Before, after and between
By the end of this chapter you will be able to
- Say the number before and the number after
- Say the number that is between two others
- Put numbers in order, smallest first and biggest first
- Say which of two numbers is greater or less
- Use the signs <, > and = correctly
You should already know
- Counting forwards and backwards to 20 (Chapter 2)
- Numbers 0 to 20 as numerals and words (Chapters 1 and 2)
Where this leads
- Number bonds to 5 (Level 1, Chapter 4)
Step-by-step practice: maths (Level 1). Small steps, repeated until fluent. Content: Say the number before and after a given number up to 20, Say the numbers between two numbers up to 20, Order numbers from 0 to 20, smallest and biggest first, Compare two numbers with more, fewer, greater and less, Use the signs <, > and = with numbers up to 20.
Exercise P Do you remember?
Non-calculatorMethod. Count on from 13 one step at a time.
- Start at 13. We begin with the number we have.13
- Count on two. Each number is one more than the one before.14, 15
- Write the answer. 14, 15
Check. Count back from 15 to 13: 15, 14, 13. It matches.
Watch out. Start with the number after 13.
Method. Count back one at a time from 10.
- Start at 10. We begin with 10 and count back.10
- Count back two. Each number is one less than the one before.9, 8
- Write the answer. 9, 8
Check. Count on from 8: 8, 9, 10. It works.
Watch out. Counting back means the numbers get smaller.
Method. The bigger number comes later when we count.
- Say the numbers in order. 9, 10, 11, 12.9, 10, 11, 12
- Find the later one. 12 comes after 9.12 is bigger
- Write the answer. 12
Check. Count from 9 to 12: that is three steps up.
Watch out. Bigger numbers come later in the count.
Method. Say the number and find its name.
- Look at the numeral. It is a ten and five more.15
- Say the number name. It is the teen word for fifteen.fifteen
- Write the answer. fifteen
Check. Count to 15 and stop on fifteen.
Watch out. Spell fifteen with f-i-f-t-e-e-n.
Method. Touch each cube once and say the last number.
- Touch each cube once. Count in order.1, 2, 3, 4, 5
- Say the last number. The last number tells how many.5
- Write the answer. 5
Check. Count back from 5 to 1. You land on 5.
Watch out. Touch each cube only once.
The number before and the number after
The number after is one more. The number before is one less.
Think of the number line. After is to the right. Before is to the left.
Key ideas
- The number after is one more.
- The number before is one less.
- Before is to the left on a number line.
Method. One less means the number just before when we count back.
- Start at the number. We begin where we are.10
- Count back one. Say the number that comes just before.10 - 1 = 9
- Write the answer. 9
Check. Count on one: 9 add 1 is 10. It works.
Watch out. One less is the number before, not the number after.
Method. One more means the next number when we count on.
- Start at the number. We begin where we are.16
- Count on one. Say the number that comes next.16 + 1 = 17
- Write the answer. 17
Check. Count back one: 17 take away 1 is 16. It works.
Watch out. One more is the next number, not the same number.
Method. The number before means one less.
- Start at 20. We begin with the number we are given.20
- Count back one. The number before is one less.20 - 1 = 19
- Write the answer. 19
Check. Count on one from 19: 20. It works.
Watch out. Do not say 21. That is after 20.
Watch out
Watch out. Before means less, after means more. Check which way you move on the number line.
Exam tip
Grown-up tip. Say a number, then ask “what comes before?” and “what comes after?” Use stairs or a number track to show left and right.
Exercise 3A Before and after
Non-calculatorMethod. One less means the number just before when we count back.
- Start at the number. We begin where we are.14
- Count back one. Say the number that comes just before.14 - 1 = 13
- Write the answer. 13
Check. Count on one: 13 add 1 is 14. It works.
Watch out. One less is the number before, not the number after.
Method. One more means the next number when we count on.
- Start at the number. We begin where we are.1
- Count on one. Say the number that comes next.1 + 1 = 2
- Write the answer. 2
Check. Count back one: 2 take away 1 is 1. It works.
Watch out. One more is the next number, not the same number.
Method. One less means the number just before when we count back.
- Start at the number. We begin where we are.17
- Count back one. Say the number that comes just before.17 - 1 = 16
- Write the answer. 16
Check. Count on one: 16 add 1 is 17. It works.
Watch out. One less is the number before, not the number after.
Method. One more means the next number when we count on.
- Start at the number. We begin where we are.11
- Count on one. Say the number that comes next.11 + 1 = 12
- Write the answer. 12
Check. Count back one: 12 take away 1 is 11. It works.
