given facts in problem solving grade 5

Related Facts – Definition With Examples

What are related facts, fact families, importance of related facts, solved examples, practice problems, frequently asked questions.

Related facts in Math are facts that are related to each other in some way. We can easily find related facts using the given facts. 

Since addition and subtraction are inverse operations, we can form their related facts. Let’s go through a related fact example:

So, A, B, and C are related facts of the given fact, $3 + 4 = 7$. 

Notice that the numbers involved in all three related facts are the same as the numbers involved in the given fact. Only the position and operation changes. 

Since multiplication and division are also inverse operations, we can form related facts for them as well.

Related Games

Fact families are sets of addition and subtraction facts or multiplication and division facts that involve the same numbers. In other words, it is a collection of related facts. Fact families are of two types:

• Addition and Subtraction
• Multiplication and Division

Related Worksheets

Addition and Subtraction Fact Family

Addition and subtraction are inverse operations. If we first add a number to a given number and then subtract the same number from the result, we get the original number back. For example, consider 10 as the given number, we add and subtract 2.

$10 + 2 = 12$

$12 – 2 = 10$ (original number)

This means that these two operations cancel each other’s effect on another number or expression. 

Let’s have a look at some fact families of addition and subtraction. 

We can assume that fact families are like parts of a whole, where the largest number is the whole, and the other two numbers are the two parts that make up the whole. In the first example above, 10 is the whole and the numbers 4 and 6 are the parts.

Multiplication and Division Fact Families

We know that multiplication and division are also inverse operations, so we can form fact families for these two operations using the related facts. Let’s have a look at some fact families of multiplication and division. 

Related facts are used so that a student can understand the relationships between the operations of addition and subtraction, and multiplication and division. It helps the students to remember that addition and subtraction are inverse operations and multiplication and division are inverse operations.

For example, if we know any one fact from a fact family, we can easily find the other related facts. 

Example 1: Identify which family the given numbers belong to. Also write all four related facts. 

Solution: 

Let’s try adding the two smaller numbers, $9 + 8 = 17$ (third number)

So, these numbers belong to the addition and subtraction fact family. 

The other related facts are: 

$8 + 9 = 17$

$17 － 8 = 9$

$17 － 9 = 8$

Example 2: Identify which fact family the given numbers belong to. Also write all four related facts. 

Let’s try adding the two smaller numbers, $5 + 7 = 12 ≠ 35$. 

Now let’s multiply these numbers. 

$5 \times 7 = 35$ (third number)

So, these numbers belong to the multiplication and division fact family. 

$7 \times 5 = 35$

$35 \div 5 = 7$

$35 \div 7 = 5$

Example 3: Use the given fact to complete the fact family. 

Solution : It is given that $10 – 3 = 7$. 

Using this fact, we can easily determine the other related facts. 

Example 4: Make a fact family of 2, 8 and 16.

Solution: 2, 8 and 16 belong to the multiplication and division fact family. 

Example 5: One of the facts is given: $5 ☐ 3 = 15$ . Identify the operation and write all other related facts. 

Solution : $5 \times 3 = 15$. 

$3 \times 5 = 15$

$15 \div 3 = 5$

#$15 \div 5 = 3$

Related Facts - Definition With Examples

Attend this quiz & Test your knowledge.

Use $6 \times 8 = 48$ to complete the fact: $48 \div$ __ $= 6$

Which of the following does not belong to the fact family of $5 \times 2 = 10$, identify the third number of the addition and subtraction fact family given that the whole is 24 and one part is 8..

What is a fact family?

Fact families are sets of addition and subtraction facts or multiplication and division facts that involve the same numbers. In other words, it is a collection of related facts.

How does multiplication facts help you divide numbers?

Multiplication and division are inverse operations. In multiplication, we combine equal groups to find the total number, whereas in division, we distribute the given number into equal groups. So, knowing a multiplication fact, we can easily find its related division fact.

Can we have a related fact of a given division fact from subtraction?

No, the related facts involve the same numbers and either the same operation or an inverse operation. So, related facts of a division fact will be either of multiplication or division involving the same set of 3 numbers.

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Problem-Solving Strategies

October 16, 2019

There are many different ways to solve a math problem, and equipping students with problem-solving strategies is just as important as teaching computation and algorithms. Problem-solving strategies help students visualize the problem or present the given information in a way that can lead them to the solution. Solving word problems using strategies works great as a number talks activity and helps to revise many skills.

Problem-solving strategies

1. create a diagram/picture, 2. guess and check., 3. make a table or a list., 4. logical reasoning., 5. find a pattern, 6. work backward, 1. create a diagram/draw a picture.

Creating a diagram helps students visualize the problem and reach the solution. A diagram can be a picture with labels, or a representation of the problem with objects that can be manipulated. Role-playing and acting out the problem like a story can help get to the solution.

Alice spent 3/4 of her babysitting money on comic books. She is left with $6. How much money did she make from babysitting?

2. Guess and check

Teach students the same strategy research mathematicians use.

