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Module 1: Problem Solving Strategies

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Unlike exercises, there is never a simple recipe for solving a problem. You can get better and better at solving problems, both by building up your background knowledge and by simply practicing. As you solve more problems (and learn how other people solved them), you learn strategies and techniques that can be useful. But no single strategy works every time.

Pólya’s How to Solve It

George Pólya was a great champion in the field of teaching effective problem solving skills. He was born in Hungary in 1887, received his Ph.D. at the University of Budapest, and was a professor at Stanford University (among other universities). He wrote many mathematical papers along with three books, most famously, “How to Solve it.” Pólya died at the age 98 in 1985.1

1. Image of Pólya by Thane Plambeck from Palo Alto, California (Flickr) [CC BY

Screen Shot 2018-08-30 at 4.43.05 PM.png

In 1945, Pólya published the short book How to Solve It , which gave a four-step method for solving mathematical problems:

First, you have to understand the problem.

After understanding, then make a plan.

Carry out the plan.

Look back on your work. How could it be better?

This is all well and good, but how do you actually do these steps?!?! Steps 1. and 2. are particularly mysterious! How do you “make a plan?” That is where you need some tools in your toolbox, and some experience to draw upon.

Much has been written since 1945 to explain these steps in more detail, but the truth is that they are more art than science. This is where math becomes a creative endeavor (and where it becomes so much fun). We will articulate some useful problem solving strategies, but no such list will ever be complete. This is really just a start to help you on your way. The best way to become a skilled problem solver is to learn the background material well, and then to solve a lot of problems!

Problem Solving Strategy 1 (Guess and Test)

Make a guess and test to see if it satisfies the demands of the problem. If it doesn't, alter the guess appropriately and check again. Keep doing this until you find a solution.

Mr. Jones has a total of 25 chickens and cows on his farm. How many of each does he have if all together there are 76 feet?

Step 1: Understanding the problem

We are given in the problem that there are 25 chickens and cows.

All together there are 76 feet.

Chickens have 2 feet and cows have 4 feet.

We are trying to determine how many cows and how many chickens Mr. Jones has on his farm.

Step 2: Devise a plan

Going to use Guess and test along with making a tab

Many times the strategy below is used with guess and test.

Make a table and look for a pattern:

Procedure: Make a table reflecting the data in the problem. If done in an orderly way, such a table will often reveal patterns and relationships that suggest how the problem can be solved.

Step 3: Carry out the plan:

Notice we are going in the wrong direction! The total number of feet is decreasing!

Better! The total number of feet are increasing!

Step 4: Looking back:

Check: 12 + 13 = 25 heads

24 + 52 = 76 feet.

We have found the solution to this problem. I could use this strategy when there are a limited number of possible answers and when two items are the same but they have one characteristic that is different.

Videos to watch:

1. Click on this link to see an example of “Guess and Test”

http://www.mathstories.com/strategies.htm

2. Click on this link to see another example of Guess and Test.

http://www.mathinaction.org/problem-solving-strategies.html

Check in question 1:

clipboard_e6298bbd7c7f66d9eb9affcd33892ef0d.png

Place the digits 8, 10, 11, 12, and 13 in the circles to make the sums across and vertically equal 31. (5 points)

Check in question 2:

Old McDonald has 250 chickens and goats in the barnyard. Altogether there are 760 feet . How many of each animal does he have? Make sure you use Polya’s 4 problem solving steps. (12 points)

Problem Solving Strategy 2 (Draw a Picture). Some problems are obviously about a geometric situation, and it is clear you want to draw a picture and mark down all of the given information before you try to solve it. But even for a problem that is not geometric thinking visually can help!

Videos to watch demonstrating how to use "Draw a Picture".

1. Click on this link to see an example of “Draw a Picture”

2. Click on this link to see another example of Draw a Picture.

Problem Solving Strategy 3 ( Using a variable to find the sum of a sequence.)

Gauss's strategy for sequences.

last term = fixed number ( n -1) + first term

The fix number is the the amount each term is increasing or decreasing by. "n" is the number of terms you have. You can use this formula to find the last term in the sequence or the number of terms you have in a sequence.

Ex: 2, 5, 8, ... Find the 200th term.