Watch out. One more is the next number, not the same number.
Method. One less means the number just before when we count back.
- Start at the number. We begin where we are.5
- Count back one. Say the number that comes just before.5 - 1 = 4
- Write the answer. 4
Check. Count on one: 4 add 1 is 5. It works.
Watch out. One less is the number before, not the number after.
Method. One more means the next number when we count on.
- Start at the number. We begin where we are.8
- Count on one. Say the number that comes next.8 + 1 = 9
- Write the answer. 9
Check. Count back one: 9 take away 1 is 8. It works.
Watch out. One more is the next number, not the same number.
Method. One less means the number just before when we count back.
- Start at the number. We begin where we are.12
- Count back one. Say the number that comes just before.12 - 1 = 11
- Write the answer. 11
Check. Count on one: 11 add 1 is 12. It works.
Watch out. One less is the number before, not the number after.
Method. One more means the next number when we count on.
- Start at the number. We begin where we are.6
- Count on one. Say the number that comes next.6 + 1 = 7
- Write the answer. 7
Check. Count back one: 7 take away 1 is 6. It works.
Watch out. One more is the next number, not the same number.
Method. One less means the number just before when we count back.
- Start at the number. We begin where we are.19
- Count back one. Say the number that comes just before.19 - 1 = 18
- Write the answer. 18
Check. Count on one: 18 add 1 is 19. It works.
Watch out. One less is the number before, not the number after.
Method. One more means the next number when we count on.
- Start at the number. We begin where we are.6
- Count on one. Say the number that comes next.6 + 1 = 7
- Write the answer. 7
Check. Count back one: 7 take away 1 is 6. It works.
Watch out. One more is the next number, not the same number.
Method. One less means the number just before when we count back.
- Start at the number. We begin where we are.12
- Count back one. Say the number that comes just before.12 - 1 = 11
- Write the answer. 11
Check. Count on one: 11 add 1 is 12. It works.
Watch out. One less is the number before, not the number after.
Method. One more means the next number when we count on.
- Start at the number. We begin where we are.1
- Count on one. Say the number that comes next.1 + 1 = 2
- Write the answer. 2
Check. Count back one: 2 take away 1 is 1. It works.
Watch out. One more is the next number, not the same number.
Method. One less means the number just before when we count back.
- Start at the number. We begin where we are.10
- Count back one. Say the number that comes just before.10 - 1 = 9
- Write the answer. 9
Check. Count on one: 9 add 1 is 10. It works.
Watch out. One less is the number before, not the number after.
Method. One more means the next number when we count on.
- Start at the number. We begin where we are.16
- Count on one. Say the number that comes next.16 + 1 = 17
- Write the answer. 17
Check. Count back one: 17 take away 1 is 16. It works.
Watch out. One more is the next number, not the same number.
Method. One less means the number just before when we count back.
- Start at the number. We begin where we are.15
- Count back one. Say the number that comes just before.15 - 1 = 14
- Write the answer. 14
Check. Count on one: 14 add 1 is 15. It works.
Watch out. One less is the number before, not the number after.
Method. One more means the next number when we count on.
- Start at the number. We begin where we are.16
- Count on one. Say the number that comes next.16 + 1 = 17
- Write the answer. 17
Check. Count back one: 17 take away 1 is 16. It works.
Watch out. One more is the next number, not the same number.
Between two numbers
A number is between two others when it comes after the smaller one and before the bigger one.
Look at 4 and 6. The number between them is 5.
Key ideas
- Between means after the smaller number and before the bigger one.
- Do not include the two end numbers.
- Two numbers can be between two others.
Method. Find the numbers in between by counting on from the smaller number.
- Start at the smaller number. Count on one at a time.4
- Count on until just before the bigger one. The numbers in between come after the smaller one.5
- Write the answer. 5
Check. Check: 5 is bigger than 4 and smaller than 6.
Watch out. Do not include the two numbers at the ends.
Method. Find the numbers in between by counting on from the smaller number.
- Start at the smaller number. Count on one at a time.10
- Count on until just before the bigger one. The numbers in between come after the smaller one.11
- Write the answer. 11
Check. Check: 11 is bigger than 10 and smaller than 12.
Watch out. Do not include the two numbers at the ends.
Method. Find the numbers in between by counting on from the smaller number.
- Start at the smaller number. Count on one at a time.7
- Count on until just before the bigger one. The numbers in between come after the smaller one.8, 9
- Write the answer. 8 and 9
Check. Check: 8 and 9 is bigger than 7 and smaller than 10.
Watch out. Do not include the two numbers at the ends.
