Making and splitting numbers
By the end of this chapter you will be able to
- I can say a number as two parts that make it
- I can find all the pairs that make 5 and make 10
- I can find the missing part when I know the whole and one part
- I can say the double of a number up to 5
- I can use fingers, ten frames and cubes to show the pairs
You should already know
- Counting to 10 (Chapter 1)
- Comparing quantities (Chapter 3)
Where this leads
- Adding within 10 (Chapter 5)
- Taking away within 10 (Chapter 6)
Early Years Foundation Stage for England, maths. Content: Show how a number to 10 is made from two parts (part and whole), Recall number bonds to 5 and to 10, Know the double facts from 1 + 1 to 5 + 5, Use fingers, ten frames and cubes to show number bonds.
Exercise P Do you remember?
Non-calculatorMethod. Count the fingers on one hand, one at a time.
- Hold up one hand. Each finger is one thing to count.1, 2, 3, 4, 5
- Count the thumb too. The thumb is one of the five.5
- Write the answer. 5
Check. Count the fingers on your other hand. It is the same. ✓
Watch out. Count the thumb as well.
Method. Find 4 on the number track. Move one box on.
- Find 4. Put your finger on it.4
- Move one box on. One more is the next number.4 + 1 = 5
- Write the answer. 5
Check. Count 4, 5. Five comes next. ✓
Watch out. One more is the next number.
Method. The number in the middle of 2 and 4 is between them.
- Find 2 and 4. Put a finger on each.2 and 4
- Count on from 2. The middle number is one more than 2.2 + 1 = 3
- Write the answer. 3
Check. Count 2, 3, 4. Three is in the middle. ✓
Watch out. Between means in the middle.
Method. Touch each side of the triangle once.
- Touch the first side. Each side is counted once.1
- Touch the other sides. Count them all.2, 3
- Write the answer. 3
Check. Count the sides again: 1, 2, 3. ✓
Watch out. Count each side once.
Method. Find 6 and 8 on the number track. The number that comes later is greater.
- Find 6 and 8. Put a finger on each number.6 and 8
- Look at which comes later. Eight comes after six when we count.6, 7, 8
- Write the answer. 8
Check. Count 6, 7, 8. Eight is greater. ✓
Watch out. The greater number comes later when we count.
Parts and wholes
Lily has 5 cubes. Some are red and some are blue.
The whole is all the cubes together. The parts are the groups that make the whole. Two parts put together make the whole. The whole is always bigger than either part.
Key ideas
- The whole is all of the things together.
- The parts make the whole when they are put together.
- If you know one part and the whole, you can find the other part.
Key words. The whole is all of the things. The parts are the groups that make it.
Method. Put the two parts together, then count them all.
- Find the first part: 2. Start with the bigger part and count on.2
- Count on 3 more. Count on one at a time from the first part.2 + 3 = 5
- Write the answer. The total is the whole.5
Check. Count the whole group one at a time: 5. ✓
Watch out. Count on from the bigger part. The total is always bigger than either part.
Key words. A missing part is the number we add to the known part to make the whole.
Method. The whole is 4. One part is 1. Find the other part.
- Start with the whole: 4. The whole has all the things.4
- Take away the part you know: 1. What is left is the other part.4 − 1 = 3
- Check by counting on. 1 and 3 must make 4.1 + 3 = 4
- Write the answer. 3
Check. Count on from 1 to 4: 3 more. ✓
Watch out. Count on from the part you know, to reach the whole.
Key words. The whole is all of the things. The parts are the groups that make it.
Method. Put the two parts together, then count them all.
- Find the first part: 3. Start with the bigger part and count on.3
- Count on 2 more. Count on one at a time from the first part.3 + 2 = 5
- Write the answer. The total is the whole.5
Check. Count the whole group one at a time: 5. ✓
Watch out. Count on from the bigger part. The total is always bigger than either part.
Watch out
Watch out: the whole is always the biggest number. A part can never be bigger than the whole.
Exam tip
Grown-up tip. Use five cubes or buttons, two in one hand and three in the other. Ask: “How many altogether? How many in each hand?” Then hide one hand and ask how many are in it.
Exercise 4A Parts and wholes
Non-calculatorKey words. The whole is all of the things. The parts are the groups that make it.
Method. Put the two parts together, then count them all.
- Find the first part: 1. Start with the bigger part and count on.1
- Count on 2 more. Count on one at a time from the first part.1 + 2 = 3
- Write the answer. The total is the whole.3
Check. Count the whole group one at a time: 3. ✓
Watch out. Count on from the bigger part. The total is always bigger than either part.
Key words. The whole is all of the things. The parts are the groups that make it.
Method. Put the two parts together, then count them all.
- Find the first part: 2. Start with the bigger part and count on.2
- Count on 3 more. Count on one at a time from the first part.2 + 3 = 5
- Write the answer. The total is the whole.5
Check. Count the whole group one at a time: 5. ✓
Watch out. Count on from the bigger part. The total is always bigger than either part.
Key words. A missing part is the number we add to the known part to make the whole.
Method. The whole is 4. One part is 1. Find the other part.
- Start with the whole: 4. The whole has all the things.4
- Take away the part you know: 1. What is left is the other part.4 − 1 = 3
- Check by counting on. 1 and 3 must make 4.1 + 3 = 4
- Write the answer. 3
Check. Count on from 1 to 4: 3 more. ✓
Watch out. Count on from the part you know, to reach the whole.
Key words. A missing part is the number we add to the known part to make the whole.
Method. The whole is 6. One part is 2. Find the other part.
- Start with the whole: 6. The whole has all the things.6
- Take away the part you know: 2. What is left is the other part.6 − 2 = 4
- Check by counting on. 2 and 4 must make 6.2 + 4 = 6
- Write the answer. 4
Check. Count on from 2 to 6: 4 more. ✓
Watch out. Count on from the part you know, to reach the whole.
