Counting and comparing · applications

Applications: Counting and Comparing

10 question types · Kindergarten · each worked step by step with a figure that follows the steps

PSLE

01

Ducks Counted One by One, Then One More Duck

strategyTouch Each Thing Once as You Count / One More Is the Next Number

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?

One counter is one duck. There are 7 counters in a row.
Draw one counter for each duck, all in a row.
step 1 of 4

Say one number for each duck. The last number you say tells you how many ducks there are.

  1. Draw one counter for each duck, all in a row.
  2. Touch each counter once and count: 1, 2, 3, 4, 5, 6, 7.
  3. (a) The last number Mei says is 7. There are 7 ducks.
  4. (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.
02

Shells in a Jumble, Crossed Off as They Are Counted

strategyCross Off Each Thing as You Count It / Then Count the Ones Not Crossed Off

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?

One counter is one shell. The 9 counters are in a jumble, not in a row.
Draw 9 counters in a jumble for the 9 shells.
step 1 of 4

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.

  1. Draw 9 counters in a jumble for the 9 shells.
  2. Cross off 6 counters. These are the shells Ben has counted: 1, 2, 3, 4, 5, 6.
  3. (a) The number after 6 is 7. Ben says 7 next.
  4. (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.
03

Buttons on a Coat, One Falls Off

strategyOne Fewer Is the Number Just Before / Cross Out the One That Goes

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?

12345678
One counter is one button. The numbers 1 to 8 are under the 8 counters.
Draw 8 counters in a row for the 8 buttons. Write the numbers 1 to 8 under them.
step 1 of 4

When one thing goes, there is one fewer. One fewer is the number just before when you count.

  1. Draw 8 counters in a row for the 8 buttons. Write the numbers 1 to 8 under them.
  2. One button falls off. Cross out the last counter, the one with 8 under it.
  3. (a) The number just before 8 is 7. There are 7 buttons on the coat now.
  4. (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.
04

A Child's Place in a Line of Six

strategyDraw the Line and Mark the Place / Count the Ones in Front and the Ones Behind

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?

frontback1st2nd3rd4th5th6th
There are 6 children in a line. The places are 1st, 2nd, 3rd, 4th, 5th and 6th from the front.
Draw 6 children in a line. Write 1st, 2nd, 3rd, 4th, 5th and 6th under them, from the front.
step 1 of 4

A word like 3rd tells you a place in the line. It does not tell you how many.

  1. Draw 6 children in a line. Write 1st, 2nd, 3rd, 4th, 5th and 6th under them, from the front.
  2. Mei is the 3rd child. Color her in.
  3. (a) Count the children in front of Mei: 1, 2. There are 2 children in front of Mei.
  4. (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.
05

A Line of Five Counted from the Front and from the Back

strategyCount Places from the End That Is Named / The First from the Front Is the Last 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?

frontbackAliBenMeiSamEvaAli is 1st from the front
There are 5 children in a line. Ali is at the front and Eva is at the back.
Draw the 5 children in a line. Ali is at the front and Eva is at the back.
step 1 of 4

A line has two ends. A place counted from the back starts at the last child.

  1. Draw the 5 children in a line. Ali is at the front and Eva is at the back.
  2. Count places from the back. Eva is 1st, Sam is 2nd, Mei is 3rd, Ben is 4th and Ali is 5th.
  3. (a) Ali is 5th from the back. The first child from the front is the last child from the back.
  4. (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.
06

Cups and Saucers Matched One to One

strategyMatch One to One / The Ones with No Partner Show Which Group Has More

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?

cupssaucers
There are 5 counters in a row for the cups and 3 counters below for the saucers.
Draw 5 counters in a row for the cups. Draw 3 counters in a row below for the saucers.
step 1 of 4

To see which group has more, match the things one to one. The group with some left over has more.

  1. Draw 5 counters in a row for the cups. Draw 3 counters in a row below for the saucers.
  2. Join each saucer to one cup with a line. There are 3 pairs.
  3. (a) Some cups have no saucer, and every saucer has a cup. So there are more cups.
  4. (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.
07

Five Fingers, Some Up and Some Down

strategyNumber Bond of Five / Put Counters in a Five Frame and Count the Empty Cells

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?

up5??
The five frame has 5 cells, one for each finger.
Draw a five frame. It has 5 cells, one for each finger.
step 1 of 4

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.

  1. Draw a five frame. It has 5 cells, one for each finger.
  2. Put in 2 counters for the 2 fingers that are up.
  3. (a) Count the empty cells: 1, 2, 3. So 2 + 3 = 5, and 3 fingers are down.
  4. (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.
08

A Box of Ten Pencils and Some Loose Pencils

strategyCount On from Ten / Write the Ten First and Then the Ones

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?

The full ten frame is the box of 10 pencils.
Draw a ten frame that is full. It is the box of 10 pencils.
step 1 of 4

You know the box holds 10, so do not count those pencils again. Count on from 10.

  1. Draw a ten frame that is full. It is the box of 10 pencils.
  2. Draw 4 counters beside the frame for the 4 loose pencils.
  3. (a) Count on from 10: 11, 12, 13, 14. There are 14 pencils altogether.
  4. (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.
09

A Ribbon and a Pencil Measured in Blocks

strategyStart Both at the Same Line / Match the Blocks and Count the Extra Ones

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?

ribbon
The ribbon is a row of 6 blocks.
Draw a row of 6 blocks for the ribbon.
step 1 of 4

To compare two lengths, both must start at the same line. Then the one that goes further is longer.

  1. Draw a row of 6 blocks for the ribbon.
  2. Draw a row of 4 blocks below for the pencil. Both rows start at the same line.
  3. (a) The row of 6 blocks goes further than the row of 4 blocks. The ribbon is longer.
  4. (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.
10

Three Plates of Buns Put in Order

strategyFind the Fewest First / Then Put the Rest in Order from Fewest to Most

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?

Ali4Mei2Sam7
There is 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.
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.
step 1 of 4

The fewest comes first when you count: 2 comes before 4, and 4 comes before 7.

  1. 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.
  2. (a) The row of 2 is the shortest row. Mei has the fewest buns.
  3. Put the rows in order from fewest to most: 2, then 4, then 7.
  4. (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.
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