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26 Snappy Answers to the Question “When Are We Ever Going to Use This Math in Real Life?”

Next time they ask, you’ll be ready.

how to solve real life problems mathematics

As a math teacher, how many times have you heard frustrated students ask, “When are we ever going to use this math in real life!?” We know, it’s maddening! Especially for those of us who love math so much we’ve devoted our lives to sharing it with others.

It may very well be true that students won’t use some of the more abstract mathematical concepts they learn in school unless they choose to work in specific fields. But the underlying skills they develop in math class—like taking risks, thinking logically and solving problems—will last a lifetime and help them solve work-related and real-world problems.

Here are 26 images and accompanying comebacks to share with your students to get them thinking about all the different and unexpected ways they might use math in their futures!

1. If you go bungee jumping, you might want to know a thing or two about trajectories.

https://giphy.com/gifs/funny-fail-5OuUiP0we57b2

Source: GIPHY

2. When you invest your money, you’ll do better if you understand concepts such as interest rates, risk vs. reward, and probability.

3. once you’re a driver, you’ll need to be able to calculate things like reaction time and stopping distance., 4. in case of a zombie apocalypse, you’re going to want to explore geometric progressions, interpret data and make predictions in order to stay human..

Trigger an outbreak of learning and infectious fun in your classroom with this Zombie Apocalypse activity from TI’s STEM Behind Hollywood series.

5. Before you tackle that home wallpaper project, you’ll need to calculate just how much wall paper glue you need per square foot.

6. when you buy your first house and apply for a 30-year mortgage, you may be shocked by the reality of what interest compounded over 30 years looks like., 7. to be a responsible pet owner, you’ll need to calculate how much hamster food to have on hand., 8. even if you’re just an armchair athlete, you can’t believe the math involved in kicking field goals.

Check out this Field Goal for the Win activity that encourages students to model, explore and explain the dynamics of kicking a football through the uprights.

9. When you double a recipe, you’re going to need to understand ratios so your dinner guests don’t look like this.

10. before you take that family road trip , you’re going to want to calculate time and distance., 11. before you go candy shopping, you’re going to have to figure out x trick or treaters times x pieces of candy equals…, 12. if  you grow up to be an ice cream scientist, you’re going to have to understand the effect of temperature and pressure at the molecular level..

https://giphy.com/gifs/ice-lick-cream-3Z1kRYmLRQm5y

Explore states of matter and the processes that change cow milk into a cone of delicious decadence with this Ice Cream, Cool Science activity .

13. Once you have little ones, you’ll need to know how many diapers to buy for the month.

14. because what if it’s your turn to organize the annual ping pong tournament, and there are 7 players at a club with 4 tables, where each player plays against each other player, 15. when dressing for the day, you might want to consider the percent likelihood of rain., 16. if you go into medical research, you’re going to have to know how to solve equations..

Learn more about inspiring careers that improve lives with STEM Behind Health , a series of free activities from TI.

17. Understanding percentages will help you get the best deal at the mall. For example, how much will something cost with 40% off? What about once the 8% tax is added? What if it’s advertised as half-off?

https://giphy.com/gifs/blue-kawaii-pink-5aplc3D2G0IrC

18. Budgeting for vacation will require figuring out how many hours at your pay rate you’ll have to work to afford the trip you want.

19. when you volunteer to host the company holiday party, you’ll need to figure out how much food to get., 20. if you grow up to be a super villain, you’re going to need to use math to determine the most effective way to slow down the superhero and keep him from saving the day..

Put your students in the role of an arch-villain’s minions with Science Friction, a STEM Behind Hollywood activity .

21. You’ll definitely want to understand how to budget your money so you don’t look like this at the grocery checkout.

22. if you don’t work the numbers out in advance, you might at some point regret choosing that expensive out-of-state college., 23. before taking on a building project, remember the old saying—measure twice, cut once., 24. if have aspirations of being a fashion designer, you’ll have to understand geometry in order to make the perfect twirling skirt.

https://giphy.com/gifs/loop-bunny-ballet-yarFJggnH24da

Geometry and fashion design intersect in this STEM Behind Cool Careers activity .

25. Everyone loves a good bargain! Figuring out the best deal is not only fun, it’s smart!

26. if you can’t manage calculations, running the numbers at the car dealership might leave you feeling like this:, you might also like.

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Using Mathematical Modeling to Get Real With Students

Unlike canned word problems, mathematical modeling plunges students into the messy complexities of real-world problem solving.  

How do you bring math to life for kids? Illustrating the boundless possibilities of mathematics can be difficult if students are only asked to examine hypothetical situations like divvying up a dessert equally or determining how many apples are left after sharing with friends, writes third- and fourth- grade teacher Matthew Kandel for Mathematics Teacher: Learning and Teaching PK-12 .

In the early years of instruction, it’s not uncommon for students to think they’re learning math for the sole purpose of being able to solve word problems or help fictional characters troubleshoot issues in their imaginary lives, Kandel says. “A word problem is a one-dimensional world,” he writes. “Everything is distilled down to the quantities of interest. To solve a word problem, students can pick out the numbers and decide on an operation.” 

But through the use of mathematical modeling, students are plucked out of the hypothetical realm and plunged into the complexities of reality—presented with opportunities to help solve real-world problems with many variables by generating questions, making assumptions, learning and applying new skills, and ultimately arriving at an answer.

In Kandel’s classroom, this work begins with breaking students into small groups, providing them with an unsharpened pencil and a simple, guiding question: “How many times can a pencil be sharpened before it is too small to use?”

Setting the Stage for Inquiry 

The process of tackling the pencil question is not unlike the scientific method. After defining a question to investigate, students begin to wonder and hypothesize—what information do we need to know?—in order to identify a course of action. This step is unique to mathematical modeling: Whereas a word problem is formulaic, leading students down a pre-existing path toward a solution, a modeling task is “free-range,” empowering students to use their individual perspectives to guide them as they progress through their investigation, Kandel says. 

Modeling problems also have a number of variables, and students themselves have the agency to determine what to ignore and what to focus their attention on. 

After inter-group discussions, students in Kandel’s classroom came to the conclusion that they’d need answers to a host of other questions to proceed with answering their initial inquiry: 

  • How much does the pencil sharpener remove? 
  • What is the length of a brand new, unsharpened pencil? 
  • Does the pencil sharpener remove the same amount of pencil each time it is used?

Introducing New Skills in Context

Once students have determined the first mathematical question they’d like to tackle (does the pencil sharpener remove the same amount of pencil each time it is used?), they are met with a roadblock. How were they to measure the pencil if the length did not fall conveniently on an inch or half inch? Kandel took the opportunity to introduce a new target skill which the class could begin using immediately: measuring to the nearest quarter inch. 

“One group of students was not satisfied with the precision of measuring to the nearest quarter inch and asked to learn how to measure to the nearest eighth of an inch,” Kandel explains. “The attention and motivation exhibited by students is unrivaled by the traditional class in which the skill comes first, the problem second.” 

Students reached a consensus and settled on taking six measurements total: the initial length of the new, unsharpened pencil as well as the lengths of the pencil after each of five sharpenings. To ensure all students can practice their newly acquired skill, Kandel tells the class that “all group members must share responsibility, taking turns measuring and checking the measurements of others.” 

Next, each group created a simple chart to record their measurements, then plotted their data as a line graph—though exploring other data visualization techniques or engaging students in alternative followup activities would work as well.

“We paused for a quick lesson on the number line and the introduction of a new term—mixed numbers,” Kandel explains. “Armed with this new information, students had no trouble marking their y-axis in half- or quarter-inch increments.” 

Sparking Mathematical Discussions

Mathematical modeling presents a multitude of opportunities for class-wide or small-group discussions, some which evolve into debates in which students state their hypotheses, then subsequently continue working to confirm or refute them. 

Kandel’s students, for example, had a wide range of opinions when it came to answering the question of how small of a pencil would be deemed unusable. Eventually, the class agreed that once a pencil reached 1 ¼ inch, it could no longer be sharpened—though some students said they would be able to still write with it. 

“This discussion helped us better understand what it means to make an assumption and how our assumptions affected our mathematical outcomes,” Kandel writes. Students then indicated the minimum size with a horizontal line across their respective graphs. 

Many students independently recognized the final step of extending their line while looking at their graphs. With each of the six points representing their measurements, the points descended downward toward the newly added horizontal “line of inoperability.” 

With mathematical modeling, Kandel says, there are no right answers, only models that are “more or less closely aligned with real-world observations.” Each group of students may come to a different conclusion, which can lead to a larger class discussion about accuracy. To prove their group had the most accurate conclusion, students needed to compare and contrast their methods as well as defend their final result. 

Developing Your Own Mathematical Models

The pencil problem is a great starting point for introducing mathematical modeling and free-range problem solving to your students, but you can customize based on what you have available and the particular needs of each group of students.

Depending on the type of pencil sharpener you have, for example, students can determine what constitutes a “fair test” and set the terms of their own inquiry. 

Additionally, Kandel suggests putting scaffolds in place to allow students who are struggling with certain elements to participate: Simplified rulers can be provided for students who need accommodations; charts can be provided for students who struggle with data collection; graphs with prelabeled x- and y-axes can be prepared in advance.

Math concepts

.css-1sk4066:hover{background:#d1ecfa;} 7 Real-World Math Strategies

Students can also explore completely different free-range problem solving and real world applications for math . At North Agincourt Jr. Public School in Scarborough, Canada, kids in grades 1-6 learn to conduct water audits. By adding, subtracting, finding averages, and measuring liquids—like the flow rate of all the water foundations, toilets, and urinals—students measure the amount of water used in their school or home in a single day. 

Or you can ask older students to bring in common household items—anything from a measuring cup to a recipe card—and identify three ways the item relates to math. At Woodrow Petty Elementary School in Taft, Texas, fifth-grade students display their chosen objects on the class’s “real-world math wall.” Even acting out restaurant scenarios can provide students with an opportunity to reinforce critical mathematical skills like addition and subtraction, while bolstering an understanding of decimals and percentages. At Suzhou Singapore International School in China, third- to fifth- graders role play with menus, ordering fictional meals and learning how to split the check when the bill arrives. 

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April 5, 2023 k-2-math-practices , k-2-measurement-and-data , 3-5-measurement-and-data , 3-5-math-practices , other-seasonal

Math in real life– strategies for planning lessons involving real-world contexts, by: allie johnston.

When are we going to use this? Why are we learning this? Why can’t I just use a calculator? If you’ve ever been asked these questions by your math students, then this article is for you! As teachers, our job is much more than teaching students math content; it is about helping students to problem solve in the real world in which they live today. The best way to do this is to allow students to learn math through the real-world situations that they encounter and that matter to them! In this article, you will learn about the relevance and usefulness of real-world applications in the math classroom and ways to implement these types of lessons in your classroom. The article includes strategies for planning lessons involving real-world contexts as well as a downloadable example that you can use in your elementary math classroom.

math-in-real-life-real-world-math-application

Benefits of Relating Math to Real Life  

The list of reasons to use real-world math applications and their benefits for students is long; they include increasing student engagement, improving how well students can remember and recall key concepts, decreasing behavior issues, and helping teachers with management. Both teachers and students enjoy the learning process more when the vehicle is a real-world problem.

Student interest and engagement are most directly impacted by the type of activity presented in class. By using math problems that mimic the real world and are relatable, students are more interested and therefore willing to work and engage with the tasks. As a result, students are more focused, and teachers worry less about classroom management. Additionally, students are better able to understand what they are learning and why they are learning it when the material is presented in a context that they can envision being in.

By using math problems that mimic the real world and are relatable, students are more interested and therefore willing to work and engage with the tasks.

Through these real-life math problems, students can develop the key thinking skills outlined by the National Council of Teachers of Mathematics in the 8 Standards of Mathematical Practice. Real-world applications often require students to decontextualize and recontextualize the task during the solving process, model with mathematics to represent the real-world situations, and push students to ask questions and persevere in problem-solving. These skills are increasingly important as technology becomes more and more accessible.

Lastly, real-world math situations enable students to transfer their learning out of the classroom and into their lives. Real-world contexts enable students to draw on existing funds of knowledge, transferring their background knowledge into the math classroom. They also enable students to apply what they have learned in new contexts, transferring their knowledge from the classroom to their lives.