Last term = 3(200-1) +2

Last term is 599.

To find the sum of a sequence: sum = [(first term + last term) (number of terms)]/ 2

Sum = (2 + 599) (200) then divide by 2

Sum = 60,100

Check in question 3: (10 points)

Find the 320 th term of 7, 10, 13, 16 …

Then find the sum of the first 320 terms.

Problem Solving Strategy 4 (Working Backwards)

This is considered a strategy in many schools. If you are given an answer, and the steps that were taken to arrive at that answer, you should be able to determine the starting point.

Videos to watch demonstrating of “Working Backwards”

https://www.youtube.com/watch?v=5FFWTsMEeJw

Karen is thinking of a number. If you double it, and subtract 7, you obtain 11. What is Karen’s number?

1. We start with 11 and work backwards.

2. The opposite of subtraction is addition. We will add 7 to 11. We are now at 18.

3. The opposite of doubling something is dividing by 2. 18/2 = 9

4. This should be our answer. Looking back:

9 x 2 = 18 -7 = 11

5. We have the right answer.

Check in question 4:

Christina is thinking of a number.

If you multiply her number by 93, add 6, and divide by 3, you obtain 436. What is her number? Solve this problem by working backwards. (5 points)

Problem Solving Strategy 5 (Looking for a Pattern)

Definition: A sequence is a pattern involving an ordered arrangement of numbers.

We first need to find a pattern.

Ask yourself as you search for a pattern – are the numbers growing steadily larger? Steadily smaller? How is each number related?

Example 1: 1, 4, 7, 10, 13…

Find the next 2 numbers. The pattern is each number is increasing by 3. The next two numbers would be 16 and 19.

Example 2: 1, 4, 9, 16 … find the next 2 numbers. It looks like each successive number is increase by the next odd number. 1 + 3 = 4.

So the next number would be

25 + 11 = 36

Example 3: 10, 7, 4, 1, -2… find the next 2 numbers.

In this sequence, the numbers are decreasing by 3. So the next 2 numbers would be -2 -3 = -5

-5 – 3 = -8

Example 4: 1, 2, 4, 8 … find the next two numbers.

This example is a little bit harder. The numbers are increasing but not by a constant. Maybe a factor?

So each number is being multiplied by 2.

16 x 2 = 32

1. Click on this link to see an example of “Looking for a Pattern”

2. Click on this link to see another example of Looking for a Pattern.

Problem Solving Strategy 6 (Make a List)

Example 1 : Can perfect squares end in a 2 or a 3?

List all the squares of the numbers 1 to 20.

1 4 9 16 25 36 49 64 81 100 121 144 169 196 225 256 289 324 361 400.

Now look at the number in the ones digits. Notice they are 0, 1, 4, 5, 6, or 9. Notice none of the perfect squares end in 2, 3, 7, or 8. This list suggests that perfect squares cannot end in a 2, 3, 7 or 8.

How many different amounts of money can you have in your pocket if you have only three coins including only dimes and quarters?

Quarter’s dimes

0 3 30 cents

1 2 45 cents

2 1 60 cents

3 0 75 cents

Videos demonstrating "Make a List"

Check in question 5:

How many ways can you make change for 23 cents using only pennies, nickels, and dimes? (10 points)

Problem Solving Strategy 7 (Solve a Simpler Problem)

Geometric Sequences:

How would we find the nth term?

Solve a simpler problem:

1, 3, 9, 27.

1. To get from 1 to 3 what did we do?

2. To get from 3 to 9 what did we do?

Let’s set up a table:

Term Number what did we do

problem solving lesson 1 7

Looking back: How would you find the nth term?

problem solving lesson 1 7

Find the 10 th term of the above sequence.

Let L = the tenth term

problem solving lesson 1 7

Problem Solving Strategy 8 (Process of Elimination)

This strategy can be used when there is only one possible solution.

I’m thinking of a number.

The number is odd.

It is more than 1 but less than 100.

It is greater than 20.

It is less than 5 times 7.

The sum of the digits is 7.

