Place value · applications

Applications: Place Value

10 question types · Primary 2 · each worked step by step with a figure that follows the steps

PSLE · GCSE Higher

01

Sticks in Bundles of Ten with Some Loose Sticks

strategyCount the Tens, Then the Ones / One More Bundle Is Ten More

Ali has 4 bundles of sticks. Each bundle has 10 sticks. He also has 6 loose sticks. (a) How many sticks does Ali have? (b) His teacher gives him 1 more bundle. How many sticks does he have now?

6 loose
Each bundle is 1 ten. Each loose stick is 1 one.
Draw the 4 bundles and the 6 loose sticks. Each bundle is 1 ten. Each loose stick is 1 one.
step 1 of 4

Each bundle is one ten and each loose stick is one one. Count the tens first, then count on the ones.

  1. Draw the 4 bundles and the 6 loose sticks. Each bundle is 1 ten. Each loose stick is 1 one.
  2. Count the bundles in tens: 10, 20, 30, 40. Then count on the loose sticks in ones: 41, 42, 43, 44, 45, 46.
  3. (a) 4 tens and 6 ones is 40 + 6 = 46. Ali has 46 sticks.
  4. (b) One more bundle is 1 more ten. Now there are 5 tens and 6 ones: 50 + 6 = 56. Ali has 56 sticks. Check: 46 + 10 = 56.

answer(a) 46 sticks; (b) 56 sticks

techniqueTens and Ones · Counting to a Hundred

examsPSLE · GCSE Higher

Common pitfalls

  • Adding the two numbers: 4 + 6 = 10. The 4 is the number of bundles, and each bundle has 10 sticks, so the 4 stands for 40 sticks.
  • Adding 1 in part (b) to get 47. One more bundle is 10 more sticks, so the tens digit goes up by 1, not the ones digit.
02

Blocks with More Than Nine Tens

strategyExchange Ten Tens for One Hundred / Then Read the Hundreds, Tens and Ones

Mei has 2 hundreds blocks, 15 tens blocks and 4 ones blocks. She swaps 10 of the tens blocks for 1 hundreds block. (a) How many hundreds blocks and how many tens blocks does she have now? (b) What number do her blocks show?

HundredsTensOnes2154
There are 2 hundreds, 15 tens and 4 ones. A place holds only one digit, and 15 is too many tens.
Put the blocks in three columns: 2 hundreds, 15 tens and 4 ones. A place holds only one digit, and 15 is too many tens for one place.
step 1 of 4

A place can hold only one digit, so there cannot be more than 9 tens in the tens place. Ten tens are exchanged for one hundred, and then the number can be read.

  1. Put the blocks in three columns: 2 hundreds, 15 tens and 4 ones. A place holds only one digit, and 15 is too many tens for one place.
  2. Ring 10 of the tens blocks. Ten tens are 100, which is the same as 1 hundreds block.
  3. (a) Swap the ringed tens for 1 hundreds block. The hundreds are 2 + 1 = 3 and the tens are 15 − 10 = 5. Mei has 3 hundreds blocks and 5 tens blocks.
  4. (b) 3 hundreds, 5 tens and 4 ones is 300 + 50 + 4 = 354. Check: 200 + 150 + 4 = 354.

answer(a) 3 hundreds blocks and 5 tens blocks; (b) 354

techniqueHundreds · Tens and Ones

examsPSLE · GCSE Higher

Common pitfalls

  • Writing the three counts side by side as 2154. Each place holds one digit, so the 15 tens must first be exchanged: 10 of them become 1 more hundred.
  • Dropping the extra tens and writing 254. The 10 tens that were swapped are still there as 1 more hundred, so the hundreds digit goes up to 3.
03

Sheets of Five Stickers with a Last Sheet That Is Not Full

strategyCount the Full Groups in Fives / Count On the Rest in Ones

Siti has 7 full sheets of stickers. Each full sheet has 5 stickers. One more sheet has only 3 stickers on it. (a) How many stickers are on the 7 full sheets? (b) How many stickers does Siti have altogether?

