Two Groups of Apples Put Together
There are 5 red apples in a bowl. There are 3 green apples in the bowl too. (a) How many apples are there altogether? (b) Mum puts 2 more apples in the bowl. How many apples are there now?
Putting two groups together is adding. Use one counter for each apple and count them all.
- Draw a ten frame. Put in 5 counters for the 5 red apples.
- Put in 3 more counters for the 3 green apples.
- (a) Count on from 5: 6, 7, 8. So 5 + 3 = 8. There are 8 apples altogether.
- (b) The frame has 2 empty cells. The 2 new apples fill them. So 8 + 2 = 10. There are 10 apples now.
answer(a) 8 apples; (b) 10 apples
techniqueAdding Within Twenty · Number Bonds to Ten
examsPSLE
Common pitfalls
- Counting on from 5 by saying 5, 6, 7 and stopping at 7. The 5 red apples are counted already, so the first green apple is 6.
- Adding 2 to the 3 green apples in part (b) to get 5. The question asks for all the apples in the bowl, so add 2 to 8.
Birds on a Fence and Some Fly Off
There are 9 birds on a fence. Then 4 birds fly off. (a) How many birds are left on the fence? (b) Then 2 more birds fly off. How many birds are left now?
When some go away, that is taking away. Cross out the ones that go and count the ones that stay.
- Draw a ten frame. Put in 9 counters for the 9 birds.
- 4 birds fly off. Cross out 4 counters.
- (a) Count the counters that are not crossed out. There are 5. So 9 − 4 = 5. There are 5 birds left.
- (b) Cross out 2 more counters. So 5 − 2 = 3. There are 3 birds left now.
answer(a) 5 birds; (b) 3 birds
techniqueTaking Away
examsPSLE
Common pitfalls
- Adding the two numbers: 9 + 4 = 13. The birds fly off, so there are fewer birds on the fence, not more.
- Taking 2 away from 9 in part (b) to get 7. Only 5 birds were still on the fence, so take 2 away from 5.
An Egg Box That Holds Ten
An egg box holds 10 eggs. There are 6 eggs in the box. (a) How many more eggs fit in the box? (b) Mum puts 2 more eggs in the box. How many more eggs fit now?
The egg box is a ten frame. The eggs and the empty cells make 10 together, so they are a number bond to 10.
- Draw a ten frame for the box. Put in 6 counters for the 6 eggs.
- Count the empty cells: 1, 2, 3, 4. The numbers 6 and 4 make 10.
- (a) 6 + 4 = 10. So 4 more eggs fit in the box.
- (b) Now there are 6 + 2 = 8 eggs in the box. There are 2 empty cells, and 8 + 2 = 10. So 2 more eggs fit.
answer(a) 4 eggs; (b) 2 eggs
techniqueNumber Bonds to Ten
Common pitfalls
- Adding the two numbers: 10 + 6 = 16. The box holds only 10 eggs. The question asks for the part that is missing from 10.
- Answering 8 in part (b). There are 8 eggs in the box now, but the question asks how many more fit, and that is the 2 empty cells.
Stickers Added by Making Ten First
Ali has 8 stickers. His teacher gives him 5 more stickers. (a) How many of the new stickers make his 8 stickers up to 10? (b) How many stickers does Ali have altogether?
It is easy to add a number to 10. So fill the ten frame first, then add what is left.
- Put 8 counters in a ten frame for the 8 stickers. There are 2 empty cells.
- (a) The numbers 8 and 2 make 10. So 2 of the new stickers fill the frame.
- Split 5 into 2 and 3. The 2 filled the frame. Put the other 3 counters in a new frame.
- (b) 8 + 5 = 8 + 2 + 3 = 10 + 3 = 13. Ali has 13 stickers altogether.
answer(a) 2 stickers; (b) 13 stickers
techniqueAdding Within Twenty · Number Bonds to Ten
examsPSLE
Common pitfalls
- Filling the frame with 2 counters and then adding all 5 again to get 15. The 2 counters are part of the 5, so only 3 more are added.
- Splitting 5 into 2 and 2. The two parts must make 5, and 2 + 3 = 5.
Two Children's Shells Matched in Pairs
Mei has 9 shells. Ben has 6 shells. (a) How many more shells does Mei have than Ben? (b) Ben finds 1 more shell. How many more shells does Mei have now?
To find how many more, put the two groups in two rows and match them in pairs. The counters with no partner show how many more.
- Draw 9 counters in a row for Mei. Draw 6 counters in a row below for Ben.
- Join each of Ben's counters to one of Mei's counters. There are 6 pairs.
- (a) 3 of Mei's counters have no partner. So 9 − 6 = 3. Mei has 3 more shells than Ben.
- (b) Ben has 6 + 1 = 7 shells now. Only 2 of Mei's counters have no partner. So 9 − 7 = 2. Mei has 2 more shells.
answer(a) 3 shells; (b) 2 shells
techniqueTaking Away · More and Fewer
examsPSLE
Common pitfalls
- Adding the two numbers: 9 + 6 = 15. That is how many shells the two children have altogether. "How many more" asks for the difference, and that is a subtraction.
- Answering 9 because Mei has 9 shells. The question asks how many more she has than Ben, so only the shells with no partner are counted.
Toy Cars with One Part Missing
Sam has 15 toy cars. 8 of the cars are red. The rest are blue. (a) How many blue cars does Sam have? (b) Sam gets 2 more blue cars. How many blue cars does he have now?
