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Primary Maths · Year 3Chapter 1 · Place value to 1000
Year 3 · Chapter 1

Place value to 1000

By the end of this chapter you will be able to

  • Say how many hundreds, tens and ones are in a three-digit number, and the value of each digit
  • Read and write numbers up to 1000 in numerals and in words
  • Count on and back in steps of 4, 8, 50 and 100
  • Find 10 more, 10 less, 100 more and 100 less than a number
  • Compare and order numbers up to 1000 using the signs <, > and =
  • Place numbers on a number line and solve problems using place value

You should already know

  • Numbers to 100, and tens and ones (Year 2, Chapter 1)
  • Counting in steps of 2, 3, 5 and tens (Year 2, Chapter 1)
  • Comparing and ordering numbers to 100 (Year 2, Chapter 1)

Where this leads

  • Adding and subtracting numbers with up to three digits (Year 3, Chapter 2)
  • Multiplying and dividing with the 3, 4 and 8 times tables (Year 3, Chapter 3)

National Curriculum for England, Key Stage 2 mathematics, Year 3. Content: Count from 0 in multiples of 4, 8, 50 and 100; find 10 or 100 more or less than a given number, Recognise the place value of each digit in a three-digit number (hundreds, tens, ones), Compare and order numbers up to 1000, Identify, represent and estimate numbers using different representations, Read and write numbers up to 1000 in numerals and in words, Solve number problems and practical problems involving these ideas.

Exercise P  Do you remember?

Non-calculator
1
FCount on in twos from 14. Say the next three numbers.
1012141618202224start
2
FHow many tens and ones are in 47?
47
3
FWhat is 10 more than 58?
4
FWhich is greater, 73 or 37? Write the greater number.
5
FWrite forty-five as a numeral.
1.1

Hundreds, tens and ones

Year 3
Recognise the place value of each digit in a three-digit number (hundreds, tens, ones)
Video lesson: Hundreds, tens and onesComing soon
Noah has a box of wooden blocks. He builds numbers with three kinds of block. The big flat squares are hundreds, the long bars are tens and the small cubes are ones.

A three-digit number has three places: hundreds, tens and ones.

A hundred is a big flat square. It is made from ten tens. A ten is a long bar, made from ten ones. A one is a single cube.

Noah builds the number 384. He uses 3 flats, 8 bars and 4 cubes.

384
The number 384: 3 hundreds, 8 tens and 4 ones.
HundredsTensOnes
384
The same number in a place-value table. Each digit sits in its own place.

Key ideas

  • The hundreds digit is on the left. It tells us the hundreds.
  • The tens digit is in the middle. It tells us the tens.
  • The ones digit is on the right. It tells us the ones.
  • A zero in a place means there are none of that place.
Worked example 1.1.1
Look at Noah's blocks. How many hundreds, tens and ones are in 384?384

Key words. A digit is one of the figures 0 to 9. The place of a digit tells us what it is worth. In a three-digit number the places are hundreds, tens and ones.

Method. Count the flats, then the bars, then the cubes, and add them.

  1. Count the flats. Each flat is one hundred.
    3 flats = 300
  2. Count the bars. Each bar is ten ones.
    8 bars = 80
  3. Count the single cubes. Each cube is one.
    4 cubes = 4
  4. Add the parts. Put the parts together.
    300 + 80 + 4 = 384
  5. Write the answer.
    384

Check. 3 hundreds, 8 tens and 4 ones make 384. ✓

Watch out. Count each block once. Do not count a bar as ten separate cubes as well.

Worked example 1.1.2
What is the value of the 6 in 362?
HundredsTensOnes
362

Key words. A digit is one of the figures 0 to 9. The place of a digit tells us what it is worth. In a three-digit number the places are hundreds, tens and ones.

Method. The value of a digit depends on its place.

