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Step-by-step practice: Maths · Level 3Chapter 3 · Comparing and ordering to 1000
Level 3 · Chapter 3

Comparing and ordering to 1000

By the end of this chapter you will be able to

  • Compare two numbers with <, > and =
  • Order up to five numbers
  • Find the greatest and least
  • Estimate a position on a number line from 0 to 1000

You should already know

  • Counting to 1000 (chapter 1)
  • Hundreds, tens and ones (chapter 2)

Where this leads

  • Adding within 1000 (chapter 4)

Step-by-step practice: maths (Level 3). Small steps, repeated until fluent. Content: Compare two numbers up to 1000 using <, > and =, Put a set of up to five numbers in order, from smallest to largest and largest to smallest, Find the greatest and least number in a set, Place a number on a 0 to 1000 number line and estimate it between two marked points.

Exercise P  Do you remember?

Non-calculator
1
FWrite <, > or = to make it true: 47 □ 74
2
FPut these numbers in order from smallest to largest: 63, 36, 58
3
FWrite <, > or = to make it true: 81 □ 18
4
FWhich number is the greatest? 27, 72, 53, 35
5
FWrite <, > or = to make it true: 640 □ 604
3.1

Comparing two numbers

Level 3
Compare two numbers up to 1000 using <, > and =
Video lesson: Comparing two numbersComing soon

The sign < means less than. The sign > means greater than. The sign = means equal to.

Compare the hundreds first. If they are the same, compare the tens. If the tens are the same, compare the ones.

Key ideas

  • Hundreds first, then tens, then ones.
  • < is less than, > is greater than.
  • The sign = means both numbers are the same.
Worked example 3.1.1
Write <, > or = to make it true: 408 □ 480

Method. Compare the hundreds first. If they are the same, compare the tens. Then compare the ones.

  1. Start with the hundreds digits. The digit in the largest place decides first.
    4 and 4
  2. The tens decide. 0 is fewer than 8 in the tens place.
    0 and 8
  3. Write the sign. 408 is less than 480.
    <

Check. 408 < 480 is true.

Watch out. Compare from the left. 480 is greater than 408.

Worked example 3.1.2
Write <, > or = to make it true: 625 □ 591

Method. Compare the hundreds first. If they are the same, compare the tens. Then compare the ones.

  1. Start with the hundreds digits. The digit in the largest place decides first.
    6 and 5
  2. The hundreds decide. 6 is more than 5 in the hundreds place.
    6 and 5
  3. Write the sign. 625 is greater than 591.
    >

Check. 625 > 591 is true.

Watch out. Compare from the left. 625 is greater than 591.

Worked example 3.1.3
Write <, > or = to make it true: 357 □ 357

Method. Compare the hundreds first. If they are the same, compare the tens. Then compare the ones.

  1. Start with the hundreds digits. The digit in the largest place decides first.
    3 and 3
  2. All the digits are the same. The numbers are equal.
    357 and 357 are the same
  3. Write the sign. 357 is equal to 357.
    =

Check. 357 = 357 is true.

Watch out. Compare from the left. 357 is greater than 357.

Watch out

Watch out. 480 is greater than 408, because 8 tens is more than 0 tens. Do not compare the ones first.

Exam tip

Grown-up tip. The sign is a little mouth that eats the bigger number. Ask: “Which number is bigger? Point to the open side.”

Exercise 3A  Practice: comparing with <, > and =

Non-calculator
1
FWrite <, > or = to make it true: 761 □ 757
2
FWrite <, > or = to make it true: 818 □ 282
3
FWrite <, > or = to make it true: 600 □ 545
4
FWrite <, > or = to make it true: 380 □ 607
5
FWrite <, > or = to make it true: 804 □ 376
6
FWrite <, > or = to make it true: 675 □ 602
7
FWrite <, > or = to make it true: 526 □ 536
8
FWrite <, > or = to make it true: 426 □ 825
9
FWrite <, > or = to make it true: 555 □ 250
10
FWrite <, > or = to make it true: 310 □ 212
11
FWrite <, > or = to make it true: 213 □ 234
12
FWrite <, > or = to make it true: 990 □ 465
13
FWrite <, > or = to make it true: 884 □ 562
14
FWrite <, > or = to make it true: 393 □ 626
15
FWrite <, > or = to make it true: 578 □ 515
16
FWrite <, > or = to make it true: 953 □ 915
3.2

Putting numbers in order

Level 3
Put a set of up to five numbers in order, from smallest to largest and largest to smallest
Video lesson: Putting numbers in orderComing soon

To put numbers in order, look at the hundreds first. The number with fewer hundreds is smaller.

If two numbers have the same hundreds, look at the tens. Then look at the ones.