Key words. A missing part is the number we add to the known part to make the whole.
Method. The whole is 7. One part is 3. Find the other part.
- Start with the whole: 7. The whole has all the things.7
- Take away the part you know: 3. What is left is the other part.7 − 3 = 4
- Check by counting on. 3 and 4 must make 7.3 + 4 = 7
- Write the answer. 4
Check. Count on from 3 to 7: 4 more. ✓
Watch out. Count on from the part you know, to reach the whole.
Key words. A missing part is the number we add to the known part to make the whole.
Method. The whole is 8. One part is 5. Find the other part.
- Start with the whole: 8. The whole has all the things.8
- Take away the part you know: 5. What is left is the other part.8 − 5 = 3
- Check by counting on. 5 and 3 must make 8.5 + 3 = 8
- Write the answer. 3
Check. Count on from 5 to 8: 3 more. ✓
Watch out. Count on from the part you know, to reach the whole.
Key words. The whole is all of the things. The parts are the groups that make it.
Method. Put the two parts together, then count them all.
- Find the first part: 2. Start with the bigger part and count on.2
- Count on 4 more. Count on one at a time from the first part.2 + 4 = 6
- Write the answer. The total is the whole.6
Check. Count the whole group one at a time: 6. ✓
Watch out. Count on from the bigger part. The total is always bigger than either part.
Key words. The whole is all of the things. The parts are the groups that make it.
Method. Put the two parts together, then count them all.
- Find the first part: 3. Start with the bigger part and count on.3
- Count on 5 more. Count on one at a time from the first part.3 + 5 = 8
- Write the answer. The total is the whole.8
Check. Count the whole group one at a time: 8. ✓
Watch out. Count on from the bigger part. The total is always bigger than either part.
Key words. A missing part is the number we add to the known part to make the whole.
Method. The whole is 9. One part is 4. Find the other part.
- Start with the whole: 9. The whole has all the things.9
- Take away the part you know: 4. What is left is the other part.9 − 4 = 5
- Check by counting on. 4 and 5 must make 9.4 + 5 = 9
- Write the answer. 5
Check. Count on from 4 to 9: 5 more. ✓
Watch out. Count on from the part you know, to reach the whole.
Key words. A missing part is the number we add to the known part to make the whole.
Method. The whole is 10. One part is 6. Find the other part.
- Start with the whole: 10. The whole has all the things.10
- Take away the part you know: 6. What is left is the other part.10 − 6 = 4
- Check by counting on. 6 and 4 must make 10.6 + 4 = 10
- Write the answer. 4
Check. Count on from 6 to 10: 4 more. ✓
Watch out. Count on from the part you know, to reach the whole.
Key words. The whole is all of the things. The parts are the groups that make it.
Method. Put the two parts together, then count them all.
- Find the first part: 3. Start with the bigger part and count on.3
- Count on 4 more. Count on one at a time from the first part.3 + 4 = 7
- Write the answer. The total is the whole.7
Check. Count the whole group one at a time: 7. ✓
Watch out. Count on from the bigger part. The total is always bigger than either part.
Method. Count 2 and 2 together.
- Count the first part. Two things.2
- Count the second part. Two more things.2
- Put them together. Count all the things.1, 2, 3, 4
- Write the answer. No. 2 and 2 make 4, not 5.
Check. Count 4 things in all: 1, 2, 3, 4. ✓
Watch out. Count all the things, do not guess.
Number bonds to 5
Ella has 5 counters. Some are red and some are yellow.
A number bond is a pair of numbers that makes a whole. Here, 2 and 3 make 5. The pairs that make 5 are 0 and 5, 1 and 4, 2 and 3, 3 and 2, 4 and 1 and 5 and 0.
Key ideas
- A number bond is two parts that make a whole.
- The pairs that make 5 are: 0 and 5, 1 and 4, 2 and 3.
- Turning the pair round does not change the total: 2 and 3, or 3 and 2.
Key words. The whole is all of the things. The parts are the groups that make it.
Method. Put the two parts together, then count them all.
- Find the first part: 2. Start with the bigger part and count on.2
- Count on 3 more. Count on one at a time from the first part.2 + 3 = 5
- Write the answer. The total is the whole.5
Check. Count the whole group one at a time: 5. ✓
Watch out. Count on from the bigger part. The total is always bigger than either part.
Key words. A missing part is the number we add to the known part to make the whole.
Method. The whole is 5. One part is 4. Find the other part.
- Start with the whole: 5. The whole has all the things.5
- Take away the part you know: 4. What is left is the other part.5 − 4 = 1
- Check by counting on. 4 and 1 must make 5.4 + 1 = 5
- Write the answer. 1
Check. Count on from 4 to 5: 1 more. ✓
Watch out. Count on from the part you know, to reach the whole.
Key words. The whole is all of the things. The parts are the groups that make it.
Method. Put the two parts together, then count them all.
- Find the first part: 1. Start with the bigger part and count on.1
- Count on 4 more. Count on one at a time from the first part.1 + 4 = 5
- Write the answer. The total is the whole.5
Check. Count the whole group one at a time: 5. ✓
Watch out. Count on from the bigger part. The total is always bigger than either part.
Watch out
Watch out: 2 and 3 make 5, and 3 and 2 make 5. But 2 and 2 do not make 5.
Exam tip
Grown-up tip. Use five buttons. Ask your child to split them into two piles and say the two numbers. Then turn the piles round and say the pair again.
Exercise 4B Bonds to 5
Non-calculatorKey words. The whole is all of the things. The parts are the groups that make it.
Method. Put the two parts together, then count them all.