Using “Windows” and “Mirrors” to Reflect Real-World Math Problems

Bringing real-life applications into the classroom requires a careful balance of offering students access to problems that they will connect with and problems that students are unfamiliar with that will help them to explore the world around them. Presenting both types of problems can help students draw connections to their own life, “mirrors,” and help students understand the lives of others through “windows.”  

“Mirror” problems can be created by relying on students' daily life experiences. Common community events and shared spaces are great places to look for possible real-world math problems. Shared developmentally appropriate interests and characteristics are another way to connect math to the students’ lives. For example, learners in early grades often enjoy playing kitchen, doctor, and teacher. Using these contexts can help them draw connections between their play and the math they are learning. For older students, using the context of video games or sports is often an effective way to increase interest in learning math concepts.

Interdisciplinary settings allow students to draw parallels and make new connections acting as both a “window” and a “mirror” to using real-world math. Oftentimes, students struggle to make connections between the learning that they are doing in each content area class. Using an application related to history or science can assist students in integrating their knowledge between settings. History is often a great connection for early math learners to begin understanding time, number lines, and basic addition and subtraction problems to discover the amount of time that has passed between different historic events.

Bringing real-life applications into the classroom requires a careful balance of offering students access to problems that they will connect with and problems that students are unfamiliar with that will help them to explore the world around them.

Equally valuable to making math problems relatable is the opportunity to expose students to the vast world around them. Sharing real-world math problems that demonstrate how mathematics is useful can open students' eyes to careers other than the common interests of most kids such as being a firefighter, teacher, or doctor. For example, math is necessary for carpentry, architecture, business analysts, and many other careers that may pique the interest of students. Math applications can also show a glimpse of how math was discovered and is continued to be used around the world. For example, looking at how numbers were initially written in ancient times may help students appreciate the number system in use today.

STEAM connections, or interdisciplinary connections among science, technology, engineering, the arts, and mathematics, abound in real-world applications and reveal to students that math connects to everything.

In any of the above types of real-world math applications, it is necessary for the teacher and the students to be able to see the context as realistic and useful. As you being to think about using and designing real-world applications in your own classroom, consider these strategies for incorporating realistic real-world math problems:

  • Include realistic word problems that your students might encounter.
  • Offer analogies as simple connections between a problem and the real world such as subtraction and the temperature dropping. Analogies can also be used to analyze a more complex concept such as comparing 0 on a number line to a mirror.
  • Set the stage through the wording of the problem or the topic and data being presented.
  • Give context and offer an entire problem that is an example of a real-world situation that students need to use math to solve.
  • Model real situations using geometric shapes and figures, equations, or technology.

The best way to get started is to give real-world application problems a try!

Math in Real Life Problems Examples

Each lesson of the Sadlier Math program opens with a real-world application and offers a STEAM connection lesson offering students both “windows” and “mirrors” with which to view problems. On April 21 we celebrate Earth Day, which makes this Protecting Our Planet STEAM Lesson both timely and relevant for students. This activity invites students to use units of measure for length to study precipitation records. After preparing models of a particular region’s record rainfall and snowfall, they explore concepts of climate change and its causes and effects. This activity connects to the United Nations Sustainable Development Goal (SDG) 13: Climate Action, which promotes awareness and education about climate change.

Math_DL_ProtectingOurPlanet_STEAMLesson_Thumb_@2X

Your students will benefit from the opportunity to enjoy math learning as they develop the skills that they need in their lives, now and in the future through real-world applications and rich interdisciplinary connections.

References:

Lee, J. E. Prospective elementary teachers’ perceptions of real-life connections reflected in posing and evaluating story problems. J Math Teacher Educ 15, 429–452 (2012). https://doi.org/10.1007/s10857-012-9220-5

Premadasa, Kirthi and Bhatia, Kavita (2013) "Real Life Applications in Mathematics: What Do Students Prefer?," International Journal for the Scholarship of Teaching and Learning: Vol. 7: No. 2, Article 20.

how to solve real life problems mathematics

Solving Real-World Problems with Mathematics

Published by excel mathematics on february 6, 2022 february 6, 2022.

In 2019, humans had, for the first time ever, a photo of a black hole. It was a feat like none before—we were all looking at a place where time stops.

This feat was not possible without math. After all, there’s no camera big enough to capture the image of a black hole.

Math solved this problem as scientists used a clever combination of carefully placed telescopes  around the world to make the impossible possible.

But this isn’t the first time, of course, that math has helped humankind reach great heights. And while we know that problems like Fermat’s last theorem —while known as the hardest math problem to ever have been solved—doesn’t work in real life, certain other things definitely do.

Trajectories and Bungee Jumping

Bungee jumping looks fun and all, but it isn’t just someone falling headfirst into a pool of water. You have to be very mindful of how you jump, and you need to get the trajectory right. A good bungee jumper will always know something about angles and trajectories before taking the dive.

Aiming for Profits

, Solving Real-World Problems with Mathematics

You’ve all heard about shares, and you all know what profit and loss mean, but is that all there is to these words? There’s actually a lot more. You need to have substantial knowledge of interest rates, probability, risks and rewards, and so on. Some basic knowledge here can help you make big profits and avoid big losses simultaneously.

Now, of course, no one goes around with the steering wheel in one hand and a notebook in the other, in a bid to try and calculate the force with which you’ll hit that pedestrian if you continue driving your car in a straight direction at a certain speed. That is, of course, a terrible idea.

Good drivers, however, are using math all the time in their heads, subconsciously, to assess their car’s velocity and its stopping speed, distance and reaction time, and so on.

Making Predictions

We’re living in the time of a pandemic. Like all other contagious diseases, the COVID-19 also has a multiplication rate. In other words, this is the rate at which the virus has spread and is spreading. Statisticians and scientists use this data to make (accurate) predictions about how far a certain pandemic will go, and this helps the medical community come up with contingency and containment plans.

Scientists have already been using  math to answer some integral questions about the virus, and Harvard scientists  are making predictions about how it will affect the world’s population. All this information is central to figuring out how to clamp down on the virus and determine the next best strategy.

If you want your child to go just as far as these scientists, start today. Sign up with Excel Mathematics for a free trial  or  contact us  to know more details about our online math classes !

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5 Teaching Mathematics Through Problem Solving

Janet Stramel

Problem Solving

In his book “How to Solve It,” George Pólya (1945) said, “One of the most important tasks of the teacher is to help his students. This task is not quite easy; it demands time, practice, devotion, and sound principles. The student should acquire as much experience of independent work as possible. But if he is left alone with his problem without any help, he may make no progress at all. If the teacher helps too much, nothing is left to the student. The teacher should help, but not too much and not too little, so that the student shall have a reasonable share of the work.” (page 1)

What is a problem  in mathematics? A problem is “any task or activity for which the students have no prescribed or memorized rules or methods, nor is there a perception by students that there is a specific ‘correct’ solution method” (Hiebert, et. al., 1997). Problem solving in mathematics is one of the most important topics to teach; learning to problem solve helps students develop a sense of solving real-life problems and apply mathematics to real world situations. It is also used for a deeper understanding of mathematical concepts. Learning “math facts” is not enough; students must also learn how to use these facts to develop their thinking skills.

According to NCTM (2010), the term “problem solving” refers to mathematical tasks that have the potential to provide intellectual challenges for enhancing students’ mathematical understanding and development. When you first hear “problem solving,” what do you think about? Story problems or word problems? Story problems may be limited to and not “problematic” enough. For example, you may ask students to find the area of a rectangle, given the length and width. This type of problem is an exercise in computation and can be completed mindlessly without understanding the concept of area. Worthwhile problems  includes problems that are truly problematic and have the potential to provide contexts for students’ mathematical development.

There are three ways to solve problems: teaching for problem solving, teaching about problem solving, and teaching through problem solving.

Teaching for problem solving begins with learning a skill. For example, students are learning how to multiply a two-digit number by a one-digit number, and the story problems you select are multiplication problems. Be sure when you are teaching for problem solving, you select or develop tasks that can promote the development of mathematical understanding.

Teaching about problem solving begins with suggested strategies to solve a problem. For example, “draw a picture,” “make a table,” etc. You may see posters in teachers’ classrooms of the “Problem Solving Method” such as: 1) Read the problem, 2) Devise a plan, 3) Solve the problem, and 4) Check your work. There is little or no evidence that students’ problem-solving abilities are improved when teaching about problem solving. Students will see a word problem as a separate endeavor and focus on the steps to follow rather than the mathematics. In addition, students will tend to use trial and error instead of focusing on sense making.

Teaching through problem solving  focuses students’ attention on ideas and sense making and develops mathematical practices. Teaching through problem solving also develops a student’s confidence and builds on their strengths. It allows for collaboration among students and engages students in their own learning.

Consider the following worthwhile-problem criteria developed by Lappan and Phillips (1998):

  • The problem has important, useful mathematics embedded in it.
  • The problem requires high-level thinking and problem solving.
  • The problem contributes to the conceptual development of students.
  • The problem creates an opportunity for the teacher to assess what his or her students are learning and where they are experiencing difficulty.
  • The problem can be approached by students in multiple ways using different solution strategies.
  • The problem has various solutions or allows different decisions or positions to be taken and defended.
  • The problem encourages student engagement and discourse.
  • The problem connects to other important mathematical ideas.
  • The problem promotes the skillful use of mathematics.
  • The problem provides an opportunity to practice important skills.

Of course, not every problem will include all of the above. Sometimes, you will choose a problem because your students need an opportunity to practice a certain skill.

Key features of a good mathematics problem includes:

  • It must begin where the students are mathematically.
  • The feature of the problem must be the mathematics that students are to learn.
  • It must require justifications and explanations for both answers and methods of solving.

Needlepoint of cats

Problem solving is not a  neat and orderly process. Think about needlework. On the front side, it is neat and perfect and pretty.

Back of a needlepoint

But look at the b ack.

It is messy and full of knots and loops. Problem solving in mathematics is also like this and we need to help our students be “messy” with problem solving; they need to go through those knots and loops and learn how to solve problems with the teacher’s guidance.

When you teach through problem solving , your students are focused on ideas and sense-making and they develop confidence in mathematics!

Mathematics Tasks and Activities that Promote Teaching through Problem Solving

Teacher teaching a math lesson

Choosing the Right Task

Selecting activities and/or tasks is the most significant decision teachers make that will affect students’ learning. Consider the following questions:

  • Teachers must do the activity first. What is problematic about the activity? What will you need to do BEFORE the activity and AFTER the activity? Additionally, think how your students would do the activity.
  • What mathematical ideas will the activity develop? Are there connections to other related mathematics topics, or other content areas?
  • Can the activity accomplish your learning objective/goals?

how to solve real life problems mathematics

Low Floor High Ceiling Tasks

By definition, a “ low floor/high ceiling task ” is a mathematical activity where everyone in the group can begin and then work on at their own level of engagement. Low Floor High Ceiling Tasks are activities that everyone can begin and work on based on their own level, and have many possibilities for students to do more challenging mathematics. One gauge of knowing whether an activity is a Low Floor High Ceiling Task is when the work on the problems becomes more important than the answer itself, and leads to rich mathematical discourse [Hover: ways of representing, thinking, talking, agreeing, and disagreeing; the way ideas are exchanged and what the ideas entail; and as being shaped by the tasks in which students engage as well as by the nature of the learning environment].

The strengths of using Low Floor High Ceiling Tasks:

  • Allows students to show what they can do, not what they can’t.
  • Provides differentiation to all students.
  • Promotes a positive classroom environment.
  • Advances a growth mindset in students
  • Aligns with the Standards for Mathematical Practice

Examples of some Low Floor High Ceiling Tasks can be found at the following sites:

  • YouCubed – under grades choose Low Floor High Ceiling
  • NRICH Creating a Low Threshold High Ceiling Classroom
  • Inside Mathematics Problems of the Month

Math in 3-Acts

Math in 3-Acts was developed by Dan Meyer to spark an interest in and engage students in thought-provoking mathematical inquiry. Math in 3-Acts is a whole-group mathematics task consisting of three distinct parts:

Act One is about noticing and wondering. The teacher shares with students an image, video, or other situation that is engaging and perplexing. Students then generate questions about the situation.

In Act Two , the teacher offers some information for the students to use as they find the solutions to the problem.

Act Three is the “reveal.” Students share their thinking as well as their solutions.