  1. Find the digit in the tens place. Look at that place in the number.
    362: the digit is 6
  2. Work out its value. Each ten is worth 10.
    6 × 10 = 60
  3. Write the answer. The value is the digit times the place, not just the digit.
    60

Check. 300 + 60 + 2 = 362, so the tens part is 60. ✓

Watch out. The digit is 6, but its value is 60.

Worked example 1.1.3
Write 504 as hundreds, tens and ones.
HundredsTensOnes
504

Key words. A digit is one of the figures 0 to 9. The place of a digit tells us what it is worth. In a three-digit number the places are hundreds, tens and ones.

Method. Write each place, using 0 for an empty place.

  1. Find the hundreds. The first digit is in the hundreds place.
    5 hundreds
  2. Find the tens. The middle digit is 0, so there are no tens.
    0 tens
  3. Find the ones. The last digit is in the ones place.
    4 ones
  4. Write the answer. The zero still counts as a place.
    5 hundreds, 0 tens and 4 ones

Check. 500 + 0 + 4 = 504. ✓

Watch out. A zero is a place with nothing in it. Do not skip it.

Watch out

Watch out: a zero still takes up a place. 504 has no tens, so it is not 54, and it is not 5 hundreds and 4 tens.

Exercise 1A  Hundreds, tens and ones

Non-calculator
1
FHow many flats (hundreds) are there in 415? Look at the hundreds digit.
415
2
FWhat digit is in the tens place of 260?
HundredsTensOnes
260
3
FWhat digit is in the ones place of 739?
HundredsTensOnes
739
4
FWhat is the value of the 7 in 782?
HundredsTensOnes
782
5
FWhat is the value of the 2 in 129?
HundredsTensOnes
129
6
FLook at the picture. Write the number that it shows.
639
7
FWrite the number that has 4 hundreds, 0 tens and 7 ones.
8
PSSplit 563 into hundreds, tens and ones. Write it as an addition.
9
PSPriya has 2 hundreds, 5 tens and 1 one. How many does she have altogether?
251
10
RTom says 370 has 3 tens and 7 hundreds. Is he right? Explain your answer.
11
RUse the digits 4, 7 and 2 once each to make the biggest three-digit number.
1.2

Reading and writing numbers to 1000

Year 3
Read and write numbers up to 1000 in numerals and in words
Video lesson: Reading and writing numbers to 1000Coming soon
Ruby finds a ticket for the school play. It says "three hundred and six". She wants to write the number using digits. Numbers can be written as numerals or as words.

A numeral uses digits, like 306. A number word uses words, like three hundred and six.

Say the hundreds first. Then say and. Then say the tens and ones.

For example, 352 is three hundred and fifty-two. Put a hyphen between fifty and two.

If there are no tens and no ones, do not say "and". 300 is three hundred.

One thousand is 1000. It is ten hundreds.

NumeralIn words
306three hundred and six
352three hundred and fifty-two
300three hundred
1000one thousand
Numerals and the same numbers in words.

Key ideas

  • Say the hundreds, then "and", then the tens and ones.
  • Put a hyphen between the tens and ones: forty-two.
  • If there are no tens or ones, do not say "and".
  • A zero in the tens place still counts: 405 is four hundred and five.
Worked example 1.2.1
Write 286 in words.
HundredsTensOnes
286

Key words. A numeral is a number written with digits, such as 352. A number word is a number written in words, such as three hundred and fifty-two.

Method. Say the hundreds, then "and", then the tens and ones.

  1. Say the hundreds. The first digit tells us the hundreds.
    2 hundreds = two hundred
  2. Say the tens and ones. Read the last two digits together.
    8 tens and 6 ones = eighty-six
  3. Join them with "and". UK English puts "and" between the hundreds and the tens and ones.
    two hundred and eighty-six
  4. Write the answer.
    two hundred and eighty-six

Check. Read the words back: two hundred and eighty-six is 286. ✓

Watch out. Put "and" after the hundreds. Do not write "and" if there are no tens or ones.

Worked example 1.2.2
Write four hundred and five in numerals.

