Ducks Counted One by One, Then One More Duck
There are 7 ducks on a pond. Mei touches each duck once as she counts. (a) What is the last number Mei says? (b) One more duck comes to the pond. How many ducks are there now?
Say one number for each duck. The last number you say tells you how many ducks there are.
All steps
- Draw one counter for each duck, all in a row.
- Touch each counter once and count: 1, 2, 3, 4, 5, 6, 7.
- (a) The last number Mei says is 7. There are 7 ducks.
- (b) Draw one more counter. The number after 7 is 8, so 7 + 1 = 8. There are 8 ducks now.
answer(a) 7; (b) 8 ducks
techniqueCounting to Ten · One and One
examsPSLE
Common pitfalls
- Touching one duck two times and saying 8 in part (a). Each duck gets one number only, so touch each duck once.
- Counting all the ducks again from 1 in part (b) and losing your place. You know there are 7, so one more is the next number, 8.
Shells in a Jumble, Crossed Off as They Are Counted
There are 9 shells in a jumble on the sand. Ben crosses off each shell as he counts it. He has crossed off 6 shells. (a) What number does Ben say next? (b) How many shells has Ben still to count?
The shells are not in a row, so it is easy to count one shell two times. Cross off each shell as you count it.
All steps
- Draw 9 counters in a jumble for the 9 shells.
- Cross off 6 counters. These are the shells Ben has counted: 1, 2, 3, 4, 5, 6.
- (a) The number after 6 is 7. Ben says 7 next.
- (b) Count the counters that are not crossed off: 1, 2, 3. Ben has 3 shells still to count.
answer(a) 7; (b) 3 shells
techniqueCounting to Ten
examsPSLE
Common pitfalls
- Counting a shell that is crossed off already. A cross means the shell has its number, so do not count it again.
- Saying 6 again for the next shell in part (a). The number 6 belongs to the last crossed shell, so the next shell is 7.
Buttons on a Coat, One Falls Off
Sam has 8 buttons on his coat. (a) One button falls off. How many buttons are on the coat now? (b) Then one more button falls off. How many buttons are on the coat now?
When one thing goes, there is one fewer. One fewer is the number just before when you count.
All steps
- Draw 8 counters in a row for the 8 buttons. Write the numbers 1 to 8 under them.
- One button falls off. Cross out the last counter, the one with 8 under it.
- (a) The number just before 8 is 7. There are 7 buttons on the coat now.
- (b) Cross out one more counter. The number just before 7 is 6. There are 6 buttons on the coat now.
answer(a) 7 buttons; (b) 6 buttons
techniqueCounting to Ten
examsPSLE
Common pitfalls
- Saying 9 in part (a). The button falls off, so there are fewer buttons, and the number goes back to 7.
- Saying 7 again in part (b). Two buttons have gone now, so go back one more number, from 7 to 6.
A Child's Place in a Line of Six
There are 6 children in a line for the slide. Mei is 3rd in the line. (a) How many children are in front of Mei? (b) How many children are behind Mei?
A word like 3rd tells you a place in the line. It does not tell you how many.
All steps
- Draw 6 children in a line. Write 1st, 2nd, 3rd, 4th, 5th and 6th under them, from the front.
- Mei is the 3rd child. Colour her in.
- (a) Count the children in front of Mei: 1, 2. There are 2 children in front of Mei.
- (b) Count the children behind Mei: 1, 2, 3. There are 3 children behind Mei.
answer(a) 2 children; (b) 3 children
techniqueOrdinal Numbers
examsPSLE
Common pitfalls
- Saying 3 children are in front of Mei because she is 3rd. Mei is one of the first three children, so only 2 children are in front of her.
- Counting Mei with the children behind her and saying 4. Mei is not behind herself, so start counting at the 4th child.
A Line of Five Counted from the Front and from the Back
There are 5 children in a line. From the front they are Ali, Ben, Mei, Sam and Eva. (a) Ali is 1st from the front. What is Ali's place from the back? (b) Who is 2nd from the back?
A line has two ends. A place counted from the back starts at the last child.
All steps
- Draw the 5 children in a line. Ali is at the front and Eva is at the back.
- Count places from the back. Eva is 1st, Sam is 2nd, Mei is 3rd, Ben is 4th and Ali is 5th.
- (a) Ali is 5th from the back. The first child from the front is the last child from the back.
- (b) Sam is 2nd from the back. From the front, Sam is 4th.
answer(a) 5th from the back; (b) Sam, who is 4th from the front
techniqueOrdinal Numbers
examsPSLE
Common pitfalls
- Saying Ben is 2nd from the back. Ben is 2nd from the front, and the question asks for the place from the back, so start counting at Eva.
- Starting the count from the back at 0, so that Sam is 1st. The child at the very back is 1st from the back, just as the child at the very front is 1st from the front.
Cups and Saucers Matched One to One
There are 5 cups and 3 saucers on a table. Dad puts one cup on each saucer. (a) Are there more cups or more saucers? (b) How many more?
To see which group has more, match the things one to one. The group with some left over has more.