- Find the first part: 1. Start with the bigger part and count on.1
- Count on 4 more. Count on one at a time from the first part.1 + 4 = 5
- Write the answer. The total is the whole.5
Check. Count the whole group one at a time: 5. ✓
Watch out. Count on from the bigger part. The total is always bigger than either part.
Key words. A missing part is the number we add to the known part to make the whole.
Method. The whole is 5. One part is 3. Find the other part.
- Start with the whole: 5. The whole has all the things.5
- Take away the part you know: 3. What is left is the other part.5 − 3 = 2
- Check by counting on. 3 and 2 must make 5.3 + 2 = 5
- Write the answer. 2
Check. Count on from 3 to 5: 2 more. ✓
Watch out. Count on from the part you know, to reach the whole.
Key words. The whole is all of the things. The parts are the groups that make it.
Method. Put the two parts together, then count them all.
- Find the first part: 4. Start with the bigger part and count on.4
- Count on 1 more. Count on one at a time from the first part.4 + 1 = 5
- Write the answer. The total is the whole.5
Check. Count the whole group one at a time: 5. ✓
Watch out. Count on from the bigger part. The total is always bigger than either part.
Key words. A missing part is the number we add to the known part to make the whole.
Method. The whole is 5. One part is 2. Find the other part.
- Start with the whole: 5. The whole has all the things.5
- Take away the part you know: 2. What is left is the other part.5 − 2 = 3
- Check by counting on. 2 and 3 must make 5.2 + 3 = 5
- Write the answer. 3
Check. Count on from 2 to 5: 3 more. ✓
Watch out. Count on from the part you know, to reach the whole.
Key words. The whole is all of the things. The parts are the groups that make it.
Method. Put the two parts together, then count them all.
- Find the first part: 5. Start with the bigger part and count on.5
- Count on 0 more. Count on one at a time from the first part.5 + 0 = 5
- Write the answer. The total is the whole.5
Check. Count the whole group one at a time: 5. ✓
Watch out. Count on from the bigger part. The total is always bigger than either part.
Method. Add the two parts in each pair. The right pair makes 5.
- Add the first pair. Check the total.2 + 2 = 4
- Add the other pairs. Only one pair makes the whole.2 + 3 = 5
- Write the answer. 2 and 3
Check. 2 + 3 = 5. ✓
Watch out. Add both parts in each pair to check.
Key words. A missing part is the number we add to the known part to make the whole.
Method. The whole is 5. One part is 4. Find the other part.
- Start with the whole: 5. The whole has all the things.5
- Take away the part you know: 4. What is left is the other part.5 − 4 = 1
- Check by counting on. 4 and 1 must make 5.4 + 1 = 5
- Write the answer. 1
Check. Count on from 4 to 5: 1 more. ✓
Watch out. Count on from the part you know, to reach the whole.
Key words. A missing part is the number we add to the known part to make the whole.
Method. The whole is 5. One part is 1. Find the other part.
- Start with the whole: 5. The whole has all the things.5
- Take away the part you know: 1. What is left is the other part.5 − 1 = 4
- Check by counting on. 1 and 4 must make 5.1 + 4 = 5
- Write the answer. 4
Check. Count on from 1 to 5: 4 more. ✓
Watch out. Count on from the part you know, to reach the whole.
Key words. A missing part is the number we add to the known part to make the whole.
Method. The whole is 5. One part is 4. Find the other part.
- Start with the whole: 5. The whole has all the things.5
- Take away the part you know: 4. What is left is the other part.5 − 4 = 1
- Check by counting on. 4 and 1 must make 5.4 + 1 = 5
- Write the answer. 1
Check. Count on from 4 to 5: 1 more. ✓
Watch out. Count on from the part you know, to reach the whole.
Key words. A missing part is the number we add to the known part to make the whole.
Method. The whole is 5. One part is 2. Find the other part.
- Start with the whole: 5. The whole has all the things.5
- Take away the part you know: 2. What is left is the other part.5 − 2 = 3
- Check by counting on. 2 and 3 must make 5.2 + 3 = 5
- Write the answer. 3
Check. Count on from 2 to 5: 3 more. ✓
Watch out. Count on from the part you know, to reach the whole.
Method. Count 3 and 3 together.
- Count the first part. Three things.3
- Count the second part. Three more things.3
- Put them together. Count all the things.1, 2, 3, 4, 5, 6
- Write the answer. No. 3 and 3 make 6.
Check. Count 6 things in all. ✓
Watch out. Count both parts, not just one.
Method. Start with 0 and 5. Then move one counter at a time from one part to the other.
- Start with all in one part. Use 0 in one part and the total in the other.0 and 5
- Move one at a time. Each time, one more goes into the first part.5 pairs in order
- Write the pairs. Include 0 and the total.0 and 5, 1 and 4, 2 and 3, 3 and 2, 4 and 1, 5 and 0
Check. Each pair adds to 5. ✓
Watch out. Keep a list in order, so you do not miss a pair.
Number bonds to 10
Mia has a ten frame. It has room for ten counters. She puts red counters in one part and yellow counters in the other.
Some pairs that make 10 are 0 and 10, 1 and 9, 2 and 8, 3 and 7, 4 and 6, 5 and 5. A full ten frame is always ten.
Key ideas
- Ten is a full ten frame.
- The pairs that make 10 include 5 and 5.
- Use the ten frame to check each pair.
Key words. The whole is all of the things. The parts are the groups that make it.
Method. Put the two parts together, then count them all.
- Find the first part: 7. Start with the bigger part and count on.7
- Count on 3 more. Count on one at a time from the first part.7 + 3 = 10
- Write the answer. The total is the whole.10
Check. Count the whole group one at a time: 10. ✓
Watch out. Count on from the bigger part. The total is always bigger than either part.