“Math in 3 Acts” is a fun way to engage your students, there is a low entry point that gives students confidence, there are multiple paths to a solution, and it encourages students to work in groups to solve the problem. Some examples of Math in 3-Acts can be found at the following websites:

  • Dan Meyer’s Three-Act Math Tasks
  • Graham Fletcher3-Act Tasks ]
  • Math in 3-Acts: Real World Math Problems to Make Math Contextual, Visual and Concrete

Number Talks

Number talks are brief, 5-15 minute discussions that focus on student solutions for a mental math computation problem. Students share their different mental math processes aloud while the teacher records their thinking visually on a chart or board. In addition, students learn from each other’s strategies as they question, critique, or build on the strategies that are shared.. To use a “number talk,” you would include the following steps:

  • The teacher presents a problem for students to solve mentally.
  • Provide adequate “ wait time .”
  • The teacher calls on a students and asks, “What were you thinking?” and “Explain your thinking.”
  • For each student who volunteers to share their strategy, write their thinking on the board. Make sure to accurately record their thinking; do not correct their responses.
  • Invite students to question each other about their strategies, compare and contrast the strategies, and ask for clarification about strategies that are confusing.

“Number Talks” can be used as an introduction, a warm up to a lesson, or an extension. Some examples of Number Talks can be found at the following websites:

  • Inside Mathematics Number Talks
  • Number Talks Build Numerical Reasoning

Light bulb

Saying “This is Easy”

“This is easy.” Three little words that can have a big impact on students. What may be “easy” for one person, may be more “difficult” for someone else. And saying “this is easy” defeats the purpose of a growth mindset classroom, where students are comfortable making mistakes.

When the teacher says, “this is easy,” students may think,

  • “Everyone else understands and I don’t. I can’t do this!”
  • Students may just give up and surrender the mathematics to their classmates.
  • Students may shut down.

Instead, you and your students could say the following:

  • “I think I can do this.”
  • “I have an idea I want to try.”
  • “I’ve seen this kind of problem before.”

Tracy Zager wrote a short article, “This is easy”: The Little Phrase That Causes Big Problems” that can give you more information. Read Tracy Zager’s article here.

Using “Worksheets”

Do you want your students to memorize concepts, or do you want them to understand and apply the mathematics for different situations?

What is a “worksheet” in mathematics? It is a paper and pencil assignment when no other materials are used. A worksheet does not allow your students to use hands-on materials/manipulatives [Hover: physical objects that are used as teaching tools to engage students in the hands-on learning of mathematics]; and worksheets are many times “naked number” with no context. And a worksheet should not be used to enhance a hands-on activity.

Students need time to explore and manipulate materials in order to learn the mathematics concept. Worksheets are just a test of rote memory. Students need to develop those higher-order thinking skills, and worksheets will not allow them to do that.

One productive belief from the NCTM publication, Principles to Action (2014), states, “Students at all grade levels can benefit from the use of physical and virtual manipulative materials to provide visual models of a range of mathematical ideas.”

You may need an “activity sheet,” a “graphic organizer,” etc. as you plan your mathematics activities/lessons, but be sure to include hands-on manipulatives. Using manipulatives can

  • Provide your students a bridge between the concrete and abstract
  • Serve as models that support students’ thinking
  • Provide another representation
  • Support student engagement
  • Give students ownership of their own learning.

Adapted from “ The Top 5 Reasons for Using Manipulatives in the Classroom ”.

any task or activity for which the students have no prescribed or memorized rules or methods, nor is there a perception by students that there is a specific ‘correct’ solution method

should be intriguing and contain a level of challenge that invites speculation and hard work, and directs students to investigate important mathematical ideas and ways of thinking toward the learning

involves teaching a skill so that a student can later solve a story problem

when we teach students how to problem solve

teaching mathematics content through real contexts, problems, situations, and models

a mathematical activity where everyone in the group can begin and then work on at their own level of engagement

20 seconds to 2 minutes for students to make sense of questions

Mathematics Methods for Early Childhood Copyright © 2021 by Janet Stramel is licensed under a Creative Commons Attribution 4.0 International License , except where otherwise noted.

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Algebra in Real Life

Table of Contents

Have you ever wondered how Algebra may be applied to solve real-life problems?

We regularly see people using Algebra in many parts of everyday life; for instance, it is utilized in our morning schedule each day to measure the time you will spend in the shower, making breakfast, or driving to work.

The absence of "X" or "Y" doesn't imply that algebra is not around us; algebra’s actual occurrences are uncountable. This exact and compact numerical language works wonderfully with practically all different subjects and everyday life. 

In this article, we will grasp instances in real life where applications of algebra are needed and examples of applications of algebra in real life.  

  • How to factorise a polynomial?

What is Algebra?

Algebra is a part of mathematics that deals with symbols and the standards for controlling those symbols. The more basic parts of algebra are called elementary algebra, and the more abstract types are called Abstract Algebra or modern algebra. 

Algebraic Expression

Let us consider the pattern below. It has been created using marbles. Here we see that the first column has 2 marbles, the second column has 3 marbles, the third column has 4 marbles and so on.

Algebraic expression image

Thus we observe that every new column increases by 1 marble. We can write the representation as 

The number of marbles used in a column =

position of the column + 1

or as 

the number of marbles used in a column = n + 1.

Here n represents the position of the column. So ‘n’ is an example for a variable that can take any value 1,2,3… so on. Thus n + 1 is the algebraic expression formed with n as variable and constant 1.

Speed of a car image

A variable is a number that does not have a fixed value. The picture and the list below show some real-life examples, where the value of a variable changes with the change in place and time. 

  • The temperature in different places also change.
  • The height of a growing child changes with time.        
  • The speed of a car changes with time.
  • The age of people keeps on increasing year by year.

Constant 

The value remains fixed for specific numbers that represent quantities or ideas that will not change. For example, the date of birth of a particular person, the normal human body temperature and capacity of a given container.

Framing algebraic expressions with given conditions

Now we will see how to frame an algebraic expression. The rules are that variables are to be represented with alphabetic letters, say lower case a-z and constants in numeric form.

1. Amanda has 10 storybooks more than Alex. Express the number of storybooks Amanda has in terms of the number of storybooks Alex has. 

Let the number of storybooks Alex has = y

Therefore the number of storybooks Amanda has = y + 10

2. Sweets from a big box are equally distributed in 10 small boxes. Express the number of sweets in one small box in terms of the total number of sweets.

Let x be the total number of sweets. 

Number of sweet boxes = 10

Therefore, the number of sweets in one box is = x/10

Solving Equations

Let us see how practical applications of algebra can be used to solve equations. You will often see equations like 3x + 4 = 5, where you want to find x.

Consider a situation from our daily life.

The cost of a book is £5 more than the cost of a pen. Let us take the cost of the pen as £x. Then the cost of the book is £ (x + 5) . If the cost of the book is £20, what is the cost of the pen?

We know that the book’s cost is x + 5 and it is given that x + 5 = 20. This is an equation in the variable x.

A table is prepared as shown below for various values of x:

It is clear from the table that x + 5 = 20 only for x = 15. So, the cost of the pen is £15. 

In general we say that x = 15 is the solution of the equation x + 5 = 20. This is the trial and error method where we substitute different values for the variable that satisfies the given equation.

An equation has two parts which are connected by an equal to sign. The two parts or sides of an equation are denoted as LHS (Left Hand Side) and RHS (Right Hand Side). If LHS = RHS we get an equation. 2x = 6 is an

algebraic equation, whereas 3x > 10 or 4x < 12 are not equations.

Solving an equation using the Principle of Balances

Consider the balance given in the figure.

Image 1

Four circles balance one square and a circle on the other side. The idea is we have to find out how many circles will balance a square. If we remove the circle from the left pan, we have only the square there. Since we removed a circle from the left pan, we have to remove the circle from the right pan also. Then there will be three circles in the right pan.

Now the balance looks like the one shown on the right. This is called the principle of balances. Using balancing equations, we can solve equations in a systematic way.

Solve using the principle of balances:

Benjamin's mother is three times as old as Benjamin. If Benjamin's mother is 39 years old, find Benjamin's age. 

Let Benjamin's age be x. 

Benjamin’s mother's age 3x = 39

3x/3 = 39/3 {Dividing by 3 on both the sides }

So, Benjamin’s age = 13.

The same quantity can be added or subtracted to both sides of the equation. If the same amount is multiplied or divided on both the sides of an equation, it remains the same.

Forming an equation to find the unknown

Translating verbal descriptions into algebraic expressions is an essential initial step in solving word problems. So let’s see another real-life example in the form of a puzzle.

Image 1 example

Detailed Solution:

Our first supposition is that Uma buys at least one ball of each kind. Now let’s say she buys x footballs, y cricket balls, and z table-tennis balls.

The question requires x + y + z = 100  [ 1 ]

It also requires 15 x + 1y + z/4 = 100  [ 2 ]Since we have 3 variables but only 2 equations we’ll have to use the trial and error method to get at the solution.

Let’s vary x the number of footballs and see what we get:

Suppose x = 1, then 

y + z =99 and y + z/ 4 = 83z/4 = 14 3z = 56 z = 56/3 which is not a whole number.

Trying for x = 2 also fails and now

If x = 3, then  z = 97 and y + z / 4 = 55 3z/4 =42 3z= 168 z = 168/3 = 56  which is a whole number! 

And if z = 56  then y = 97 - z = 97 - 56 = 41 

So the set of balls Uma buys is { 3 footballs, 41 cricket balls and 56 table tennis balls }

Algebra in Geometry

In Algebraic Geometry we study geometric objects and their assortment that are characterized by polynomial equations. 

Examples of algebraic varieties’ most studied classes are plane algebraic curves, including lines, circles, parabolas, ellipses, hyperbolas. There are also cubic curves like elliptic curves and quartic curves like lemniscates and Cassini ovals.

In real life, algebraic geometry can be used to study the dynamics properties of robotics mechanisms.

Algebraic geometry image

   Source: Pinterest

A robot can move in continuous space with an infinite set of possible actions and states. When the robot has arms and legs that must also be controlled and the search space becomes many-dimensional. Robot’s kinematics can be formulated as a polynomial equation system that can be solved using algebraic geometry tools.

Algebraic geometry is also widely used in statistics, control theory, and geometric modelling. There are also connections to string theory, game theory, graph matchings and integer programming.

Algebra in Computer Programming

The mathematical languages unite fields such as science, technology, and engineering into itself. That is why an individual intrigued by the field of computer programming and coding should figure out how to comprehend and control mathematical logic.

Strong comprehension of algebra incorporates characterizing the connections between objects, critical thinking with restricted factors, and analytical skill development to help execute decision making. 

One such use of Algebra can be seen in Inference procedures used in Knowledge engineering. Variables and constant symbols are used as terms representing objects in real life. 

The knowledge engineer adds a set of facts and specifies what is true, and the inference procedure figures out how to turn the facts into a solution to the problem. 

Besides, because a fact is true regardless of what task one is trying to solve, knowledge bases can be reused for various tasks without modification. 

Example for the  task of inference

Take a sentence,

Everyone likes ice cream.

It is represented in First-order logic as 

 x Likes ( x, ice cream ) 

where x is the variable and is the universal quantifier that generalizes to all persons liking icecream. 

If another sentence found in the knowledge base is as follows:

    John likes ice cream

It is represented as Likes( John, ice cream)

The inference procedure will reason out from x Likes ( x, ice cream ) with the substitution {x/John} and infers Likes(John, ice cream) and concludes that John likes icecreams.

                                                                                                                                                      Biostatistics University of Florida

Other uses of algebra in programming are  Ontology, error correction algorithms, Natural language processing, Neural networks,  designing artificial intelligence programming languages such as LISP and PROLOG and theorem provers such as OTTER.

In real life there are a plethora of instances where Algebra is being used. It’s utility is being universally quantified in all walks of our lives. For instance, take a shopping domain where we need to be budgeted with the cart items and some algebraic formulation is applied.

Algebra in real life image

The economy of every country is analysed with the help of economists taking the help of algebra to solve the problems related to debts or loans.

Tom Evans's ANALOGY program (1968) solved geometric analogy problems that appear in IQ tests such as the one shown below.

Anology image 1

                                                                                                                                                 Source: Artificial Intelligence by Stuart Russell

The use of algebra is multipurpose, and it goes handy in every sphere of our lives.  It isn't just mathematicians, however, even most academicians, educationists, researchers, and experts from all different backgrounds collectively

agree with the adaptability of algebra. 

Real-World Applications of Linear Algebra

What is linear algebra.

Linear algebra is the branch of mathematics concerning linear equations such as linear maps and their representations in vector spaces and matrices.

