Solving Word Questions

With LOTS of examples!

In Algebra we often have word questions like:

Example: Sam and Alex play tennis.

On the weekend Sam played 4 more games than Alex did, and together they played 12 games.

How many games did Alex play?

How do we solve them?

The trick is to break the solution into two parts:

Turn the English into Algebra.

Then use Algebra to solve.

Turning English into Algebra

To turn the English into Algebra it helps to:

  • Read the whole thing first
  • Do a sketch if possible
  • Assign letters for the values
  • Find or work out formulas

You should also write down what is actually being asked for , so you know where you are going and when you have arrived!

Also look for key words:

Thinking Clearly

Some wording can be tricky, making it hard to think "the right way around", such as:

Example: Sam has 2 dollars less than Alex. How do we write this as an equation?

  • Let S = dollars Sam has
  • Let A = dollars Alex has

Now ... is that: S − 2 = A

or should it be: S = A − 2

or should it be: S = 2 − A

The correct answer is S = A − 2

( S − 2 = A is a common mistake, as the question is written "Sam ... 2 less ... Alex")

Example: on our street there are twice as many dogs as cats. How do we write this as an equation?

  • Let D = number of dogs
  • Let C = number of cats

Now ... is that: 2D = C

or should it be: D = 2C

Think carefully now!

The correct answer is D = 2C

( 2D = C is a common mistake, as the question is written "twice ... dogs ... cats")

Let's start with a really simple example so we see how it's done:

Example: A rectangular garden is 12m by 5m, what is its area ?

Turn the English into Algebra:

  • Use w for width of rectangle: w = 12m
  • Use h for height of rectangle: h = 5m

Formula for Area of a Rectangle : A = w × h

We are being asked for the Area.

A = w × h = 12 × 5 = 60 m 2

The area is 60 square meters .

Now let's try the example from the top of the page:

tennis

Example: Sam and Alex play Tennis. On the weekend Sam played 4 more games than Alex did, and together they played 12 games. How many games did Alex play?

  • Use S for how many games Sam played
  • Use A for how many games Alex played

We know that Sam played 4 more games than Alex, so: S = A + 4

And we know that together they played 12 games: S + A = 12

We are being asked for how many games Alex played: A

Which means that Alex played 4 games of tennis.

Check: Sam played 4 more games than Alex, so Sam played 8 games. Together they played 8 + 4 = 12 games. Yes!

A slightly harder example:

table

Example: Alex and Sam also build tables. Together they make 10 tables in 12 days. Alex working alone can make 10 in 30 days. How long would it take Sam working alone to make 10 tables?

  • Use a for Alex's work rate
  • Use s for Sam's work rate

12 days of Alex and Sam is 10 tables, so: 12a + 12s = 10

30 days of Alex alone is also 10 tables: 30a = 10

We are being asked how long it would take Sam to make 10 tables.

30a = 10 , so Alex's rate (tables per day) is: a = 10/30 = 1/3

Which means that Sam's rate is half a table a day (faster than Alex!)

So 10 tables would take Sam just 20 days.

Should Sam be paid more I wonder?

And another "substitution" example:

track

Example: Jenna is training hard to qualify for the National Games. She has a regular weekly routine, training for five hours a day on some days and 3 hours a day on the other days. She trains altogether 27 hours in a seven day week. On how many days does she train for five hours?

  • The number of "5 hour" days: d
  • The number of "3 hour" days: e

We know there are seven days in the week, so: d + e = 7

And she trains 27 hours in a week, with d 5 hour days and e 3 hour days: 5d + 3e = 27

We are being asked for how many days she trains for 5 hours: d

The number of "5 hour" days is 3

Check : She trains for 5 hours on 3 days a week, so she must train for 3 hours a day on the other 4 days of the week.

3 × 5 hours = 15 hours, plus 4 × 3 hours = 12 hours gives a total of 27 hours

Some examples from Geometry:

Example: A circle has an area of 12 mm 2 , what is its radius?

  • Use A for Area: A = 12 mm 2
  • Use r for radius

And the formula for Area is: A = π r 2

We are being asked for the radius.

We need to rearrange the formula to find the area

Example: A cube has a volume of 125 mm 3 , what is its surface area?

Make a quick sketch:

  • Use V for Volume
  • Use A for Area
  • Use s for side length of cube
  • Volume of a cube: V = s 3
  • Surface area of a cube: A = 6s 2

We are being asked for the surface area.

First work out s using the volume formula:

Now we can calculate surface area:

An example about Money:

pizza

Example: Joel works at the local pizza parlor. When he works overtime he earns 1¼ times the normal rate. One week Joel worked for 40 hours at the normal rate of pay and also worked 12 hours overtime. If Joel earned $660 altogether in that week, what is his normal rate of pay?

  • Joel's normal rate of pay: $N per hour
  • Joel works for 40 hours at $N per hour = $40N
  • When Joel does overtime he earns 1¼ times the normal rate = $1.25N per hour
  • Joel works for 12 hours at $1.25N per hour = $(12 × 1¼N) = $15N
  • And together he earned $660, so:

$40N + $(12 × 1¼N) = $660

We are being asked for Joel's normal rate of pay $N.

So Joel’s normal rate of pay is $12 per hour

Joel’s normal rate of pay is $12 per hour, so his overtime rate is 1¼ × $12 per hour = $15 per hour. So his normal pay of 40 × $12 = $480, plus his overtime pay of 12 × $15 = $180 gives us a total of $660

More about Money, with these two examples involving Compound Interest

Example: Alex puts $2000 in the bank at an annual compound interest of 11%. How much will it be worth in 3 years?

This is the compound interest formula:

So we will use these letters:

  • Present Value PV = $2,000
  • Interest Rate (as a decimal): r = 0.11
  • Number of Periods: n = 3
  • Future Value (the value we want): FV

We are being asked for the Future Value: FV

Example: Roger deposited $1,000 into a savings account. The money earned interest compounded annually at the same rate. After nine years Roger's deposit has grown to $1,551.33 What was the annual rate of interest for the savings account?

The compound interest formula:

  • Present Value PV = $1,000
  • Interest Rate (the value we want): r
  • Number of Periods: n = 9
  • Future Value: FV = $1,551.33

We are being asked for the Interest Rate: r

So the annual rate of interest is 5%

Check : $1,000 × (1.05) 9 = $1,000 × 1.55133 = $1,551.33

And an example of a Ratio question:

Example: At the start of the year the ratio of boys to girls in a class is 2 : 1 But now, half a year later, four boys have left the class and there are two new girls. The ratio of boys to girls is now 4 : 3 How many students are there altogether now?

  • Number of boys now: b
  • Number of girls now: g

The current ratio is 4 : 3

Which can be rearranged to 3b = 4g

At the start of the year there was (b + 4) boys and (g − 2) girls, and the ratio was 2 : 1

b + 4 g − 2 = 2 1

Which can be rearranged to b + 4 = 2(g − 2)

We are being asked for how many students there are altogether now: b + g

There are 12 girls !

And 3b = 4g , so b = 4g/3 = 4 × 12 / 3 = 16 , so there are 16 boys

So there are now 12 girls and 16 boys in the class, making 28 students altogether .

There are now 16 boys and 12 girls, so the ratio of boys to girls is 16 : 12 = 4 : 3 At the start of the year there were 20 boys and 10 girls, so the ratio was 20 : 10 = 2 : 1

And now for some Quadratic Equations :

Example: The product of two consecutive even integers is 168. What are the integers?

Consecutive means one after the other. And they are even , so they could be 2 and 4, or 4 and 6, etc.