Key words. A missing part is the number we add to the known part to make the whole.
Method. The whole is 10. One part is 6. Find the other part.
- Start with the whole: 10. The whole has all the things.10
- Take away the part you know: 6. What is left is the other part.10 − 6 = 4
- Check by counting on. 6 and 4 must make 10.6 + 4 = 10
- Write the answer. 4
Check. Count on from 6 to 10: 4 more. ✓
Watch out. Count on from the part you know, to reach the whole.
Key words. The whole is all of the things. The parts are the groups that make it.
Method. Put the two parts together, then count them all.
- Find the first part: 8. Start with the bigger part and count on.8
- Count on 2 more. Count on one at a time from the first part.8 + 2 = 10
- Write the answer. The total is the whole.10
Check. Count the whole group one at a time: 10. ✓
Watch out. Count on from the bigger part. The total is always bigger than either part.
Watch out
Watch out: 6 and 3 make 9, not 10. Check each pair by counting the whole ten frame.
Exam tip
Grown-up tip. Draw a ten frame on paper (two rows of five). Fill it with counters or beans in two colours. Ask: “How many of each colour? What is the total?”
Exercise 4C Bonds to 10
Non-calculatorKey words. The whole is all of the things. The parts are the groups that make it.
Method. Put the two parts together, then count them all.
- Find the first part: 7. Start with the bigger part and count on.7
- Count on 3 more. Count on one at a time from the first part.7 + 3 = 10
- Write the answer. The total is the whole.10
Check. Count the whole group one at a time: 10. ✓
Watch out. Count on from the bigger part. The total is always bigger than either part.
Key words. The whole is all of the things. The parts are the groups that make it.
Method. Put the two parts together, then count them all.
- Find the first part: 2. Start with the bigger part and count on.2
- Count on 8 more. Count on one at a time from the first part.2 + 8 = 10
- Write the answer. The total is the whole.10
Check. Count the whole group one at a time: 10. ✓
Watch out. Count on from the bigger part. The total is always bigger than either part.
Key words. A missing part is the number we add to the known part to make the whole.
Method. The whole is 10. One part is 6. Find the other part.
- Start with the whole: 10. The whole has all the things.10
- Take away the part you know: 6. What is left is the other part.10 − 6 = 4
- Check by counting on. 6 and 4 must make 10.6 + 4 = 10
- Write the answer. 4
Check. Count on from 6 to 10: 4 more. ✓
Watch out. Count on from the part you know, to reach the whole.
Key words. A missing part is the number we add to the known part to make the whole.
Method. The whole is 10. One part is 3. Find the other part.
- Start with the whole: 10. The whole has all the things.10
- Take away the part you know: 3. What is left is the other part.10 − 3 = 7
- Check by counting on. 3 and 7 must make 10.3 + 7 = 10
- Write the answer. 7
Check. Count on from 3 to 10: 7 more. ✓
Watch out. Count on from the part you know, to reach the whole.
Key words. The whole is all of the things. The parts are the groups that make it.
Method. Put the two parts together, then count them all.
- Find the first part: 9. Start with the bigger part and count on.9
- Count on 1 more. Count on one at a time from the first part.9 + 1 = 10
- Write the answer. The total is the whole.10
Check. Count the whole group one at a time: 10. ✓
Watch out. Count on from the bigger part. The total is always bigger than either part.
Key words. The whole is all of the things. The parts are the groups that make it.
Method. Put the two parts together, then count them all.
- Find the first part: 4. Start with the bigger part and count on.4
- Count on 6 more. Count on one at a time from the first part.4 + 6 = 10
- Write the answer. The total is the whole.10
Check. Count the whole group one at a time: 10. ✓
Watch out. Count on from the bigger part. The total is always bigger than either part.
Key words. The whole is all of the things. The parts are the groups that make it.
Method. Put the two parts together, then count them all.
- Find the first part: 10. Start with the bigger part and count on.10
- Count on 0 more. Count on one at a time from the first part.10 + 0 = 10
- Write the answer. The total is the whole.10
Check. Count the whole group one at a time: 10. ✓
Watch out. Count on from the bigger part. The total is always bigger than either part.
Key words. A missing part is the number we add to the known part to make the whole.
Method. The whole is 10. One part is 7. Find the other part.
- Start with the whole: 10. The whole has all the things.10
- Take away the part you know: 7. What is left is the other part.10 − 7 = 3
- Check by counting on. 7 and 3 must make 10.7 + 3 = 10
- Write the answer. 3
Check. Count on from 7 to 10: 3 more. ✓
Watch out. Count on from the part you know, to reach the whole.
Key words. A missing part is the number we add to the known part to make the whole.
Method. The whole is 10. One part is 4. Find the other part.
- Start with the whole: 10. The whole has all the things.10
- Take away the part you know: 4. What is left is the other part.10 − 4 = 6
- Check by counting on. 4 and 6 must make 10.4 + 6 = 10
- Write the answer. 6
Check. Count on from 4 to 10: 6 more. ✓
Watch out. Count on from the part you know, to reach the whole.
Method. Add the two parts in each pair. The right pair makes 10.
- Add the first pair. Check the total.4 + 5 = 9
- Add the other pairs. Only one pair makes the whole.3 + 7 = 10, 2 + 9 = 11
- Write the answer. 3 and 7
Check. 3 + 7 = 10. ✓
Watch out. Add both parts in each pair to check.
Key words. A missing part is the number we add to the known part to make the whole.
Method. The whole is 10. One part is 8. Find the other part.
- Start with the whole: 10. The whole has all the things.10
- Take away the part you know: 8. What is left is the other part.10 − 8 = 2
- Check by counting on. 8 and 2 must make 10.8 + 2 = 10
- Write the answer. 2
Check. Count on from 8 to 10: 2 more. ✓
Watch out. Count on from the part you know, to reach the whole.