Key ideas

  • Order by hundreds, then tens, then ones.
  • Smallest to largest: the smallest number comes first.
  • Largest to smallest: the largest number comes first.
Worked example 3.2.1
Put these numbers in order from smallest to largest: 512, 409, 527, 415

Method. Put the numbers in order, smallest to largest. Compare hundreds first, then tens, then ones.

  1. Compare the hundreds of each number. The number with fewer hundreds is smaller.
    512: 5 hundreds, 409: 4 hundreds, 527: 5 hundreds, 415: 4 hundreds
  2. Find the first number in the order. It is the smallest, or the largest if we go the other way.
    409
  3. Write all the numbers in order. Check each one fits between the ones next to it.
    409, 415, 512, 527

Check. Read the list again. Each number is bigger than the one before it.

Watch out. Compare hundreds first. 508 is less than 521, because 5 hundreds is the same but 0 tens is less than 2 tens.

Worked example 3.2.2
Put these numbers in order from largest to smallest: 640, 604, 46, 460

Method. Put the numbers in order, largest to smallest. Compare hundreds first, then tens, then ones.

  1. Compare the hundreds of each number. The number with fewer hundreds is smaller.
    640: 6 hundreds, 604: 6 hundreds, 46: 0 hundreds, 460: 4 hundreds
  2. Find the first number in the order. It is the smallest, or the largest if we go the other way.
    640
  3. Write all the numbers in order. Check each one fits between the ones next to it.
    640, 604, 460, 46

Check. Read the list again. Each number is smaller than the one before it.

Watch out. Compare hundreds first. 508 is less than 521, because 5 hundreds is the same but 0 tens is less than 2 tens.

Worked example 3.2.3
Put these numbers in order from smallest to largest: 250, 205, 520, 502

Method. Put the numbers in order, smallest to largest. Compare hundreds first, then tens, then ones.

  1. Compare the hundreds of each number. The number with fewer hundreds is smaller.
    250: 2 hundreds, 205: 2 hundreds, 520: 5 hundreds, 502: 5 hundreds
  2. Find the first number in the order. It is the smallest, or the largest if we go the other way.
    205
  3. Write all the numbers in order. Check each one fits between the ones next to it.
    205, 250, 502, 520

Check. Read the list again. Each number is bigger than the one before it.

Watch out. Compare hundreds first. 508 is less than 521, because 5 hundreds is the same but 0 tens is less than 2 tens.

Watch out

Watch out. 46 is less than 460, not greater. Check the number of hundreds, not just the first digit you see.

Exam tip

Grown-up tip. Write each number on a card and move the cards into order. Ask: “Which one comes first?”

Exercise 3B  Practice: putting numbers in order

Non-calculator
1
FPut these numbers in order from smallest to largest: 634, 208, 466, 636, 885
2
FPut these numbers in order from largest to smallest: 904, 161, 197, 157, 120
3
FPut these numbers in order from largest to smallest: 148, 557, 961, 842
4
FPut these numbers in order from largest to smallest: 716, 805, 264, 303
5
FPut these numbers in order from largest to smallest: 914, 604, 201, 774
6
FPut these numbers in order from smallest to largest: 968, 849, 863, 938, 325
7
FPut these numbers in order from smallest to largest: 276, 621, 132, 925, 389
8
FPut these numbers in order from largest to smallest: 941, 532, 176
9
FPut these numbers in order from smallest to largest: 947, 673, 425
10
FPut these numbers in order from largest to smallest: 114, 777, 331, 999, 301
11
FPut these numbers in order from largest to smallest: 845, 864, 164
12
FPut these numbers in order from largest to smallest: 886, 599, 748, 496
13
FPut these numbers in order from smallest to largest: 575, 509, 652, 580
14
FPut these numbers in order from largest to smallest: 314, 200, 195, 461
15
FPut these numbers in order from smallest to largest: 979, 722, 557
16
FPut these numbers in order from largest to smallest: 577, 525, 806
3.3

Greatest and least numbers

Level 3
Find the greatest and least number in a set
Video lesson: Greatest and least numbersComing soon

The greatest number is the one furthest to the right on a number line. The least number is the one furthest to the left.

Compare hundreds first, then tens, then ones, to find them.

Key ideas

  • Greatest: the biggest number.
  • Least: the smallest number.
  • Use hundreds, tens and ones to compare.
Worked example 3.3.1
Which number is the greatest? 731, 713, 371, 137

Method. Find the greatest number by comparing hundreds, then tens, then ones.