We will call the smaller integer n , and so the larger integer must be n+2

And we are told the product (what we get after multiplying) is 168, so we know:

n(n + 2) = 168

We are being asked for the integers

That is a Quadratic Equation , and there are many ways to solve it. Using the Quadratic Equation Solver we get −14 and 12.

Check −14: −14(−14 + 2) = (−14)×(−12) = 168 YES

Check 12: 12(12 + 2) = 12×14 = 168 YES

So there are two solutions: −14 and −12 is one, 12 and 14 is the other.

Note: we could have also tried "guess and check":

  • We could try, say, n=10: 10(12) = 120 NO (too small)
  • Next we could try n=12: 12(14) = 168 YES

But unless we remember that multiplying two negatives make a positive we might overlook the other solution of (−14)×(−12).

Example: You are an Architect. Your client wants a room twice as long as it is wide. They also want a 3m wide veranda along the long side. Your client has 56 square meters of beautiful marble tiles to cover the whole area. What should the length of the room be?

Let's first make a sketch so we get things right!:

  • the length of the room: L
  • the width of the room: W
  • the total Area including veranda: A
  • the width of the room is half its length: W = ½L
  • the total area is the (room width + 3) times the length: A = (W+3) × L = 56

We are being asked for the length of the room: L

This is a quadratic equation , there are many ways to solve it, this time let's use factoring :

And so L = 8 or −14

There are two solutions to the quadratic equation, but only one of them is possible since the length of the room cannot be negative!

So the length of the room is 8 m

L = 8, so W = ½L = 4

So the area of the rectangle = (W+3) × L = 7 × 8 = 56

There we are ...

... I hope these examples will help you get the idea of how to handle word questions. Now how about some practice?

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Problems with Solutions and Answers for Grade 10

Grade 10 math word problems with answers and solutions are presented.

A real estate agent received a 6% commission on the selling price of a house. If his commission was $8,880, what was the selling price of the house?

Pin it!

  • An airplane flies against the wind from A to B in 8 hours. The same airplane returns from B to A, in the same direction as the wind, in 7 hours. Find the ratio of the speed of the airplane (in still air) to the speed of the wind.

Solutions to the Above Problems

  • 6% x = 8,880 : x = selling price of house. x = $148,000 : solve for x.
  • 3000 revolutions / minute = 3000×360 degrees / 60 seconds = 18,000 degrees / second
  • L × W = 300 : area , L is the length and W is the width. 2 L + 2 W = 70 : perimeter L = 35 - w : solve for L (35 - W) × W = 300 : substitute in the area equation W = 15 and L = 20 : solve for W and find L using L = 35 - w.
  • Let h be the height of the trapezoid. area = (1/2) × h × (10 + 10 + 3 + 4) = 270 h = 20 : solve for h 20 2 + 3 2 = L 2 : Pythagora's theorem applied to the right triangle on the left. L = sqrt(409) 20 2 + 4 2 = R 2 : Pythagora's theorem applied to the right triangle on the right. R = sqrt(416) perimeter = sqrt(409) + 10 + sqrt(416) + 17 = 27 + sqrt(409) + sqrt(416)
  • 400 rev / minute = 400 × 60 rev / 60 minutes = 24,000 rev / hour 24,000 × C = 72,000 m : C is the circumference C = 3 meters
  • Let x be the price of one shirt, y be the price of one pair of trousers and z be the price of one hat. 4x + 4y + 2z = 560 : 9x + 9y + 6z = 1,290 3x + 3y + 2z = 430 : divide all terms of equation C by 3 x + y = 130 : subtract equation D from equation B 3(x + y) + 2z = 430 : equation D with factored terms. 3*130 + 2z = 430 z = 20 : solve for z x + y + z = 130 + 20 = $150
  • x : the total number of toys x/10 : the number of toys for first child x/10 + 12 : the number of toys for second child x/10 + 1 : the number of toys for the third child 2(x/10 + 1) : the number of toys for the fourth child x/10 + x/10 + 12 + x/10 + 1 + 2(x/10 + 1) = x x = 30 toys : solve for x
  • Let n the number of students who scored below 60 and N the number of students who scored 60 or more. Xi the grades below 60 and Yi the grades 60 or above. [sum(Xi) + sum(Yi)] / 20 = 70 : class average sum(Xi) / n = 50 : average for less that 60 sum(Yi) / N = 75 : average for 60 or more 50n + 75N = 1400 : combine the above equations n + N = 20 : total number of students n = 4 and N = 16 : solve the above system
  • f(x) = -3(x - 10)(x - 4) = -3 x 2 + 42 x - 120 : expand and obtain a quadratic function h = -b/2a = - 42/(-6) = 7 : h is the value of x for which f has a maximum value f(h) = f(7) = 27 : maximum value of f.
  • (1 - 1/10)(1 - 1/11)(1 - 1/12)...(1 - 1/99)(1 - 1/100) = (9/10)(10/11)(11/12)...(98/99)(99/100) = 9/100 : simplify
  • Let: S be the speed of the boat in still water, r be the rate of the water current and d the distance between A and B. d = 3(S + r) : boat travelling down river d = 5(S - r) : boat travelling up river 3(S + r) = 5(S - r) r = S / 4 : solve above equation for r d = 3(S + S/4) : substitute r by S/4 in equation B d / S = 3.75 hours = 3 hours and 45 minutes.
  • Let: S be the speed of the airplane in still air, r be the speed of the wind and d the distance between A and B. d = 8(S - r) : airplane flies against the wind d = 7(S + r) : airplane flies in the same direction as the wind 8(S - r) = 7(S + r) S/r = 15

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  • Math Article
  • Word Problems On Integers

Integers: Word Problems On Integers

An arithmetic operation is an elementary branch of mathematics. Arithmetical operations include addition, subtraction, multiplication and division. Arithmetic operations are applicable to different types of numbers including integers.

Integers are a special group of numbers that do not have a fractional or a decimal part. It includes positive numbers, negative numbers and zero.  Arithmetic operations on integers are similar to that of whole numbers. Since integers can be positive or negative numbers i.e. as these numbers are preceded either by a positive (+) or a negative sign (-), it makes them a little confusing concept. Therefore, they are different from whole numbers . Let us now see how various arithmetical operations can be performed on integers with the help of a few word problems. Solve the following word problems using various rules of operations of integers.

Word problems on integers Examples:

Example 1: Shyak has overdrawn his checking account by Rs.38.  The bank debited him Rs.20 for an overdraft fee.  Later, he deposited Rs.150.  What is his current balance?

Solution:  Given,

Total amount deposited= Rs. 150

Amount overdrew by Shyak= Rs. 38

Amount charged by bank= Rs. 20

⇒ Debit amount= -20

Total amount debited = (-38) + (-20) = -58

Current balance= Total deposit +Total Debit

Hence, the current balance is Rs. 92.

Example 2: Anna is a microbiology student. She was doing research on optimum temperature for the survival of different strains of bacteria. Studies showed that bacteria X need optimum temperature of -31˚C while bacteria Y need optimum temperature of -56˚C. What is the temperature difference?

Solution: Given,

Optimum temperature for bacteria X = -31˚C

Optimum temperature for bacteria Y= -56˚C

Temperature difference= Optimum temperature for bacteria X – Optimum temperature for bacteria Y

⇒ (-31) – (-56)

Hence, temperature difference is 25˚C.

Example 3: A submarine submerges at the rate of 5 m/min. If it descends from 20 m above the sea level, how long will it take to reach 250 m below sea level?