It is evenly divisible by 5.

a. We know it is an odd number between 1 and 100.

b. It is greater than 20 but less than 35

21, 23, 25, 27, 29, 31, 33, 35. These are the possibilities.

c. The sum of the digits is 7

21 (2+1=3) No 23 (2+3 = 5) No 25 (2 + 5= 7) Yes Using the same process we see there are no other numbers that meet this criteria. Also we notice 25 is divisible by 5. By using the strategy elimination, we have found our answer.

Check in question 6: (8 points)

Jose is thinking of a number.

The number is not odd.

The sum of the digits is divisible by 2.

The number is a multiple of 11.

It is greater than 5 times 4.

It is a multiple of 6

It is less than 7 times 8 +23

What is the number?

Click on this link for a quick review of the problem solving strategies.

https://garyhall.org.uk/maths-problem-solving-strategies.html

problem solving lesson 1 7

Problem Solving Activities: 7 Strategies

  • Critical Thinking

problem solving lesson 1 7

Problem solving can be a daunting aspect of effective mathematics teaching, but it does not have to be! In this post, I share seven strategic ways to integrate problem solving into your everyday math program.

In the middle of our problem solving lesson, my district math coordinator stopped by for a surprise walkthrough. 

I was so excited!

We were in the middle of what I thought was the most brilliant math lesson– teaching my students how to solve problem solving tasks using specific problem solving strategies. 

It was a proud moment for me!

Each week, I presented a new problem solving strategy and the students completed problems that emphasized the strategy. 

Genius right? 

After observing my class, my district coordinator pulled me aside to chat. I was excited to talk to her about my brilliant plan, but she told me I should provide the tasks and let my students come up with ways to solve the problems. Then, as students shared their work, I could revoice the student’s strategies and give them an official name. 

What a crushing blow! Just when I thought I did something special, I find out I did it all wrong. 

I took some time to consider her advice. Once I acknowledged she was right, I was able to make BIG changes to the way I taught problem solving in the classroom. 

When I Finally Saw the Light

To give my students an opportunity to engage in more authentic problem solving which would lead them to use a larger variety of problem solving strategies, I decided to vary the activities and the way I approached problem solving with my students. 

Problem Solving Activities

Here are seven ways to strategically reinforce problem solving skills in your classroom. 

This is an example of seasonal problem solving activities.

Seasonal Problem Solving

Many teachers use word problems as problem solving tasks. Instead, try engaging your students with non-routine tasks that look like word problems but require more than the use of addition, subtraction, multiplication, and division to complete. Seasonal problem solving tasks and daily challenges are a perfect way to celebrate the season and have a little fun too!

Cooperative Problem Solving Tasks

Go cooperative! If you’ve got a few extra minutes, have students work on problem solving tasks in small groups. After working through the task, students create a poster to help explain their solution process and then post their poster around the classroom. Students then complete a gallery walk of the posters in the classroom and provide feedback via sticky notes or during a math talk session.

Notice and Wonder

Before beginning a problem solving task, such as a seasonal problem solving task, conduct a Notice and Wonder session. To do this, ask students what they notice about the problem. Then, ask them what they wonder about the problem. This will give students an opportunity to highlight the unique characteristics and conditions of the problem as they try to make sense of it. 

Want a better experience? Remove the stimulus, or question, and allow students to wonder about the problem. Try it! You’ll gain some great insight into how your students think about a problem.

This is an example of a math starter.

Math Starters

Start your math block with a math starter, critical thinking activities designed to get your students thinking about math and provide opportunities to “sneak” in grade-level content and skills in a fun and engaging way. These tasks are quick, designed to take no more than five minutes, and provide a great way to turn-on your students’ brains. Read more about math starters here ! 

Create your own puzzle box! The puzzle box is a set of puzzles and math challenges I use as fast finisher tasks for my students when they finish an assignment or need an extra challenge. The box can be a file box, file crate, or even a wall chart. It includes a variety of activities so all students can find a challenge that suits their interests and ability level.

Calculators

Use calculators! For some reason, this tool is not one many students get to use frequently; however, it’s important students have a chance to practice using it in the classroom. After all, almost everyone has access to a calculator on their cell phones. There are also some standardized tests that allow students to use them, so it’s important for us to practice using calculators in the classroom. Plus, calculators can be fun learning tools all by themselves!

