Small steps, explained properly

1 Group things in tens

Counting one by one gets slow. Group objects into piles of ten, then count the piles first and the leftovers after.

10, 20, 30 … then 31, 32, 33

2 Every digit has a job

In a two-digit number the left digit counts tens and the right digit counts ones.

34 = 3 tens + 4 ones = 30 + 4

3 Read before you write

Say the number as tens and ones out loud before writing the digits down.

4 tens and 7 ones → 47

1 Make ten first

Fill the first number up to ten, then add what is left over.

8 + 5 → 8 + 2 = 10, then 10 + 3 = 13

2 Start from the bigger number

Counting on is faster when you begin at the larger number and add the smaller one.

3 + 9 → start at 9, count on 3 → 12

3 Use doubles

Doubles are easy to remember, and near doubles are only one more or less.

6 + 7 → 6 + 6 = 12, then +1 = 13

1 Count up instead

For numbers that are close together, count up from the smaller one to the bigger one.

12 − 9 → 9 to 12 is 3, so the answer is 3

2 Take tens, then ones

Split the number you are taking away into tens and ones.

45 − 23 → 45 − 20 = 25, then 25 − 3 = 22

3 Check with addition

Add your answer back to the number you took away. If you land on the start, you are right.

22 + 23 = 45 ✓

1 Think in equal groups

Multiplication counts how many equal groups you have and how big each group is.

4 × 3 = four groups of three = 12

2 Order does not matter

Swapping the two numbers gives the same total, so learn the easier version.

3 × 4 = 4 × 3 = 12

3 Build from facts you know

Split a hard fact into two easy ones and add the results.

6 × 7 → 6 × 5 = 30, plus 6 × 2 = 12 → 42

1 Share into equal piles

Deal the total out one at a time into the number of piles you need.

12 ÷ 3 → three piles of four

2 Turn it into a times table question

Ask yourself what you multiply by to reach the total.

12 ÷ 3 → 3 × ? = 12 → 4

3 Leftovers are remainders

When it does not divide exactly, the extra is called the remainder.

13 ÷ 4 → 3 each, remainder 1

1 A fraction is a fair share

The bottom number says how many equal parts, the top number says how many you take.

1/4 of 12 → split into 4 groups of 3

2 Different names, same size

Multiplying top and bottom by the same number keeps the value but changes the name.

1/2 = 2/4 = 4/8

3 Compare by the pieces

With the same top number, a bigger bottom number means smaller pieces.

3/5 is bigger than 3/8