# Lesson 91: Understanding fact families

🧮 MATH (40 Lessons) • 🔵 B. Addition and Subtraction

← Back to Level 1

## Objective

I can explain what a fact family is. I can find the three numbers in a fact family and write the addition and subtraction sentences that belong together.

## Materials

- Small counters (buttons, blocks, or toy animals)
- Number line from 0 to 20 (on paper or a card strip)
- Pencil and notebook or scrap paper

## Mini-lesson — What is a fact family?

A fact family is a group of addition and subtraction facts that use the same three numbers.

Parts and whole

- The two parts are the smaller numbers.
- The whole is the bigger number.
- Together, they make a fact family.

Example fact family: 3, 4, and 7

- Parts: 3 and 4
- Whole: 7
- Addition facts: 3 + 4 = 7 and 4 + 3 = 7
- Subtraction facts: 7 − 3 = 4 and 7 − 4 = 3

Example fact family: 5, 2, and 7

- Parts: 5 and 2; whole: 7
- Addition: 5 + 2 = 7 and 2 + 5 = 7
- Subtraction: 7 − 5 = 2 and 7 − 2 = 5

In this lesson we stay within 20. We will use part–part–whole models and number lines to see how addition and subtraction are linked in a fact family.

Picture strip: Fact family houses

Fact family: 3, 4, 7

Fact family: 5, 2, 7

## Guided Practice — Build a fact family

You will use counters and a part–part–whole model to build a fact family. Then you will use the tracing pad to write key fact family words.

1. Choose a whole: Pick a number from 5–12. For example, choose 7.
2. Split it into two parts: Use counters to show two parts that make 7 (for example 3 and 4).
3. Say the parts and whole: “3 and 4 are parts. 7 is the whole.”
4. Write the two addition facts in your notebook: 3 + 4 = 7 and 4 + 3 = 7.
5. Write the two subtraction facts for the same family: 7 − 3 = 4 and 7 − 4 = 3.
6. Try a new family: Pick another whole within 12 (for example 9) and find two parts that make it (like 5 and 4). Repeat the steps.
7. Use the tracing pad: Trace words like family, fact, or whole. You can also trace one of your numbers, such as 7 or 9.

Tracing Pad
Lines
Trace
Pen

## Practice 1 — Fact family houses

[PLACEHOLDER PRACTICE 1]

## Practice 2 — Part–part–whole models

[PLACEHOLDER PRACTICE 2]

## Practice 3 — Complete the fact families

[PLACEHOLDER PRACTICE 3]

## Quick Check — Understanding fact families

Answer each question about fact families. You may use counters or a number line to help you.

1) What is a fact family?

A group of shapes A list of random numbers Facts that use the same three numbers
A fact family is a group of addition and subtraction facts that share the same three numbers.

2) Which three numbers could make a fact family?

3, 4, 7 2, 5, 10 1, 2, 4
3 and 4 are parts and 7 is the whole: 3 + 4 = 7.

3) In the fact family 3, 4, and 7, which number is the whole?

3 7 4
7 is the biggest number, so it is the whole.

4) Which sentence is part of the fact family for 3, 4, and 7?

3 + 3 = 6 7 + 4 = 11 7 − 3 = 4
7 − 3 = 4 uses the same three numbers: 3, 4, and 7.

5) Which two addition facts belong to the family 5, 2, and 7?

5 + 2 = 7 and 2 + 5 = 7 7 + 2 = 9 and 7 + 5 = 12 5 + 7 = 12 and 2 + 7 = 9
Addition facts in the family must equal the whole, 7.

6) Which two subtraction facts belong to the family 5, 2, and 7?

5 − 2 = 3 and 2 − 5 = 3 7 − 5 = 2 and 7 − 2 = 5 7 − 7 = 0 and 5 − 5 = 0
In a fact family, you always subtract from the whole, 7.

7) In a part–part–whole model, what are the parts?

Only the biggest number Any two numbers The two smaller numbers that make the whole
The parts are the smaller numbers that join to make the whole.

8) Which set could be a fact family?

6, 4, 10 6, 5, 2 10, 1, 12
6 and 4 are parts and 10 is the whole: 6 + 4 = 10.

9) For the family 6, 4, and 10, which subtraction fact is correct?

6 − 10 = 4 10 − 4 = 6 4 − 6 = 10
We subtract a part from the whole: 10 − 4 = 6.

10) Which sentence does NOT belong to the fact family 3, 5, and 8?

3 + 5 = 8 8 − 3 = 5 5 + 5 = 10
5 + 5 = 10 uses numbers outside the family 3, 5, and 8.

11) In a fact family, which number do we always start with in subtraction?

The whole The smallest part Any number
In subtraction we always start from the whole and take away a part.

12) The numbers 9, 1, and 10 make a fact family. Which is an addition fact from this family?

10 − 1 = 9 9 + 1 = 10 10 − 9 = 2
9 + 1 = 10 uses all three numbers and is an addition fact.

13) Why are fact families helpful?

They make numbers bigger. They help us draw better pictures. They show how addition and subtraction are connected.
Fact families help us see the link between adding and subtracting.

14) In the fact family 8, 2, and 10, which sentence is true?

10 − 2 = 8 8 + 10 = 2 2 − 8 = 10
Taking away a part from the whole gives the other part: 10 − 2 = 8.

15) A student says: "3, 6, and 9 are a fact family because 3 + 6 = 9." What else do they need to write to show the full family?

Only one subtraction fact One more addition fact and two subtraction facts Three more unrelated facts
A full fact family has two addition facts and two subtraction facts.

## Assessment (parent/teacher)

Student can explain what a fact family is. Student can identify the parts and whole in a fact family. Student can write the two addition facts for a simple fact family. Student can write the two subtraction facts for a simple fact family. Student can use counters or a model to show how the facts are connected.

## Exit ticket (student)

😀 I understand fact families very well. 🙂 I understand some fact families but need more practice. 😅 Fact families still feel tricky for me.

#### Next time I will practise…

Finding the three numbers in a fact family Writing addition facts in a family Writing subtraction facts in a family
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