Watch out
Watch out. The numbers at the ends are not between. For 4 and 6, the answer is 5, not 4 or 6.
Exam tip
Grown-up tip. Count from the smaller number to the bigger one. Say the numbers out loud and stop before the last one.
Exercise 3B Between two numbers
Non-calculatorMethod. Find the numbers in between by counting on from the smaller number.
- Start at the smaller number. Count on one at a time.8
- Count on until just before the bigger one. The numbers in between come after the smaller one.9
- Write the answer. 9
Check. Check: 9 is bigger than 8 and smaller than 10.
Watch out. Do not include the two numbers at the ends.
Method. Find the numbers in between by counting on from the smaller number.
- Start at the smaller number. Count on one at a time.9
- Count on until just before the bigger one. The numbers in between come after the smaller one.10, 11
- Write the answer. 10 and 11
Check. Check: 10 and 11 is bigger than 9 and smaller than 12.
Watch out. Do not include the two numbers at the ends.
Method. Find the numbers in between by counting on from the smaller number.
- Start at the smaller number. Count on one at a time.15
- Count on until just before the bigger one. The numbers in between come after the smaller one.16
- Write the answer. 16
Check. Check: 16 is bigger than 15 and smaller than 17.
Watch out. Do not include the two numbers at the ends.
Method. Find the numbers in between by counting on from the smaller number.
- Start at the smaller number. Count on one at a time.16
- Count on until just before the bigger one. The numbers in between come after the smaller one.17, 18
- Write the answer. 17 and 18
Check. Check: 17 and 18 is bigger than 16 and smaller than 19.
Watch out. Do not include the two numbers at the ends.
Method. Find the numbers in between by counting on from the smaller number.
- Start at the smaller number. Count on one at a time.7
- Count on until just before the bigger one. The numbers in between come after the smaller one.8
- Write the answer. 8
Check. Check: 8 is bigger than 7 and smaller than 9.
Watch out. Do not include the two numbers at the ends.
Method. Find the numbers in between by counting on from the smaller number.
- Start at the smaller number. Count on one at a time.3
- Count on until just before the bigger one. The numbers in between come after the smaller one.4, 5
- Write the answer. 4 and 5
Check. Check: 4 and 5 is bigger than 3 and smaller than 6.
Watch out. Do not include the two numbers at the ends.
Method. Find the numbers in between by counting on from the smaller number.
- Start at the smaller number. Count on one at a time.9
- Count on until just before the bigger one. The numbers in between come after the smaller one.10
- Write the answer. 10
Check. Check: 10 is bigger than 9 and smaller than 11.
Watch out. Do not include the two numbers at the ends.
Method. Find the numbers in between by counting on from the smaller number.
- Start at the smaller number. Count on one at a time.0
- Count on until just before the bigger one. The numbers in between come after the smaller one.1, 2
- Write the answer. 1 and 2
Check. Check: 1 and 2 is bigger than 0 and smaller than 3.
Watch out. Do not include the two numbers at the ends.
Method. Find the numbers in between by counting on from the smaller number.
- Start at the smaller number. Count on one at a time.16
- Count on until just before the bigger one. The numbers in between come after the smaller one.17
- Write the answer. 17
Check. Check: 17 is bigger than 16 and smaller than 18.
Watch out. Do not include the two numbers at the ends.
Method. Find the numbers in between by counting on from the smaller number.
- Start at the smaller number. Count on one at a time.0
- Count on until just before the bigger one. The numbers in between come after the smaller one.1, 2
- Write the answer. 1 and 2
Check. Check: 1 and 2 is bigger than 0 and smaller than 3.
Watch out. Do not include the two numbers at the ends.
Method. Find the numbers in between by counting on from the smaller number.
- Start at the smaller number. Count on one at a time.18
- Count on until just before the bigger one. The numbers in between come after the smaller one.19
- Write the answer. 19
Check. Check: 19 is bigger than 18 and smaller than 20.
Watch out. Do not include the two numbers at the ends.
Method. Find the numbers in between by counting on from the smaller number.
- Start at the smaller number. Count on one at a time.13
- Count on until just before the bigger one. The numbers in between come after the smaller one.14, 15
- Write the answer. 14 and 15
Check. Check: 14 and 15 is bigger than 13 and smaller than 16.
Watch out. Do not include the two numbers at the ends.
Method. Find the numbers in between by counting on from the smaller number.
- Start at the smaller number. Count on one at a time.15
- Count on until just before the bigger one. The numbers in between come after the smaller one.16
- Write the answer. 16
Check. Check: 16 is bigger than 15 and smaller than 17.
