Mathematics notes, unit 2

Addition and Subtraction

Textbook Mathematics Year 1 (DLP), Textbook Part 1 and Part 2, pages Part 1, 55–114

What this chapter covers

You can say what add, subtract, total, difference and balance mean (2.1.1)
You can add numbers within 18 and then within 100, with and without regrouping (2.2.1, 2.2.2)
You can subtract numbers within 18 and then within 100, with and without regrouping (2.3.1, 2.3.2)
You can make up and tell a story for an addition or subtraction number sentence (2.4.1)
You can solve one-step problems about adding and subtracting (2.4.2)
You can write repeated addition and repeated subtraction for equal groups (2.5.1, 2.6.1)

2.1What add and subtract mean

Add (+) means put together to make a total. Subtract (−) means take away to find what is left. The sign = means "is equal to".

4 blue balls and 1 orange ball — 4 balls and 1 more ball. 4 + 1 = 5. There are 5 balls altogether.

6 balls where 2 are crossed out — 6 balls, take away 2. 6 − 2 = 4. There are 4 balls left.

The difference tells how many more or how many less. The difference of 9 and 7 is 2, because 9 − 7 = 2. The balance is what is left.

When we add, the number gets bigger. When we subtract, the number gets smaller.

There are 12 sandwiches. 3 are sold. How many are left?

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12 − 3 = 9 sandwiches.

Based on the Year 1 textbook, pages 56 to 59 and 74 to 77.

2.2Adding

Add numbers up to 18

Count on from the bigger number. For 8 + 3, say 9, 10, 11. Or make 10 first: 8 + 2 = 10, then 10 + 1 = 11.

Adding 0 does not change a number: 6 + 0 = 6. The order does not change the total: 3 + 4 = 4 + 3 = 7.

Add numbers up to 100

4 tens blocks and 3 ones blocks — 43 is 4 tens and 3 ones.

Number line from 25 to 28 with three jumps of plus 1 — 25 + 3: count on 3 steps. The answer is 28.

Write the numbers in columns. Ones go under ones and tens go under tens. Add the ones first, then the tens.

Worked example: 43 + 52

Step 1. Ones: 3 + 2 = 5.
Step 2. Tens: 4 + 5 = 9.
Step 3. 43 + 52 = 95.

Add with regrouping

If the ones make 10 or more, change 10 ones into 1 ten. This is regrouping.

Worked example: 29 + 6

Step 1. Ones: 9 + 6 = 15 ones = 1 ten and 5 ones. Write 5, carry 1 ten.
Step 2. Tens: 2 + 0 + 1 = 3.
Step 3. 29 + 6 = 35.

Do not forget the carried ten. 18 + 34 is 52, not 42.

Find 17 + 30, and then 38 + 25.

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17 + 30 = 47 (1 ten + 3 tens = 4 tens, ones stay 7). 38 + 25: 8 + 5 = 13, write 3 carry 1; 3 + 2 + 1 = 6. The answer is 63.

Based on the Year 1 textbook, pages 58 to 73.

2.3Subtracting

Subtract numbers up to 18

Count back from the bigger number. For 11 − 4, count back 4 steps: 10, 9, 8, 7. The answer is 7.

Addition and subtraction are partners. 3 + 4 = 7, so 7 − 4 = 3 and 7 − 3 = 4.

Subtract numbers up to 100

Number line from 19 back to 14 with five jumps of minus 1 — 19 − 5: count back 5 steps. 14 are left.

Subtract the ones first, then the tens. Always put the bigger number on top.

Worked example: 68 − 25

Step 1. Ones: 8 − 5 = 3.
Step 2. Tens: 6 − 2 = 4.
Step 3. 68 − 25 = 43.

Subtract with regrouping

If the top ones digit is too small, change 1 ten into 10 ones.

Worked example: 63 − 7

Step 1. 3 ones is less than 7. Change 1 ten to 10 ones: 13 ones − 7 ones = 6 ones.
Step 2. Tens: 5 tens left, 5 − 0 = 5.
Step 3. 63 − 7 = 56.

Do not turn the ones round. In 63 − 7, you cannot do 3 − 7 by saying 7 − 3 = 4. That gives 64, which is wrong. Regroup instead to get 56.

Check subtraction by adding. 56 + 7 = 63, so 63 − 7 = 56 is right.

Find 59 − 28, and then 50 − 24.

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59 − 28: 9 − 8 = 1 and 5 − 2 = 3, so 31. 50 − 24: regroup, 10 − 4 = 6 and 4 − 2 = 2, so 26.

Based on the Year 1 textbook, pages 76 to 92.

2.4Stories and problems

A number sentence can tell a story. 18 + 7 = 25 can be: "There are 18 red cars and 7 blue cars. There are 25 cars altogether."

Words in the problem	What to do
altogether, total, more	add
left, balance, give away, difference	subtract

To solve a problem, read it, find the numbers, write the number sentence, work it out and write the answer.

Worked example

Lina's father has 17 corn plants. 4 plants die. How many are left?
17 − 4 = 13 plants.

Sometimes a number is missing: 58 − ? = 12. Think "58 take away what makes 12?" The answer is 46, because 12 + 46 = 58.

Ho has 10 oranges. He gives 6 to Raju. How many are left?

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10 − 6 = 4 oranges.

Based on the Year 1 textbook, pages 93 to 107.

2.5Repeated addition and subtraction

3 plates with 2 sweets on each plate — 3 groups of 2: 2 + 2 + 2 = 6.

Repeated addition means adding the same number again and again. 3 groups of twos are 2 + 2 + 2 = 6.

Repeated subtraction means taking away the same number again and again until none is left. 10 − 5 − 5 = 0, so 10 shared between 2 friends is 5 each.

Write the repeated addition for 4 groups of 5.

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5 + 5 + 5 + 5 = 20.

Based on the Year 1 textbook, pages 108 to 113.

Summary

Add to find the total. Subtract to find what is left or the difference.
Add and subtract the ones first, then the tens.
If the ones make 10 or more, carry 1 ten. If the top ones are too small, change 1 ten to 10 ones.
Check subtraction with addition.
Repeated addition adds equal groups. Repeated subtraction takes away equal groups.