Initial position = 20 m    (above sea level)

Final position = 250 m    (below sea level)

Total depth it submerged = (250+20) = 270 m

Thus, the submarine travelled 270 m below sea level.

Time taken to submerge 1 meter = 1/5 minutes

Time taken to submerge 270 m = 270 (1/5) = 54 min

Hence, the submarine will reach 250 m below sea level in 54 minutes.

To solve more problems on the topic, download BYJU’S – The Learning App and watch interactive videos. Also, take free tests to practice for exams.

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how to solve word problems in maths class 10

Strategies for Solving Word Problems – Math

how to solve word problems in maths class 10

It’s one thing to solve a math equation when all of the numbers are given to you but with word problems, when you start adding reading to the mix, that’s when it gets especially tricky.

The simple addition of those words ramps up the difficulty (and sometimes the math anxiety) by about 100!

How can you help your students become confident word problem solvers? By teaching your students to solve word problems in a step by step, organized way, you will give them the tools they need to solve word problems in a much more effective way.

Here are the seven strategies I use to help students solve word problems.

1. read the entire word problem.

Before students look for keywords and try to figure out what to do, they need to slow down a bit and read the whole word problem once (and even better, twice). This helps kids get the bigger picture to be able to understand it a little better too.

2. Think About the Word Problem

Students need to ask themselves three questions every time they are faced with a word problem. These questions will help them to set up a plan for solving the problem.

Here are the questions:

A. what exactly is the question.

What is the problem asking? Often times, curriculum writers include extra information in the problem for seemingly no good reason, except maybe to train kids to ignore that extraneous information (grrrr!). Students need to be able to stay focused, ignore those extra details, and find out what the real question is in a particular problem.

B. What do I need in order to find the answer?

Students need to narrow it down, even more, to figure out what is needed to solve the problem, whether it’s adding, subtracting, multiplying, dividing, or some combination of those. They’ll need a general idea of which information will be used (or not used) and what they’ll be doing.

This is where key words become very helpful. When students learn to recognize that certain words mean to add (like in all, altogether, combined ), while others mean to subtract, multiply, or to divide, it helps them decide how to proceed a little better

Here’s a Key Words Chart I like to use for teaching word problems. The handout could be copied at a smaller size and glued into interactive math notebooks. It could be placed in math folders or in binders under the math section if your students use binders.

One year I made huge math signs (addition, subtraction, multiplication, and divide symbols) and wrote the keywords around the symbols. These served as a permanent reminder of keywords for word problems in the classroom.

If you’d like to download this FREE Key Words handout, click here:

how to solve word problems in maths class 10

C. What information do I already have?

This is where students will focus in on the numbers which will be used to solve the problem.

3. Write on the Word Problem

This step reinforces the thinking which took place in step number two. Students use a pencil or colored pencils to notate information on worksheets (not books of course, unless they’re consumable). There are lots of ways to do this, but here’s what I like to do:

  • Circle any numbers you’ll use.
  • Lightly cross out any information you don’t need.
  • Underline the phrase or sentence which tells exactly what you’ll need to find.

4. Draw a Simple Picture and Label It

Drawing pictures using simple shapes like squares, circles, and rectangles help students visualize problems. Adding numbers or names as labels help too.

For example, if the word problem says that there were five boxes and each box had 4 apples in it, kids can draw five squares with the number four in each square. Instantly, kids can see the answer so much more easily!

5. Estimate the Answer Before Solving

Having a general idea of a ballpark answer for the problem lets students know if their actual answer is reasonable or not. This quick, rough estimate is a good math habit to get into. It helps students really think about their answer’s accuracy when the problem is finally solved.

6. Check Your Work When Done

This strategy goes along with the fifth strategy. One of the phrases I constantly use during math time is, Is your answer reasonable ? I want students to do more than to be number crunchers but to really think about what those numbers mean.

Also, when students get into the habit of checking work, they are more apt to catch careless mistakes, which are often the root of incorrect answers.

7. Practice Word Problems Often

Just like it takes practice to learn to play the clarinet, to dribble a ball in soccer, and to draw realistically, it takes practice to become a master word problem solver.

When students practice word problems, often several things happen. Word problems become less scary (no, really).

They start to notice similarities in types of problems and are able to more quickly understand how to solve them. They will gain confidence even when dealing with new types of word problems, knowing that they have successfully solved many word problems in the past.

If you’re looking for some word problem task cards, I have quite a few of them for 3rd – 5th graders.

This 3rd grade math task cards bundle has word problems in almost every one of its 30 task card sets..

There are also specific sets that are dedicated to word problems and two-step word problems too. I love these because there’s a task card set for every standard.

CLICK HERE to take a look at 3rd grade:

3rd Grade Math Task Cards Mega Bundle | 3rd Grade Math Centers Bundle

This 4th Grade Math Task Cards Bundle also has lots of word problems in almost every single of its 30 task card sets. These cards are perfect for centers, whole class, and for one on one.

CLICK HERE to see 4th grade:

th Grade 960 Math Task Cards Mega Bundle | 4th Grade Math Centers

This 5th Grade Math Task Cards Bundle is also loaded with word problems to give your students focused practice.

CLICK HERE to take a look at 5th grade:

5th Grade Math Task Cards Mega Bundle - 5th Grade Math Centers

Want to try a FREE set of math task cards to see what you think?

3rd Grade: Rounding Whole Numbers Task Cards

4th Grade: Convert Fractions and Decimals Task Cards

5th Grade: Read, Write, and Compare Decimals Task Cards

Thanks so much for stopping by!

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  • Equation Problems of Age

Equation Problems of Age are part of the quantitative aptitude section. In the equation problems of age, the questions are such that they result in equations. These equations could become either linear or non-linear and they will have solutions that will represent the age of the people in the question. In the following sections, we will some of the examples of these problems and also learn about the various shortcuts that we can use to solve them. Let us start with some easier examples and concepts below.

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Equations are a convenient way to represent conditions or relations between two or more quantities . An equation could have one, two or more unknowns. The basic rule is that if the number of unknowns is equal to the number of conditions, then these equations are solvable, otherwise not. We will see some important examples here but first, let us see the following tricks.

If the age of a person is ‘x’, then ‘n’ years after today, the age = x + n. Similarly, n years in the past, the age of this would have been x – n years.

Example 1: A father and his son decide to sum their age. The sum is equal to sixty years. Six years ago the age of the father was five times the age of the son. Six years from now the son’s age will be:

A) 23 years               B) 19 years                  C) 20 years                        D) 22 years

Answer: Suppose that the present age of the son is = x years. Then the father’s age is (60 -x) years. Notice that we are trying to reduce the problem into as few variables as possible. As per the second condition of the question, we have:

The age of the father six years ago = (60 – x) – 6 years = 54 – x years.

Similarly the age of the son six years ago will be x – 6 years. Therefore as per the second condition , we have;

54 – x = 5(x – 6) or 54 – x = 5x – 30 and we can write 6x = 84

Hence, we have x = 14 years. Thus the son’s age after 6 years = (x+ 6) = (14 + 6) = 20 years. Hence the correct option is C) 20 years.

More Solved Examples

Example 2: The difference in the age of two people is 20 years. If 5 years ago, the elder one of the two was 5 times as old as the younger one, then their present ages are equal to:

A) 20 and 30 years respectively

B) 30 and 10 years respectively

C) 15 and 35 years respectively

D) 32 and 22 years respectively

Answer: The first step is to find the equation. Let the age of the younger person be x. Then the age of the second person will be (x + 20) years. Five years ago their ages would have been x – 5 years and x + 20 years. Therefore as per the question, we have: 5 (x – 5) = (x + 20 – 5) or 4x = 40 or x = 10. Therefore the ages are 10 years for the younger one and (10 + 20) years = 30 years for the elder one.