Key words. A numeral is a number written with digits, such as 352. A number word is a number written in words, such as three hundred and fifty-two.

Method. Write the hundreds first, then the tens, then the ones.

  1. Find the hundreds word. The word before "hundred" gives the hundreds digit.
    four hundred → 4 hundreds = 400
  2. Find the tens and ones. The words after "and" are the last two digits.
    five → 5
  3. Put the digits in order. Write the hundreds, then the tens, then the ones. Use 0 for an empty place.
    4 0 5 → 405
  4. Write the answer.
    405

Check. 400 + 5 = 405, so the digits are right. ✓

Watch out. A zero in the tens place is still a digit. Do not leave the place out.

Worked example 1.2.3
How many hundreds make 1000? Count on in hundreds to find out.

Key words. A numeral is a number written with digits, such as 352. A number word is a number written in words, such as three hundred and fifty-two.

Method. Count on in hundreds until you reach 1000, and count how many numbers you said.

  1. Count on in hundreds from 0. Each step is one hundred.
    100, 200, 300, 400, 500, 600, 700, 800, 900, 1000
  2. Count how many numbers you said. Each number is one hundred more than the one before.
    10 numbers
  3. Write the answer. Ten hundreds make one thousand.
    10

Check. 10 × 100 = 1000. ✓

Watch out. Count the numbers carefully. Do not count 0 as one of the hundreds.

Watch out

Watch out: "one hundred and five" is 105. Do not write it as 1005, and do not write it as 150.

Exercise 1B  Reading and writing numbers to 1000

Non-calculator
1
FWrite 258 in words.
HundredsTensOnes
258
2
FWrite "seven hundred and six" in numerals.
3
FWrite 900 in words.
4
FWrite "three hundred and seventy" in numerals.
5
FWrite 1000 in words.
6
FWrite each number in words.
(a)117
(b)240
(c)602
7
FWrite each number in numerals.
(a)"three hundred and nine"
(b)"eight hundred and forty"
(c)"five hundred"
8
PSMia writes the number of her stickers in words: "three hundred and one". Write the number of stickers in numerals.
9
PSWrite in words the number that has 8 hundreds, 0 tens and 3 ones.
10
RTom says that "two hundred and forty" is written as 204. Is he right? Explain.
11
RWrite "three hundred and fifty" in numerals. Is it the same as "three hundred and five"? Explain.
1.3

Counting in steps of 4, 8, 50 and 100

Year 3
Count from 0 in multiples of 4, 8, 50 and 100
Video lesson: Counting in steps of 4, 8, 50 and 100Coming soon
Mei is packing cups into boxes. Each box holds four cups, so she counts the cups in fours. Her friend Leo counts tins on a shelf in eights.

When we count in steps, we jump by the same amount each time.

Counting in fours goes 4, 8, 12, 16, 20.

Counting in eights goes 8, 16, 24, 32, 40.

Counting in fifties goes 50, 100, 150, 200.

Counting in hundreds goes 100, 200, 300, 400.

We can count back too. Take the step away each time.

010020030040050150250350
Counting in fifties from 0. Each jump is 50.

Key ideas

  • Keep the step the same every time.
  • Counting in fours: 4, 8, 12, 16, 20, 24.
  • Counting in eights: 8, 16, 24, 32, 40, 48.
  • Counting in fifties and hundreds changes the tens and hundreds.
Worked example 1.3.1
Count in fours from 0. Say the first six numbers.

Key words. A count in steps jumps by the same amount each time. The numbers we say are multiples of the step: 8, 16 and 24 are multiples of 8.

Method. Count on in steps of 4.