Three-Act Math Tasks

Use a three-act math task to engage students with a content-focused, real-world problem! These math tasks were created with math modeling in mind– students are presented with a scenario and then given clues and hints to help them solve the problem. There are several sites where you can find these awesome math tasks, including Dan Meyer’s Three-Act Math Tasks and Graham Fletcher’s 3-Acts Lessons . 

Getting the Most from Each of the Problem Solving Activities

When students participate in problem solving activities, it is important to ask guiding, not leading, questions. This provides students with the support necessary to move forward in their thinking and it provides teachers with a more in-depth understanding of student thinking. Selecting an initial question and then analyzing a student’s response tells teachers where to go next. 

Ready to jump in? Grab a free set of problem solving challenges like the ones pictured using the form below. 

Which of the problem solving activities will you try first? Respond in the comments below.

problem solving lesson 1 7

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problem solving lesson 1 7

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This is a very cool site. I hope it takes off and is well received by teachers. I work in mathematical problem solving and help prepare pre-service teachers in mathematics.

Thank you, Scott! Best wishes to you and your pre-service teachers this year!

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Brought to you by CU Engineering (University of Colorado Boulder)

FREE K-12 standards-aligned STEM

curriculum for educators everywhere!

Find more at TeachEngineering.org .

  • TeachEngineering
  • Problem Solving

Lesson Problem Solving

Grade Level: 8 (6-8)

(two 40-minute class periods)

Lesson Dependency: The Energy Problem

Subject Areas: Physical Science, Science and Technology

Partial design

  • Print lesson and its associated curriculum

Curriculum in this Unit Units serve as guides to a particular content or subject area. Nested under units are lessons (in purple) and hands-on activities (in blue). Note that not all lessons and activities will exist under a unit, and instead may exist as "standalone" curriculum.

  • Energy Forms and States Demonstrations
  • Energy Conversions
  • Watt Meters to Measure Energy Consumption
  • Household Energy Audit
  • Light vs. Heat Bulbs
  • Efficiency of an Electromechanical System
  • Efficiency of a Water Heating System
  • Solving Energy Problems
  • Energy Projects

TE Newsletter

Engineering connection, learning objectives, worksheets and attachments, more curriculum like this, introduction/motivation, associated activities, user comments & tips.

Engineering… designed to work wonders

Scientists, engineers and ordinary people use problem solving each day to work out solutions to various problems. Using a systematic and iterative procedure to solve a problem is efficient and provides a logical flow of knowledge and progress.

  • Students demonstrate an understanding of the Technological Method of Problem Solving.
  • Students are able to apply the Technological Method of Problem Solving to a real-life problem.

Educational Standards Each TeachEngineering lesson or activity is correlated to one or more K-12 science, technology, engineering or math (STEM) educational standards. All 100,000+ K-12 STEM standards covered in TeachEngineering are collected, maintained and packaged by the Achievement Standards Network (ASN) , a project of D2L (www.achievementstandards.org). In the ASN, standards are hierarchically structured: first by source; e.g. , by state; within source by type; e.g. , science or mathematics; within type by subtype, then by grade, etc .

Ngss: next generation science standards - science.

View aligned curriculum

Do you agree with this alignment? Thanks for your feedback!

International Technology and Engineering Educators Association - Technology

State standards, national science education standards - science.

Scientists, engineers, and ordinary people use problem solving each day to work out solutions to various problems. Using a systematic and iterative procedure to solve a problem is efficient and provides a logical flow of knowledge and progress.

In this unit, we use what is called "The Technological Method of Problem Solving." This is a seven-step procedure that is highly iterative—you may go back and forth among the listed steps, and may not always follow them in order. Remember that in most engineering projects, more than one good answer exists. The goal is to get to the best solution for a given problem. Following the lesson conduct the associated activities Egg Drop and Solving Energy Problems for students to employ problem solving methods and techniques. 

Lesson Background and Concepts for Teachers

The overall concept that is important in this lesson is: Using a standard method or procedure to solve problems makes the process easier and more effective.

1) Describe the problem, 2) describe the results you want, 3) gather information, 4) think of solutions, 5) choose the best solution, 6) implement the solution, 7) evaluate results and make necessary changes. Reenter the design spiral at any step to revise as necessary.