The concept of classification can be simulated with the help of neural network structures that use a linear regression model. Here the training set is compared with the test data so that the learning algorithms generate outcomes to predict data related to decision making, medical diagnosis, statistical inferences, etc.

Example 1

Applications

The most generally utilized use of linear algebra is certainly optimization, and the most broadly utilized sort of advancement is linear algebra. You can upgrade spending plans, your eating regimen, and your course to work 

utilizing linear algebra, and this uniqueness starts to expose a lot of applications. 

Other real-world applications of linear algebra include ranking in search engines, decision tree induction, testing software code in software engineering, graphics, facial recognition, prediction and so on.

In real life, algebra can be compared to a universally handy device or a sorcery wand that can help manage regular issues of life. Whenever life throws a maths problem at you, for example when you have to solve an equation or work out a geometrical problem, algebra is usually the best way to attack it. 

Written by Jesy Margaret, Cuemath teacher

About Cuemath

Cuemath, a student-friendly mathematics and coding platform, conducts regular Online Classes for academics and skill-development, and their Mental Math App, on both iOS and Android , is a one-stop solution for kids to develop multiple skills. Understand the Cuemath Fee structure and sign up for a free trial.

How to Use Real-World Problems to Teach Elementary School Math: 6 Tips

how to solve real life problems mathematics

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When you think back on elementary school math, do you have fond memories of the countless worksheets you completed on adding fractions or solving division problems? Probably not.

Researchers and educators have been pushing for years for schools to move away from teaching math through a set of equations with no context around them, and towards an approach that pushes kids to use numerical reasoning to solve real problems, mirroring the way that they’ll encounter the use of math as adults.

The strategy is largely about setting kids up for success in the professional world, and educators can lay the groundwork decades earlier, even in kindergarten .

Here are some tips for using a real world problem-solving approach to teaching math to elementary school students.

1. There’s more than one right answer and more than one right method

A “real world task” can be as simple as asking students to think of equations that will get them to a particular “target” number, say, 14. Students could say 7 plus 7 is 14 or they could say 25 minus 11 is 14. Neither answer is better than the other, and that lesson teaches kids that there are multiple ways to use math to solve problems.

2. Give kids a chance to explain their thinking

The process you use to solve a real world math problem can be just as important as arriving at the correct answer, said Robbi Berry, who teaches 5th grade in Las Cruces, N.M. Her students have learned not to ask her if a particular answer is correct, she said, because she’ll turn the question back on them, asking them to explain how they know that it is right. She also gives her students a chance to explain to one another how they arrived at a particular solution, “We always share our strategies so that the kids can see the different ways” to arrive at an answer, she said. Students get excited, she said, when one of their classmates comes up with an approach they never would have thought of. “Math is creative,” Berry said. “It’s not just learning and memorizing.”

3. Be willing to deal with some off-the-wall answers

Problem solving does not necessarily mean going to the word problems in your textbook, said Latrenda Knighten, a mathematics instructional coach in Baton Rouge, La. For little kids, it can be as simple as showing a group of geometric shapes and asking what they have in common. Students may go off track a bit by talking about things like color, she said, but teachers can steer them towards thinking about things like how a rectangle differs from a triangle.

4. Let your students push themselves

Tackling these richer, real-world problems can be tougher than solving equations on a worksheet. And that is a good thing, said Jo Boaler, a professor at Stanford University and an expert on math education. “It’s really good for your brain to struggle,” she said. “We don’t want kids getting right answers all the time because that’s not giving their brains a really good workout.” These types of problems require collaboration, a skill that many don’t associate with math, but that is key to how math reasoning works beyond the classroom. The complexity and difficulty of the tasks means that students “have to talk to each other and really figure out what to do, what’s a good method?”

5. Celebrate ‘favorite mistakes’ to encourage intellectual risk taking

Wrong answers should be viewed as learning opportunities, Berry said. When one of her students makes an error, she asks if she can share it with the class as a “favorite mistake.” Most of the time, students are comfortable with that, and the class will work together to figure how the misstep happened.

6. Remember there’s no such thing as a being born with a ‘math brain’

Some teachers believe that certain students are just naturally good at math, and others are not, Boaler said. But that’s not true. “Brains are constantly shaping, changing, developing, connecting, and there is no fixed anything,” said Boaler, who often works alongside neuroscientists. What’s more, many elementary school teachers lack confidence in their own math abilities, she said. “They think they can’t do [math],” Boaler said. “And they often pass those ideas on” to their students.

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7 Examples of Algebra in Everyday Life (Simplified Real-Life Applications)

Do you ever feel like algebra is just a bunch of meaningless equations and symbols? Well, think again! Algebra is actually all around us in everyday life. In this blog post, we will discuss seven examples of how algebra is used in the real world.

We will also provide real-life applications for each example. So whether you’re a student trying to understand why you’re learning this stuff or a teacher looking for ways to make it more relevant to your students, read on!

Examples of Algebra in everyday life

Whilst algebra has many applications in daily life, here are my favorite ways of using algebra to solve problems.

1. Calculating discounts at the store

You’re at the store and you see a shirt that’s on sale for 20% off. How much will it cost? This is a great opportunity to use some algebra!

Here’s how we can set this up:

Let x represent the original price of the shirt

Then, we know that:

x – 0.20x = the new price of the shirt

We can simplify x – 0.20x to 0.8x.

So then the new price of the shirt is 0.8x

If the original price of the shirt is $30,

then the new price of the shirt = 0.8 x 30 = $24

2. Are we there yet? Calculating how long it will take to get somewhere

Remember Bart Simpson asking ‘Are we there yet?’ on repeat.

Well, we can use algebra, specifically the formula linking distance, speed and time, to calculate how long it will take to arrive at your destination.

how to solve real life problems mathematics

Say your car is traveling at 60 miles per hour, then the formula would be:

how to solve real life problems mathematics

So instead of asking ‘Are we there yet?’, you could look out the window for a sign that shows how many miles to your destination then use the Distance-Speed-Time formula.

The Sign Says You've Got 72 Miles to Go Before the End of Your Road Trip.  It's Lying. - Bloomberg

So the time to get to Las Vegas will be 72 divided by 60 which is just over 1. So it will be just over 1 hour to get there.

how to solve real life problems mathematics

The distance – speed – time formula is a useful math formula to remember.

3. Figuring out how many pizzas to order

You’re having 7 friends over and you want pizza.

You each can eat at least 4 slices.

If there are 8 slices in a pizza, how many pizzas should you order?

You can use algebra to find how many pizzas you should order by writing an equation and solving it.

Let x represent the number of pizzas you should order.

So then you and 7 friends is 1 + 7, which is 8.

If each person eats 4 slices, the total number of slices is 8 x 4 = 32

Since each pizza has 8 slices, the number of slices in total will be 8x.

Here’s what it looks like as an algebraic equation:

how to solve real life problems mathematics

So you will need to order at least 4 pizzas.

If your friend eat more than 4 slices each you need to order more pizzas.

If your mom and dad, brothers & sisters want pizza too, you will need to order more.

So we could write it as an algebraic inequality like this:

how to solve real life problems mathematics

4. Calculating how many hours you need to work

Imagine there is a new pair of jeans you want that cost $75.

If your parents give you $25 towards them, how many hours of babysitting do you have to work in order to buy them?

Well you only need $50 right because $75 – $25 = $50

Let us say you earn $5 an hour for babysitting.

Then you will need to work for 10 hours.

Here’s what it looks like in algebra:

how to solve real life problems mathematics

5. When adjusting amounts in a recipe when cooking

Let’s say you want to make some choc-chip cookies but the recipe requires 2 eggs and you only have 1 egg.

You will need to adjust the amounts of the rest of the ingredients.

This is a simple example where you can simply halve each ingredient.

Alternatively, you could use your knowledge of algebra to write an algebraic equation to calculate all the other quantities.

This is useful when its not a simple case of doubling or halving amounts.

For example if you wanted to make choc-chip cookies but you only have 2 cups of flour and you need 3 cups.

This means your recipe will be 2/3 of the original recipe.

So your formula will be:

new amount = 2/3 x recipe amount

how to solve real life problems mathematics

6. Planning a budget and sticking to it

Budgeting is so important, whether you’re an individual, a family or a business. And algebra can help!

Let’s say you have $200 income in a month. You want to budget this out so that you don’t overspend and can even save money each month. Perhaps for an end-of-school holiday, a car or college.

List all your expenses, for example:

  • $16 cell phone
  • $30 monthly bus pass
  • $50 going out with friends

Add up your expenses to find your monthly expenses.

16 + 30 +50 = 96

You should track your expenses in an app or spreadsheet to see what you are actually spending your money on. These days with apple pay and a cashless society it is very easy to spend money and not realize how much we are spending over. a month.

Subtract your total monthly expenses from your income to calculate the amount leftover that you can save (or invest).

Using algebra this could be done like this:

Let x represent your monthly expenditure.

Then we know that:

200-x = the amount we can save each month

Of course, this is just a simple example. In reality, you may use a spreadsheet (which is what I use). But you will need to understand the mathematics so you can enter a formula in your spreadsheet. This way when your expenses vary each month your savings will be automatically calculated.

So algebra can help you to create a budget, stick to it and even save or invest.

how to solve real life problems mathematics

7. Comparing cell phone plans

The time will come when your parents stop paying your cell bill. In order to find the best value for money, you need to be able to compare different cell phone plans.

Algebra can help you do this!

Let’s say you’re looking at two different cell phone plans:

Plan A: $60/month with unlimited talk and text and 5GB data

Plan B: $20/month with unlimited talk and text and 1GB data plus $10/GB over this amount.

In order to compare cell phone plans, we need to find out how much data we use each month. You may need to look at past statements for this information.

Just say you use roughly 3GB of data each month.

On Plan A, the 3GB is included so your total bill would be $60

On Plan B, 3GB is over the 1GB of included data so you will need to pay extra. Each plan will have different costs.

The amount you will pay is calculated as follows:

# of GB over plan = 3GB minus 1GB = 2 GB

Cost for extra GB = 2 x $10/GB = $20

Total monthly cost = $20 + $20 = $40

So plan B ends up being $20 cheaper.

You could write this as a formula as:

Total monthly cost = 20 + (# GB used – 1GB) x 10

Since the amount of data used each month may vary, it Is called a variable.

Different plans may charge different excess data costs too.

You could set up a spreadsheet to calculate the different monthly costs for the varying amount of data used to help you decide which cell phone plan is best for your needs.

Using Algebra to compare cell phone plans in a spreadsheet

You can see that once you use over 5GB of data the monthly cost for plan B will be more than $60. This is when plan A is the best value.

So knowing how to write a formula can help you compare cell phone plans.

Wrapping up and my experience with using examples of Algebra in everyday life in the classroom.

There are countless other examples of how algebra is used in daily life. These are just a few of the ways that I use it on a regular basis to problem solve. I’m sure you can think of many more!

From my 14+ years of teaching high school mathematics to students of all abilities, I have observed that some students need to see the relevance of abstract concepts like Algebra in order to be interested.

Start the lesson with a hook or example of how they can use algebra in real life so they buy into the topic and are more engaged.

If you’re a teacher, try incorporating some real-life examples into your lessons. And if you’re a student, pay attention to the ways that you use algebra in your daily life. It will help you to better understand the concepts and make them more relevant to your own life.

I hope this article has helped you to see how algebra is used in everyday life.

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The Ways We Use Math in the Real World: 8 Examples

Created: December 21, 2023

Last updated: January 9, 2024

math in the real world

You may not realize it, but many children ask themselves: What relevance do abstract equations have in my life? Why practice math problems like ‘John bought 45 watermelons’ equations when nobody ever buys 45 watermelons in real life?

Yes, it happens, and sometimes schools fail to address these doubts correctly or even recognize them. Getting kids to understand math formulas and processes has become second nature to teachers. However, getting them to learn math using real world math problems is another story altogether.

In What Ways Does Math Exist in The Real World?

To a lot of individuals, math serves little practical purpose. We do not use all those equations after leaving school. However, the simple truth is that we unknowingly use mathematical concepts daily. Numerical calculations are part of going shopping, cooking, and working, amongst other activities.

Fluency in math equals success in countless real-world activities that involve logical thinking and spatial skills. Moreover, it also enables different brain parts to utilize them well. Nevertheless, if you view math at its full scale, you will see that the civilization that exists at present was brought by ancient Greek mathematics. Everything, from architecture, machines, and medicines to iPads, came out of calculation.