  1. Start at the number we are counting from. We start at 0.
    0
  2. Add 4 to find the next number. The step is always 4.
    0 + 4 = 4
  3. Add 4 to find the next number. The step is always 4.
    4 + 4 = 8
  4. Add 4 to find the next number. The step is always 4.
    8 + 4 = 12
  5. Add 4 to find the next number. The step is always 4.
    12 + 4 = 16
  6. Add 4 to find the next number. The step is always 4.
    16 + 4 = 20
  7. Add 4 to find the next number. The step is always 4.
    20 + 4 = 24
  8. Write the answer. Say the numbers in order.
    4, 8, 12, 16, 20, 24

Check. 0 + 6 × 4 = 24. ✓

Watch out. Keep the step the same every time. Each number is one step from the number before it.

Worked example 1.3.2
Count on in fifties from 150. Say the next three numbers.

Key words. A count in steps jumps by the same amount each time. The numbers we say are multiples of the step: 8, 16 and 24 are multiples of 8.

Method. Count on in steps of 50.

  1. Start at the number we are counting from. We start at 150.
    150
  2. Add 50 to find the next number. The step is always 50.
    150 + 50 = 200
  3. Add 50 to find the next number. The step is always 50.
    200 + 50 = 250
  4. Add 50 to find the next number. The step is always 50.
    250 + 50 = 300
  5. Write the answer. Say the numbers in order.
    200, 250, 300

Check. 150 + 3 × 50 = 300. ✓

Watch out. Keep the step the same every time. Each number is one step from the number before it.

Worked example 1.3.3
Count back in eights from 80. Say the next three numbers.

Key words. A count in steps jumps by the same amount each time. The numbers we say are multiples of the step: 8, 16 and 24 are multiples of 8.

Method. Count back in steps of 8.

  1. Start at the number we are counting from. We start at 80.
    80
  2. Take 8 away to find the next number. The step is always 8.
    80 − 8 = 72
  3. Take 8 away to find the next number. The step is always 8.
    72 − 8 = 64
  4. Take 8 away to find the next number. The step is always 8.
    64 − 8 = 56
  5. Write the answer. Say the numbers in order.
    72, 64, 56

Check. 80 − 3 × 8 = 56. ✓

Watch out. Keep the step the same every time. Each number is one step from the number before it.

Watch out

Watch out: the step must stay the same. In eights, 8, 16, 24 is right, but 8, 16, 26 is wrong.

Exercise 1C  Counting in steps of 4, 8, 50 and 100

Non-calculator
1
FCount in fours from 0. Say the first five numbers.
2
FCount in eights from 0. Say the first five numbers.
3
FFill in the missing numbers in each count.
(a)4, 8, __, 16
(b)24, __, 32, 36
(c)40, 48, __, 64
4
FCount on in fifties from 100. Say the next four numbers.
5
FCount on in hundreds from 200. Say the next five numbers.
6
FCount back in fifties from 500. Say the next three numbers.
7
FCount back in fours from 40. Say the next four numbers.
8
RIs 36 in the count in eights from 0? Explain how you know.
9
PSMei packs cups in boxes of 8. She has 5 boxes. How many cups does she have?
10
PSA shop sells pens in packs of 4. Priya buys 6 packs. How many pens does she get?
04812162024?
11
RWhich number greater than 0 and up to 150 is in both the count in fours and the count in fifties?
1.4

10 more, 10 less, 100 more and 100 less

Year 3
Find 10 or 100 more or less than a given number
Video lesson: 10 more, 10 less, 100 more and 100 lessComing soon
Priya has 340 stickers in her book. Her friend gives her 100 more stickers. Then Priya gives 10 stickers to her brother.

When you add or take away 10, only the tens digit changes. The hundreds and ones stay the same.

When you add or take away 100, only the hundreds digit changes. The tens and ones stay the same.

Sometimes a change crosses a hundred. Then the tens digit goes past 9, and the hundreds digit changes too.

NumberHundredsTensOnes
340340
440440
340 plus 100 makes 440. Only the hundreds digit changed.

Key ideas

  • 10 more or less: change the tens digit.
  • 100 more or less: change the hundreds digit.
  • The other digits stay the same.
  • If the tens digit is 0 and you take 10 away, exchange 1 hundred for 10 tens.
Worked example 1.4.1
What is 10 more than 348?
HundredsTensOnes
348

Key words. More means add. Less means take away. When you change a number by 10 or 100, the number changes in one place value.

