Operations & Algebraic Thinking

Addition and Subtraction within 20

Grade 1

✓By the end of this lesson students will be able to solve word problems involving addition and subtraction within 20.
✓By the end of this lesson students will be able to apply properties of operations (commutative and associative properties) as strategies to add and subtract.
✓By the end of this lesson students will be able to use counting on as a strategy to add and subtract within 20.
✓By the end of this lesson students will be able to understand the relationship between addition and subtraction.

Key concepts

Addition

Addition is when you put two or more groups of things together to find how many there are in all. We use the plus sign (+).

Subtraction

Subtraction is when you take away from a group or find the difference between two groups. We use the minus sign (-).

Word Problems

Word problems are math stories that tell you about a situation and ask you to find a number answer. You need to read carefully to decide if you should add or subtract.

Counting On

Counting on is a strategy to add or subtract. To add, you start with the bigger number and count up the smaller number. To subtract, you can count up from the smaller number to the larger number to find the difference.

Commutative Property of Addition

This property means that you can add numbers in any order and still get the same sum. For example, 3 + 5 is the same as 5 + 3.

a + b = b + a

Associative Property of Addition

This property means that when you add three or more numbers, how you group them does not change the sum. For example, (2 + 3) + 4 is the same as 2 + (3 + 4). This helps us make tens!

(a + b) + c = a + (b + c)

Identity Property of Addition

This property means that when you add zero to any number, the number stays the same. For example, 7 + 0 = 7.

a + 0 = a

Relationship between Addition and Subtraction

Addition and subtraction are related! They are opposite operations. If you know that 3 + 5 = 8, then you also know that 8 - 5 = 3 and 8 - 3 = 5. These are called fact families.

Key facts to remember

1Addition means putting groups together to find the total.
2Subtraction means taking away from a group or finding the difference.
3Counting on is a helpful strategy for both addition and subtraction.
4You can add numbers in any order and get the same sum (Commutative Property of Addition).
5You can group numbers differently when adding and still get the same sum (Associative Property of Addition).
6Adding zero to a number does not change the number (Identity Property of Addition).
7Addition and subtraction are related; they are inverse operations.
8Using strategies like 'making a ten' can make adding easier.

Worked examples

Example 1

Lily has 7 red apples and 5 green apples. How many apples does Lily have in all?

I1. Understand the problem: Lily has two groups of apples, and we want to find the total. This means we need to add.

II2. Write an addition sentence: 7 + 5 = ?

III3. Use a strategy (Counting On): Start at 7 and count on 5 more: 7... 8, 9, 10, 11, 12.

IV4. Write the answer.

Answer

Lily has 12 apples in all.

You can also use a number line or draw pictures to help you count on.

Example 2

There are 12 birds on a branch. 4 birds fly away. How many birds are left on the branch?

I1. Understand the problem: We start with a group of birds, and some fly away. We want to find how many are left. This means we need to subtract.

II2. Write a subtraction sentence: 12 - 4 = ?

III3. Use a strategy (Counting On to find the difference): Start at 4 and count up to 12: 4... 5, 6, 7, 8, 9, 10, 11, 12. We counted 8 numbers.

IV4. Write the answer.

Answer

There are 8 birds left on the branch.

Another way to solve this is to count back 4 from 12: 12, 11, 10, 9, 8.

Example 3

Use a property of addition to solve 6 + 8.

I1. Understand the problem: We need to add 6 and 8. We can use a property to make it easier, like making a ten.

II2. Think about making a ten: We can take some from 6 to make 8 a ten. We need 2 more to make 8 into 10 (because 8 + 2 = 10).

III3. Break apart the 6: We can break 6 into 2 and 4 (because 2 + 4 = 6).

IV4. Rewrite the problem using the Associative Property: 6 + 8 = (4 + 2) + 8 = 4 + (2 + 8).

V5. Add the numbers that make ten first: 4 + (2 + 8) = 4 + 10.

VI6. Add the remaining numbers: 4 + 10 = 14.

VII7. Write the answer.

Answer

6 + 8 = 14

This strategy helps you add quickly by using your knowledge of tens!

Common mistakes

✗Not understanding if a word problem requires addition or subtraction.
✗Miscounting when using the 'counting on' strategy.
✗Forgetting to check their answer to see if it makes sense.
✗Not showing their work or the strategy they used to solve a problem.
✗Confusing the plus (+) and minus (-) signs.

Exam tips

★Read every word problem carefully, sometimes twice, to understand what it is asking.
★Draw pictures or use objects (like counters) to help you visualize and solve problems.
★Use a number line or your fingers to help you with counting on and counting back.
★Always check your answer to make sure it is correct and makes sense for the problem.

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