Method. Add the two numbers together.
- Count 5. Five things.5
- Add 6 more. Count on six from five.5 + 6 = 11
- Compare with 10. Eleven is more than ten.11 is not 10
- Write the answer. No. 5 and 6 make 11, not 10.
Check. Count on from 5 to 11, six steps. ✓
Watch out. The pair must add to 10, not more or less.
Doubles
Leo has two rows of cubes. Both rows are the same. He has the same number in each row.
A double is when you add a number to itself. Two 3s make 6: 3 + 3 = 6.
Key ideas
- A double is a number added to itself.
- Two equal rows make a double.
- Doubles are easy to check by counting both rows.
Key words. A double is two of the same number.
Method. A double is two equal parts. Add the number to itself.
- Find the two equal rows of 3. The two rows are the same length.3 and 3
- Count the total. Count both rows together.3 + 3 = 6
- Write the answer. 6
Check. Count on from 3 another 3: the answer is 6. ✓
Watch out. Doubles have two equal parts. Check that both rows match.
Key words. A double is two of the same number.
Method. A double is two equal parts. Add the number to itself.
- Find the two equal rows of 4. The two rows are the same length.4 and 4
- Count the total. Count both rows together.4 + 4 = 8
- Write the answer. 8
Check. Count on from 4 another 4: the answer is 8. ✓
Watch out. Doubles have two equal parts. Check that both rows match.
Key words. A double is two of the same number.
Method. A double is two equal parts. Add the number to itself.
- Find the two equal rows of 5. The two rows are the same length.5 and 5
- Count the total. Count both rows together.5 + 5 = 10
- Write the answer. 10
Check. Count on from 5 another 5: the answer is 10. ✓
Watch out. Doubles have two equal parts. Check that both rows match.
Watch out
Watch out: 2 + 2 is a double, but 2 + 3 is not. A double has two equal parts.
Exam tip
Grown-up tip. Put two equal rows of buttons on a table. Ask: “Are the rows the same?” Count both rows, then count again with the rows the other way round.
Exercise 4D Doubles
Non-calculatorKey words. A double is two of the same number.
Method. A double is two equal parts. Add the number to itself.
- Find the two equal rows of 1. The two rows are the same length.1 and 1
- Count the total. Count both rows together.1 + 1 = 2
- Write the answer. 2
Check. Count on from 1 another 1: the answer is 2. ✓
Watch out. Doubles have two equal parts. Check that both rows match.
Key words. A double is two of the same number.
Method. A double is two equal parts. Add the number to itself.
- Find the two equal rows of 2. The two rows are the same length.2 and 2
- Count the total. Count both rows together.2 + 2 = 4
- Write the answer. 4
Check. Count on from 2 another 2: the answer is 4. ✓
Watch out. Doubles have two equal parts. Check that both rows match.
Key words. A double is two of the same number.
Method. A double is two equal parts. Add the number to itself.
- Find the two equal rows of 3. The two rows are the same length.3 and 3
- Count the total. Count both rows together.3 + 3 = 6
- Write the answer. 6
Check. Count on from 3 another 3: the answer is 6. ✓
Watch out. Doubles have two equal parts. Check that both rows match.
Key words. A double is two of the same number.
Method. A double is two equal parts. Add the number to itself.
- Find the two equal rows of 4. The two rows are the same length.4 and 4
- Count the total. Count both rows together.4 + 4 = 8
- Write the answer. 8
Check. Count on from 4 another 4: the answer is 8. ✓
Watch out. Doubles have two equal parts. Check that both rows match.
Key words. A double is two of the same number.
Method. A double is two equal parts. Add the number to itself.
- Find the two equal rows of 5. The two rows are the same length.5 and 5
- Count the total. Count both rows together.5 + 5 = 10
- Write the answer. 10
Check. Count on from 5 another 5: the answer is 10. ✓
Watch out. Doubles have two equal parts. Check that both rows match.
Key words. A double is two of the same number.
Method. A double is two equal parts. Add the number to itself.
- Find the two equal rows of 2. The two rows are the same length.2 and 2
- Count the total. Count both rows together.2 + 2 = 4
- Write the answer. 4
Check. Count on from 2 another 2: the answer is 4. ✓
Watch out. Doubles have two equal parts. Check that both rows match.
Key words. A double is two of the same number.
Method. A double is two equal parts. Add the number to itself.
- Find the two equal rows of 4. The two rows are the same length.4 and 4
- Count the total. Count both rows together.4 + 4 = 8
- Write the answer. 8
Check. Count on from 4 another 4: the answer is 8. ✓
Watch out. Doubles have two equal parts. Check that both rows match.
Key words. A double is two of the same number.
Method. A double is two equal parts. Add the number to itself.
- Find the two equal rows of 3. The two rows are the same length.3 and 3
- Count the total. Count both rows together.3 + 3 = 6
- Write the answer. 6
Check. Count on from 3 another 3: the answer is 6. ✓
Watch out. Doubles have two equal parts. Check that both rows match.
Key words. A double is two of the same number.
Method. A double is two equal parts. Add the number to itself.
- Find the two equal rows of 4. The two rows are the same length.4 and 4
- Count the total. Count both rows together.4 + 4 = 8
- Write the answer. 8
Check. Count on from 4 another 4: the answer is 8. ✓
Watch out. Doubles have two equal parts. Check that both rows match.
Key words. A double is two of the same number.
Method. A double is two equal parts. Add the number to itself.
- Find the two equal rows of 5. The two rows are the same length.5 and 5
- Count the total. Count both rows together.5 + 5 = 10
- Write the answer. 10
Check. Count on from 5 another 5: the answer is 10. ✓
Watch out. Doubles have two equal parts. Check that both rows match.