Example 3: Yasir is fifteen years elder than Mujtaba. Five years ago, Yasir was three times as old as Mujtaba. Then Yasir’s present age will be:

A) 29 years                  B) 30 years                     C) 31 years                        D) 32 years

Answer: Let the age of Yasir be = x years. Then the age of Mujtaba will be equal to x – 15 years. Now let us move on to the second condition. Five years ago the age of Yasir will be equal to x – 5 years. Also, the age of Mujtaba five years ago will be x – 15 – 6 years = x – 21 years. As per the question, we have:

3(x – 21) = x – 5 or 3x – 63 = x  – 5. Therefore we have: 2x = 58 and hence x = 29 years. Therefore Yasir’s present age is 29 years and the correct option is A) 29 years.

Example 4: Ten years ago, the age of a person’s mother was three times the age of her son. Ten years hence, the mother’s age will be two times the age of her son. The ratio of their present ages will be:

A) 10:19                        B) 9: 5                                 C) 7: 4                                      D) 7: 3

Answer: Let the age of the son ten years ago be equal to x years. Therefore the age of the mother ten years ago will be equal to 3x. Following this logic, we see that the present age of the son will be equal to x + 10 years and that of the mother will be equal to 3x + 10 years.

The second condition says that ten years from the present, the mother’s age will be twice that of her son. After ten year’s the mother’s age will be 3x + 10 + 10 years and that of the son will be x + 10 + 10 years. As per the question we have:

(3x + 10) +10 = 2 [(x + 10) + 10] or (3x + 20) = 2[x + 20]. In other words , we can write:

x = 20 years. Thus the present age of the mother = 3(20) + 10 = 70 years. Also the present age of the son = 20 + 10 = 30 years. Thus the ratio is 7:3 and the correct option is D) 7:3.

Practice Questions

Q 1: The age of a man is 24 years more than his son. In two years, the father’s age will be twice that of his son. Then the present age of his son is: A) 18 years                   B) 21 years               C) 22 years                 D) 24 years

Ans: C) 22 years.

Q 2: After 15 years Ramesh’s age will be 5 times his age 5 years ago. What is the present age of Ramesh? A) 5 years                     B) 10 years               C) 15 years                  D) 20 years

Ans: B) 10 years

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6 responses to “Ratio Based Age Problems”

3 peoples ages = 100,the older is 5 years older than the second,the age of the third is half of the seconds age ,whats the age of the thrid person ?

The ages of zaira and angel are in the ratio 7:9. Five years ago, the sum of their ages is 54. What are their present ages?

Am I crazy or is Q1 not the right answer? I got 24. I even looked this up elsewhere and people were reporting 24 is the correct answer (or rather none of the above in this case).

5 Read the information given. Form simultaneous equations and solve :

Present age of Raju is X years

Present age of Sanju is y years

Add 4 years , to their ages

The ratio of their ages is

Equation 121

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  • \mathrm{Lauren's\:age\:is\:half\:of\:Joe's\:age.\:Emma\:is\:four\:years\:older\:than\:Joe.\:The\:sum\:of\:Lauren,\:Emma,\:and\:Joe's\:age\:is\:54.\:How\:old\:is\:Joe?}
  • \mathrm{Kira\:went\:for\:a\:drive\:in\:her\:new\:car.\:She\:drove\:for\:142.5\:miles\:at\:a\:speed\:of\:57\:mph.\:For\:how\:many\:hours\:did\:she\:drive?}
  • \mathrm{The\:sum\:of\:two\:numbers\:is\:249\:.\:Twice\:the\:larger\:number\:plus\:three\:times\:the\:smaller\:number\:is\:591\:.\:Find\:the\:numbers.}
  • \mathrm{If\:2\:tacos\:and\:3\:drinks\:cost\:12\:and\:3\:tacos\:and\:2\:drinks\:cost\:13\:how\:much\:does\:a\:taco\:cost?}
  • \mathrm{You\:deposit\:3000\:in\:an\:account\:earning\:2\%\:interest\:compounded\:monthly.\:How\:much\:will\:you\:have\:in\:the\:account\:in\:15\:years?}
  • How do you solve word problems?
  • To solve word problems start by reading the problem carefully and understanding what it's asking. Try underlining or highlighting key information, such as numbers and key words that indicate what operation is needed to perform. Translate the problem into mathematical expressions or equations, and use the information and equations generated to solve for the answer.
  • How do you identify word problems in math?
  • Word problems in math can be identified by the use of language that describes a situation or scenario. Word problems often use words and phrases which indicate that performing calculations is needed to find a solution. Additionally, word problems will often include specific information such as numbers, measurements, and units that needed to be used to solve the problem.
  • Is there a calculator that can solve word problems?
  • Symbolab is the best calculator for solving a wide range of word problems, including age problems, distance problems, cost problems, investments problems, number problems, and percent problems.
  • What is an age problem?
  • An age problem is a type of word problem in math that involves calculating the age of one or more people at a specific point in time. These problems often use phrases such as 'x years ago,' 'in y years,' or 'y years later,' which indicate that the problem is related to time and age.

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300 Primary School Maths Word Problems: Includes Examples And Answers

Sophie bartlett.

Solving word problems at KS1 and KS2 is an essential part of the new maths curriculum. Here you can find expert guidance on how to solve maths word problems as well as examples of the many different types of word problems primary school children will encounter with links to hundreds more .

What is a word problem?

Mastery helps children to explore maths in greater depth, how to teach children to solve word problems , word problems in year 1, word problems in year 2, word problems in year 3 , word problems in year 4, word problems in year 5, word problems in year 6, place value word problems, addition and subtraction word problems, multiplication and division word problems, fraction word problems, how important are word problems when it comes to the sats , remember: the word problems can change but the maths won’t .

A word problem in maths is a maths question written as one sentence or more that requires children to apply their maths knowledge to a ‘real-life’ scenario. 

This means that children must be familiar with the vocabulary associated with the mathematical symbols they are used to, in order to make sense of the word problem. 

For example:

Importance of word problems within the national curriculum

The National Curriculum states that its mathematics curriculum “aims to ensure that all pupils:

  • become fluent in the fundamentals of mathematics, including through varied and frequent practice with increasingly complex problems over time , so that pupils develop conceptual understanding and the ability to recall and apply knowledge rapidly and accurately;
  • reason mathematically by following a line of enquiry, conjecturing relationships and generalisations, and developing an argument, justification or proof using mathematical language;
  • can solve problems by applying their mathematics to a variety of routine and non-routine problems with increasing sophistication , including breaking down problems into a series of simpler steps and persevering in seeking solutions.”

To support this schools are adopting a ‘mastery’ approach to maths

The National Centre for Excellence in the Teaching of Mathematics (NCETM) have defined “teaching for mastery”, with some aspects of this definition being: 

  • Maths teaching for mastery rejects the idea that a large proportion of people ‘just can’t do maths’.  
  • All pupils are encouraged by the belief that by working hard at maths they can succeed. 
  • Procedural fluency and conceptual understanding are developed in tandem because each supports the development of the other. 
  • Significant time is spent developing deep knowledge of the key ideas that are needed to underpin future learning. The structure and connections within the mathematics are emphasised, so that pupils develop deep learning that can be sustained.