Math for Kids

Math in the Real World

Often, teachers take situations from everyday life to teach math in a meaningful and real-world sense. Check these real life math problems below:

Which Popcorn Container Is Better?

While in the cinema, you look forward to getting a big popcorn box in your mouth, which should keep it occupied till the end of the film. However, upon getting closer to the popcorn stand, you notice two bags of the same product: cone-shaped and cylindrical. They are the same size, but the only ones selling anything for $5.

Which Popcorn Container Is Better?

Which one should you choose? You can hardly tell them apart at a glance. However, mathematicians are brilliant and understand that you’ll be forced to pay much more for a coned bag. Therefore, the cone has a constant ratio of one-third of cylinders with the same height. Therefore, this cylindrical bag will hold the acorn and allow you to pick up various snack foods.

What Makes Bees Build Hexagons Inside Their Hives?

Bees are among Earth’s most complex working creatures, yet their buzzing critters are economical with space for all their work. Their hives always take the form of a hexagon, not any other shape.

Why Do Bees Construct Hexagons in Their Hives?

The question is: Why not round honeycombs? They will not fit since they would leave large cavities with round cells. Why should triangle or square cells, then? They won’t be efficient either. Many of such operations with numbers take place in those hexagon cells. A hexagon has the lowest circumference and maximum area.

As one of the math in the real world examples, we can also consider if the hexagon has a side length of five centimeters. The formula of a perimeter is the sum of all sides: 5 x 6 = 30. Thus, the hexagon of the 5 cm side becomes a 30 cm long line. The hexagon’s surface area formula is The quotient of (3 √3 x S2)/2, with S as the hexagon’s side length. For our hexagon, we have the following formula: The area of the body is equal to (3 × √3 × 25) ÷ 2 = 64.95 sq cms.

As such, let us apply the same to an equilateral triangle with a perimeter measuring 30 centimeters. It will have sides measuring 10 centimeters each and an area of 43.3 square centimeters. To construct a triangle with a surface area of 64.95cm^{2}, its perimeter measures 37.75cm, about 25% larger than a hexagon’s side.

Therefore, had the bees been triangulators, they would have needed 25% more wax to cover a hexagonal cell’s surface area. Additionally, a hexagon provides six wall stiffeners that share loads more evenly than triangles and squares.

Folding Paper Problem

Have you heard about paper-folding and its magical theory? You have probably learned that folding a regular letter-size paper more than eight times is impossible.

A paper sheet 1:219 KM long has been used for the current world record of noon. It is also believed that if you fold a piece of paper forty-two times, it will be as thick as the distance between you and the moon. Firstly, it increases in thickness as it folds exponentially. Consider a typical sheet with a thickness of 0.1 mm (similar to an A4 paper). Here is how thick it will be with each fold:

  • No fold – 0.1 mm thickness
  • One fold is equal to 2 times the thickness. The paper has two layers. It has a depth of not more than 0.2mm.
  • Two folds = 2². Upon folding, you will have two layers of material, after which the process is repeated.
  • Three folds = 2³. You will double four layers. There will be eight layers.
  • Four folds = 2⁴. This is doubling eight layers for a total of 16.
  • Five folds = 2⁵. Doubling 16 results in 32.
  • Six folds = 2⁶. Doubling 32 equals 64.
  • Seven folds = 2⁷. Doubling 64 equals 128.

To illustrate, a paper sheet of 7 folds consists of 128 layers. It will be 12.8 mm thick (128 x 0.1 equals 12.8mm). The paper is now too thick, and insufficient surface spaces support further folding.

Folding Paper to the Moon

What about 42 folds? These products will have 4,398,046,511,104 or 4.39 trillion levels each year. Theoretically, the paper thickness should be 439,800 millimeters / 439.8 billion meters. Consequently, 439.8 million meters is similar to 439804 km, which is precisely equal to the Earth and moon’s distance of 384,400km.

To answer the question of how is math used in the real world, take this example. When you fold a flat piece of paper enough times, it will exceed the distance from here to the moon. However, while being folded, the visible area of the paper diminishes by a factor ½ (1/2), but the actual area does not. The first fold reduces the paper to half its original size, making it 50% of its original size. It then will be one-fourth of the first fold.

After 42 folds, the visible surface area becomes less than an atom’s. Essentially, you cannot have it shrunk to that tiny size. Hence, kids can understand why saying you cannot fold a piece of paper more than seven times is an oversimplification. This is one of the direct math in real life examples.

Math in Real world

Saving Money

Help kids start a simple savings plan to introduce them to financial literacy. Motivate them to have manageable targets, such as putting aside money for a toy or an excursion. Teach them to track savings and decisions related to spending as they earn or receive Money. Such an approach is based on practice, helping to reinforce addition and subtraction while teaching children how to save or budget.

Investment Using Geometric Progression

There are many jokes related to math when speaking of school money matters. For examples of math in the real world, when individuals walk into a store to purchase 49 watermelons, in the case of math. You could, for instance, talk about Money in terms of stock markets and interest rates as an elementary instance of simple interest — or just fortune and wealth.

Considering that you invested $1,000 in banks and stocks, what would be your returns in a few years? Over time, the prices of various stocks go up, and $1,000 could rise to $10,000 or even $100,000 as a geometrical proportion. However, this is just a one-time investment. How about using $150 each month in stocks and banks?

One of the real world math examples is the crypto market, which has become faster several times. However, there are some occasions whereby fortunate investors amass millions within seconds due to rapid variations in the value of varied digital currencies.

Such instances demonstrate that math is an integral part of daily life, which will help improve the children’s knowledge of finance. This practice gives them answers to some of the most relatable questions: What’s the way to break the rat race? How to become independent?

Measurements

Jobs requiring measurements are numerous, such as in construction and post, meteorology, etc. Measurements count for everyone; hence, you should prove them to your child if they need to mail a package or find out whether their PlayStation fits the table.

Now, give them a meter rule and ask them to measure things instead. For real life math problems examples, get them to assist you in posting a parcel to your grandparents. Allow them to record the dimensions along with the weight of the packing box, or keep a note about the temperature record on a thermometer.

Searching For Discounts While Practicing Percentages

Take them through Amazon and eBay if your child is uncomfortable with percentages. One can learn percentages best while online shopping because of the off-percentage discounts. Their favorite shoes cost $100. How many can be saved with a twenty percent sign-in discount? This integration of a math problem into something they love will serve as an encouragement to young brains to master percentages.

In some cases, it is just as easy to calculate the percentage of a number by multiplication. For example, to determine what 20% of 5 is, multiply it by 0.2.

Grocery Shopping

They are giving kids a chance to understand addition and subtraction while grocery shopping, which is very beneficial. Have them tally items in the cart as they walk past each item. Ask them to take discount calculations and explain why prices decrease when a promotion occurs. This kind of hands-on experience will revisit the basics of real life situation math problems and show how math is needed daily in real-life situations.

Time Management

For most students, the notion of time is difficult to comprehend. It is an inevitable skill that the child must be familiar with from the beginning of their childhood. Children will also learn to use the clock to tell the time and thus be able to assign and finish tasks.

Organizational skills include being able to tell time and manage schedules, among others, which are very important for teaching children—using a clock to schedule activities/setting timers for tasks to help them understand time in terms of hours, minutes, and seconds. This approach further enhances math skills, which also helps instill discipline and self-responsibility in children. However, time management is an invaluable skill that transcends math and constitutes one of the essential attributes in individual development in general.

Building and Construction

Building projects like a birdhouse or a small shelf can be an engaging activity, showing kids how math real life problems are applied in real life. They also learn about measurements, geometry, and spatial relationships using materials. Building something with their hands gives them a tangible understanding of length, width, and height. This increases achievement experience, giving kids a chance to appreciate mathematics truly.

Sports Scores and Statistics

Venture into scores, statistics, averages, and other numbers that give meaning to the thrill of sports. Mathematical ideas such as averages, percentages, and basic arithmetic can be presented when discussing player statistics or team performance. The relationship between sport and math is established by kids who can determine a batting average, points per game, etc., relating them to their cherished activity.

Map Reading and Navigation

Map reading and navigation are other examples of how math is used in the real world to introduce basic geometry and measurement skills. Encourage your kids while planning trips and exploring neighborhoods by allowing them to understand distances, directions, and scale markings on maps.

Besides developing their spatial awareness, they learn that units are used in measuring for real world math problems examples. Length, weight, area, or volume, as well as geometric relations, help them solve real world problems math, which also become a part of how they explore and understand the world around them.

Budgeting for Allowance

Giving kids an allowance that will teach them about budgeting is a great way to empower them with financial skills, as they will learn how best they can save, spend, and give out, as well as how to budget for things. Motivating them to save a portion of their income and spending the rest while giving to others would not be wrong. It shows them how Money is essential while they are still young and makes it possible for them to learn the essential qualities of responsibility for finances at an early age. These skills in budgeting pave the way for further financial literacy.

Math in real world for children demonstrates why they learn such mathematics and engages them to understand such mathematics better. Children will develop a strong understanding of the relevance and application of mathematical concepts in their daily lives using math in real life scenarios to create the necessary base for further advancement.

Temperature and Weather

Speak about changes in temperature — those happening during the day and in different seasons. Assist them in recording temperatures, highs, and lows and their observation patterns. This activity also strengthens mathematics education by teaching students to gather, evaluate, and analyze information, leading to another skill—understanding statistics. Kids can also make simple graphs and charts that will help them understand the use of weather data as a mathematical representation.

Planting and Gardening

Evaluate plant spacing, developmental rates, and observational data on plant growth during time. Talk about counting the plant’s height, seeds sprouting time, and land size for various plants. Through gardening, one can relate math to the natural world as maths in the real world is applied in simple tasks such as planting and watering plants, where you are expected to achieve specific results at certain periods.

When cooking, little kids wonder about how much math is involved. So, allow your child to get closer with kitchen math: three pounds of tomatoes, four ounces of ice cream, one teaspoon of ground coffee, or 1/2 ounce of cinnamon. How much is the 1–1 proportion?

Moreover, when it comes to cooking, most recipes require you to have math skills, so this is an excellent opportunity to connect mathematics in the real world. Ratios, proportions, and basic math operations in cooking make sense.

A good presentation of math in fundamental topics using relatable examples helps children understand that this field is essential for their future. Compared to other approaches, this provides more chances of attracting children’s attention and inspiring interest in mathematical studies.

You may also register your child with Brighterly’s online math classes for further math real world problems practice. This recommendation is for kids to learn more effectively when they are in a relaxed manner. Your children will benefit from being made to use everyday language, math in the real world word problem sheets and worksheets, and engaging activities.

Jessica is a a seasoned math tutor with over a decade of experience in the field. With a BSc and Master’s degree in Mathematics, she enjoys nurturing math geniuses, regardless of their age, grade, and skills. Apart from tutoring, Jessica blogs at Brighterly. She also has experience in child psychology, homeschooling and curriculum consultation for schools and EdTech websites.

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Praxis Core Math

Course: praxis core math   >   unit 1.

  • Algebraic properties | Lesson
  • Algebraic properties | Worked example
  • Solution procedures | Lesson
  • Solution procedures | Worked example
  • Equivalent expressions | Lesson
  • Equivalent expressions | Worked example
  • Creating expressions and equations | Lesson
  • Creating expressions and equations | Worked example

Algebraic word problems | Lesson

  • Algebraic word problems | Worked example
  • Linear equations | Lesson
  • Linear equations | Worked example
  • Quadratic equations | Lesson
  • Quadratic equations | Worked example

What are algebraic word problems?

What skills are needed.

  • Translating sentences to equations
  • Solving linear equations with one variable
  • Evaluating algebraic expressions
  • Solving problems using Venn diagrams

How do we solve algebraic word problems?

  • Define a variable.
  • Write an equation using the variable.
  • Solve the equation.
  • If the variable is not the answer to the word problem, use the variable to calculate the answer.

What's a Venn diagram?