Seven sheets are full, with 5 stickers on each. The last sheet has only 3 stickers.
Draw the 7 full sheets with 5 stickers on each. Draw the last sheet with 3 stickers.
step 1 of 4

The full sheets are equal groups of 5, so they can be counted in fives. The last sheet is not a full group, so its stickers are counted on in ones.

  1. Draw the 7 full sheets with 5 stickers on each. Draw the last sheet with 3 stickers.
  2. Count the full sheets in fives: 5, 10, 15, 20, 25, 30, 35.
  3. (a) There are 35 stickers on the 7 full sheets.
  4. (b) The last sheet is not a full five, so count on in ones: 36, 37, 38. Siti has 38 stickers altogether. Check: 35 + 3 = 38.

answer(a) 35 stickers; (b) 38 stickers

techniqueSkip Counting

Common pitfalls

  • Counting the last sheet as another five and getting 40. The last sheet has only 3 stickers, so after 35 the count goes on in ones, not in fives.
  • Counting the sheets and answering 8. The question asks for stickers, and each full sheet is 5 stickers, not 1.
04

Children Walking in Pairs

strategyPut the Objects in Twos / One Left Over Means an Odd Number

17 children line up to walk to the hall in pairs. (a) How many pairs can they make? (b) How many children have no partner? Is 17 odd or even?

17 children
One dot is one child. There are 17 dots.
Draw one dot for each child. There are 17 dots.
step 1 of 4

An even number of objects can all be put in pairs. An odd number has one object left over. Draw the children as dots and ring them in twos.

  1. Draw one dot for each child. There are 17 dots.
  2. Ring the dots in twos. Count in twos as you ring: 2, 4, 6, 8, 10, 12, 14, 16.
  3. (a) There are 8 rings, so the children make 8 pairs. The pairs use 16 children.
  4. (b) 17 − 16 = 1, so 1 child has no partner. A number with one left over after pairing is odd, so 17 is odd.

answer(a) 8 pairs; (b) 1 child, so 17 is odd

techniqueOdd and Even Numbers · Skip Counting

examsPSLE

Common pitfalls

  • Looking at the tens digit to decide. The ones digit decides whether a number is odd or even. The ones digit of 17 is 7, and 7 is odd, so 17 is odd.
  • Saying there are 9 pairs. The ninth ring would have only 1 child in it, and a pair needs 2 children.
05

House Numbers on One Side of a Street

strategyCount On in Twos / Count the Houses as You Go

The houses on one side of a street have odd numbers. The first house is number 21. The numbers go up in twos. (a) What is the number of the fifth house? (b) Ravi lives at number 35. Which house in the row is his?

211st2nd3rd4th5thEach next house is 2 more
The first house is number 21. Each next house is 2 more.
Draw a row of houses. Write 21 on the first house. Each next house is 2 more.
step 1 of 5

Each house number is 2 more than the one before it. Draw the row of houses and count on in twos, keeping count of the houses.

  1. Draw a row of houses. Write 21 on the first house. Each next house is 2 more.
  2. Count on in twos to the fifth house: 21, 23, 25, 27, 29.
  3. (a) The fifth house is number 29.
  4. Keep counting in twos until you reach 35: 31, 33, 35. These are the sixth, seventh and eighth houses.
  5. (b) Number 35 is the eighth house in the row. Every number in the row is odd, because 2 more than an odd number is odd again.

answer(a) number 29; (b) the 8th house

techniqueSkip Counting · Odd and Even Numbers

examsPSLE

Common pitfalls

  • Adding five twos to 21 to get 31. The first house is already number 21, so the fifth house is only 4 steps of 2 away: 21 + 8 = 29.
  • Counting on in ones: 21, 22, 23. The even numbers are on the other side of the street, so this side goes up in twos.
06

A Number in Words with an Empty Place

strategyPlace-Value Chart / Write a Zero in the Empty Place

Tom's ticket says four hundred and six. Ben's ticket says 640. (a) Write the number on Tom's ticket in digits. (b) Write the number on Ben's ticket in words.

four hundred and sixHundredsTensOnes46
Four hundred is 4 in the hundreds place. Six is 6 in the ones place.
Draw a chart with three places: hundreds, tens and ones. Four hundred goes in the hundreds place as 4. Six goes in the ones place as 6.
step 1 of 5

A three-digit number has a hundreds place, a tens place and a ones place. When the words leave a place out, that place still needs the digit 0.