Watch out. Do not include the two numbers at the ends.
Method. Find the numbers in between by counting on from the smaller number.
- Start at the smaller number. Count on one at a time.12
- Count on until just before the bigger one. The numbers in between come after the smaller one.13, 14
- Write the answer. 13 and 14
Check. Check: 13 and 14 is bigger than 12 and smaller than 15.
Watch out. Do not include the two numbers at the ends.
Method. Find the numbers in between by counting on from the smaller number.
- Start at the smaller number. Count on one at a time.13
- Count on until just before the bigger one. The numbers in between come after the smaller one.14
- Write the answer. 14
Check. Check: 14 is bigger than 13 and smaller than 15.
Watch out. Do not include the two numbers at the ends.
Method. Find the numbers in between by counting on from the smaller number.
- Start at the smaller number. Count on one at a time.12
- Count on until just before the bigger one. The numbers in between come after the smaller one.13, 14
- Write the answer. 13 and 14
Check. Check: 13 and 14 is bigger than 12 and smaller than 15.
Watch out. Do not include the two numbers at the ends.
Putting numbers in order
To put numbers in order, look at them all first.
Smallest first means the list goes up. Biggest first means the list goes down.
Key ideas
- Smallest first: the list goes up.
- Biggest first: the list goes down.
- Check each number is bigger than the one before.
Method. Find the smallest first, then put the rest in order.
- Find the smallest number. Six is the smallest.6
- Put the others in order. Eleven is next, then fourteen.6, 11, 14
- Write the answer. 6, 11, 14
Check. Each number is bigger than the one before. It is in order.
Watch out. Compare the tens first. Fourteen is more than eleven.
Method. Find the biggest first, then put the rest in order.
- Find the biggest number. Seventeen is the biggest.17
- Put the others in order. Nine is next, then three.17, 9, 3
- Write the answer. 17, 9, 3
Check. Each number is smaller than the one before. It is in order.
Watch out. The list goes down when it is biggest first.
Method. Find the smallest first, then the rest.
- Find the smallest number. Two is the smallest.2
- Put the others in order. Twelve comes before twenty.2, 12, 20
- Write the answer. 2, 12, 20
Check. Count from 2 to 20. The numbers appear in the same order.
Watch out. Do not read 20 before 12. Twenty is the biggest.
Watch out
Watch out. Do not put 9 after 10. Nine is smaller than ten, so it comes first.
Exam tip
Grown-up tip. Write three numbers on cards. Mix them up, then put them in order. Ask: “Which is smallest? Which is next?”
Exercise 3C Putting numbers in order
Non-calculatorMethod. Put the numbers in order from the smallest. Start with the smallest.
- Find the smallest number. It goes first in the list.6
- Put the rest in order. Each number is bigger than the one before.6, 19, 20
- Write the answer. 6, 19, 20
Check. Read the list again. Each number is bigger than the one before. ✓
Watch out. Compare the tens digit first when the numbers are big.
Method. Put the numbers in order from the biggest. Start with the biggest.
- Find the biggest number. It goes first in this list.20
- Put the rest in order. Each number is smaller than the one before.20, 15, 13
- Write the answer. 20, 15, 13
Check. Read the list again. Each number is smaller than the one before. ✓
Watch out. Biggest first means the list goes down.
Method. Put the numbers in order from the smallest. Start with the smallest.
- Find the smallest number. It goes first in the list.9
- Put the rest in order. Each number is bigger than the one before.9, 16, 19
- Write the answer. 9, 16, 19
Check. Read the list again. Each number is bigger than the one before. ✓
Watch out. Compare the tens digit first when the numbers are big.
Method. Put the numbers in order from the biggest. Start with the biggest.
- Find the biggest number. It goes first in this list.13
- Put the rest in order. Each number is smaller than the one before.13, 12, 3
- Write the answer. 13, 12, 3
Check. Read the list again. Each number is smaller than the one before. ✓
Watch out. Biggest first means the list goes down.
Method. Put the numbers in order from the smallest. Start with the smallest.
- Find the smallest number. It goes first in the list.1
- Put the rest in order. Each number is bigger than the one before.1, 12, 13
- Write the answer. 1, 12, 13
Check. Read the list again. Each number is bigger than the one before. ✓
Watch out. Compare the tens digit first when the numbers are big.
Method. Put the numbers in order from the biggest. Start with the biggest.
- Find the biggest number. It goes first in this list.19
- Put the rest in order. Each number is smaller than the one before.19, 14, 3
- Write the answer. 19, 14, 3
Check. Read the list again. Each number is smaller than the one before. ✓
Watch out. Biggest first means the list goes down.