  • Your answer should be
  • an integer, like 6 ‍  
  • a simplified proper fraction, like 3 / 5 ‍  
  • a simplified improper fraction, like 7 / 4 ‍  
  • a mixed number, like 1   3 / 4 ‍  
  • an exact decimal, like 0.75 ‍  
  • a multiple of pi, like 12   pi ‍   or 2 / 3   pi ‍  
  • (Choice A)   $ 4 ‍   A $ 4 ‍  
  • (Choice B)   $ 5 ‍   B $ 5 ‍  
  • (Choice C)   $ 9 ‍   C $ 9 ‍  
  • (Choice D)   $ 14 ‍   D $ 14 ‍  
  • (Choice E)   $ 20 ‍   E $ 20 ‍  
  • (Choice A)   10 ‍   A 10 ‍  
  • (Choice B)   12 ‍   B 12 ‍  
  • (Choice C)   24 ‍   C 24 ‍  
  • (Choice D)   30 ‍   D 30 ‍  
  • (Choice E)   32 ‍   E 32 ‍  
  • (Choice A)   4 ‍   A 4 ‍  
  • (Choice B)   10 ‍   B 10 ‍  
  • (Choice C)   14 ‍   C 14 ‍  
  • (Choice D)   18 ‍   D 18 ‍  
  • (Choice E)   22 ‍   E 22 ‍  

Things to remember

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Real-Life Math Problems with Solutions

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How can you save money? How should a building be designed? How do you train for a competition? In the real world, math problems involve many disciplines, are complicated, and don’t have an answer key. In a math classroom, the problems usually need to be smaller scale and more focused. These problems still mimic and provide insight into the real world and can serve as a “diving board” into the sorts of math problems students encounter outside of math class.

Below are three open-ended math problems for Grades K, 2, and 4, which encourage students to explore math in real-life contexts. They get students thinking about how math can be used to solve problems in gardening, biology, and music.

Real-World Math Problems with Answers

These problems, which can all be found in HMH Into Math , do have clear solutions. Even though in all three cases many answers are possible, you can assess students’ understanding based on how they respond.

Kindergarten: 5-and-More Garden

  • Key Standard: Represent addition within 10 with drawings and objects.
  • Key Standard: Model with mathematics.

“ 5-and-More Garden ” asks students to create a visual representation of a garden bed by spinning a wheel and then “planting” different quantities of lettuce and carrots.

how to solve real life problems mathematics

In this activity, students will make groups to show 5 and the number on the spinner. Answers can be represented in a variety of ways: drawn on the provided garden teacher resource, created using paper and counters, or possibly built out of clay and other materials. If students use the spinner provided, there should be between 5–10 carrots and 5–10 lettuce plants. If there are only 5 of both, make sure the student did in fact spin 0 on the spinner both times! The image on the first page of the activity shows a possible model if students build a garden using clay.

Sample answers for the Challenge questions:

  • Carrots: 5 + 1 = 6
  • Lettuce: 5 + 3 = 8
  • If I pick 3 carrots, then 3 carrots will be left.

Grade 2: By the Sea

  • Key Standard: Understand that the three digits of a three-digit number represent the amounts of hundreds, tens, and ones.
  • Key Standard: Reason quantitatively.

“ By the Sea ” challenges students to imagine various quantities of plants and animals that they might observe by the sea and demonstrates the efficiency of using place value to denote three-digit numbers. They make a math storybook about the wildlife, choosing a number for each organism, writing the number two ways, and drawing to show the number using hundreds, tens, and ones.

how to solve real life problems mathematics

In this activity, students should choose a number between 100 and 999 for snails, pieces of seaweed, starfish, and clams. They should record each value accurately, matching the models they make with manipulatives. Drawings should match the values chosen. For example, if they chose 583 starfish, then for starfish, they should note there are 5 hundreds, 8 tens, and 3 ones and draw 5 large starfish, 8 medium starfish, and 3 small starfish.

  • Each page is made up of two types of plants and animals. On page 2, there are 583 starfish and 215 clams, so there are 798 animals total.
  • There are four types of plants or animals in the whole journal. On page 1, there are 296 snails and 317 pieces of seaweed. On page 2, there are 583 starfish and 215 clams. So, there are 1,411 plants and animals total. That is 14 hundreds, 1 ten, and 1 one.

Grade 4: Concert Calculations

  • Key Standard: Fluently add and subtract numbers through 1,000,000.
  • Key Standard: Make sense of problems and persevere in solving them.

“ Concert Calculations ” gives students a budget of $300,000 to spend on a tour for their band; students must use their critical thinking and decision-making skills to weigh cities with the appropriate stadium capacity against tour costs. Their goal is to reach a million attendees.

how to solve real life problems mathematics

In this activity, students select different cities around the U.S. They will need to keep track of costs (stadium + hotel + food for each city) and capacities (add the capacities for each city). If they find a successful answer for the activity, check the totals. The total cost should be under $300,000, and the total capacities should be over 1 million.

Sample answers for the Reflection Questions :

  • The numbers being added included 2-, 3-, and 5-digit numbers. I had to ensure I was adding ones, tens, hundreds, thousands, and ten thousands, paying attention to which digit was contained in which place value.
  • I decided to visit Atlanta because the stadiums had a high capacity (138,258) but low cost ($15,678). Evidence that this was a good decision is that I succeeded in having a total capacity of over 1,000,000 but did not go over $300,000.
  • Authors do not need stadiums like popular musicians do. I would plan a book tour similar to the concert tour, but I would look at the capacity for different bookstores in each city and go to as many as possible to make the total amount of people who can meet the author as high as possible.

HMH Into Math is a core mathematics curriculum for Grades K­­–8 that inspires students to see the value and purpose of math in their daily lives through rewarding, real-life activities and lessons.

To learn more about the indicators of a powerful math task and strategies to promote math talk in the classroom, watch our webinar The Power of a Great Math Task.

Get our FREE guide "Optimizing the Math Classroom: 6 Best Practices."

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5 Real Life Algebra Problems That You Solve Everyday

Algebra has a reputation for not being very useful in daily life. In fact, in my experience as a high school math teacher, the complaint that I get the most often is that we don’t spend enough time solving real life algebra problems.

You might be surprised to hear that I understand the frustration that my students experience. Unless we are solving real life algebra problems related to money in some way, algebra can feel very “artificial” or disconnected from real life.

My goal here is to walk you through 5 real life algebra problems that will give you a whole new appreciation for the application of algebra to the real-world. I am excited to help you see how many algebraic equations and algebraic concepts are applicable beyond just algebra word problems in your math class!

What is an Example of Algebra in Real Life?

While it is often seen as an abstract branch of mathematics, there are many real-life applications of algebra in everyday life. Now, it is unlikely that you will be solving quadratic equations while walking your dog, or solving real-world problems with linear equations while you play video games. But you can see examples of real life algebra problems all around you!

A simple example is when you want to quickly determine the total cost of a product including taxes, or the total cost after a discount from the original price. Knowing the total amount of money something will cost is a real-life scenario that everyone can relate to!

Depending on your chosen career path, you may see the use of algebra more often than others (I know I see it a lot in my daily life as a math teacher…!).

For example, if you are a business owner, you may use algebra to determine the number of labor hours to spread amongst your staff, or the lowest price you can sell your product for to break even.

For more uses of algebra, check out my list of 20  examples of algebra in real life !

What is an Example of an Algebra Problem in Real Life?

An algebra problem is a mathematical problem that requires the use of algebraic concepts and strategies to determine unknown values or unknown variables. Much like how the order of operations are required to evaluate numerical expressions, algebra problems require the problem solver to apply a set of rules in order to arrive at a solution.

Real world problems that require the use of algebra usually involve modelling real-life situations with  algebraic formulas . A formula is a specific equation that can be applied to solve a problem. Formulas make it possible to make predictions about a given real-life scenario.

For example, consider the following problem:

You are saving up for a new smartphone and currently have $200 in your savings account. Your plan is to save a certain amount of money each week from your allowance. If the smartphone costs $600, and you want to have enough money to buy it in 8 weeks, how much money should you save each week?

cell phone pixel art

To solve this problem, we first need to use the information provided in the problem to create an equation that models the real-life scenario. Thinking about the problem in terms of variables, we can define T as the total of the savings, and variable x as the amount saved each week.

Since we know that we have a fixed value of 200, we can use the following equation to model this real world problem:

$$T=200+8x$$

This equation says “the total saved is equal to the original $200 plus whatever amount is saved per week, for 8 weeks”.

Substituting the total of the smartphone allows us to begin solving for the unknown variable x. Remember, when solving algebraic equations, you must apply the same operation to both sides of the equation.

$$ \begin{split} T&=200+8x  \\ \\ 600&=200+8x  \\ \\ 600-200 &= 8x \\ \\ 400 &= 8x \\ \\ \frac{400}{8} &= \frac{8x}{8} \\\\ 50 &= x \end{split} $$

Therefore, since x = 50, you should save $50 each week in order to save enough money for the smartphone. For more practice with the algebra used in this solution, check out this free collection of  solving two step equations worksheets !

5 Real Life Algebra Problems with Step-By-Step Solutions

There are so many real-life examples of algebra problems, but I want to focus on 5 here that I believe will convince you of just how applicable algebra is to the real-world! So let’s dig into these 5 real-world algebraic word problems!

Example #1: Comparing Cell Phone Plans

Link is considering two different cell phone plans. Plan A charges a monthly fee of $30 and an additional $0.10 per minute of talk time. Plan B charges a monthly fee of $45 regardless of how much time is used talking. How many minutes of total time talking will make the plans equal in cost?

The best way to start this problem is by writing two equations to represent each scenario. If C represents total cost, and x represents minutes of talk time used, the equations can be written as follows:

  • Plan A: \(C=30+0.1x\)
  • Plan B: \(C=45\)

Setting the first equation equal to the second equation will allow us to employ algebra to solve for the number of minutes that makes the two plans equal.

$$ \begin{split}  30+0.1x&=45 \\ \\ 30-30+0.1x&=45-30 \\ \\ 0.1x&=15 \\ \\ \frac{0.1x}{0.1}&=\frac{15}{0.1} \\ \\ x&=150 \end{split} $$

Therefore, the two cell phone plans are equal when 150 minutes of total time talking are used.

Example #2: Calculating Gallons of Gas

Zelda is driving from Hyrule to the Mushroom Kingdom, which are 180 miles apart. Her car can travel 30 miles per gallon of gas. Write an equation to represent the number of gallons of gas, G, that Zelda needs for the trip in terms of the distance, d, she needs to travel. Then calculate how many gallons of gas she needs for this trip.

jerry can pixel art

The number of gallons of gas (G) Zelda needs for any trip can be represented by the equation \(G = \frac{d}{30}\). Since the distance between Hyrule and the Mushroom Kingdom is 180 miles, we can substitute 180 into the equation for  d  to determine the number of gallons of gas needed:

$$G=\frac{180}{30}=6$$

Therefore, Zelda needs 6 gallons of gas for her trip.

Example #3: Basketball Players in Action!

A basketball player shoots a basketball from a height of 6 feet above the ground. Unfortunately he completely misses the net and the ball bounces off court. A sports analyst models the path of the basketball using the equation \(h(t) = -16t^2 + 16t + 6\), where h(t) represents the height of the basketball above the ground in feet at time t seconds after the shot. Determine the time it takes for the basketball to hit the ground.

basketball pixel art

Since we are asked for when the ball hits the ground and  h(t)  is given as the height above the ground, we know that we are looking for the x-intercepts of this quadratic function. We therefore set the equation equal to zero and solve for x. 

Note that we cannot use  trinomial factoring  here since the quadratic is not factorable! Thankfully quadratic equations are solvable using the quadratic formula!

$$ \begin{split}  x&=\frac{-b \pm \sqrt{b^2-4ac}}{2a} \\\\ &=\frac{-16 \pm \sqrt{16^2-4(-16)(6)}}{2(-16)}\\\\ &=\frac{-16 \pm \sqrt{640}}{-32}\\\\ x&=-0.291 \\\\ x&=1.291 \end{split}$$

Therefore, the ball hits the ground after approximately 1.3 seconds. Remember that time cannot be negative, so the first answer is inadmissible and rejected!

Example #4: Saving for a Computer Game

You are saving to buy a new computer game that costs $90. You decide to save up for the computer game by depositing some money into a savings account that earns an annual interest rate of 5% (compounded monthly). You start with an initial deposit of $30 and plan to save for 22 months. Will you have enough to purchase the computer game?

pixel art cd

This is an example of a math problem that connects to financial problems people encounter everyday! Since the account you chose earns  interest , we can apply a compound interest formula to help us out here:

$$A=P(1+i)^n$$

In this formula:

  • A(t)  is the total amount of money.
  • P  is the initial deposit (which is $30 in this case).
  • i  is the monthly interest rate (5% annual interest, compounded monthly means that  i  is approximately 0.004167).
  • n  is the time that has elapsed (since we are working with months, we multiply by 12)

We can set up our equation and see if our total amount of money is greater than $90:

$$\begin{split}  A(22)&=30(1.004167)^{22 \times 12} \\\\ &=$89.93 \end{split} $$

Remember to always include a dollar sign in your answer and to round to two decimal places when working with money!