  1. Draw a chart with three places: hundreds, tens and ones. Four hundred goes in the hundreds place as 4. Six goes in the ones place as 6.
  2. The words say nothing about tens, so there are 0 tens. Write 0 in the tens place. The 0 keeps the 4 in the hundreds place.
  3. (a) The number on Tom's ticket is 406.
  4. Now put 640 in the chart: 6 hundreds, 4 tens and 0 ones. Say the hundreds first and then the tens.
  5. (b) 6 hundreds is six hundred and 4 tens is forty. There are no ones to say. The number on Ben's ticket is six hundred and forty.

answer(a) 406; (b) six hundred and forty

techniqueNumber Words to a Thousand · Hundreds

examsPSLE · GCSE Higher

Common pitfalls

  • Writing 46 for four hundred and six. Without the 0, the 4 moves into the tens place and the number becomes forty-six.
  • Writing 4006. Four hundred and six is 400 + 6, which has only three places. It is not 400 with a 6 written after it.
07

Three Numbers Put in Order

strategyCompare the Hundreds First / Then the Tens, Then the Ones

Three children count their stickers. Amy has 253, Bala has 235 and Chen has 325. (a) Who has the most stickers? (b) Write the three numbers in order. Begin with the smallest.

HundredsTensOnesAmy253Bala235Chen325
The three numbers are in a chart, so the hundreds, the tens and the ones line up.
Write the numbers one under another in a chart, so that the hundreds, the tens and the ones line up.
step 1 of 5

A hundred is worth more than any number of tens and ones in a three-digit number, so the hundreds are compared first. The tens are compared only when the hundreds are the same.

  1. Write the numbers one under another in a chart, so that the hundreds, the tens and the ones line up.
  2. Look at the hundreds first. 325 has 3 hundreds. The other two numbers have only 2 hundreds.
  3. (a) 325 is the greatest number, so Chen has the most stickers.
  4. 253 and 235 have the same hundreds, so look at the tens. 5 tens is more than 3 tens, so 253 is greater than 235.
  5. (b) In order from the smallest, the numbers are 235, 253, 325.

answer(a) Chen, with 325 stickers; (b) 235, 253, 325

techniqueOrdering Numbers · Hundreds

examsPSLE

Common pitfalls

  • Looking at the ones first and saying that 235 is greater than 253 because 5 is more than 3. The ones are worth the least, so they are compared last.
  • Writing the order as 325, 253, 235. The question says to begin with the smallest, so 235 comes first and 325 comes last.
08

A Mystery Number from Clues

strategyList Every Number That Fits the First Clues / Test the Last Clue on the List

Lina thinks of a number. It is less than 100. It has 5 tens. (a) How many numbers fit these two clues? (b) The ones digit of her number is 2 more than its tens digit. What is Lina's number?

Tens5Ones?
The number is less than 100 and has 5 tens, so it has two digits and its tens digit is 5.
A number less than 100 that has 5 tens is a two-digit number. Its tens digit is 5.
step 1 of 5

Each clue tells something about one digit. Write the numbers that fit the first clues, then use the last clue to choose one of them.