The specific process of problem solving used in this unit was adapted from an eighth-grade technology textbook written for New York State standard technology curriculum. The process is shown in Figure 1, with details included below. The spiral shape shows that this is an iterative, not linear, process. The process can skip ahead (for example, build a model early in the process to test a proof of concept) and go backwards (learn more about the problem or potential solutions if early ideas do not work well).

This process provides a reference that can be reiterated throughout the unit as students learn new material or ideas that are relevant to the completion of their unit projects.

Brainstorming about what we know about a problem or project and what we need to find out to move forward in a project is often a good starting point when faced with a new problem. This type of questioning provides a basis and relevance that is useful in other energy science and technology units. In this unit, the general problem that is addressed is the fact that Americans use a lot of energy, with the consequences that we have a dwindling supply of fossil fuels, and we are emitting a lot of carbon dioxide and other air pollutants. The specific project that students are assigned to address is an aspect of this problem that requires them to identify an action they can take in their own live to reduce their overall energy (or fossil fuel) consumption.

The Seven Steps of Problem Solving

1.  Identify the problem

Clearly state the problem. (Short, sweet and to the point. This is the "big picture" problem, not the specific project you have been assigned.)

2.  Establish what you want to achieve

  • Completion of a specific project that will help to solve the overall problem.
  • In one sentence answer the following question: How will I know I've completed this project?
  • List criteria and constraints: Criteria are things you want the solution to have. Constraints are limitations, sometimes called specifications, or restrictions that should be part of the solution. They could be the type of materials, the size or weight the solution must meet, the specific tools or machines you have available, time you have to complete the task and cost of construction or materials.

3.  Gather information and research

  • Research is sometimes needed both to better understand the problem itself as well as possible solutions.
  • Don't reinvent the wheel – looking at other solutions can lead to better solutions.
  • Use past experiences.

4.  Brainstorm possible solutions

List and/or sketch (as appropriate) as many solutions as you can think of.

5.  Choose the best solution

Evaluate solution by: 1) Comparing possible solution against constraints and criteria 2) Making trade-offs to identify "best."

6.  Implement the solution

  • Develop plans that include (as required): drawings with measurements, details of construction, construction procedure.
  • Define tasks and resources necessary for implementation.
  • Implement actual plan as appropriate for your particular project.

7.  Test and evaluate the solution

  • Compare the solution against the criteria and constraints.
  • Define how you might modify the solution for different or better results.
  • Egg Drop - Use this demonstration or activity to introduce and use the problem solving method. Encourages creative design.
  • Solving Energy Problems - Unit project is assigned and students begin with problem solving techniques to begin to address project. Mostly they learn that they do not know enough yet to solve the problem.
  • Energy Projects - Students use what they learned about energy systems to create a project related to identifying and carrying out a personal change to reduce energy consumption.

The results of the problem solving activity provide a basis for the entire semester project. Collect and review the worksheets to make sure that students are started on the right track.

problem solving lesson 1 7

Learn the basics of the analysis of forces engineers perform at the truss joints to calculate the strength of a truss bridge known as the “method of joints.” Find the tensions and compressions to solve systems of linear equations where the size depends on the number of elements and nodes in the trus...

preview of 'Doing the Math: Analysis of Forces in a Truss Bridge' Lesson

Through role playing and problem solving, this lesson sets the stage for a friendly competition between groups to design and build a shielding device to protect humans traveling in space. The instructor asks students—how might we design radiation shielding for space travel?

preview of 'Shielding from Cosmic Radiation: Space Agency Scenario' Lesson

A process for technical problem solving is introduced and applied to a fun demonstration. Given the success with the demo, the iterative nature of the process can be illustrated.

preview of 'Egg Drop' Activity

The culminating energy project is introduced and the technical problem solving process is applied to get students started on the project. By the end of the class, students should have a good perspective on what they have already learned and what they still need to learn to complete the project.

preview of 'Solving Energy Problems' Activity

Hacker, M, Barden B., Living with Technology , 2nd edition. Albany NY: Delmar Publishers, 1993.

Other Related Information

This lesson was originally published by the Clarkson University K-12 Project Based Learning Partnership Program and may be accessed at http://internal.clarkson.edu/highschool/k12/project/energysystems.html.