(The Essence of Maths Teaching for Mastery, 2016)

Year 3 to 6 Rapid Reasoning Worksheet for Weeks 1-6

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One of NCETM’s Five Big Ideas in Teaching for Mastery (2017) is “ Mathematical Thinking: if taught ideas are to be understood deeply, they must not merely be passively received but must be worked on by the student: thought about, reasoned with and discussed with others”.

In other words – yes, fluency in arithmetic is important; however, with this often lies the common misconception that once a child has learnt the number skills appropriate to their level/age, they should be progressed to the next level/age of number skills. 

The mastery approach encourages exploring the breadth and depth of these concepts (once fluency is secure) through reasoning and problem solving. 

See the following example:

What sort of word problems might my child encounter at school.

In Key Stage 2, there are nine ‘strands’ of maths – these are then further split into ‘sub-strands’.  For example, ‘number and place value’ is the first strand: a Year 3 sub-strand of this is to “find 10 or 100 more or less than a given number”; a Year 6 sub-strand of this is to “determine the value of each digit in numbers up to 10 million”. The table below shows how the ‘sub-strands’ are distributed across each strand and year group in KS2.

Here are two simple strategies that can be applied to many word problems before solving them.

  • What do you already know?
  • How can this problem be drawn/represented pictorially?

Let’s see how this can be applied to a word problem to help achieve the answer.

Solving a simple word problem

There are 28 pupils in a class. The teacher has 8 litres of orange juice. She pours 225 millilitres of orange juice for every pupil. How much orange juice is left over?

1. What do you already know?

  • There are 1,000ml in 1 litre
  • Pours = liquid leaving the bottle = subtraction
  • For every = multiply
  • Left over = requires subtraction at some point

2. How can this problem be drawn/represented pictorially?

The bar model is always a brilliant way of representing problems, but if you are not familiar with this, there are always other ways of drawing it out. 

Read more: What is a bar model

For example, for this question, you could draw 28 pupils (or stick man x 28) with ‘225 ml’ above each one and then a half-empty bottle with ‘8 litres’ marked at the top.

Now to put the maths to work. This is a Year 6 multi-step problem, so we need to use what we already know and what we’ve drawn to break down the steps.

Solving a more complex word problem

Mara is in a bookshop. She buys one book for £6.99 and another that costs £3.40 more than the first book. She pays using a £20 notes. What change does Mara get?

  • More than = add
  • Using decimals means I will have to line up the decimal points correctly in calculations
  • Change from money = subtract

See this example of bar modelling for this question:

Now to put the maths to work using what we already know and what we’ve drawn to break down the steps.

Mara is in a bookshop. 

She buys one book for £6.99 and another that costs £3.40 more than the first book. 1) £6.99 + (£6.99 + £3.40) = £17.38

She pays using a £20 note. What change does Mara get? 2) £20 – £17.38 = £2.62

Maths word problems for years 1 to 6

The more children learn about maths as the go through primary school, the trickier the word problems they face will become.

Below you will find some information about the types of word problems your child will be coming up against on a year by year basis, and how word problems apply to each primary year group

Throughout Year 1 a child is likely to be introduced to word problems with the help of concrete resources (pieces of physical apparatus like coins, cards, counters or number lines) to help them understand the problem.

An example of a word problem for Year 1 would be:

Chris is going to buy a cake for his mum which costs 80p. How many 20p coins would he need to do this? 

Year 2 is a continuation of Year 1 when it comes to word problems, with children still using concrete maths resources to help them understand and visualise the problems they are working on

An example of a word problem for Year 2 would be:

A class of 10 children each have 5 pencils in their pencil cases. How many pencils are there in total?

With word problems for year 3 , children will move away from using concrete resources when solving word problems, and move towards using written methods. Teachers will begin to demonstrate the four operations such as addition and subtraction word problems, multiplication and division problems too.

This is also the year in which 2-step word problems will be introduced. This is a problem which requires two individual calculations to be completed.

Year 3 word problem: Geometry properties of shape

Shaun is making 3-D shapes out of plastic straws.

At the vertices where the straws meet, he uses blobs of modelling clay to fix them together

Here are some of the shapes he makes:

One of Sean’s shapes is a cuboid. Which is it? Explain your answer.

Answer: shape B as a cuboid has 12 edges (straws) and 8 vertices (clay)

Year 3 word problem: Statistics

Year 3 are collecting pebbles. This pictogram shows the different numbers of pebbles each group finds.

Answer: a) 9   b) 3 pebbles drawn

Top tip By the time children are in Year 3 many of the word problems, even one-step story problems tend to be a variation on a multiplication problem. For this reason learning times tables becomes increasingly essential at this stage. One of the best things you can do to help with Year 3 maths at home is support your child to do this. You can also help children while they are developing this skill by providing 100 squares to help them solve these word problems.

At this stage of their primary school career, children should feel confident using the written method for each of the four operations. 

Word problems for year 4 will include a variety of problems, including 2-step problems and be children will be expected to work out the appropriate method required to solve each one. 

Year 4 word problem: Number and place value

My number has four digits and has a 7 in the hundreds place. The digit which has the highest value in my number is 2. The digit which has the lowest value in my number is 6. My number has 3 fewer tens than hundreds. What is my number?

Answer: 2,746

One and 2-step word problems continue with word problems for year 5 , but this is also the year that children will be introduced to word problems containing decimals.

These are some examples of Year 5 maths word problems .

Year 5 word problem: Fractions, decimals and percentages

Stan, Frank and Norm are washing their cars outside their houses. Stan has washed 0.5 of his car. Frank has washed 1/5 of his car. Norm has washed 5% of his car.

Who has washed the most?

Explain your answer.

Answer: Stan (he has washed 0.5 whereas Frank has only washed 0.2 and Norm 0.05)

Word problems for year 6 shift from 2-step word problems to multi-step word problems. These will include fractions, decimals, percentages and time word problems. 

Here are some examples of the types of maths word problems Year 6 will have to solve.

Year 6 word problem – Ratio and proportion

This question is from the 2018 key stage 2 SATs paper. It is worth 1 mark.

The Angel of the North is a large statue in England. It is 20 metres tall and 54 metres wide. 

Ally makes a scale model of the Angel of the North. Her model is 40 centimetres tall. How wide is her model?

Answer: 108cm

Year 6 word problem – Algebra

This question is from the 2018 KS2 SATs paper. It is worth 2 marks as there are 2 parts to the answer.

Amina is making designs with two different shapes.

She gives each shape a value.

Calculate the value of each shape.

Answer: 36 (hexagon) and 25 . 

Year 6 word problem: Measurement

This question is from the 2018 KS2 SATs paper. It is worth 3 marks as it is a multi-step problem.

Answer: 1.7 litres or 1,700ml

Topic based word problems

The following examples give you an idea of the kinds of maths word problems your child will encounter for each of the 9 strands of maths in KS2.

Place value word problem Year 5

This machine subtracts one hundredth each time the button is pressed. The starting number is 8.43. What number will the machine show if the button is pressed six times? Answer: 8.37

Download free number and place value word problems for Years 3, 4, 5 and 6

Addition and subtraction word problem Year 3

In Year 3 pupils will solve addition word problems and subtraction word problems with 2 and 3 digits.