Method. 10 more changes the tens place, and the other places stay the same.

  1. Write the number in place-value columns. Hundreds, tens and ones.
    3 hundreds, 4 tens, 8 ones
  2. Change the tens digit. 10 more changes the tens place.
    4 tens + 1 ten = 5 tens
  3. Keep the other places the same. Only the place that changed moves.
    3 hundreds, 5 tens, 8 ones
  4. Write the answer.
    358

Check. 358 − 10 = 348. ✓

Watch out. Only change the place that is named. Watch for a change that crosses a hundred.

Worked example 1.4.2
What is 100 less than 720?
HundredsTensOnes
720

Key words. More means add. Less means take away. When you change a number by 10 or 100, the number changes in one place value.

Method. 100 less changes the hundreds place, and the other places stay the same.

  1. Write the number in place-value columns. Hundreds, tens and ones.
    7 hundreds, 2 tens, 0 ones
  2. Change the hundreds digit. 100 less changes the hundreds place.
    7 hundreds − 1 hundred = 6 hundreds
  3. Keep the other places the same. Only the place that changed moves.
    6 hundreds, 2 tens, 0 ones
  4. Write the answer.
    620

Check. 620 + 100 = 720. ✓

Watch out. Only change the place that is named. Watch for a change that crosses a hundred.

Worked example 1.4.3
What is 10 less than 500?
HundredsTensOnes
500

Key words. More means add. Less means take away. When you change a number by 10 or 100, the number changes in one place value.

Method. 10 less changes the tens place, and the other places stay the same.

  1. Write the number in place-value columns. Hundreds, tens and ones.
    5 hundreds, 0 tens, 0 ones
  2. Change the tens digit. 10 less changes the tens place.
    0 tens − 1 ten: exchange 1 hundred for 10 tens, then 10 tens − 1 ten = 9 tens
  3. Keep the other places the same. Only the place that changed moves.
    4 hundreds, 9 tens, 0 ones
  4. Write the answer.
    490

Check. 490 + 10 = 500. ✓

Watch out. Only change the place that is named. Watch for a change that crosses a hundred.

Watch out

Watch out: 195 + 10 is 205, not 105. The 9 tens become 0 tens, and 1 more hundred is made.

Exercise 1D  10 more, 10 less, 100 more and 100 less

Non-calculator
1
FWhat is 10 more than 417?
HundredsTensOnes
417
2
FWhat is 10 less than 263?
3
FWhat is 100 more than 286?
4
FWhat is 100 less than 650?
5
FWhat is 10 more than 298?
6
FWhat is 10 less than 300?
7
FWork out each answer.
(a)10 more than 340
(b)100 less than 340
(c)10 less than 340
(d)100 more than 340
8
FFind the missing number in each sentence.
(a)10 more than __ is 380
(b)100 less than __ is 300
9
PSPriya has 340 stickers. Her friend gives her 100 more. Then she gives 10 stickers to her brother. How many does she have now?
10
PSA school library has 480 books. Ten more books arrive each week for three weeks. How many books are there after three weeks?
11
RRavi says that 10 more than 195 is 105. Is he right? Explain.
1.5

Comparing and ordering numbers

Year 3
Compare and order numbers up to 1000
Video lesson: Comparing and ordering numbersComing soon
Jack and Zainab each collect bags of beads. Jack has 245 beads. Zainab has 254 beads. Who has more beads?

We compare numbers place by place. First compare the hundreds. If the hundreds are the same, compare the tens. If the tens are the same, compare the ones.

We use three signs: > means greater than, < means less than, and = means equal to.

Jack has 245 and Zainab has 254. The hundreds are the same. The tens are 4 and 5. Five tens is more than four tens, so 254 is greater than 245.