Contributors

Supporting program, acknowledgements.

This lesson was developed under National Science Foundation grants no. DUE 0428127 and DGE 0338216. However, these contents do not necessarily represent the policies of the National Science Foundation, and you should not assume endorsement by the federal government.

Last modified: August 16, 2023

Curriculum  /  Math  /  7th Grade  /  Unit 6: Geometry  /  Lesson 1

Lesson 1 of 21

Criteria for Success

Tips for teachers, anchor problems, problem set, target task, additional practice.

Identify and determine values of angles in complementary and supplementary relationships.

Common Core Standards

Core standards.

The core standards covered in this lesson

7.G.B.5 — Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.

Foundational Standards

The foundational standards covered in this lesson

Measurement and Data

4.MD.C.5 — Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement:

4.MD.C.7 — Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure.

The essential concepts students need to demonstrate or understand to achieve the lesson objective

  • Understand that complementary angles are angles whose measures add up to 90°, and supplementary angles are angles whose measures add up to 180°.  
  • Identify pairs of complementary and supplementary angles in angle diagrams.
  • Find the values of angles using complementary and supplementary angle relationships and equations.

Suggestions for teachers to help them teach this lesson

Students studied angles in fourth grade, where they recognized angles as shapes formed when two rays share a common endpoint. They understood that angle measures are additive, and they solved addition and subtraction problems to find missing angles. In this lesson, students formally define complementary and supplementary angles , and they start to develop their understanding of angle relationships and how they can represent these relationships using equations. 

Unlock features to optimize your prep time, plan engaging lessons, and monitor student progress.

Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding

problem solving lesson 1 7

a.   Name an acute angle.

b.   Name an obtuse angle.

c.   Name a right angle.

d.   Name two adjacent angles.

e.   Name two nonadjacent angles.

Guiding Questions

Two angle diagrams are shown below. Use the information about each diagram to find the measure of the angle described.

a.   Points $$Q$$ , $$R$$ , and $$T$$  lie on a straight line, as shown below. Find the measure of $$\angle SRT$$ .

problem solving lesson 1 7

b.   Angle  $${ABC}$$ is a right angle. Find the value of  $$x$$ .

problem solving lesson 1 7

In the diagram below, point $$P$$  lies on line $${QT}$$ .

problem solving lesson 1 7

a.   Write and solve an equation to find the measure of $$x$$ .

b.   What is the measure of $$\angle RPT$$ ?

A set of suggested resources or problem types that teachers can turn into a problem set

Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.

A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved

In the diagram below, point $$A$$  lies on line  $${BD}$$  and  $$\angle CAE$$ is a right angle.

problem solving lesson 1 7

a.   Describe the relationship between $$\angle DAE$$  and $$\angle EAB$$ .

b.   Name two angles that are complementary.

c.   If the measure of angle  $$DAC$$  is 74°, what is the measure of angle $$ DAE$$ ?

Student Response

The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.

  • Include problems where students practice identifying and determining angles in supplementary and complementary angle relationships.
  • Include problems where students write simple equations to represent the relationship between a missing angle and its supplementary or complementary pair. 
  • Open Up Resources Grade 7 Unit 7 Practice Problems — Lesson 2
  • EngageNY Mathematics Grade 7 Mathematics > Module 6 > Topic A > Lesson 1 — Exercises and Problem Set; note, these problems incorporate verbal expressions to describe angle relationships, for example, the measurement of a larger angle is three times the measurement of a complementary smaller angle

Topic A: Angle Relationships

Use vertical, complementary, and supplementary angle relationships to find missing angles. 

Use equations to solve for unknown angles. (Part 1)

Use equations to solve for unknown angles. (Part 2)

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Topic B: Circles

Define circle and identify the measurements radius, diameter, and circumference. 

Determine the relationship between the circumference and diameter of a circle and use it to solve problems. 

Solve real-world and mathematical problems using the relationship between the circumference of a circle and its diameter. 

Determine the relationship between the area and radius of a circle and use it to solve problems.

Solve real-world and mathematical problems using the relationship between the area of a circle and its radius.

Solve problems involving area and circumference of two-dimensional figures (Part 1).