Sam has 364 sweets. He gets given 142 more. He then gives 277 away. How many sweets is he left with? Answer: 229

Download free addition and subtraction word problems for Years 3, 4, 5 and 6

Addition word problem Year 3

Alfie thinks of a number. He subtracts 70. His new number is 12. What was the number Alfie thought of? Answer: 82

Subtraction word problem Year 6

The temperature at 7pm was 4oC. By midnight, it had dropped by 9 degrees. What was the temperature at midnight? Answer: -5oC

More here: 25 addition and subtraction word problems

Multiplication and division word problem Year 3

A baker is baking chocolate cupcakes. She melts 16 chocolate buttons to make the icing for 9 cakes. How many chocolate buttons will she need to melt to make the icing for 18 cakes? Answer: 32

Multiplication word problem Year 4

E ggs are sold in boxes of 12. The egg boxes are delivered to stores in crates. Each crate holds 9 boxes. How many eggs are in a crate? Answer: 108

Download free multiplication word problems for Years 3, 4, 5 and 6

Division word problem Year 6

A factory produces 1,692 paintbrushes every day. They are packaged into boxes of 9. How many boxes does the factory produce every day? Answer: 188

Download our free division word problems worksheets for Years 3, 4, 5 and 6.

More here: 20 multiplication word problems More here: 25 division word problems

Free resource: Use these four operations word problems to practise addition, subtraction, multiplication and division all together.

Fraction word problem Year 5

At the end of every day, a chocolate factory has 1 and 2/6 boxes of chocolates left over. How many boxes of chocolates are left over by the end of a week? Answer: 9 and 2/6 or 9 and 1/3

Download free fractions and decimals word problems worksheets for Years 3, 4, 5 and 6

More here: 28 fraction word problems

Decimals word problem Year 4 (crossover with subtraction)

Which two decimals that have a difference of 0.5? 0.2, 0.25, 0.4, 0.45, 0.6, 0.75. Answer: 0.25 and 0.75

Download free decimals and percentages word problems resources for Years 3, 4, 5 and 6

Percentage word problem Year 5

There are 350 children in a school. 50% are boys. How many boys are there? Answer: 175

Measurement word problem Year 3 (crossover with subtraction)

Lucy and Ffion both have bottles of strawberry smoothie. Each bottle contains 1 litre. Lucy drinks ½ of her bottle. Ffion drinks 300ml of her bottle. How much does each person have left in both bottles? Answer: Lucy = 500ml, Ffion = 300ml

More here: 25 percentage word problems

Money word problem Year 3

James and Lauren have different amounts of money. James has twelve 2p coins. Lauren has seven 5p coins. Who has the most money and by how much? Answer: Lauren by 11p.

More here: 25 money word problems

Area word problem Year 4

A rectangle measures 6cm by 5cm.

What is its area? Answer: 30cm2

Perimeter word problem Year 4

The swimming pool at the Sunshine Inn hotel is 20m long and 7m wide. Mary swims around the edge of the pool twice. How many metres has she swum? Answer: 108m

Ratio word problem Year 6 (crossover with measurement)

A local council has spent the day painting double yellow lines. They use 1 pot of yellow paint for every 100m of road they paint. How many pots of paint will they need to paint a 2km stretch of road? Answer: 20 pots

More here: 24 ratio word problems

Bodmas word problem Year 6

Draw a pair of brackets in one of these calculations so that they make two different answers. What are the answers?

50 – 10 × 5 =

50 – 10 × 5 =

Volume word problem Year 6

This large cuboid has been made by stacking shipping containers on a boat. Each individual shipping container has a length of 6m, a width of 4m and a height of 3m. What is the volume of the large cuboid? Answer: 864m3

In the KS1 SATs, 58% (35/60 marks) of the test is comprised of maths ‘reasoning’ (word problems). 

In KS2, this increases to 64% (70/110 marks) spread over two reasoning papers, each worth 35 marks. Considering children have, in the past, needed approximately 55-60% to reach the ‘expected standard’, it’s clear that children need regular exposure to and a solid understanding of how to solve a variety of word problems.

Children have the opportunity to practice SATs style word problems in Third Space Learning’s online one-to-one SATs revision programme. Personalised to meet the needs of each student, our programme helps to fill gaps and give students more confidence going in to the SATs exams.

It can be easy for children to get overwhelmed when they first come across word problems in KS2, but it is important that you remind them that whilst the context of the problem may be presented in a different way, the maths behind it remains the same. 

Word problems are a good way to bring maths into the real world and make maths more relevant for your child, so help them practise, or even ask them to turn the tables and make up some word problems for you to solve. 

This article while written by a teacher for teachers is also suitable for those at home supporting children with home learning . More free home learning resources are also available.

Do you have pupils who need extra support in maths? Every week Third Space Learning’s maths specialist tutors support thousands of pupils across hundreds of schools with weekly online 1-to-1 lessons and maths interventions designed to address learning gaps and boost progress. Since 2013 we’ve helped over 150,000 primary and secondary school pupils become more confident, able mathematicians. Learn more or request a personalised quote for your school to speak to us about your school’s needs and how we can help.

Subsidised one to one maths tutoring from the UK’s most affordable DfE-approved one to one tutoring provider.

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1. Phonics Instruction

2. graphic organizers, 3. think-pair-share, 4. vocabulary instruction, 5. story mapping, 6. kwl charts (know, want to know, learned), 7. interactive read-alouds, 8. guided reading, 9. writing workshops, 10. literature circles.

Today, literacy is not just about learning to read and write ; it’s a crucial tool that opens doors to a world of knowledge and opportunities. It’s the foundation upon which we build our ability to communicate, understand, and interact with the world around us. It is the cornerstone that supports all other learning.

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But how do we ensure every student learns to read and write, loves the process, and excels in it? This is where literacy strategies for teachers come into play. 

In the modern classroom, literacy strategies are essential for several reasons. They help cater to diverse learning styles , engage students more effectively, and promote a deeper understanding of the material.

These strategies are vital in an era of abundant information and attention spans are challenged. They equip teachers with innovative methods to make reading and writing more interactive and meaningful. 

In this blog, we will talk about some of the best literacy strategies that can make a significant difference in your classroom!

Literacy Strategy Definition

Literacy strategies are various methods and approaches used in teaching reading and writing. These are not just standard teaching practices but innovative, interactive, and tailored techniques designed to improve literacy skills. They include activities like group discussions, interactive games , and creative writing exercises, all part of a broader set of literacy instruction strategies.

The Role of Literacy Strategies in Enhancing Reading and Writing Skills

Teaching literacy strategies enhance students’ reading and writing skills. These strategies help break down complex texts, making them more understandable and relatable for students. They encourage students to think critically about what they read and express their thoughts clearly in writing. Teachers can use literacy strategies to address different learning styles, helping students find their path to literacy success.

15 Best Literacy Strategies for Teachers

Phonics instruction is fundamental in building foundational reading skills , especially for young learners. This method teaches students the relationships between letters and sounds , helping them decode words. Through phonics, students learn to sound out words, which is crucial for reading fluency and comprehension. Phonics instruction can be made fun and interactive with games, songs, and puzzles .

You can begin here:

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Graphic organizers are powerful visual tools that aid in better comprehension and organization of information. As part of literacy practice examples, they help students visually map out ideas and relationships between concepts. This can include charts, diagrams, or concept maps. Using graphic organizers, teachers can help students structure their thoughts, making complex ideas more accessible and understandable. It’s an effective way to break down reading materials or organize writing drafts visually.

Think Pair Share worksheet

Think-pair-share is an essential literacy strategy that fosters collaborative learning. In this activity, students first think about a question or topic individually, then pair up with a classmate to discuss their thoughts, and finally share their ideas with the larger group. This strategy encourages active participation and communication, allowing students to learn from each other. It’s a simple yet powerful way to engage students in critical thinking and discussion.