Method. Put the numbers in order from the smallest. Start with the smallest.
- Find the smallest number. It goes first in the list.2
- Put the rest in order. Each number is bigger than the one before.2, 11, 12
- Write the answer. 2, 11, 12
Check. Read the list again. Each number is bigger than the one before. ✓
Watch out. Compare the tens digit first when the numbers are big.
Method. Put the numbers in order from the biggest. Start with the biggest.
- Find the biggest number. It goes first in this list.20
- Put the rest in order. Each number is smaller than the one before.20, 9, 5
- Write the answer. 20, 9, 5
Check. Read the list again. Each number is smaller than the one before. ✓
Watch out. Biggest first means the list goes down.
Method. Put the numbers in order from the smallest. Start with the smallest.
- Find the smallest number. It goes first in the list.2
- Put the rest in order. Each number is bigger than the one before.2, 18, 19
- Write the answer. 2, 18, 19
Check. Read the list again. Each number is bigger than the one before. ✓
Watch out. Compare the tens digit first when the numbers are big.
Method. Put the numbers in order from the biggest. Start with the biggest.
- Find the biggest number. It goes first in this list.17
- Put the rest in order. Each number is smaller than the one before.17, 16, 8
- Write the answer. 17, 16, 8
Check. Read the list again. Each number is smaller than the one before. ✓
Watch out. Biggest first means the list goes down.
Method. Put the numbers in order from the smallest. Start with the smallest.
- Find the smallest number. It goes first in the list.1
- Put the rest in order. Each number is bigger than the one before.1, 10, 18
- Write the answer. 1, 10, 18
Check. Read the list again. Each number is bigger than the one before. ✓
Watch out. Compare the tens digit first when the numbers are big.
Method. Put the numbers in order from the biggest. Start with the biggest.
- Find the biggest number. It goes first in this list.18
- Put the rest in order. Each number is smaller than the one before.18, 11, 2
- Write the answer. 18, 11, 2
Check. Read the list again. Each number is smaller than the one before. ✓
Watch out. Biggest first means the list goes down.
Method. Put the numbers in order from the smallest. Start with the smallest.
- Find the smallest number. It goes first in the list.2
- Put the rest in order. Each number is bigger than the one before.2, 12, 20
- Write the answer. 2, 12, 20
Check. Read the list again. Each number is bigger than the one before. ✓
Watch out. Compare the tens digit first when the numbers are big.
Method. Put the numbers in order from the biggest. Start with the biggest.
- Find the biggest number. It goes first in this list.15
- Put the rest in order. Each number is smaller than the one before.15, 12, 5
- Write the answer. 15, 12, 5
Check. Read the list again. Each number is smaller than the one before. ✓
Watch out. Biggest first means the list goes down.
Method. Put the numbers in order from the smallest. Start with the smallest.
- Find the smallest number. It goes first in the list.2
- Put the rest in order. Each number is bigger than the one before.2, 14, 17
- Write the answer. 2, 14, 17
Check. Read the list again. Each number is bigger than the one before. ✓
Watch out. Compare the tens digit first when the numbers are big.
Method. Put the numbers in order from the biggest. Start with the biggest.
- Find the biggest number. It goes first in this list.18
- Put the rest in order. Each number is smaller than the one before.18, 13, 10
- Write the answer. 18, 13, 10
Check. Read the list again. Each number is smaller than the one before. ✓
Watch out. Biggest first means the list goes down.
Greater, less and the signs
We can compare two numbers. The greater number is bigger. The less number is smaller.
The sign > means greater than. The sign < means less than. The sign = means equal.
The open end of the sign always faces the bigger number. The point faces the smaller one.
Key ideas
- Greater means bigger. Less means smaller.
- > means greater than.
- < means less than.
- = means the same as.
Method. Compare the two numbers.
- Say the two numbers. Eight and thirteen.8 and 13
- Compare them. 13 comes later, so it is bigger.8 is less than 13
- Choose the sign. The point faces the smaller number, 8.<
Check. The sign faces the smaller number. 8 < 13 is right.
Watch out. The point of the sign always faces the smaller number.
Method. Compare the two numbers.
- Say the two numbers. Fifteen and nine.15 and 9
- Compare them. 15 comes later, so it is bigger.15 is greater than 9
- Choose the sign. The open end faces the bigger number.>
Check. The open end faces 15. 15 > 9 is right.
Watch out. The open end of the sign faces the bigger number.
Method. Look at both numbers.