With this strategy, students solve problems by making a reasonable guess depending on the information given. Then they check to see if the answer is correct and they improve it accordingly.  By repeating this process, a student can arrive at a correct answer that has been checked. It is recommended that the students keep a record of their guesses by making a chart, a table or a list. This is a flexible strategy that works for many types of problems. When students are stuck, guessing and checking helps them start and explore the problem. However, there is a trap. Exactly because it is such a simple strategy to use, some students find it difficult to consider other strategies. As problems get more complicated, other strategies become more important and more effective.

Find two numbers that have sum 11 and product 24.

Try/guess  5 and 6  the product is 30 too high

  adjust  to 4 and 7 with product 28 still high

  adjust  again 3 and 8 product 24

3. Make a table or a list

Carefully organize the information on a table or list according to the problem information. It might be a table of numbers, a table with ticks and crosses to solve a logic problem or a list of possible answers. Seeing the given information sorted out on a table or a list will help find patterns and lead to the correct solution.

To make sure you are listing all the information correctly read the problem carefully.

Find the common factors of 24, 30 and 18

Logical reasoning is the process of using logical, systemic steps to arrive at a conclusion based on given facts and mathematic principles. Read and understand the problem. Then find the information that helps you start solving the problem. Continue with each piece of information and write possible answers.

Thomas, Helen, Bill, and Mary have cats that are black, brown, white, or gray. The cats’ names are Buddy, Lucky, Fifi, and Moo. Buddy is brown. Thoma’s cat, Lucky, is not gray. Helen’s cat is white but is not named Moo. The gray cat belongs to Bill. Which cat belongs to each student, and what is its color?

A table or list is useful in solving logic problems.

Since Lucky is not gray it can be black or brown. However, Buddy is brown so Lucky has to be black.

Buddy is brown so it cannot be Helen’s cat. Helen’s cat cannot be Moo, Buddy or Lucky, so it is Fifi.

Therefore, Moo is Bill’s cat and Buddy is Mary’s cat.

5. Find a pattern.

Finding a pattern is a strategy in which students look for patterns in the given information in order to solve the problem. When the problem consists of data like numbers or events that are repeated then it can be solved using the “find a pattern” problem-solving strategy. Data can be organized in a table or a list to reveal the pattern and help discover the “rule” of the pattern.

 The “rule” can then be used to find the answer to the question and complete the table/list.

Shannon’s Pizzeria made 5 pizzas on Sunday, 10 pizzas on Monday, 20 pizzas on Tuesday, and 40 pizzas on Wednesday. If this pattern continues, how many pizzas will the pizzeria make on Saturday?

6. Working backward

Problems that can be solved with this strategy are the ones that  list a series of events or a sequence of steps .

In this strategy, the students must start with the solution and work back to the beginning. Each operation must be reversed to get back to the beginning. So if working forwards requires addition, when students work backward they will need to subtract. And if they multiply working forwards, they must divide when working backward.

Mom bought a box of candy. Mary took 5 of them, Nick took 4 of them and 31 were given out on Halloween night. The next morning they found 8 pieces of candy in the box. How many candy pieces were in the box when mom bought it.

For this problem, we know that the final number of candy was 8, so if we work backward to “put back” the candy that was taken from the box we can reach the number of candy pieces that were in the box, to begin with.

The candy was taken away so we will normally subtract them. However, to get back to the original number of candy we need to work backward and do the opposite, which is to add them.

8 candy pieces were left + the 31 given out + plus the ones Mary took + the ones Nick took

8+31+5+4= 48   Answer: The box came with 48 pieces of candy.

Selecting the best strategy for a problem comes with practice and often problems will require the use of more than one strategies.

Print and digital activities

I have created a collection of print and digital activity cards and worksheets with word problems (print and google slides) to solve using the strategies above. The collection includes 70 problems (5 challenge ones) and their solution s and explanations.

sample below

How to use the activity cards

Allow the students to use manipulatives to solve the problems. (counters, shapes, lego blocks, Cuisenaire blocks, base 10 blocks, clocks) They can use manipulatives to create a picture and visualize the problem. They can use counters for the guess and check strategy. Discuss which strategy/strategies are better for solving each problem. Discuss the different ways. Use the activities as warm-ups, number talks, initiate discussions, group work, challenge, escape rooms, and more.

Ask your students to write their own problems using the problems in this resource, and more, as examples. Start with a simple type. Students learn a lot when trying to compose a problem. They can share the problem with their partner or the whole class. Make a collection of problems to share with another class.

For the google slides the students can use text boxes to explain their thinking with words, add shapes and lines to create diagrams, and add (insert) tables and diagrams.

Many of the problems can be solved faster by using algebraic expressions. However, since I created this resource for grades 4 and up I chose to show simple conceptual ways of solving the problems using the strategies above. You can suggest different ways of solving the problems based on the grade level.

Find the free and premium versions of the resource below. The premium version includes 70 problems (challenge problems included) and their solutions

There are 2 versions of the resource

70 google slides with explanations + 70 printable task cards

70 google slides with explanations + 11 worksheets

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