  1. Look at the hundreds of each number. For the greatest, look for the most hundreds, then the most tens.
    731, 713, 371, 137
  2. Find the greatest hundreds. Keep only numbers with that many hundreds.
    731, 713
  3. Compare the tens, then the ones, of the numbers left. The one with the most or fewest tens, then ones, is the answer.
    731
  4. Write the answer. This is the greatest number.
    731

Check. Compare 731 with each other number in the list. It is the greatest.

Watch out. Compare hundreds first. The greatest number is not always the first one in the list.

Worked example 3.3.2
Which number is the least? 504, 540, 450, 405

Method. Find the least number by comparing hundreds, then tens, then ones.

  1. Look at the hundreds of each number. For the least, look for the fewest hundreds, then the fewest tens.
    504, 540, 450, 405
  2. Find the least hundreds. Keep only numbers with that many hundreds.
    450, 405
  3. Compare the tens, then the ones, of the numbers left. The one with the most or fewest tens, then ones, is the answer.
    405
  4. Write the answer. This is the least number.
    405

Check. Compare 405 with each other number in the list. It is the least.

Watch out. Compare hundreds first. The least number is not always the first one in the list.

Worked example 3.3.3
Which number is the greatest? 292, 929, 299, 92

Method. Find the greatest number by comparing hundreds, then tens, then ones.

  1. Look at the hundreds of each number. For the greatest, look for the most hundreds, then the most tens.
    292, 929, 299, 92
  2. Find the greatest hundreds. Keep only numbers with that many hundreds.
    929
  3. Compare the tens, then the ones, of the numbers left. The one with the most or fewest tens, then ones, is the answer.
    929
  4. Write the answer. This is the greatest number.
    929

Check. Compare 929 with each other number in the list. It is the greatest.

Watch out. Compare hundreds first. The greatest number is not always the first one in the list.

Watch out

Watch out. 92 is less than 929, even though 92 has a 9 in it. The number of hundreds matters most.

Exam tip

Grown-up tip. Ask the child to say which number has the most hundreds first, before looking at any other digit.

Exercise 3C  Practice: greatest and least

Non-calculator
1
FWhich number is the least? 535, 879, 154, 825
2
FWhich number is the least? 875, 653, 308, 565, 271
3
FWhich number is the greatest? 461, 457, 605, 555, 424
4
FWhich number is the least? 350, 838, 892, 653
5
FWhich number is the greatest? 429, 287, 998, 674, 452
6
FWhich number is the least? 966, 872, 586, 377, 263
7
FWhich number is the greatest? 930, 984, 748
8
FWhich number is the least? 382, 338, 386, 946
9
FWhich number is the least? 305, 646, 209, 330, 914
10
FWhich number is the greatest? 474, 155, 930, 692
11
FWhich number is the least? 767, 912, 336, 558
12
FWhich number is the least? 771, 601, 253, 237, 465
13
FWhich number is the least? 823, 888, 969, 579, 239
14
FWhich number is the greatest? 606, 453, 589, 781
15
FWhich number is the least? 139, 263, 442
16
FWhich number is the least? 145, 126, 873
3.4

Estimating on a number line from 0 to 1000

Level 3
Place a number on a 0 to 1000 number line and estimate it between two marked points
Video lesson: Estimating on a number line from 0 to 1000Coming soon

On a number line from 0 to 1000, the hundreds are marked. A number between two hundreds is about halfway if it ends in 50.

To estimate, round to the nearest hundred. Look at the tens and ones.

01002003004005006007008009001000
A number line from 0 to 1000 with each hundred marked.

Key ideas

  • Count the hundreds marked on the line.
  • Round to the nearest hundred when you estimate.
  • If the tens and ones are 50 or more, the number is nearer to the next hundred.
Worked example 3.4.1
Round 738 to the nearest hundred.

Method. Find the hundreds either side. The nearer one is the answer.

  1. Find the hundreds either side of 738. These are the two hundreds the number is between.
    700 and 800
  2. Find which hundred is nearer. 738 - 700 = 38, and 800 - 738 = 62.
    38 is less than 62
  3. Write the nearest hundred. This is the answer.
    700

Check. 700 is 38 away from 738, and the other hundred is further away.

Watch out. Look at the tens and ones. If they are 50 or more, round up. If less than 50, round down.

Worked example 3.4.2
Round 412 to the nearest hundred.

Method. Find the hundreds either side. The nearer one is the answer.

  1. Find the hundreds either side of 412. These are the two hundreds the number is between.
    400 and 500
  2. Find which hundred is nearer. 412 - 400 = 12, and 500 - 412 = 88.
    12 is less than 88
  3. Write the nearest hundred. This is the answer.
    400

Check. 400 is 12 away from 412, and the other hundred is further away.

Watch out. Look at the tens and ones. If they are 50 or more, round up. If less than 50, round down.