- Say the two numbers. Six and six.6 and 6
- Check whether they are the same. They are the same amount.6 is equal to 6
- Choose the sign. Equal means the same.=
Check. Both numbers are 6, so the sign is =.
Watch out. Use = only when the two numbers are the same.
Watch out
Watch out. The sign does not care about the size of the symbol. Look at which number is bigger.
Exam tip
Grown-up tip. Use two groups of counters. Ask: “Which group has more?” Then show the sign that matches the answer.
Exercise 3D Greater, less and the signs
Non-calculatorMethod. Compare the two numbers. Which one comes later when we count?
- Say both numbers. The numbers are 12 and 11.12 and 11
- Compare them. The number further along the count is bigger.12 is greater than 11
- Write the answer. 12
Check. Count from 11 to 12. 12 comes later, so it is bigger. ✓
Watch out. Bigger numbers come later in the count, even when the digits look different.
Method. Compare the two numbers. Which one comes later when we count?
- Say both numbers. The numbers are 18 and 11.18 and 11
- Compare them. The number further along the count is bigger.11 is less than 18
- Write the answer. 11
Check. Count from 11 to 18. 18 comes later, so it is bigger. ✓
Watch out. Bigger numbers come later in the count, even when the digits look different.
Method. Compare the two numbers. Which one comes later when we count?
- Say both numbers. The numbers are 11 and 17.11 and 17
- Compare them. The number further along the count is bigger.11 is less than 17, so the sign is <
- Write the answer. <
Check. Count from 11 to 17. 17 comes later, so it is bigger. ✓
Watch out. Bigger numbers come later in the count, even when the digits look different.
Method. Compare the two numbers. Which one comes later when we count?
- Say both numbers. The numbers are 2 and 0.2 and 0
- Compare them. The number further along the count is bigger.2 is further along the count
- Write the answer. 2
Check. Count from 0 to 2. 2 comes later, so it is bigger. ✓
Watch out. Bigger numbers come later in the count, even when the digits look different.
Method. Compare the two numbers. Which one comes later when we count?
- Say both numbers. The numbers are 20 and 5.20 and 5
- Compare them. The number further along the count is bigger.20 is greater than 5
- Write the answer. 20
Check. Count from 5 to 20. 20 comes later, so it is bigger. ✓
Watch out. Bigger numbers come later in the count, even when the digits look different.
Method. Compare the two numbers. Which one comes later when we count?
- Say both numbers. The numbers are 16 and 5.16 and 5
- Compare them. The number further along the count is bigger.5 is less than 16
- Write the answer. 5
Check. Count from 5 to 16. 16 comes later, so it is bigger. ✓
Watch out. Bigger numbers come later in the count, even when the digits look different.
Method. Compare the two numbers.
- Say the two numbers. They are the same number.19 and 19
- Check whether they are the same. Equal means the same amount.19 is equal to 19
- Choose the sign. Equal is written with two short lines.=
Check. Both numbers are 19, so the sign is =. ✓
Watch out. Use = only when the two numbers are the same.
Method. Compare the two numbers. Which one comes later when we count?
- Say both numbers. The numbers are 18 and 0.18 and 0
- Compare them. The number further along the count is bigger.18 is further along the count
- Write the answer. 18
Check. Count from 0 to 18. 18 comes later, so it is bigger. ✓
Watch out. Bigger numbers come later in the count, even when the digits look different.
Method. Compare the two numbers. Which one comes later when we count?
- Say both numbers. The numbers are 10 and 1.10 and 1
- Compare them. The number further along the count is bigger.10 is greater than 1
- Write the answer. 10
Check. Count from 1 to 10. 10 comes later, so it is bigger. ✓
Watch out. Bigger numbers come later in the count, even when the digits look different.
Method. Compare the two numbers. Which one comes later when we count?
- Say both numbers. The numbers are 19 and 6.19 and 6
- Compare them. The number further along the count is bigger.6 is less than 19
- Write the answer. 6
Check. Count from 6 to 19. 19 comes later, so it is bigger. ✓
Watch out. Bigger numbers come later in the count, even when the digits look different.
Method. Compare the two numbers. Which one comes later when we count?
- Say both numbers. The numbers are 15 and 17.15 and 17
- Compare them. The number further along the count is bigger.15 is less than 17, so the sign is <
- Write the answer. <
Check. Count from 15 to 17. 17 comes later, so it is bigger. ✓
Watch out. Bigger numbers come later in the count, even when the digits look different.
Method. Compare the two numbers. Which one comes later when we count?