7.G.B.4 7.G.B.6

Solve problems involving area and circumference of two-dimensional figures (Part 2).

Topic C: Building Polygons and Triangles

Draw two-dimensional geometric shapes using rulers, protractors, and compasses. 

7.G.A.2 7.G.B.5

Determine if three side lengths will create a unique triangle or no triangle. 

Identify unique and identical triangles. 

Determine if conditions describe a unique triangle, no triangle, or more than one triangle.

Topic D: Solid Figures

Identify and describe two-dimensional figures that result from slicing three-dimensional figures.

Find the surface area of right prisms.

 Find the surface area of right pyramids.

Find the volume of right prisms and pyramids.

Solve real-world and mathematical problems involving volume.

Distinguish between and solve real-world problems involving volume and surface area.

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Chapter 1, Lesson 1: A Plan for Problem Solving

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  1. Lesson 8 Problem Solving Practice Financial Literacy Answer Key

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  2. Problem Solving

    problem solving lesson 1 7

  3. Printable Problem Solving Worksheets Grade 1 Free Printable First Grade

    problem solving lesson 1 7

  4. Problem Solving

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  5. problem solving lesson plans

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  6. Problem-Solving Lesson Plan for Pre-K

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VIDEO

  1. Problem Solving Lesson 2 Thursday 11 16 2023

  2. Lesson 02 Problem Solving on Tries

  3. Easy math problem

  4. SSC Selection Post Reasoning Class 2024

  5. Lesson 1.7 Multiply by 2-Digit Numbers

  6. Solve if you're A genius

COMMENTS

  1. Problem Solving

    Problem Solving - Tens and Ones - Lesson 1.7 - YouTube 0:00 / 6:54 Problem Solving - Tens and Ones - Lesson 1.7 Mrmathblog 25K subscribers 16K views 6 years ago 2nd Grade This...

  2. 2nd Grade Math 1.7, Word Problem Solving, Tens and Ones

    105 11K views 3 years ago 2nd Grade Math Course ...more ...more 2nd Grade Math 1.8, Counting Patterns Within 100 JoAnn's School A pattern is an ordered set of numbers or objects that helps us to...

  3. Math Topic 1-7 Problem Solving: Look For and Use Structure

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  4. Module 1: Problem Solving Strategies

    Step 2: Devise a plan. Going to use Guess and test along with making a tab. Many times the strategy below is used with guess and test. Make a table and look for a pattern: Procedure: Make a table reflecting the data in the problem.

  5. Problem Solving Activities: 7 Strategies

    Problem Solving Activities: 7 Strategies 2 Comments Critical Thinking Problem solving can be a daunting aspect of effective mathematics teaching, but it does not have to be! In this post, I share seven strategic ways to integrate problem solving into your everyday math program.

  6. Problem Solving

    Introduction/Motivation Scientists, engineers, and ordinary people use problem solving each day to work out solutions to various problems. Using a systematic and iterative procedure to solve a problem is efficient and provides a logical flow of knowledge and progress.

  7. PDF Practice Workbook

    TO THE STUDENTThisPractice Workbookgives you additional examples and problems for the concept exercises in each lesson.The exercises are designed to aid your study of mathematics by reinforcing important mathematical skills needed to succeed in the everyday world.The materials are organized by chapter and lesson, with one Practiceworksheet for e...

  8. PDF Practice and Homework Name 1.7 Lesson Problem Solving • Tens and Ones

    Lesson 1.7 Chapter 1 fifty-three 53 1. Ann is grouping 38 rocks. She can put them into groups of 10 rocks or as ... ways Mr. Grant can buy the felt? Problem Solving • Tens and Ones Find a pattern to solve. Groups of 10 rocks Single rocks Packs of 10 pieces Single pieces 3. Math Choose one of the problems above. Describe how you organized the ...

  9. Lesson 1

    Expressions and Equations. 7.EE.B.4.A — Solve word problems leading to equations of the form px + q = r and p (x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach.

  10. Lesson 1

    4.MD.C.5. Measurement and Data. 4.MD.C.5 — Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: Search. 4.MD.C.7. Measurement and Data. 4.MD.C.7 — Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle ...