NumberHundredsTensOnes
245245
254254
The two numbers in place-value columns. Compare the tens digits.

Key ideas

  • Compare the hundreds first, then the tens, then the ones.
  • The wide end of the sign faces the bigger number.
  • To order numbers, put them in size order from the smallest to the largest.
  • A bigger ones digit does not make a bigger number.
Worked example 1.5.1
Jack has 245 beads and Zainab has 254 beads. Fill in the box with <, > or =: 245 [ ] 254

Key words. > means greater than. < means less than. = means equal to. The wide end of the sign faces the bigger number.

Method. Compare the hundreds first, then the tens, then the ones.

  1. Compare the hundreds digits. Start on the left. The bigger hundreds digit gives the bigger number.
    245 has 2 hundreds, 254 has 2 hundreds
  2. The hundreds are the same, so compare the tens. Look at the middle digit next.
    4 tens and 5 tens
  3. Choose the sign. The wide end of the sign faces the bigger number.
    245 < 254
  4. Write the answer.
    <

Check. 254 is the bigger number, so the sign points to it. ✓

Watch out. Do not compare the ones first. Start with the hundreds.

Worked example 1.5.2
Which is greater, 698 or 701?
NumberHundredsTensOnes
698698
701701

Key words. > means greater than. < means less than. = means equal to. The wide end of the sign faces the bigger number.

Method. Compare the hundreds first, then the tens, then the ones.

  1. Compare the hundreds digits. Start on the left. The bigger hundreds digit gives the bigger number.
    698 has 6 hundreds, 701 has 7 hundreds
  2. Choose the greater number. The number with the bigger place values is greater.
    701 is greater
  3. Write the answer.
    701

Check. 701 is the bigger number, so the sign points to it. ✓

Watch out. Do not compare the ones first. Start with the hundreds.

Worked example 1.5.3
Put 412, 124 and 421 in order from smallest to largest.
NumberHundredsTensOnes
412412
124124
421421

Key words. > means greater than. < means less than. = means equal to. The wide end of the sign faces the bigger number.

Method. Compare the hundreds, then the tens, then the ones.

  1. Look at the hundreds digit of each number. The hundreds digit gives the first clue.
    412 has 4 hundreds, 124 has 1 hundreds, 421 has 4 hundreds
  2. Put the numbers in order. If two hundreds digits are the same, compare the tens. Then compare the ones.
    124 → 412 → 421
  3. Write the answer. The numbers go from smallest to largest.
    124, 412, 421

Check. The first number is the smallest, and the last is the largest. ✓

Watch out. Compare the tens and ones only when the hundreds are the same.

Watch out

Watch out: 352 is bigger than 349. Compare the tens first: 5 tens is more than 4 tens, even though 9 is more than 2.

Exercise 1E  Comparing and ordering numbers

Non-calculator
1
FFill in the box with <, > or =: 380 [ ] 308
2
FFill in the box with <, > or =: 415 [ ] 415
3
FFill in the box with <, > or =: 527 [ ] 572
4
FFill in the box with <, > or =: 600 [ ] 599
5
FFill in each box with <, > or =.
(a)234 [ ] 243
(b)709 [ ] 690
(c)186 [ ] 186
6
FWhich is greater: 614 or 641?
7
FWhich is the largest number: 207, 270 or 702?
8
FPut these numbers in order from smallest to largest: 503, 530, 305, 350.
9
PSRavi says 349 is bigger than 352, because 9 is bigger than 2. Is he right? Explain.
10
PSMei has three bags of beads. Bag A has 286 beads, Bag B has 268 beads and Bag C has 306 beads. Which bag has the most beads?
11
RUse the digits 3, 5 and 8 once each to make the largest and the smallest three-digit numbers. What is the difference between them?
1.6

Number lines and solving problems

Year 3
Identify, represent and estimate numbers on a number line, Solve number problems and practical problems
Video lesson: Number lines and solving problemsComing soon
Aisha is drawing a number line for a bus route. The marks go up in steps of 10. She needs to place the number 370 on the line.