Vocabulary instruction is crucial in expanding language comprehension. This strategy involves teaching students new words and phrases in terms of their definitions, context, and usage. Effective vocabulary instruction can include word mapping , sentence creation , and word games. By enriching students’ vocabulary , teachers equip them with the tools to understand and articulate ideas more effectively, enhancing their overall literacy.

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Story mapping is a technique where students break down the narrative elements of a story, such as characters, setting, plot, and conflict. This strategy helps in enhancing comprehension and analytical skills. By visually organizing the elements of a story, students can better understand the structure and themes of the text. It’s an engaging way to dissect stories and can be done individually or as a group activity .

A KWL chart

KWL charts are an effective tool for structuring learning objectives. This strategy involves creating a chart with three columns: What students already Know, What they Want to know, and What they have Learned. This approach helps activate prior knowledge, set learning goals , and reflect on new information. It’s a great way to engage students in the learning process from start to finish, making them active participants in their education. KWL Charts can be used across various subjects, making them versatile and essential in the classroom.

Kids in a classroom

Interactive read-alouds are a cornerstone among literacy instructional strategies. In this activity, the teacher reads a story aloud, using expressive tones and gestures to bring the story to life. This method engages students in dynamic storytelling , sparking their imagination and interest. It’s an essential literacy strategy that enhances listening skills, vocabulary, and comprehension. Teachers can pause to ask questions, encouraging students to think and predict, making it an interactive and inclusive learning experience.

kids in guided reading session

Guided reading is a tailored approach that addresses the diverse reading levels within a classroom. In this strategy, teachers work with small groups of students, providing focused reading instruction at their specific level of development. This allows for more personalized attention and support, helping students progress at their own pace.

Kids in a writing workshop

Writing workshops are a dynamic way to foster creative expression among students. These workshops provide a platform for students to write , share, and receive feedback on their work. It’s an interactive process where students learn to develop their writing style, voice, and technique. Writing Workshops encourage creativity, critical thinking, and peer collaboration, making them a vital part of literacy development.

Depiction of collaborative learning

Literature circles are a collaborative and student-centered approach to reading and discussing books. In these circles, small groups of students choose and read a book together, then meet to discuss it, often taking on different roles like discussion leader or summarizer. This strategy promotes discussion, critical thinking, and a deeper understanding of literature. It’s an engaging way for students to explore texts and share their perspectives, enhancing their analytical and communication skills.

11. Scaffolding

Scaffolding technique

Scaffolding is a teaching method that provides students with step-by-step guidance to help them better understand new concepts. This approach breaks down learning into manageable chunks, gradually moving students towards stronger comprehension and greater independence. Scaffolding can include techniques like asking leading questions, providing examples, or offering partial solutions. It’s especially effective in building confidence and skill in students, as they feel supported throughout their learning journey.

12. Word Walls

A word board

Word walls are a visual and interactive way to display vocabulary in the classroom . As one of the essential literacy strategy examples, they help students learn new words and reinforce their spelling and meaning. Teachers can add words related to current lessons or themes, encouraging students to use and explore these words in their writing and speaking. Word walls are educational and serve as a reference tool that students can continually interact with.

13. Reader’s Theater

Kids in a readers theatre

Reader’s theater is an engaging literacy activity that combines reading and performance. In this strategy, students read scripts aloud, focusing on expression rather than memorization or props. This method helps improve reading fluency, comprehension, and confidence as students practice reading with emotion and emphasis. Reader’s Theater is also a fun way to bring literature to life and encourage a love for reading and storytelling.

14. Dramatization of Text

Kids dramatizing text

Dramatization of text involves bringing stories and texts to life through acting and role-play. This strategy allows students to interpret and enact narratives, deepening their understanding of the characters, plot, and themes. It’s an interactive way to engage students with literature, encouraging them to explore texts creatively and collaboratively. Dramatization can enhance comprehension, empathy, and public speaking skills.

15. Inquiry-Based Learning

Inquiry based learning wallpaper

Inquiry-Based Learning is a student-centered approach that promotes curiosity-driven research and exploration. In this method, learning starts with questions, problems, or scenarios rather than simply presenting facts. Students are encouraged to investigate topics, ask questions , and discover answers through research and discussion. This strategy fosters critical thinking, problem-solving skills, and a love for learning .

These literacy strategies for teachers offer a diverse and dynamic toolkit for teachers to enhance reading, writing, and comprehension skills in their classrooms. By incorporating these methods, educators can create a more engaging, inclusive, and effective learning environment , paving the way for students to become confident and proficient learners.

Frequently Asked Questions (FAQs)

What are the key benefits of using literacy strategies in the classroom.

Literacy strategies enhance classroom engagement, improve comprehension, and foster critical thinking skills. They make learning more interactive and meaningful, helping students to connect with the material more deeply.

How can teachers effectively integrate literacy strategies into existing curricula?

Teachers can integrate literacy strategies by aligning them with current lesson objectives, using them as complementary tools for existing content. Start small, incorporate strategies gradually, and tailor them to fit the lesson’s context.

Are these literacy strategies suitable for all age groups?

Yes, these strategies can be adapted for different age groups and learning levels. The key is to modify the complexity and delivery of the strategy to suit the developmental stage and abilities of the students.

How do digital literacy strategies for teachers differ from traditional ones?

Digital literacy strategies incorporate technology, focusing on skills like navigating online information, digital communication, and critical evaluation of online content, which are essential in the digital age.

Can literacy strategies be used in subjects other than language arts?

Absolutely, literacy strategies can be applied cross-curricularly. For example, graphic organizers can be used in science for hypothesis mapping, or story mapping can be used in history to outline events.

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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 ‍  

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10 Best AI Tools for Solving Math Problems Effortlessly [Free + Paid]

Mathematics is intimidating for many students. AI transforms how math is understood and remembered, making it more enjoyable. You can learn about the top 10 best AI tools for solving math problems effortlessly with pros and cons.

These tools will enhance your mathematical abilities and help you excel. Whether you are struggling to learn new math concepts or want to gain the next level of proficiency in this subject, these tools are helpful.

1. Photomath

2. socratic, 4. wolfram alpha, 5. maple calculator, 6. cameramath, 7. microsoft math solver, 8. symbolab, 9. quickmath, 10. mathpix, 10 best ai tools for solving math problems effortlessly.

Here are the 10 Best AI tools for solving math problems effortlessly along with their features, pricing, pros, and cons.

Photomath

Photomath – AI tool for solving Math Problems

Photomath is a mobile app that offers the best solutions for people struggling to solve math problems. Using this AI tool for math students , users can scan the handwritten math problems handwritten using their smartphone camera and get the solution for this problem in real-time.

  • Improve the math skills of students by getting quick feedback.
  • Offer solutions to various math topics such as arithmetic, algebra, calculus, etc.
  • Ideal for research students, parents, and teachers to use this app to teach math to students.
  • Photomath, math AI solver free offers accurate solutions to math problems with the help of photo scanning.
  • Give you animated instructions on how to solve the math problem, enhancing the visual experience.
  • Limited to solving only math problems and does not focus on other subjects.
  • To solve complicated issues, you will need to take a subscription to get the solutions in steps.
  • Basic version – free.
  • Photomath Plus – subscription based.
Link : https://photomath.com/

Socratic

Socratic – AI tools for Mathematics

Socratic is one of the best AI tools for mathematics that Google developed, and it is a mobile app. The app is also designed to help you with other subjects such as science, history, and more.