Since our answer is approximately equal to $90, we can say that you will have enough money after 22 months! It’s time to get saving!

Example #5: How Many Tickets Did the Movie Theater Sell?

A movie theater charges $10 per ticket for adults and $6 per ticket for children. On a particular day, the theater sold a total of 150 tickets, and the total revenue for the day was $1350. Write a system of equations to represent this real-life scenario and then solve for the number of adult and child tickets sold.

movie tickets pixel art

Let’s assume that variable  x  represents the number of adult tickets sold and variable  y  represents the number of child tickets sold. We can set up two linear equations as follows:

  • First Equation (the total number of tickets sold): \(x+y=150\) 
  • Second Equation (the total revenue from ticket sales is 1350): \(10x+6y=1350\) 

We can use substitution to solve this linear system by rearranging the first equation and substituting it into the second equation. You can catch a quick overview of the substitution process by checking out  this substitution video  on my YouTube channel!

Rearranging the first equation into a different form to solve for  y  results in \(y=-x+150\). Substituting this expression for  y  into the second equation results in: 

$$ \begin{split}  10x+6(-x+150)&=1350 \\ \\ 10x-6x+900&=1350 \\ \\ 4x&=450\\ \\ x&=112.5\\ \\ \end{split}  $$

We then substitute this value for  x  into our expression for  y: 

$$ \begin{split}  y&=-x+150 \\ \\ &=-112.50+150 \\ \\ &=37.5\\ \\ \end{split}  $$

Since we can’t have fractional ticket sales, we can say that approximately 112 adult tickets were sold and 38 child tickets were sold.

Appreciating Real Life Algebra Problems

While algebra is often seen as an abstract topic, I am hopeful that I have shown you just how applicable it can be to real-life situations! Some of these examples you may have even encountered in your own life!

Even if you aren’t drawing up complex equations and solving them while you are playing basketball, combining basic math and problem solving is one of the most important skills people can have in both their work and their lives. 

I hope that I have helped you further your understanding of algebra, while growing an appreciation for the different ways it can be used in your own life!

Did you find this guide to real life algebra problems helpful? Share this post and subscribe to Math By The Pixel on YouTube for more helpful mathematics content!

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Using mathematics to solve real world problems: the role of enablers

  • Original Article
  • Published: 21 June 2017
  • Volume 30 , pages 7–19, ( 2018 )

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  • Vincent Geiger   ORCID: orcid.org/0000-0002-0379-4753 1 ,
  • Gloria Stillman 2 ,
  • Jill Brown 3 ,
  • Peter Galbriath 4 &
  • Mogens Niss 5  

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The purpose of this article is to report on a newly funded research project in which we will investigate how secondary students apply mathematical modelling to effectively address real world situations. Through this study, we will identify factors, mathematical, cognitive, social and environmental that “enable” year 10/11 students to successfully begin the modelling process, that is, formulate and mathematise a real world problem. The 3-year study will take a design research approach in working intensively with six schools across two educational jurisdictions. It is anticipated that this research will generate new theoretical and practical insights into the role of “enablers” within the process of mathematisation, leading to the development of principles for the design and implementation for tasks that support students’ development as modellers.

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ACARA (2016). Australian Curriculum: Mathematics Aims Retrieved 27 Sept 2016 from http://www.australiancurriculum.edu.au/mathematics/aims .

Australian Industry Group (2015). Progressing STEM skills in Australia . Sydney: Author.

Blum, W. (2011). Can modelling be taught and learnt? Some answers from empirical research. In G. Kaiser, W. Blum, R. Borromeo Ferri, & G. Stillman (Eds.), Trends in teaching and learning of mathematical modelling (pp. 15–30). Dordrecht: Springer.

Chapter   Google Scholar  

Brown, J. (2015). Complexities of digital technology use and the teaching and learning of function. Computers & Education, 87 , 112–122.

Article   Google Scholar  

Burns, R. (2000). Introduction to research methods (4th ed.). Sydney: Longman.

Google Scholar  

Cai, J., & Melino, F. J. (2011). Metaphors: a powerful means for assessing students’ mathematical disposition. In D. J. Brahier & W. R. Speer (Eds.), Motivation and disposition: pathways to learning mathematics (pp. 147–156). Reston, VA: NCTM.

Cobb, P., Confrey, J., diSessa, A., Lehrer, R., & Schauble, L. (2003). Design experiments in educational research. Educational Researcher, 32 (1), 9–13.

English, L. D. (2016). Advancing mathematics education research within a STEM environment. In K. Makar, S. Dole, J. Visnovska, M. Goos, A. Bennison, & K. Fry (Eds.), Research in mathematics education in Australasia 2012–2015 (pp. 353–372). Singapore: Springer.

Flavell, J., Miller, P., & Miller, S. (2002). Cognitive development (4th ed.). Upper Saddle River, NJ: Prentice Hall.

Galbraith, P. (2015). “Noticing” in the practice of modelling as real world problem solving. In G. Kaiser & H.-W. Henn (Eds.), Werner Blum und seine Beiträge zum Modellieren im Mathematikunterricht: Realitätsbezüge im Mathematikunterricht (pp. 151–166). Wiesbaden: Springer.

Galbraith, P., Stillman, G., & Brown, J. (2010). Turning ideas into modeling problems. In R. Lesh, P. L. Galbraith, C. R. Haines, & A. Hurford (Eds.), Modeling students’mathematical competencies (pp. 133–144). New York: Springer.

Geiger, V., Faragher, R., & Goos, M. (2010). CAS-enabled technologies as ‘agents provocateurs’ in teaching and learning mathematical modelling in secondary school classrooms. Mathematics Education Research Journal, 22 (2), 48–68.

Geiger, V., Goos, M., & Dole, S. (2015a). The role of digital technologies in numeracy teaching and learning. International Journal of Science and Mathematics Education, 13 (5), 1115–1137. doi: 10.1007/s10763-014-9530-4 .

Geiger, V., Goos, M., & Forgasz, H. (2015b). A rich interpretation of numeracy for the 21 st century: a survey of the state of the field. ZDM–Mathematics Education, 47 (4), 531–548. doi: 10.1007/s11858-015-0708-1 .

Gould, H., & Wasserman, N. H. (2014). Striking a balance: students’ tendencies to oversimplify or overcomplicate in mathematical modelling. Journal of Mathematics Education at Teachers’ College, 5 (1), 27–34.

Jorgensen, R., & Lowrie, T. (2012). Digital games for learning mathematics: possibilities and limitations. In J. Dindyal, L. P. Cheng, & S. F. Ng (Eds.), Mathematics education: expanding horizons (pp. 378–384). Adelaide: MERGA.

Kaiser, G., & Maaβ, K. (2007). Modelling in lower secondary mathematics classroom—problems and opportunities. In W. Blum, P. Galbraith, H.-W. Henn, & M. Niss (Eds.), Modelling and applications in mathematics education (pp. 99–108). New York: Springer.

Marginson, S., Tytler, R., Freeman, B. & Roberts, K. (2013). STEM country comparisons: international comparisons of science, technology, engineering and mathematics (STEM) education. Report for the Australian Council of Learned Academies. Retrieved from www.acola.org.au on 5 Feb 2017.

Maaß, K. (2006). What are modelling competencies? ZDM –Mathematics Education, 38 (2), 113–142.

New York Academy of Sciences. (2015). The global STEM paradox . New York: Author.

Niss, M. (2010). Modeling a crucial aspect of students’ mathematical modeling. In R. Lesh, P. L. Galbraith, C. R. Haines, & A. Hurford (Eds.), Modeling students’ mathematical competencies (pp. 43–59). New York: Springer.

OECD. (2009). Mathematics framework. In OECD PISA 2009 assessment framework (pp. 83–123). Paris: OECD Publishing.

Office of the Chief Scientist. (2012). Mathematics, engineering and science in the national interest . Canberra: Commonwealth of Australia.

Paulos, J. A. (2000). Innumeracy: mathematical illiteracy and its consequences . London: Penguin.

Stacey, K., & Turner, R. (2015). PISA’s reporting of mathematical processes. In K. Beswick, T. Muir, & J. Wells (Eds.), Proceedings of the 39th conference of IGPME (Vol. 4, pp. 201–208). Hobart: PME.

STEM Task Force Report. (2014). Innovate: a blueprint for science, technology, engineering, and mathematics in California public education . Dublin, CA: Californians Dedicated to Education Foundation.

Stillman, G. (2004). Strategies employed by upper secondary students for overcoming or exploiting conditions affecting accessibility of applications task. Mathematics Education Research Journal, 16 (1), 41–70.

Stillman, G. (2010). Implementing applications and modelling in secondary school: issues for teaching and learning. In B. Kaur & J. Dindyal (Eds.), Mathematical applications and modelling (pp. 300–322). Singapore: World Scientific.

Stillman, G. (2011). Applying metacognitive knowledge and strategies in applications and modelling tasks at secondary school. In G. Kaiser, W. Blum, R. Borrromeo Ferri, & G. Stillman (Eds.), Trends in teaching and learning of mathematical modelling (pp. 165–180). Dordrecht: Springer.

Stillman, G., Brown, J., & Galbraith, P. (2010). Identifying challenges within transition phases of mathematical modelling activities at year 9. In R. L. Lesh, P. L. Galbraith, C. L. Haines, & A. Hurford (Eds.), Modeling students mathematical modeling competencies (pp. 385–398). New York: Springer.

Stillman, G., & Brown, J. (2014). Evidence of “implemented anticipation” in mathematising by beginning modellers. Mathematics Education Research Journal, 26 (4), 763–789. doi: 10.1007/s13394-014-0119-6 .

Stillman, G., Brown, J., & Geiger, V. (2015). Facilitating mathematisation in modelling by beginning modellers in secondary schools. In G. A. Stillman, W. Blum, & M. S. Biembengut (Eds.), Mathematical modelling in education, research and practice: cultural, social, and cognitive influences (pp. 93–103). Cham: Springer.

Thomson, S., De Bortoli, L., & Underwood, C. (2016a). PISA 2015: a first look at Australia’s results . Melbourne: ACER.

Thomson, S., Wernert, N., O’Grady, E., & Rodrigues, S. (2016b). TIMSS 2015: a first look at Australia’s results . Melbourne: ACER.

Treilibs, V. (1979). Formulation processes in mathematical modelling. – Thesis submitted to the University of Nottingham for the degree of Master of Philosophy.

Wijaya, A., Van den Heuvel-Panhuizen, M., Doorman, M., & Robitzsch, A. (2014). Difficulties in solving context based PISA mathematics tasks: an analysis of students’ errors. The Mathematics Enthusiast, 11 (3), 555–584.

Witzel, A., & Reiter, H. (2012). The problem-centred interview . London: Sage.

Book   Google Scholar  

Wood, L., Petocz, P., & Reid, A. (2012). Becoming a mathematician: an international perspective . Dordrecht: Springer.

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Geiger, V., Stillman, G., Brown, J. et al. Using mathematics to solve real world problems: the role of enablers. Math Ed Res J 30 , 7–19 (2018). https://doi.org/10.1007/s13394-017-0217-3

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How to Solve a Life Problem Mathematically?

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What is a Life Problem, and Why Solve it Mathematically?

In math, a problem is defined as a question or set of questions that can be solved using a given set of tools. In contrast, a life problem is any question or challenge that you encounter in your day-to-day existence. ¹ While some life problems can be easily solved using common sense and experience, others may be more difficult to figure out. This is where math can come in handy.

By applying mathematical principles to your problem, you can often find a more efficient solution than you would have otherwise. In addition, the process of solving a problem mathematically can help you develop new skills and improve your analytical thinking.

How Can You Solve a Life Problem Using Math?

Many people think of math as a dry and abstract discipline, but math is an incredibly powerful tool that can solve all sorts of problems. In fact, some of the most famous mathematicians in history have been able to solve complex life problems using nothing more than simple equations. For example, in the 18th century, French mathematician Pierre-Simon Laplace used math to predict the future position of planets. 2

What are Examples of Life Problems Solved Using Math?