  11. Ready Mathematics: Practice and Problem Solving Grade 7

    Chapter Unit 1: The Number System Section 1: Understand Addition of Positive and Negative Integers Section 2: Understand Subtracting of Positive and Negative Integers Section 3: Add and Subtract Positive and Negative Integers Section 4: Multiple and Divide Positive and Negative Integers Section 5: Terminating and Repeating Decimals Section 6:

  12. IXL skill plan

    Lesson 1-7: Practice Solving Problems: Add To 1. "Add to" word problems with change unknown - up to 10 ... Lesson 11-7: Math Practices & Problem Solving: Model with Math 12 Topic 12. Measure Lengths Lesson 12-1: Compare and Order by Length 1. Compare objects: length and height Lesson 12-1: Compare and Order by ...

  13. 7th Grade Math

    Article Area of circles review Area and circumference of circles Article Complementary and supplementary angles review Vertical, complementary, and supplementary angles Unit 1: Proportional relationships 0/1600 Mastery points

  14. Chapter 1: Introduction to Algebra and Functions

    Lesson Resources Extra Examples Group Activity Cards Personal Tutor Self-Check Quizzes. Hotmath Homework Help Math Review Math Tools Multilingual eGlossary Visual Vocabulary Cards Online Calculators Study to Go. Mathematics. Home > Chapter 1. Math Connects: Concepts, Skills, and Problem Solving, Course 2. Chapter 1: Introduction to Algebra and ...

  15. 10 ways to teach problem solving (with FREE curriculum!)

    10. Connect students with change makers. Entrepreneurs all over the world are using the processes students use in GPS: The Series. Put your students in touch with them to bring concepts to life. GPS: The Series offers six videos called "The Putri Files", where GPS team leader Putri interviews these entrepreneurs.

  16. PDF Word Problem Practice Workbook

    To the StudentThis Word Problem Practice Workbookgives you additional examples and problems for the concept exercises in each lesson.The exercises are designed to aid your study of mathematics by reinforcing important mathematical skills needed to succeed in the everyday world.The materials are organized by chapter and lesson, with one Word Prob...

  17. Grade 1 Math 7.4, Problem solving, Compare numbers

    How a model will help us solve word problems and compare tens and ones. We can use counters, draw a picture of counters, or use cards to model numbers. Seve...

  18. PDF Lesson 1: Section 1.1 Mathematics and Problem Solving Assoc. Prof. Lisa

    Lesson 1: Section 1.1 Mathematics and Problem Solving Assoc. Prof. Lisa Brown 1 Notes and Class Participation Directions: Print this handout. Use this handout to take notes as you read pages 4 - 13, watch the lecture video, and view the PowerPoint slides. After you complete this handout, scan pages 2, 3, 4, 6, and 7, and

  19. Overcoming Obstacles

    2. Students apply the steps of the decision making process to problem solving. Divide the class into groups of four or five students. Assign each group one character from the starter (Marta, Ali, or Rodrigo). Give each group one copy of the "Problem Solving" activity sheet and a character to focus on. Reread the starter to the class.

  20. enVisionmath 2.0: Grade 7 Volume 1

    Expert Solutions enVisionmath 2.0: Grade 7 Volume 1 ISBN: 9780328908783 Scott Foresman Textbook solutions Verified Chapter 1: Integers and Rational Numbers Section 1.0: Review What You Know! Section 1.1: Relate Integers and Their Opposites Section 1.2: Understand Rational Numbers Section 1.3: Add Integers Section 1.4: Subtract Integers Section 1.5:

  21. Lesson 7

    Understand the problem. To be able to solve a problem, understanding what the problem asks for is very important. 2. Devise a plan. Successful problems solvers uses a variety of techniques when they attempt to solve a. problem. The following techniques are most useful: Techniques. 1.

  22. Chapter 1, Lesson 1: A Plan for Problem Solving

    Chapter 1, Lesson 1: A Plan for Problem Solving. Mathematics.

  23. 2nd Grade Go Math Lesson 1.7

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  24. Rivers Edge RV Resort on Instagram: "1. Freedom to Roam: With an RV

    riversedgervresort on February 6, 2024: "1. Freedom to Roam: With an RV, the open road becomes your playground. Escape the confines of rou..."