- Say both numbers. The numbers are 12 and 0.12 and 0
- Compare them. The number further along the count is bigger.12 is further along the count
- Write the answer. 12
Check. Count from 0 to 12. 12 comes later, so it is bigger. ✓
Watch out. Bigger numbers come later in the count, even when the digits look different.
Method. Count the cubes in each row. Then say which group has more or fewer.
- Count group A. Touch each cube once.A has 6
- Count group B. Touch each cube once.B has 7
- Compare the two numbers. 7 is bigger than 6, so one group has more.Group B
Check. The difference is 7 take away 6, which is 1. ✓
Watch out. Read the letter first. A is the top row, B is the bottom row.
Method. Count the cubes in each row. Then say which group has more or fewer.
- Count group A. Touch each cube once.A has 5
- Count group B. Touch each cube once.B has 8
- Compare the two numbers. 8 is bigger than 5, so one group has fewer.Group A
Check. The difference is 8 take away 5, which is 3. ✓
Watch out. Read the letter first. A is the top row, B is the bottom row.
Method. Count the cubes in each row. Then say which group has more or fewer.
- Count group A. Touch each cube once.A has 4
- Count group B. Touch each cube once.B has 5
- Compare the two numbers. 5 is bigger than 4, so one group has more.Group B
Check. The difference is 5 take away 4, which is 1. ✓
Watch out. Read the letter first. A is the top row, B is the bottom row.
Method. Count the cubes in each row. Then say which group has more or fewer.
- Count group A. Touch each cube once.A has 1
- Count group B. Touch each cube once.B has 2
- Compare the two numbers. 2 is bigger than 1, so one group has fewer.Group A
Check. The difference is 2 take away 1, which is 1. ✓
Watch out. Read the letter first. A is the top row, B is the bottom row.
Chapter summary
| Skill | Method |
|---|---|
| Before and after | Before is one less. After is one more |
| Between | Numbers after the smaller one and before the bigger one |
| Order | Smallest first goes up. Biggest first goes down |
| Compare | Use greater, less, more or fewer. Signs: < > = |
Can you…?
- I can say the number before and the number after
- I can say the number between two numbers
- I can put numbers up to 20 in order
- I can say which number is greater or less
- I can use the signs <, > and = correctly
Key terms
- before
- one less than a number
- after
- one more than a number
- between
- bigger than the smaller number and smaller than the bigger one
- greater than
- bigger than; written >
- less than
- smaller than; written <
- equal to
- the same as; written =
Exercise 3Z Check-up
Non-calculatorMethod. One less means the number just before when we count back.
- Start at the number. We begin where we are.8
- Count back one. Say the number that comes just before.8 - 1 = 7
- Write the answer. 7
Check. Count on one: 7 add 1 is 8. It works.
Watch out. One less is the number before, not the number after.
Method. One more means the next number when we count on.
- Start at the number. We begin where we are.14
- Count on one. Say the number that comes next.14 + 1 = 15
- Write the answer. 15
Check. Count back one: 15 take away 1 is 14. It works.
Watch out. One more is the next number, not the same number.
Method. One less means the number just before when we count back.
- Start at the number. We begin where we are.12
- Count back one. Say the number that comes just before.12 - 1 = 11
- Write the answer. 11
Check. Count on one: 11 add 1 is 12. It works.
Watch out. One less is the number before, not the number after.
Method. One more means the next number when we count on.
- Start at the number. We begin where we are.0
- Count on one. Say the number that comes next.0 + 1 = 1
- Write the answer. 1
Check. Count back one: 1 take away 1 is 0. It works.
Watch out. One more is the next number, not the same number.
Method. Find the numbers in between by counting on from the smaller number.
- Start at the smaller number. Count on one at a time.15
- Count on until just before the bigger one. The numbers in between come after the smaller one.16
- Write the answer. 16
Check. Check: 16 is bigger than 15 and smaller than 17.
Watch out. Do not include the two numbers at the ends.
Method. Find the numbers in between by counting on from the smaller number.
- Start at the smaller number. Count on one at a time.14
- Count on until just before the bigger one. The numbers in between come after the smaller one.15, 16
- Write the answer. 15 and 16
Check. Check: 15 and 16 is bigger than 14 and smaller than 17.
Watch out. Do not include the two numbers at the ends.
Method. Put the numbers in order from the smallest. Start with the smallest.
- Find the smallest number. It goes first in the list.9
- Put the rest in order. Each number is bigger than the one before.9, 16, 18
- Write the answer. 9, 16, 18
Check. Read the list again. Each number is bigger than the one before. ✓
Watch out. Compare the tens digit first when the numbers are big.