All steps
- Draw 5 counters in a row for the cups. Draw 3 counters in a row below for the saucers.
- Join each saucer to one cup with a line. There are 3 pairs.
- (a) Some cups have no saucer, and every saucer has a cup. So there are more cups.
- (b) Count the cups with no saucer: 1, 2. There are 2 more cups than saucers.
answer(a) There are more cups. (b) 2 more cups
techniqueMore and Fewer
examsPSLE · GCSE Higher
Common pitfalls
- Spreading the 3 saucers out so that their row looks as long as the row of cups. A longer row does not mean more things, so match them one to one.
- Saying there are 5 more cups in part (b). There are 5 cups altogether, and only the 2 cups with no saucer are the extra ones.
Five Fingers, Some Up and Some Down
Eva has 5 fingers on one hand. (a) She holds 2 fingers up. How many fingers are down? (b) Now she holds 4 fingers up. How many fingers are down?
The fingers that are up and the fingers that are down make 5 together. Two numbers that make 5 are a number bond of 5.
All steps
- Draw a five frame. It has 5 cells, one for each finger.
- Put in 2 counters for the 2 fingers that are up.
- (a) Count the empty cells: 1, 2, 3. So 2 + 3 = 5, and 3 fingers are down.
- (b) Put in 4 counters for the 4 fingers that are up. There is 1 empty cell. So 4 + 1 = 5, and 1 finger is down.
answer(a) 3 fingers; (b) 1 finger
techniqueNumber Bonds to Five
Common pitfalls
- Saying 2 fingers are down because 2 fingers are up. The two parts do not have to be the same. They have to make 5 together.
- Putting the numbers together in part (b) to get 4 + 5 = 9. The 4 fingers are part of the 5 fingers, so count the empty cells.
A Box of Ten Pencils and Some Loose Pencils
There are 10 pencils in a box. There are 4 loose pencils beside the box. (a) How many pencils are there altogether? (b) Ben writes the number. He writes 1 first for the one ten. What does he write next?
You know the box holds 10, so do not count those pencils again. Count on from 10.
All steps
- Draw a ten frame that is full. It is the box of 10 pencils.
- Draw 4 counters beside the frame for the 4 loose pencils.
- (a) Count on from 10: 11, 12, 13, 14. There are 14 pencils altogether.
- (b) The number 14 is one ten and 4 ones. Ben writes 1 for the ten, and then he writes 4 for the ones.
answer(a) 14 pencils; (b) 4
techniqueWriting Numbers to Twenty · Counting to Ten
examsPSLE
Common pitfalls
- Saying 10 again for the first loose pencil and ending at 13. The box is 10 already, so the first loose pencil is 11.
- Writing the 4 first and then the 1, which is 41. The ten is written first and the ones are written after it, so the number is 14.
A Ribbon and a Pencil Measured in Blocks
A ribbon is 6 blocks long. A pencil is 4 blocks long. (a) Which is longer, the ribbon or the pencil? (b) How many blocks longer is it?
To compare two lengths, both must start at the same line. Then the one that goes further is longer.
All steps
- Draw a row of 6 blocks for the ribbon.
- Draw a row of 4 blocks below for the pencil. Both rows start at the same line.
- (a) The row of 6 blocks goes further than the row of 4 blocks. The ribbon is longer.
- (b) Count the ribbon's blocks that go past the pencil: 1, 2. The ribbon is 2 blocks longer.
answer(a) The ribbon is longer. (b) 2 blocks longer
techniqueLonger and Shorter · More and Fewer
examsPSLE · GCSE Higher
Common pitfalls
- Starting the pencil's row further along, so that both rows end at the same place. Then the two look the same length. Both rows must start at the same line.
- Saying the ribbon is 6 blocks longer. The ribbon is 6 blocks long. Only the 2 blocks that go past the pencil are extra.
Three Plates of Buns Put in Order
Ali has 4 buns on his plate. Mei has 2 buns on her plate. Sam has 7 buns on his plate. (a) Who has the fewest buns? (b) The plates are put in order from fewest to most. Whose plate is in the middle?
The fewest comes first when you count: 2 comes before 4, and 4 comes before 7.
All steps
- Draw a row of counters for each plate: 4 for Ali, 2 for Mei and 7 for Sam. All the rows start at the same line.
- (a) The row of 2 is the shortest row. Mei has the fewest buns.
- Put the rows in order from fewest to most: 2, then 4, then 7.
- (b) The middle row has 4 counters. Ali's plate is in the middle.
answer(a) Mei, with 2 buns; (b) Ali, with 4 buns. The order is 2, 4, 7.
techniqueMore and Fewer · Counting to Ten
examsPSLE · GCSE Higher
Common pitfalls
- Picking Ali for the fewest because his name comes first in the question. Look at the numbers: 2 is fewer than 4.
- Putting the plates in order from most to fewest, 7, 4, 2. The question asks for fewest to most, so start with 2.
One More Sticker on a Chart Each Day
Ben gets 1 sticker for his chart every day. On Monday he has 4 stickers. (a) He gets 1 more on Tuesday and 1 more on Wednesday. How many stickers does he have on Wednesday? (b) He gets 1 more every day after that. How many stickers will he have on Friday?