The red cars and the blue cars are the two parts of the 15 cars. One part is known, so the other part is found by taking away.
- Put 15 counters in two ten frames for the 15 cars. There are 10 in the first frame and 5 in the next.
- Mark 8 of the counters for the red cars. The other counters are the blue cars.
- (a) Count on from 8. 2 more make 10, and 5 more make 15. 2 + 5 = 7, so 15 − 8 = 7. Sam has 7 blue cars. Check: 8 + 7 = 15.
- (b) Sam gets 2 more blue cars. So 7 + 2 = 9. He has 9 blue cars now.
answer(a) 7 blue cars; (b) 9 blue cars
techniqueTaking Away · Number Bonds to Ten
examsPSLE
Common pitfalls
- Adding the two numbers: 15 + 8 = 23. The 8 red cars are part of the 15 cars already, so they are taken away from 15.
- Adding 2 to 15 in part (b) to get 17. That is all of Sam's cars. The question asks for the blue cars only, so add 2 to 7.
Three Bunches of Flowers with a Ten Inside
Lina picks 4 red flowers. She picks 5 white flowers and 6 yellow flowers. (a) How many red and yellow flowers does she pick? (b) How many flowers does she pick altogether?
Three numbers can be added in any order. Look for two numbers that make 10 and add them first.
- Put 4 counters in a ten frame for the red flowers. There are 6 empty cells.
- The 6 counters for the yellow flowers fill the 6 empty cells. The numbers 4 and 6 make 10.
- (a) 4 + 6 = 10. Lina picks 10 red and yellow flowers.
- Put the 5 counters for the white flowers in a new frame.
- (b) 4 + 5 + 6 = 10 + 5 = 15. Lina picks 15 flowers altogether.
answer(a) 10 flowers; (b) 15 flowers
techniqueNumber Bonds to Ten · Adding Within Twenty
examsPSLE
Common pitfalls
- Adding only the first two numbers: 4 + 5 = 9. There are three groups of flowers, and all three are added in part (b).
- Adding the 10 from part (a) to all three numbers again. The 10 is the red and the yellow flowers already, so only the 5 white flowers are added to it.
Balloons That Pop, Taken Away Through Ten
There are 13 balloons at a party. 5 of the balloons pop. (a) How many balloons must pop to leave 10 balloons? (b) How many balloons are left after all 5 pop?
It is easy to take a number away from 10. So take away down to 10 first, then take away the rest.
- Put 13 counters in two ten frames. There are 10 in the first frame and 3 in the next.
- (a) Cross out the 3 counters in the second frame. 13 − 3 = 10. So 3 balloons must pop to leave 10.
- Split 5 into 3 and 2. The 3 are crossed out. Cross out 2 more from the full frame.
- (b) 13 − 5 = 13 − 3 − 2 = 10 − 2 = 8. There are 8 balloons left.
answer(a) 3 balloons; (b) 8 balloons
techniqueTaking Away · Number Bonds to Ten
examsPSLE
Common pitfalls
- Taking away 3 and then taking away all 5 again to get 5. The 3 are part of the 5, so only 2 more are taken away.
- Taking the small digit from the big digit: 5 − 3 = 2, and writing 12. The 5 is taken away from all 13 balloons, and that leaves fewer than 10.
Children Get On a Bus and Then Get Off
There are 8 children on a bus. At the first stop 6 children get on. At the next stop 5 children get off. (a) How many children are on the bus after the first stop? (b) How many children are on the bus after the next stop?
The story has two steps. Children get on, so add. Then children get off, so take away from the new number.
- Put 8 counters in a ten frame for the 8 children on the bus.
- 6 children get on. 2 counters fill the first frame. The other 4 go in a new frame.
- (a) 8 + 6 = 8 + 2 + 4 = 14. There are 14 children on the bus after the first stop.
- 5 children get off. Cross out the 4 counters in the second frame and 1 more.
- (b) 14 − 5 = 14 − 4 − 1 = 9. There are 9 children on the bus after the next stop.
answer(a) 14 children; (b) 9 children
techniqueAdding Within Twenty · Taking Away
examsPSLE
Common pitfalls
- Taking 5 away from 8 in part (b) to get 3. When the 5 children get off, there are 14 children on the bus, not 8.
- Adding all three numbers: 8 + 6 + 5 = 19. The 5 children get off the bus, so they are taken away.
Cookies Baked and Eaten, One Fact Family
Mum bakes 7 round cookies and 5 star cookies. (a) How many cookies does Mum bake altogether? (b) The family eats the 5 star cookies. How many cookies are left?
The numbers 7, 5 and 12 are in one number bond. The same bond gives an addition and a subtraction.
- Put in 7 counters for the round cookies. Put in 5 counters for the star cookies.
- (a) 7 + 3 = 10, and 2 more make 12. So 7 + 5 = 12. Mum bakes 12 cookies altogether.
- The family eats the 5 star cookies. Cross out the 5 counters for the star cookies.
- (b) The 7 round cookies are left. 7 + 5 = 12, so 12 − 5 = 7. There are 7 cookies left.
answer(a) 12 cookies; (b) 7 cookies
techniqueAdding Within Twenty · Taking Away
examsPSLE
Common pitfalls
- Taking 5 away from 7 in part (b) to get 2. The family eats 5 of the 12 cookies, so the subtraction is 12 − 5.
- Counting back 5 from 12 and saying 12 as the first count, which gives 8. The first cookie eaten leaves 11. The fact 7 + 5 = 12 gives 12 − 5 = 7 with no counting back.