Math is often viewed as an abstract area. However, it has several common applications in our daily life. Math can be used to solve all sorts of problems, big and small. For example, mathematical optimization can be used to find the most efficient route for a delivery truck or the best way to schedule employees at a call center. It can also be used to design more fuel-efficient cars and planes. That’s just the beginning!

Are There Limitations to Using Math to Solve Life Problems?

  • Not all life problems can be expressed in mathematical terms. For example, questions of morality and personal preferences cannot be reduced to numbers and equations. 
  • Even when a problem can be expressed mathematically, there may not be a clear solution. In many cases, math can only provide clues and possible approaches rather than a definitive answer. 
  • Calculation mistakes can lead to incorrect solutions, which can cause more problems than they solve.

Despite these limitations, math remains a powerful tool for understanding and solving many problems we face in life.

How to Know When You’ve Solved a Life Problem Mathematically?

Some general steps can be followed to arrive at a mathematical solution. 

  • First, identify the problem that needs to be solved. Next, gather information about the problem, including relevant data or background information. 
  • Once you clearly understand the problem, begin brainstorming possible solutions. Once you have generated a list of potential solutions, it’s time to start testing them out. 
  • Try to find a way to model the problem mathematically, and then experiment with different solutions to see which ones produce the best results.
  • Ultimately, the goal is to find a logical and effective solution. If you can do that, you can be confident that you’ve found a mathematical solution to your life problem.

Tips to Successfully Solve Life Problems Mathematically

Here are a few tips for solving life problems mathematically:

1) Break the problem down into smaller pieces. This will make it easier to find a pattern or solution.

2) Write down what you know about the problem. This will help you see what information is missing and what assumptions you are making.

3) Draw a picture or diagram. This can help visualize the problem and see relationships between different elements.

4) Persevere. There is no unsolvable problem in real life, so don’t give up! Keep working at it until you find a solution.

The Benefits of Using Math to Solve Life Problems

Math can be useful in solving all sorts of problems we face in everyday life. For example, math can help us budget our money, and calculate how much time we need to complete a task. Learning to use math to solve problems can make our lives simpler and more efficient.

In addition, using math can help in developing critical thinking skills that can be applied to other areas of our lives. For instance, if we learn to break down a complex problem into smaller pieces, we can apply this process to problems at work or in our relationships. Ultimately, learning how to use math to solve problems can positively impact every aspect of our lives.  If you are looking for ways to help your children with real-world problems,  BYJU’S FutureSchool blog  is a great resource. The blog posts offer mathematical solutions to everyday issues, from budgeting and travel to cooking and gardening. You can also find helpful tips for parents on how to support their children’s learning. Check out the blog today and see how you and your family can start using math to solve real-life problems!

References Mathematics as a Complex Problem-Solving Activity | Generation Ready. (2021, January 6). Mathematics as a Complex Problem-Solving Activity | Generation Ready. Retrieved November 9, 2022, from https://www.generationready.com/white-papers/mathematics-as-a-complex-problem-solving-activity/ Pierre Simon de Laplace and his true love for Astronomy and Mathematics Generation Ready. (2018, March 18). Pierre Simon de Laplace and his true love for Astronomy and Mathematics. Retrieved November 9, 2022, from http://scihi.org/laplace-astronomy-mathematics/

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  • Applications Of Linear Equations

Linear Equations : Applications

There are various applications of linear equations in Mathematics as well as in real life. An algebraic equation is an equality that includes variables and equal sign (=). A linear equation is an equation of degree one.

The knowledge of mathematics is frequently applied through word problems, and the applications of linear equations are observed on a wide scale to solve such word problems. Here, we are going to discuss the linear equation applications and how to use them in the real world with the help of an example.

What is Linear Equation?

A linear equation is an algebraic expression with a variable and equality sign (=), whose highest degree is equal to 1. For example, 2x – 1 = 5 is a linear equation.

  • A linear equation with one variable and degree one is called a linear equation in one variable. (Eg, 3x + 5 = 0)
  • A linear equation with degrees one and two variables is called a linear equation in two variables. (Eg, 3x + 5y = 0)

The graphical representation of linear equation is ax + by + c = 0, where,

  • a and b are coefficients
  • x and y are variables
  • c is a constant term

What are the Applications of Linear Equations?

In real life, the applications of linear equations are vast. To tackle real-life problems using algebra, we convert the given situation into mathematical statements in such a way that it clearly illustrates the relationship between the unknowns (variables) and the information provided. The following steps are involved while restating a situation into a mathematical statement:

  • Translate the problem statement into a mathematical statement and set it up in the form of algebraic expression in a manner it illustrates the problem aptly.
  • Identify the unknowns in the problem and assign variables ( quantity whose value can change depending upon the mathematical context ) to these unknown quantities.
  • Read the problem thoroughly multiple times and cite the data, phrases and keywords. Organize the information obtained sequentially.
  • Frame an equation with the help of the algebraic expression and the data provided in the problem statement and solve it using systematic techniques of equation solving.
  • Retrace your solution to the problem statement and analyze if it suits the criterion of the problem.

There you go!! Using these steps and applications of linear equations word problems can be solved easily.

Applications of Linear equations in Real life

  • Finding unknown age
  • Finding unknown angles in geometry
  • For calculation of speed, distance or time
  • Problems based on force and pressure

Let us look into an example to analyze the applications of linear equations in depth.

Applications of Linear Equations Solved Example

Rishi is twice as old as Vani. 10 years ago his age was thrice of Vani. Find their present ages.

In this word problem, the ages of Rishi and Vani are unknown quantities. Therefore as discussed above, let us first choose variables for the unknowns.

Let us assume that Vani’s present age is ‘x’ years. Since Rishi’s present age is 2 times that of Vani, therefore his present age can be assumed to be ‘2x’.

10 years ago, Vani’s age would have been ‘x – 10 ’, and Rishi’s age would have been ‘2x – 10’. According to the problem statement, 10 years ago, Rishi’s age was thrice of Vani, i.e. 2x – 10 = 3(x – 10).

We have our linear equation in the variable ‘x’ which clearly defines the problem statement. Now we can solve this linear equation easily and get the result.

Linear Equations

This implies that the current age of Vani is 20 years, and Rishi’s age is ‘2x,’ i.e. 40 years. Let us retrace our solution. If the present age of Vani is 20 years then 10 years ago her age would have been 10 years, and Rishi’s age would have been 30 years which satisfies our problem statement. Thus, applications of linear equations enable us to tackle such real-world problems.

Video Lesson on Applications of Linear Equation

how to solve real life problems mathematics

Related Articles

  • Solving Linear Equations
  • Algebra – Linear Equations Applications
  • Difference Between Linear and Nonlinear Equations
  • Graphing of Linear Equations
  • Linear Equation in One Variable
  • Linear Equations In Two Variables

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Authentic Assessment Methods for Mathematics

The foundation of authentic assessment revolves around evaluating a student’s ability to apply what they have learned in mathematics to a “real world” context.

Rather than rote learning and passive test-taking, authentic assessment math tests focus on a student’s analytical skills and the ability to integrate what they have learned along with creativity with written and oral skills. Also evaluated are the results of collaborative efforts of group projects. It is not just learning the process of computation that is important to know, but also how to take the finished product and apply it to another situation.

This need for an improved test to accurately assess a student’s growth has been developed. It is called the authentic assessment math test. Multiple choice tests do not often accurately reflect the individual student’s understanding of the material. It reflects whether a student is successful at memorization. Instead of tests that focus on recalling specific facts, the authentic assessment math test has students demonstrate the various skills and concepts they have learned and explain when it would be appropriate to use those facts and problem-solving skills in their own lives.

Six ways to use authentic assessment math in the classroom

Performance assessment.

Students can demonstrate what they have learned and how to solve problems through a collaborative effort in solving a complex problem together. Not only do they learn how to work in a team, but also how to brainstorm and utilize their separate grains of knowledge to benefit the whole.

Short investigations

Typically, a short investigation starts with a basic math problem (or can be adapted to any other school subject) in which the student can demonstrate how he or she has mastered the basic concepts and skills. As the teacher, ask the students to interpret, calculate, explain, describe or predict whatever it is they are analyzing. These are generally 60- to-90 minute tasks for an individual (or group projects) on which to work independently, writing answers to questions and then interviewed separately.

Open-response questions

A teacher can assess the student’s real-world understanding and how the analytical processes relate by, in a quiz setting, requesting open responses, like:

  • a brief written or oral answer
  • a mathematical solution
  • a diagram, chart or graph

These open-ended questions can be approximately 15-minute assessments and can be converted into a larger-scale project.

As students learn concepts throughout the school year, they can be documented and will reveal progress and improvements as well as allow for self-assessment, edits and revisions. They can be recorded in a number of ways, including:

  • journal writing
  • review by peers
  • artwork and diagrams
  • group reports
  • student notes and outlines
  • rough drafts to finished work

Self-assessment

After the teacher has clearly explained and provided the expectations prior to the project and then, once the projects are complete, ask the students to evaluate their own projects and participation. Responding to the following questions will help students learn to assess themselves and their work objectively:

  • What was the most difficult part of this project for you?
  • What do you think you should do next?
  • If you could do this task again, would you do anything differently? If yes, what?
  • What did you learn from this project?

Multiple-choice questions

Usually, multiple-choice questions do not reflect an authentic assessment math context. There are multiple-choice questions being developed that reveal an understanding of the mathematical ideas required as well as integrating more than one concept. These questions are designed to take about 2 or 3 minutes each.

Traits developed through authentic assessment math tests

This situational type of learning in which students are learning lessons on how to solve real-life problems can be utilized in mathematics. These ideas are presented as follows:

  • Thinking and reasoning:  Causing students to interact in such activities that include gathering data, exploration, investigation, interpretation, reasoning, modeling, designing, analyzing, formation of hypotheses, use of trial and error, generalization and solution-checking.
  • Settings:  Allowing the students to work individually or in smaller groups.
  • Mathematical tools: The students learn to use symbols, tables, graphs, drawings, calculators and computers.
  • Attitudes and dispositions:  Students in this type of learning environment learn persistence, self-regulating behaviors and reflection, participation and a special enthusiasm for learning various kinds of situations.

Learn educational techniques to improve student outcomes in mathematics. A master’s degree in math education helps you know about best practices for successful teaching in a mathematics class. 

You may also like to read

  • Advice on Using Authentic Assessment in Teaching
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Watch CBS News

Read the full decision in Trump's New York civil fraud case

By Graham Kates

Edited By Stefan Becket, Paula Cohen

Updated on: February 16, 2024 / 8:27 PM EST / CBS News

The judge overseeing the civil fraud case in New York against former President Donald Trump and the Trump Organization has issued his long-awaited ruling , five weeks after the  trial in the case concluded . 

Judge Arthur Engoron ordered Trump and his company to pay $354 million in fines — a total that jumps to $453.5 million when pre-judgment interest is factored in. It also bars them from seeking loans from financial institutions in New York for a period of three years, and includes a three-year ban on Trump serving as an officer or director of any New York corporation. 

Additional penalties were ordered for Trump's sons, Eric and Donald Trump Jr., who are executives at the company, and two former executives, Allen Weisselberg and Jeffrey McConney.

New York Attorney General Letitia James  brought the civil suit  in 2022, seeking a  penalty that grew to $370 million  and asking the judge to bar Trump from doing business in the state. 

Judge Engoron had already ruled in September that Trump and the other defendants were  liable for fraud , based on the evidence presented through pretrial filings. 

The judge had largely affirmed James' allegations that Trump and others at his company had inflated valuations of his properties by hundreds of millions of dollars over a the course of a decade and misrepresented his wealth by billions in a scheme, the state said, intended to trick banks and insurers into offering more favorable deal terms.

Trump and his legal team long expected a defeat, with the former president decrying the case as "rigged" and a "sham" and his lawyers laying the groundwork for an appeal before the decision was even issued. He is expected to appeal.

Read Judge Engoron's decision here :

  • The Trump Organization
  • Donald Trump
  • Letitia James

Graham Kates is an investigative reporter covering criminal justice, privacy issues and information security for CBS News Digital. Contact Graham at [email protected] or [email protected]

More from CBS News

Trump fraud verdict includes 3-year ban on running a New York business

Fulton County prosecutors decline to call DA Fani Willis back for questioning

Sen. Tim Scott: Voters "more focused on their future than Donald Trump's past"

Full transcript of "Face the Nation," Feb. 18, 2024

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