Key words. A double is two of the same number.
Method. A double is two equal parts. Add the number to itself.
- Find the two equal rows of 2. The two rows are the same length.2 and 2
- Count the total. Count both rows together.2 + 2 = 4
- Write the answer. 4
Check. Count on from 2 another 2: the answer is 4. ✓
Watch out. Doubles have two equal parts. Check that both rows match.
Method. A double has two equal parts. Check whether the two parts are the same.
- Look at 3 and 4. Are they the same number?3 and 4
- Check the parts. Three is not the same as four.3 is not 4
- Write the answer. No. A double has two equal parts. 3 and 4 are not equal.
Check. A double would be 3 + 3 or 4 + 4. ✓
Watch out. Both parts must be the same number.
Finding missing parts
Tom has 9 stickers. Some are stars and some are hearts. He tells his friend, "Four are stars."
To find the hearts, start with the stars you know. Count on until you reach 9. The number you counted on by is the missing part.
Key ideas
- Start with the part you know.
- Count on to reach the whole.
- The number you counted on by is the missing part.
Key words. A missing part is the number we add to the known part to make the whole.
Method. The whole is 9. One part is 4. Find the other part.
- Start with the whole: 9. The whole has all the things.9
- Take away the part you know: 4. What is left is the other part.9 − 4 = 5
- Check by counting on. 4 and 5 must make 9.4 + 5 = 9
- Write the answer. 5
Check. Count on from 4 to 9: 5 more. ✓
Watch out. Count on from the part you know, to reach the whole.
Key words. A missing part is the number we add to the known part to make the whole.
Method. The whole is 10. One part is 3. Find the other part.
- Start with the whole: 10. The whole has all the things.10
- Take away the part you know: 3. What is left is the other part.10 − 3 = 7
- Check by counting on. 3 and 7 must make 10.3 + 7 = 10
- Write the answer. 7
Check. Count on from 3 to 10: 7 more. ✓
Watch out. Count on from the part you know, to reach the whole.
Method. Start with 0 and 4. Then move one counter at a time from one part to the other.
- Start with all in one part. Use 0 in one part and the total in the other.0 and 4
- Move one at a time. Each time, one more goes into the first part.4 pairs in order
- Write the pairs. Include 0 and the total.0 and 4, 1 and 3, 2 and 2, 3 and 1, 4 and 0
Check. Each pair adds to 4. ✓
Watch out. Keep a list in order, so you do not miss a pair.
Watch out
Watch out: the missing part is not always the number you see last. Count on from the part you know.
Exam tip
Grown-up tip. Hide one part of a set of cubes with your hand. Ask: “How many are hidden?” Count the visible part, then count on to the whole.
Exercise 4E Finding missing parts
Non-calculatorKey words. A missing part is the number we add to the known part to make the whole.
Method. The whole is 6. One part is 2. Find the other part.
- Start with the whole: 6. The whole has all the things.6
- Take away the part you know: 2. What is left is the other part.6 − 2 = 4
- Check by counting on. 2 and 4 must make 6.2 + 4 = 6
- Write the answer. 4
Check. Count on from 2 to 6: 4 more. ✓
Watch out. Count on from the part you know, to reach the whole.
Key words. A missing part is the number we add to the known part to make the whole.
Method. The whole is 9. One part is 5. Find the other part.
- Start with the whole: 9. The whole has all the things.9
- Take away the part you know: 5. What is left is the other part.9 − 5 = 4
- Check by counting on. 5 and 4 must make 9.5 + 4 = 9
- Write the answer. 4
Check. Count on from 5 to 9: 4 more. ✓
Watch out. Count on from the part you know, to reach the whole.
Method. Start with 0 and 4. Then move one counter at a time from one part to the other.
- Start with all in one part. Use 0 in one part and the total in the other.0 and 4
- Move one at a time. Each time, one more goes into the first part.4 pairs in order
- Write the pairs. Include 0 and the total.0 and 4, 1 and 3, 2 and 2, 3 and 1, 4 and 0
Check. Each pair adds to 4. ✓
Watch out. Keep a list in order, so you do not miss a pair.
Method. Start with 0 and 3. Then move one counter at a time from one part to the other.
- Start with all in one part. Use 0 in one part and the total in the other.0 and 3
- Move one at a time. Each time, one more goes into the first part.3 pairs in order
- Write the pairs. Include 0 and the total.0 and 3, 1 and 2, 2 and 1, 3 and 0
Check. Each pair adds to 3. ✓
Watch out. Keep a list in order, so you do not miss a pair.
Key words. A missing part is the number we add to the known part to make the whole.
Method. The whole is 7. One part is 3. Find the other part.
- Start with the whole: 7. The whole has all the things.7
- Take away the part you know: 3. What is left is the other part.7 − 3 = 4
- Check by counting on. 3 and 4 must make 7.3 + 4 = 7
- Write the answer. 4
Check. Count on from 3 to 7: 4 more. ✓
Watch out. Count on from the part you know, to reach the whole.
Key words. A missing part is the number we add to the known part to make the whole.
Method. The whole is 10. One part is 8. Find the other part.
- Start with the whole: 10. The whole has all the things.10
- Take away the part you know: 8. What is left is the other part.10 − 8 = 2
- Check by counting on. 8 and 2 must make 10.8 + 2 = 10
- Write the answer. 2
Check. Count on from 8 to 10: 2 more. ✓
Watch out. Count on from the part you know, to reach the whole.
Method. Add the two parts in each pair. The right pair makes 6.