  1. A number less than 100 that has 5 tens is a two-digit number. Its tens digit is 5.
  2. List the numbers with 5 tens: 50, 51, 52, 53, 54, 55, 56, 57, 58, 59.
  3. (a) The ones digit can be any digit from 0 to 9, so 10 numbers fit the two clues.
  4. The ones digit is 2 more than the tens digit, so the ones digit is 5 + 2 = 7.
  5. (b) Lina's number is 57. Check: 57 is less than 100, it has 5 tens, and 7 is 2 more than 5.

answer(a) 10 numbers; (b) 57

techniqueTens and Ones · Ordering Numbers

examsPSLE · GCSE Higher

Common pitfalls

  • Writing 75. That number has 7 tens and 5 ones, so it does not fit the clue that the number has 5 tens.
  • Writing 52. The clue does not say that the ones digit is 2. It says that the ones digit is 2 more than the tens digit, which is 5 + 2 = 7.
09

Ten More, Ten Less and a Hundred More

strategyMove One Row on the Hundred Chart / Only One Digit Changes

Devi puts a counter on 64 on a hundred chart. Each row of the chart has ten numbers. (a) What number is just below 64, and what number is just above it? (b) What number is 100 more than 64?

51525354555657585960616263656667686970717273747576777879806464 is in the row from 61 to 70
Here are three rows of the hundred chart. 64 is in the row that goes from 61 to 70.
Find 64 on the chart. It is in the row that goes from 61 to 70.
step 1 of 5

Each row of a hundred chart has ten numbers, so moving down one row adds 10 and moving up one row takes away 10. Only the tens digit changes. Adding 100 changes only the hundreds digit.

  1. Find 64 on the chart. It is in the row that goes from 61 to 70.
  2. One row down is 10 more. The tens digit goes up by 1 and the ones digit stays the same: 64 + 10 = 74.
  3. One row up is 10 less. The tens digit goes down by 1: 64 − 10 = 54.
  4. (a) The number just below 64 is 74, and the number just above it is 54.
  5. (b) 100 more is 1 more hundred. The tens and the ones stay the same: 64 + 100 = 164.

answer(a) 74 is below and 54 is above; (b) 164

techniqueCounting to a Hundred · Hundreds · Tens and Ones

examsPSLE · GCSE Higher

Common pitfalls

  • Saying that the number below 64 is 65. The number 65 is next to 64 in the same row, which is 1 more. One row down is 10 more.
  • Writing 1064 for 100 more than 64. One more hundred puts a 1 in the hundreds place, so the number is 1 hundred, 6 tens and 4 ones, which is 164.
10

Two Numbers Made from the Same Two Digits

strategyCompare the Tens First / Count On to Find the Difference

Sam has 52 marbles. Tim has 25 marbles. Both numbers are made from the digits 5 and 2. (a) Who has more marbles? (b) How many more marbles does he have?

Sam= 52Tim= 25
52 is 5 tens and 2 ones. 25 is 2 tens and 5 ones.
Show each number as tens and ones. 52 is 5 tens and 2 ones. 25 is 2 tens and 5 ones.
step 1 of 5

The same digit has a different value in a different place. Show each number as tens and ones, compare the tens, and then count on from the smaller number to the greater one.

  1. Show each number as tens and ones. 52 is 5 tens and 2 ones. 25 is 2 tens and 5 ones.
  2. (a) Compare the tens first. 5 tens is more than 2 tens, so 52 is greater than 25. Sam has more marbles.
  3. To find how many more, count on from 25 to 52. First go to the next ten: 25 + 5 = 30.
  4. Then go from 30 to 50, which is 20 more, and from 50 to 52, which is 2 more.
  5. (b) 5 + 20 + 2 = 27. Sam has 27 more marbles than Tim. Check: 25 + 27 = 52.

answer(a) Sam, with 52 marbles; (b) 27 more marbles

techniqueOrdering Numbers · Tens and Ones

examsPSLE

Common pitfalls

  • Saying that the two boys have the same number because the digits are the same. The place of a digit gives its value: the 5 in 52 is worth 50, and the 5 in 25 is worth only 5.
  • Saying that Tim has more because 25 ends in the bigger digit. The tens are compared first, and 5 tens is more than 2 tens.
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