  • Provide you with step-by-step solutions to solve the problem and understand it.
  • Solve issues related to basic arithmetic to advanced calculus.
  • Analyze the problem and offer you a comprehensive explanation.
  • Come with videos to solve the issues and tackle challenging coursework.
  • Give clear-cut explanations with visual aids to solve the math problem.
  • Cover topics such as algebra, geometry, calculus, and so on.
  • Users find the explanations for the math problem to be too simplified.
  • Limited functionality is available to provide solutions for advanced math topics.

Price: Free

Link: https://socratic.org/

Mathway

Mathway – AI Mathematics tool

Mathway is an AI-powered tool that will quickly solve math problems and give you a clear-cut explanation. It is one of the best AI tools for mathematics students that offers you a comprehensive explanation that will be helpful for students to solve math problems at diverse levels.

  • Solve math problems related to various concepts such as calculus, algebra, trigonometry, and graphing.
  • Offer extra support for students to help them solve math homework.
  • Available for both online and mobile apps to let you access this on the move.
  • User-friendly interface to find solutions for the math problem with ease.
  • Advanced features will need you to subscribe to the Mathway Plus subscription.
  • It does not provide you with alternative methods or approaches to solving the problem.
  • Basic version is free.
  • Premium – starts at $19.99/month.
Link: https://www.mathway.com/

Wolfram-Alpha

Wolfram Alpha – Best AI Math Tool

The Wolfram Alpha application is made of a computational engine that will leverage the power of AI to access your math queries. It is one of the AI math problem solvers that can also answer questions related to science and engineering.

  • Solve math problems and graph functions and offer you with step by step solution.
  • Vast library for math concepts, formulas, and equations.
  • Visualize the data and offer you highly interactive graphs and plots.
  • Easy to handle complex calculations with its solutions.
  • Great tool for students who want to master Mathematics.
  • You will need internet connectivity to access this application.
  • A few features are not available in the free version of the app.
  • Free version is available.
  • Pro – $5/month,
  • Pro premium – $8.25/month.
Link : https://www.wolframalpha.com/

MapleSoft

MapleSoft – AI based math tool

Maple calculation is one of the best AI-based math tools that students use. You can solve different problems using this application, such as algebra, trigonometry, calculus, and so on. Widely used tool by engineers, scientists, and mathematicians across the globe

  • Help students learn math and get knowledge on advanced functions and graphing tools.
  • Many educational games and puzzles are available to boost your math skill.
  • User-friendly interface is available to gain in-depth knowledge on the subject.
  • Different mathematical functions are available to solve the problems.
  • Graphical representation of complicated concepts of math.
  • Advanced concepts will need additional support to understand.
  • Minimal access is offered to access this app online.
Link: https://www.maplesoft.com/
Related Articles: 10 Best AI Tools For Students 2024 10 Best AI Tools to Boost Productivity in 2024

CameraMath

CameraMath – AI tool for Math Students

CameraMath is one of the innovative yet powerful AI tools for math students that is available for students to solve problems briskly. You can take a picture of the math expression or problem. Using image recognition and algorithms, it offers you with the best solutions.

  • Let students ask questions and get personalized answers from tutors.
  • The bank feature present will give you access to different math concepts, formulas, and equations.
  • Scientific calculators, graphing calculators, and geometry calculators are available for students who want to improve their math skills.
  • Easy to solve math problems by capturing the image with equations.
  • Offer steps to improve the learning experience of users.
  • Can only be used to solve the math problems.
  • Stable internet connectivity is required to solve math problems.
  • Basic – Free.
  • Premium- $3.33/month.
Link: https://cameramath.com/

Microfsoft Mathsolver

AI Math Solver

Microsoft Math Solver is the AI math solver used to solve math problems innovatively. It also teaches math to students. The app is designed to solve arithmetic to advanced calculus problems.

  • Come with visual explanation to help students understand how the problem was solved.
  • You can get any equation in a graph format to understand the variables relationship.
  • Recognize the handwritten problems and let students solve the problem on paper and verify.
  • Easy to use and solve different types of mathematical problems.
  • Supports multiple languages like German, Hindi, Spanish and more.
  • You will need internet connectivity to access all the functionalities in the tool.
  • You will have limited access to the handwritten input.
Link : https://math.microsoft.com/

Symbolab

Symbolab – AI Math Tool

Symbolab is one of the AI-powered math tools used to solve different types of mathematical problems, such as calculus, trigonometry, and algebra. Progress can be tracked in the form of reports and analytics in the dashboard.

  • AI math solver online is used to solve all complicated math problems, such as graphing and geometry.
  • Help college students prepare for the exams when pursuing math-related fields.
  • Solve math in different subjects comprehensively.
  • Offer step-by-step solutions to solve the problem to help the students easily understand.
  • Advanced features in the tool are available only after paying for the subscription.
  • Limited access to some of the features.
  • Pro plans – monthly $6.99/month, semi annual – $4.15/month, annual – $2.49/month.
Link: https://www.symbolab.com/

QuickMath

QuickMath – AI Math Tool

Quickmath is the AI math tool that is used to solve algebraic equations accurately along with calculus problems with the help of large language models. The mobile app is available for Android and iOS devices.

  • Easy-to-understand tutorials are available to solve complex concepts and calculations.
  • Robust offline support is available for users to continue learning without any internet.
  • Easy to use to solve complicated math problems with the help of this math companion.
  • The interface is highly interactive and intuitive.
  • The user interface could be more straightforward for users to understand and use this tool.
  • Could not give accurate solutions for some of the complicated equations.

Price – Free

Link: https://quickmath.com/

Mathpix

Mathpix – AI math problem solver

Mathpix is one of the best math AI solver word problems to solve printed and handwritten math and science problems including simple, advanced levels and chemical diagrams. It will recognize the math symbols, equations, and graphs on paper and give solutions.

  • Digital Ink – Offers live drawing in app and support actions like erase and scribble.
  • On-premise PDF Cloud – Easily converts PDFs, or images to machine readable formats like Latex, Docx, and Markdown.
  • Handwriting Recognition – It uses OCR technology to recognize math and provide you with accurate solutions in different languages.
  • You can get real-time assistance to solve issues related to equations.
  • Supports multiple languages includes printed Latin, Asian, Semitic, and Cyrillic alphabet languages.
  • Does not solve complicated problems, as it cannot accurately recognize.
  • Advanced features of the tool can be accessed only through a subscription.
  • Pro – $4.99/month.
  • Pro Yearly – $49.90/month.
  • Organization – $9.99/month.
  • Organization Yearly – $99.90/month.
  • Custom pricing plans also available for OCR API.
Link: https://mathpix.com/
Related Articles: Top 12 AI Tools for Remote Learning and Online Education Top 7 AI Studying Tools for Effective Study and Exam Preparation 2024

AI-powered tools cater to every math student’s needs, irrespective of their academic level. There are free and paid best AI tools for solving math problems available to get detailed solutions to understand how the problem was solved so that you can solve the same problem when it is given in an exam.

Out of all the top tools we have listed to solve math using AI, Wolfram Alpha helps professionals and students solve complicated math problems with ease and offers insights into challenging mathematical topics. It will also generate graphs and visualizations to explain math concepts clearly to users.

FAQs – Best AI Tools for Solving Math Problems

How do i choose the best ai math tool for me.

You can choose the math AI bot tool based on your needs and educational level. Secondary students can choose Symbolab or Photomath, whereas college students who tackle complicated problems can choose Wolfram Alpha.

Are there free AI tools available for math?

Yes, Free tools are available. Maple Calculator is great math tool that gives answers including 2D, 3D graphs.

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