- Add the first pair. Check the total.2 + 3 = 5
- Add the other pairs. Only one pair makes the whole.4 + 2 = 6, 1 + 6 = 7
- Write the answer. 4 and 2
Check. 4 + 2 = 6. ✓
Watch out. Add both parts in each pair to check.
Key words. A missing part is the number we add to the known part to make the whole.
Method. The whole is 8. One part is 3. Find the other part.
- Start with the whole: 8. The whole has all the things.8
- Take away the part you know: 3. What is left is the other part.8 − 3 = 5
- Check by counting on. 3 and 5 must make 8.3 + 5 = 8
- Write the answer. 5
Check. Count on from 3 to 8: 5 more. ✓
Watch out. Count on from the part you know, to reach the whole.
Key words. A missing part is the number we add to the known part to make the whole.
Method. The whole is 10. One part is 6. Find the other part.
- Start with the whole: 10. The whole has all the things.10
- Take away the part you know: 6. What is left is the other part.10 − 6 = 4
- Check by counting on. 6 and 4 must make 10.6 + 4 = 10
- Write the answer. 4
Check. Count on from 6 to 10: 4 more. ✓
Watch out. Count on from the part you know, to reach the whole.
Method. Add the two parts together and compare with 5.
- Count 2. Two things.2
- Add 4 more. Count on four from two.2 + 4 = 6
- Compare with 5. Six is not five.6 is not 5
- Write the answer. No. 2 and 4 make 6.
Check. Count on from 2: 3, 4, 5, 6. Six. ✓
Watch out. Count on all four, not just to 5.
Key words. A missing part is the number we add to the known part to make the whole.
Method. The whole is 9. One part is 4. Find the other part.
- Start with the whole: 9. The whole has all the things.9
- Take away the part you know: 4. What is left is the other part.9 − 4 = 5
- Check by counting on. 4 and 5 must make 9.4 + 5 = 9
- Write the answer. 5
Check. Count on from 4 to 9: 5 more. ✓
Watch out. Count on from the part you know, to reach the whole.
Method. Start with the known part, then count on to the whole.
- Start with the known part. Begin at the part you know.known part
- Count on to the whole. Count on one at a time until you reach the whole.count on to whole
- Write the answer. The number of steps is the missing part.Accept any answer: count on from the known part until you reach the whole. The count is the missing part.
Check. Count on from a part to the whole, and count your steps. ✓
Watch out. Count the steps, not the whole.
Chapter summary
| Skill | Method |
|---|---|
| Parts and wholes | The parts put together make the whole. |
| Bonds to 5 | The pairs that make 5: 0 and 5, 1 and 4, 2 and 3, and turned round. |
| Bonds to 10 | Pairs that make 10, such as 3 and 7, and 5 and 5. |
| Doubles | A double is a number added to itself: 4 + 4 = 8. |
| Missing parts | Count on from the known part until you reach the whole. |
Can you…?
- I can say a number as two parts that make it
- I can find the pairs that make 5 and the pairs that make 10
- I can find a missing part when I know the whole and one part
- I can say the double of a number up to 5
- I can use fingers, ten frames and cubes to show number bonds
Key terms
- whole
- all of the things together
- part
- one of the groups that makes the whole
- number bond
- a pair of numbers that make a whole
- double
- a number added to itself
- missing part
- the number that completes the whole
Exercise 4Z Check-up
Non-calculatorKey words. The whole is all of the things. The parts are the groups that make it.
Method. Put the two parts together, then count them all.
- Find the first part: 2. Start with the bigger part and count on.2
- Count on 4 more. Count on one at a time from the first part.2 + 4 = 6
- Write the answer. The total is the whole.6
Check. Count the whole group one at a time: 6. ✓
Watch out. Count on from the bigger part. The total is always bigger than either part.
Key words. The whole is all of the things. The parts are the groups that make it.
Method. Put the two parts together, then count them all.
- Find the first part: 3. Start with the bigger part and count on.3
- Count on 2 more. Count on one at a time from the first part.3 + 2 = 5
- Write the answer. The total is the whole.5
Check. Count the whole group one at a time: 5. ✓
Watch out. Count on from the bigger part. The total is always bigger than either part.
Key words. A missing part is the number we add to the known part to make the whole.
Method. The whole is 5. One part is 3. Find the other part.
- Start with the whole: 5. The whole has all the things.5
- Take away the part you know: 3. What is left is the other part.5 − 3 = 2
- Check by counting on. 3 and 2 must make 5.3 + 2 = 5
- Write the answer. 2
Check. Count on from 3 to 5: 2 more. ✓
Watch out. Count on from the part you know, to reach the whole.
Key words. The whole is all of the things. The parts are the groups that make it.
Method. Put the two parts together, then count them all.
- Find the first part: 6. Start with the bigger part and count on.6
- Count on 4 more. Count on one at a time from the first part.6 + 4 = 10
- Write the answer. The total is the whole.10
Check. Count the whole group one at a time: 10. ✓
Watch out. Count on from the bigger part. The total is always bigger than either part.
Key words. A missing part is the number we add to the known part to make the whole.
Method. The whole is 10. One part is 7. Find the other part.
- Start with the whole: 10. The whole has all the things.10
- Take away the part you know: 7. What is left is the other part.10 − 7 = 3
- Check by counting on. 7 and 3 must make 10.7 + 3 = 10
- Write the answer. 3
Check. Count on from 7 to 10: 3 more. ✓
Watch out. Count on from the part you know, to reach the whole.
Key words. A double is two of the same number.
Method. A double is two equal parts. Add the number to itself.
- Find the two equal rows of 4. The two rows are the same length.4 and 4
- Count the total. Count both rows together.4 + 4 = 8
- Write the answer. 8
Check. Count on from 4 another 4: the answer is 8. ✓
Watch out. Doubles have two equal parts. Check that both rows match.
Key words. A double is two of the same number.