A number line shows numbers in order. The numbers get bigger to the right.

To place a number, first find the two marks that it is between. Then count the steps from a mark you know. Work out how much one step is worth.

On this line, the marks are 10 apart. From 300 the arrow is 7 steps on. Each step is 10, so the arrow is at 370.

300350400?
A number line from 300 to 400. Each small step is 10.

Key ideas

  • Find the two marks that the number is between.
  • Work out how much one step is worth.
  • Count the steps from a mark you know.
  • A number halfway between two marks is in the middle of them.
Worked example 1.6.1
What number is the arrow pointing to? The marks go up in tens from 300 to 400.300350400?

Key words. On a number line the numbers get bigger as you move to the right. An estimate is a sensible guess that is close to the true value.

Method. Count the steps from a mark you know, then work out the value.

  1. Find the two marks the arrow is between. The marks go up by 10.
    300 and 310 are the first two marks
  2. Count the steps from the start mark. Each step is 10.
    370 is 7 steps from 300
  3. Work out the value. Multiply the steps by the step size, then add the start.
    300 + 7 × 10 = 370
  4. Write the answer.
    370

Check. 7 steps of 10 from 300 is 370. ✓

Watch out. Check that the value is between the two marks on either side of it.

Worked example 1.6.2
The arrow is at 620 on a line from 0 to 1000 with a mark every 100. Which two hundreds is it between?01002003004005006007008009001000?

Key words. On a number line the numbers get bigger as you move to the right. An estimate is a sensible guess that is close to the true value.

Method. Find the two hundreds marks, then check where 620 sits between them.

  1. Find the two hundreds marks. The marks are 100 apart, so the hundreds are 600 and 700.
    600 and 700
  2. Check where 620 sits. 620 is more than 600 and less than 700.
    600 is less than 620, and 620 is less than 700
  3. Write the answer. It is 20 past 600, so it sits just after the 600 mark.
    600 and 700

Check. 600 + 100 = 700. ✓

Watch out. The arrow is near 600, not near 700.

Worked example 1.6.3
Jack has 245 stickers. Zainab has 100 more stickers than Jack. How many stickers does Zainab have? Use the bar model.Jack: 245+ 100Zainab: 345

Key words. More means add. Less means take away. When you change a number by 10 or 100, the number changes in one place value.

Method. Start with Jack's number, then add the extra 100.

  1. Read Jack's number. Jack has 245 stickers.
    245
  2. Find the extra stickers. Zainab has 100 more than Jack.
    100 more
  3. Add them. Add the extra 100 to Jack's number.
    245 + 100 = 345
  4. Write the answer.
    345

Check. 345 − 100 = 245. ✓

Watch out. The extra 100 changes the hundreds digit only.

Watch out

Watch out: the marks may be 10 apart, 50 apart or 100 apart. Check the step size before you count.

Exercise 1F  Number lines and solving problems

Non-calculator
1
FWhat number is the arrow pointing to? The marks go up in tens.500550600?
2
FWhat number is the arrow pointing to? The marks go up in twenties.200220240260280300?
3
FThe arrow is halfway between 700 and 800. What number is it?700750800?
4
FOn a line from 0 to 1000 with a mark every 100, where does 450 go? Which two marks is it between?01002003004005006007008009001000?
5
FThe number line goes from 600 to 700 in steps of 10. Write the number at each arrow.600650700AB
(a)Arrow A
(b)Arrow B
6
PSOn a number line, which number is nearer to 500: 430 or 580?
7
FThe numbers go up in tens from 320. The arrow is 5 tens past 320. What number is the arrow pointing to?320340360380400420?
8
PSMia has 4 bags with 100 beads in each bag, and 27 loose beads. How many beads does she have altogether?
427
9
PSA shop has 580 apples. It sells 10 apples. Then 100 more apples arrive. How many apples are there now?
10
PSA hall has 400 seats in all. 150 of them are in the balcony. How many seats are on the ground floor? Use the bar model.
150?400 seats in all
11
RRavi says "1 hundred and 3 tens" is 103. Ava says it is 130. Who is right? Explain.