Method. Put the numbers in order from the biggest. Start with the biggest.
- Find the biggest number. It goes first in this list.18
- Put the rest in order. Each number is smaller than the one before.18, 12, 1
- Write the answer. 18, 12, 1
Check. Read the list again. Each number is smaller than the one before. ✓
Watch out. Biggest first means the list goes down.
Method. Compare the two numbers. Which one comes later when we count?
- Say both numbers. The numbers are 17 and 15.17 and 15
- Compare them. The number further along the count is bigger.17 is greater than 15
- Write the answer. 17
Check. Count from 15 to 17. 17 comes later, so it is bigger. ✓
Watch out. Bigger numbers come later in the count, even when the digits look different.
Method. Compare the two numbers. Which one comes later when we count?
- Say both numbers. The numbers are 4 and 9.4 and 9
- Compare them. The number further along the count is bigger.4 is less than 9
- Write the answer. 4
Check. Count from 4 to 9. 9 comes later, so it is bigger. ✓
Watch out. Bigger numbers come later in the count, even when the digits look different.
Total 18 marks. Allow about 18 minutes.
Exercise 3X Practice test questions
Non-calculatorMethod. One less means the number just before when we count back.
- Start at the number. We begin where we are.18
- Count back one. Say the number that comes just before.18 - 1 = 17
- Write the answer. 17
Check. Count on one: 17 add 1 is 18. It works.
Watch out. One less is the number before, not the number after.
Method. One more means the next number when we count on.
- Start at the number. We begin where we are.14
- Count on one. Say the number that comes next.14 + 1 = 15
- Write the answer. 15
Check. Count back one: 15 take away 1 is 14. It works.
Watch out. One more is the next number, not the same number.
Method. Find the numbers in between by counting on from the smaller number.
- Start at the smaller number. Count on one at a time.6
- Count on until just before the bigger one. The numbers in between come after the smaller one.7
- Write the answer. 7
Check. Check: 7 is bigger than 6 and smaller than 8.
Watch out. Do not include the two numbers at the ends.
Method. Find the numbers in between by counting on from the smaller number.
- Start at the smaller number. Count on one at a time.2
- Count on until just before the bigger one. The numbers in between come after the smaller one.3, 4
- Write the answer. 3 and 4
Check. Check: 3 and 4 is bigger than 2 and smaller than 5.
Watch out. Do not include the two numbers at the ends.
Method. Put the numbers in order from the smallest. Start with the smallest.
- Find the smallest number. It goes first in the list.3
- Put the rest in order. Each number is bigger than the one before.3, 13, 19
- Write the answer. 3, 13, 19
Check. Read the list again. Each number is bigger than the one before. ✓
Watch out. Compare the tens digit first when the numbers are big.
Method. Put the numbers in order from the biggest. Start with the biggest.
- Find the biggest number. It goes first in this list.14
- Put the rest in order. Each number is smaller than the one before.14, 6, 1
- Write the answer. 14, 6, 1
Check. Read the list again. Each number is smaller than the one before. ✓
Watch out. Biggest first means the list goes down.
Method. Compare the two numbers. Which one comes later when we count?
- Say both numbers. The numbers are 6 and 5.6 and 5
- Compare them. The number further along the count is bigger.6 is greater than 5
- Write the answer. 6
Check. Count from 5 to 6. 6 comes later, so it is bigger. ✓
Watch out. Bigger numbers come later in the count, even when the digits look different.
Method. Compare the two numbers. Which one comes later when we count?
- Say both numbers. The numbers are 1 and 19.1 and 19
- Compare them. The number further along the count is bigger.1 is less than 19
- Write the answer. 1
Check. Count from 1 to 19. 19 comes later, so it is bigger. ✓
Watch out. Bigger numbers come later in the count, even when the digits look different.
Method. Count the cubes in each row. Then say which group has more or fewer.
- Count group A. Touch each cube once.A has 4
- Count group B. Touch each cube once.B has 5
- Compare the two numbers. 5 is bigger than 4, so one group has more.Group B
Check. The difference is 5 take away 4, which is 1. ✓
Watch out. Read the letter first. A is the top row, B is the bottom row.
Method. Count the cubes in each row. Then say which group has more or fewer.
- Count group A. Touch each cube once.A has 6
- Count group B. Touch each cube once.B has 4
- Compare the two numbers. 6 is bigger than 4, so one group has fewer.Group B
Check. The difference is 6 take away 4, which is 2. ✓
Watch out. Read the letter first. A is the top row, B is the bottom row.