Method. A double is two equal parts. Add the number to itself.
- Find the two equal rows of 5. The two rows are the same length.5 and 5
- Count the total. Count both rows together.5 + 5 = 10
- Write the answer. 10
Check. Count on from 5 another 5: the answer is 10. ✓
Watch out. Doubles have two equal parts. Check that both rows match.
Method. Start with 0 and 5. Then move one counter at a time from one part to the other.
- Start with all in one part. Use 0 in one part and the total in the other.0 and 5
- Move one at a time. Each time, one more goes into the first part.5 pairs in order
- Write the pairs. Include 0 and the total.0 and 5, 1 and 4, 2 and 3, 3 and 2, 4 and 1, 5 and 0
Check. Each pair adds to 5. ✓
Watch out. Keep a list in order, so you do not miss a pair.
Method. Add the two parts in each pair. The right pair makes 5.
- Add the first pair. Check the total.1 + 3 = 4
- Add the other pairs. Only one pair makes the whole.2 + 3 = 5
- Write the answer. 2 and 3
Check. 2 + 3 = 5. ✓
Watch out. Add both parts in each pair to check.
Method. A double has two equal parts.
- Look at the parts. Each part is 3.3 and 3
- Check they are equal. Two equal parts make a double.3 = 3
- Write the answer. Accept any answer: 3 and 3 are two equal parts, so they are a double.
Check. Count 3 + 3 = 6. ✓
Watch out. The two parts must be the same number.
Total 20 marks. Allow about 20 minutes.
Exercise 4X Practice test questions
Non-calculatorKey words. The whole is all of the things. The parts are the groups that make it.
Method. Put the two parts together, then count them all.
- Find the first part: 2. Start with the bigger part and count on.2
- Count on 5 more. Count on one at a time from the first part.2 + 5 = 7
- Write the answer. The total is the whole.7
Check. Count the whole group one at a time: 7. ✓
Watch out. Count on from the bigger part. The total is always bigger than either part.
Key words. A missing part is the number we add to the known part to make the whole.
Method. The whole is 9. One part is 4. Find the other part.
- Start with the whole: 9. The whole has all the things.9
- Take away the part you know: 4. What is left is the other part.9 − 4 = 5
- Check by counting on. 4 and 5 must make 9.4 + 5 = 9
- Write the answer. 5
Check. Count on from 4 to 9: 5 more. ✓
Watch out. Count on from the part you know, to reach the whole.
Method. Add the two parts in each pair. The right pair makes 4.
- Add the first pair. Check the total.1 + 2 = 3
- Add the other pairs. Only one pair makes the whole.2 + 2 = 4
- Write the answer. 2 and 2
Check. 2 + 2 = 4. ✓
Watch out. Add both parts in each pair to check.
Key words. A missing part is the number we add to the known part to make the whole.
Method. The whole is 10. One part is 4. Find the other part.
- Start with the whole: 10. The whole has all the things.10
- Take away the part you know: 4. What is left is the other part.10 − 4 = 6
- Check by counting on. 4 and 6 must make 10.4 + 6 = 10
- Write the answer. 6
Check. Count on from 4 to 10: 6 more. ✓
Watch out. Count on from the part you know, to reach the whole.
Method. Start with 0 and 4. Then move one counter at a time from one part to the other.
- Start with all in one part. Use 0 in one part and the total in the other.0 and 4
- Move one at a time. Each time, one more goes into the first part.4 pairs in order
- Write the pairs. Include 0 and the total.0 and 4, 1 and 3, 2 and 2, 3 and 1, 4 and 0
Check. Each pair adds to 4. ✓
Watch out. Keep a list in order, so you do not miss a pair.
Key words. A missing part is the number we add to the known part to make the whole.
Method. The whole is 10. One part is 6. Find the other part.
- Start with the whole: 10. The whole has all the things.10
- Take away the part you know: 6. What is left is the other part.10 − 6 = 4
- Check by counting on. 6 and 4 must make 10.6 + 4 = 10
- Write the answer. 4
Check. Count on from 6 to 10: 4 more. ✓
Watch out. Count on from the part you know, to reach the whole.
Method. Add 5 and 5 together.
- Count the first 5. Five things.5
- Count the second 5. Five more things.5 + 5
- Count all the things. Count on from 5 to 10.1, 2, 3, 4, 5, 6, 7, 8, 9, 10
- Write the answer. No. 5 and 5 make 10.
Check. Count 10 things in all. ✓
Watch out. Count both fives, not just one.
Method. Start with the part you know, then count on to the whole.
- Start with 4 fingers. The part you know is 4.4
- Count on to 9. Count on one at a time: 5, 6, 7, 8, 9.5, 6, 7, 8, 9
- Count your steps. You counted on 5 steps.5 steps
- Write the answer. 5. Four and 5 make 9.
Check. Count 4 and 5 fingers: 9 in all. ✓
Watch out. Count on from the part you know.
Method. Choose two pairs and check each pair adds to 10.
- Choose a pair. Pick two numbers that you think make 10.3 and 7
- Check it. Add the two numbers.3 + 7 = 10
- Choose another pair and check it. Add them to see if the total is 10.4 + 6 = 10
- Write the answer. Accept any two pairs that add to 10, such as 3 and 7, or 4 and 6, because each pair makes 10.
Check. Both pairs add to 10. ✓
Watch out. Check the total of each pair.
Method. Start with the red cubes, and count on to 8.
- Start with 5. Lily has 5 red cubes.5
- Count on to 8. Count on one at a time: 6, 7, 8.6, 7, 8
- Count the steps. Three steps to reach 8.3
- Write the answer. 3. Five and three make 8.
Check. Count 5 and 3 together: 8. ✓
Watch out. Count on from the part you know.