Chapter summary

SkillMethod
Hundreds, tens and onesThe first digit is the hundreds, the middle digit is the tens and the last digit is the ones.
Value of a digitMultiply the digit by its place: a 6 in the tens place is worth 6 × 10 = 60.
Numerals and wordsSay the hundreds, then "and", then the tens and ones. Leave out "and" when there are no tens or ones.
Counting in stepsKeep the step the same. Use 4, 8, 50 or 100 each time, and count on or back.
10 or 100 more or lessChange only the tens digit for 10, or only the hundreds digit for 100. Exchange when a place goes past 9 or below 0.
Comparing numbersCompare the hundreds first, then the tens, then the ones. The wide end of the sign faces the bigger number.
Ordering numbersCompare the hundreds, then the tens, then the ones, and put the numbers in order.
Number linesFind the two marks the number is between, work out one step, then count the steps.
ProblemsRead the problem, write the numbers in place-value columns, then add or subtract and check the answer.

Can you…?

  • I can say how many hundreds, tens and ones are in a three-digit number.
  • I can say the value of a digit by its place.
  • I can write numbers up to 1000 in numerals and in words.
  • I can count on and back in steps of 4, 8, 50 and 100.
  • I can find 10 more, 10 less, 100 more and 100 less than a number.
  • I can compare and order numbers up to 1000 using the signs <, > and =.
  • I can place a number on a number line and estimate its position.
  • I can use place value to solve problems about numbers up to 1000.

Key terms

Digit
One of the figures 0 to 9 that make up a number.
Place value
The value of a digit, which depends on its place in the number.
Hundreds
The place for the third digit from the right. A hundred is ten tens.
Tens
The place for the second digit from the right. A ten is ten ones.
Ones
The place for the digit on the right. A one is a single unit.
Numeral
A number written with digits, such as 352.
Number word
A number written in words, such as three hundred and fifty-two.
Multiple
A number that we say when we count in steps of a given size.
Number line
A line with numbers in order, getting bigger to the right.
Estimate
A sensible guess of a value, close to the true answer.
Greater than
A number that is bigger. The sign is >.
Less than
A number that is smaller. The sign is <.

Exercise 1Z  Check-up

Non-calculator
1
How many tens are in 470?
2
What is the value of the 9 in 596?
HundredsTensOnes
596
3
Write 406 in words.
4
Write "nine hundred and twenty" in numerals.
5
Count on in fifties from 200. Say the next three numbers.
6
Count back in fours from 40. Say the next three numbers.
7
What is 100 less than 845?
8
What is 10 more than 699?
9
Fill in the box with <, > or =: 480 [ ] 408
10
Put these numbers in order from smallest to largest: 317, 371, 137, 713.

Total 20 marks. Allow about 20 minutes.

Exercise 1X  Practice test questions

Non-calculator
1
FWhat is the value of the 3 in 436?[1 mark]
2
FWrite 530 in words.[1 mark]
3
FWrite "six hundred and four" in numerals.[1 mark]
4
FCount on in eights from 56. Say the next three numbers.[2 marks]
5
FWhat is 100 less than 540? Show your working.[2 marks]
6
FWrite the missing number in each count.[2 marks]
(a)450, 500, __, 600
(b)120, 110, __, 90
7
FBen says 10 more than 386 is 396. Is he right? Explain.[2 marks]
8
FRavi has three cards: 402, 420 and 240. Write them in order from largest to smallest.[3 marks]
9
FAmira has 3 bags of 100 beads, 4 tens and 6 loose beads. She gives 10 beads to a friend. How many beads does she have now?[3 marks]
10
FLeo says 709 has 7 tens. Is he right? Explain fully, using the place of each digit.[3 marks]
Chapter 2: Adding and subtracting →

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