Worked example 3.4.3
Which hundred is 683 nearer to: 600 or 700?

Method. Find the distance from the number to each hundred. The shorter distance is the nearer one.

  1. Find the two hundreds. 683 is between 600 and 700.
    600 < 683 < 700
  2. Compare the distances. 683 - 600 = 83, 700 - 683 = 17.
    83 and 17
  3. Write the nearer hundred. The smaller distance is the nearer hundred.
    700

Check. 700 is nearer to 683 than the other hundred.

Watch out. The number is nearer to 600 than to 700 when it is less than 650.

Watch out

Watch out. 738 is nearer to 700 than to 800, because it is only 38 more than 700. Do not round to the wrong hundred.

Exam tip

Grown-up tip. Draw a number line on paper and mark the hundreds. Ask: “Is the number closer to the left or the right?”

Exercise 3D  Practice: estimating on a number line

Non-calculator
1
FWhich hundred is 903 nearer to: 900 or 1000?
01002003004005006007008009001000903
2
FRound 708 to the nearest hundred.
01002003004005006007008009001000708
3
FRound 822 to the nearest hundred.
01002003004005006007008009001000822
4
FRound 966 to the nearest hundred.
01002003004005006007008009001000966
5
FWhich hundred is 976 nearer to: 900 or 1000?
01002003004005006007008009001000976
6
FRound 848 to the nearest hundred.
01002003004005006007008009001000848
7
FWhich hundred is 826 nearer to: 800 or 900?
01002003004005006007008009001000826
8
FRound 357 to the nearest hundred.
01002003004005006007008009001000357
9
FRound 849 to the nearest hundred.
01002003004005006007008009001000849
10
FWhich hundred is 982 nearer to: 900 or 1000?
01002003004005006007008009001000982
11
FWhich hundred is 141 nearer to: 100 or 200?
01002003004005006007008009001000141
12
FRound 443 to the nearest hundred.
01002003004005006007008009001000443
13
FRound 433 to the nearest hundred.
01002003004005006007008009001000433
14
FWhich hundred is 744 nearer to: 700 or 800?
01002003004005006007008009001000744
15
FRound 232 to the nearest hundred.
01002003004005006007008009001000232
16
FRound 811 to the nearest hundred.
01002003004005006007008009001000811

Chapter summary

SkillMethod
Compare two numbersCompare hundreds, then tens, then ones; use <, > or =
Order a setCompare hundreds, then tens, then ones; write the numbers in order
Greatest and leastFind the most (or fewest) hundreds, then the tens and ones
Estimate on a number lineFind the two hundreds either side; the nearer one is the estimate

Can you…?

  • I can compare two numbers up to 1000 with <, > and =
  • I can put up to five numbers in order, both ways
  • I can find the greatest and least number in a set
  • I can estimate where a number goes on a 0 to 1000 number line

Key terms

less than
smaller than; the sign is <
greater than
bigger than; the sign is >
estimate
a sensible guess that is close to the exact answer
nearest
the one that is closest in value to the number

Exercise 3Z  Check-up

Non-calculator
1
Put these numbers in order from largest to smallest: 209, 333, 352
2
Round 622 to the nearest hundred.
01002003004005006007008009001000622
3
Which number is the greatest? 680, 287, 669
4
Which number is the greatest? 200, 780, 428
5
Which number is the greatest? 466, 829, 897, 641
6
Which hundred is 506 nearer to: 500 or 600?
01002003004005006007008009001000506
7
Write <, > or = to make it true: 803 □ 384
8
Which number is the least? 197, 904, 438
9
Write <, > or = to make it true: 807 □ 792
10
Put these numbers in order from smallest to largest: 841, 116, 611

Total 19 marks. Allow about 19 minutes.

Exercise 3X  Practice test questions

Non-calculator
1
FWhich number is the least? 307, 124, 910, 113, 719[1 mark]
2
FPut these numbers in order from smallest to largest: 178, 991, 453, 103[1 mark]
3
FWrite <, > or = to make it true: 441 □ 328[1 mark]
4
FPut these numbers in order from smallest to largest: 266, 146, 350, 490, 736[1 mark]
5
FWrite <, > or = to make it true: 875 □ 875[2 marks]
6
FWhich hundred is 316 nearer to: 300 or 400?[2 marks]
01002003004005006007008009001000316
7
FPut these numbers in order from largest to smallest: 501, 847, 587, 687, 616[2 marks]
8
FWhich number is the greatest? 678, 504, 737, 131, 725[3 marks]
9
FPut these numbers in order from smallest to largest: 583, 887, 803, 948, 639[3 marks]
10
FRound 947 to the nearest hundred.[3 marks]
01002003004005006007008009001000947

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