Each day Ben gets one more sticker. One more is the next number when you count, so you do not need to count all the stickers again.
All steps
- Draw 4 counters in a row for the 4 stickers Ben has on Monday.
- On Tuesday he gets 1 more. The number after 4 is 5, so 4 + 1 = 5. He has 5 stickers on Tuesday.
- (a) On Wednesday he gets 1 more. The number after 5 is 6, so 5 + 1 = 6. He has 6 stickers on Wednesday.
- (b) Say the next number for each new day. Thursday is 7 and Friday is 8. Ben will have 8 stickers on Friday.
answer(a) 6 stickers; (b) 8 stickers
techniqueOne and One · Counting to Ten
examsPSLE
Common pitfalls
- Stopping at Tuesday and saying 5 in part (a). Ben gets 1 more on Tuesday and 1 more again on Wednesday, so the count goes up two times: 5, then 6.
- Adding 1 for Monday too and saying 9 in part (b). Monday's 4 stickers are counted already. The new stickers come on Tuesday, Wednesday, Thursday and Friday, one each day: 5, 6, 7, 8.
Skips Counted in Ten Frames, Then Written in Digits
Eva skips with a rope. For each skip, she puts 1 counter in a ten frame. When a frame is full, she starts a new frame. At the end, 1 frame is full and the next frame has 6 counters. (a) Eva says the number of skips: sixteen. Write sixteen in digits. (b) The next day, Eva fills 2 frames and has no counters left over. Write that number of skips in digits.
A full ten frame is one ten. A number from 11 to 19 is one ten and some ones. It is written with the 1 for the ten first and the ones after it, even when its word says the ones first.
All steps
- Look at the frames. The full frame is 1 ten. The other frame has 6 counters, which are 6 ones.
- The word sixteen says the six first. But a number is written with the tens first, on the left, and the ones after them.
- (a) Write 1 for the ten and then 6 for the ones. Sixteen is written 16.
- (b) Two full frames are 2 tens. There are no ones, so write 0 for the ones. The number is 20.
answer(a) 16; (b) 20 skips
techniqueWriting Numbers to Twenty
Common pitfalls
- Writing 61 because the word says six first. 61 is 6 tens and 1 one, which would fill 6 frames. Eva filled only 1 frame, so the 1 goes first: 16.
- Writing 60 because sixteen sounds like sixty. A word that ends in teen is 1 ten and some ones. Sixty is 6 full tens.
Seats on a Little Train, Some Taken and Some Free
A little train at the fair has 5 seats. 3 children are sitting in it. (a) How many seats are free? (b) Later, only 1 seat is free. How many children are sitting in the train now?
The seats that are taken and the seats that are free make 5 together. When you know the whole and one part, you can find the other part.
All steps
- Draw a number bond. The whole is the 5 seats. One part is the seats that are taken. The other part is the seats that are free.
- 3 children are sitting, so 3 seats are taken. Put 3 in one part. The other part is missing.
- (a) Count up from 3 to 5: four, five. That is 2 counts, so 2 seats are free. Check: 3 + 2 = 5.
- (b) Now 1 seat is free. Take the free part from the whole: 5 − 1 = 4. So 4 seats are taken, and 4 children are sitting in the train. Check: 4 + 1 = 5.
answer(a) 2 seats; (b) 4 children
techniqueNumber Bonds to Five
Common pitfalls
- Saying 3 seats are free because 3 children are sitting. The two parts do not have to be the same. They must make 5 together, and 3 + 3 is 6, not 5.
- Saying 1 child in part (b). The 1 is the free seat. The children sit in the seats that are taken, and that part is 5 − 1 = 4.
Three Toy Snakes Lined Up and Put in Order by Length
Jo has 3 toy snakes: a red one, a blue one and a green one. At first, the snakes are not lined up. The end of the green snake sticks out the furthest. Then Jo lines up all 3 snakes at the edge of a book. Now the red snake reaches the furthest. The green snake stops before the blue snake. (a) Which snake is the longest? (b) Put the snakes in order from the shortest to the longest.
To compare lengths, all the snakes must start at the same line. Then the one that reaches the furthest is the longest, and the one that stops first is the shortest.
All steps
- Draw a start line for the edge of the book. Draw the 3 snakes side by side, all starting at that line.
- Look at where each snake stops. The red snake reaches the furthest.
- (a) All 3 snakes start at the same line, and the red one reaches the furthest. So the red snake is the longest.
- The green snake stops before the blue snake. It does not reach as far, so the green snake is shorter than the blue one.
- (b) From the shortest to the longest, the order is green, blue, red.
answer(a) the red snake; (b) green, blue, red
techniqueLonger and Shorter
Common pitfalls
- Saying the green snake is the longest because its end stuck out the furthest at first. At first the snakes were not lined up, so the green snake did not start where the others started. Only when all 3 start at the same line does the furthest end show the longest snake.
- Reading 'the green snake stops before the blue snake' as green being longer. A snake that stops before another one does not reach as far, so it is the shorter one.