The pattern
Large numbers and operation order
Group digits by place value, then do brackets and multiplication or division before addition or subtraction.
Large numbers add up correctly only when digits of the same place value sit under each other: ones under ones, tens under tens, hundreds under hundreds. Line the numbers up this way before adding, and carry any digit that makes a column reach ten into the column on its left. Ordering numbers compares the hundreds digit first, moving to tens only if the hundreds match.
How to spot it
Two numbers to add with carrying, several numbers to put in order, or a sum mixing addition, multiplication and brackets, all point here.
Common mistake
Children forget to carry a ten into the next column, or compare digits from the left without first checking the numbers have the same number of digits.
104 worked solutions
Standard
- add three-digit numbers Calculate 357 + 216.
- add three-digit numbers Calculate 248 + 156.
- add two-digit numbers mentally Calculate 94 + 38 mentally.
- add two-digit numbers mentally Calculate 68 + 27 mentally.
- add with a four-digit algorithm Calculate 3857 + 2416.
- add with a four-digit algorithm Calculate 2748 + 1356.
- calculate mentally by place value Calculate 605 + 7 mentally.
- calculate mentally by place value Calculate 348 + 20 mentally.
- calculate mentally within multiplication tables Calculate 8 × 7 mentally.
- calculate mentally within multiplication tables Calculate 9 × 4 mentally.
- calculate with brackets Calculate (72 + 8) × 5.
- calculate with brackets Calculate (48 + 6) × 7.
- calculate within multiplication tables Calculate 4 × 7.
- calculate within multiplication tables Calculate 3 × 9.
- calculate within multiplication tables Calculate 5 × 7.
- calculate within multiplication tables Calculate 4 × 8.
- calculate within multiplication tables Calculate 2 × 9.
- calculate within multiplication tables Calculate 10 × 6.
- compare and order numbers Arrange 78,216, 78,162 and 78,612 in ascending order.
- compare and order numbers Arrange 60,540, 65,004 and 60,450 in ascending order.
- compare and order numbers Arrange 6305, 6350 and 6035 in ascending order.
- compare and order numbers Arrange 4827, 4782 and 4872 in ascending order.
- compare and order numbers Arrange 605, 650 and 506 from least to greatest.
- compare and order numbers Arrange 482, 428 and 824 from least to greatest.
- connect factors and multiples Explain the factor-and-multiple relationship between 9 and 72.
- connect factors and multiples Explain the factor-and-multiple relationship between 8 and 56.
- connect multiplication with division Use 6 × 4 = 24 to complete 24 ÷ 6 = __.
- connect multiplication with division Use 5 × 8 = 40 to complete 40 ÷ 5 = __.
- continue a number sequence Continue the sequence: 4,275, 4,400, 4,525, 4,650, __.
- continue a number sequence Continue the sequence: 18,300, 18,700, 19,100, 19,500, __.
- count by hundreds and thousands Count on by 1000 from 3000: 3000, 4000, 5000, __. What comes next?
- count by hundreds and thousands Count on by 100 from 2400: 2400, 2500, 2600, __. What comes next?
- count by tens and hundreds 300, 400, 500, __. What comes next?
- count by tens and hundreds 240, 250, 260, __. What comes next?
- distinguish odd and even numbers Is 247 odd or even?
- distinguish odd and even numbers Is 608 odd or even?
- divide by a multiple of a power of ten Calculate 960,000 ÷ 3,000 without a calculator.
- divide by a multiple of a power of ten Calculate 84,000 ÷ 700 without a calculator.
- divide up to three digits by one digit Calculate 936 ÷ 6.
- divide up to three digits by one digit Calculate 728 ÷ 7.
- divide with a remainder Calculate 67 ÷ 8. Give the quotient and remainder.
- divide with a remainder Calculate 53 ÷ 6. Give the quotient and remainder.
- divide within multiplication tables Calculate 72 ÷ 8.
- divide within multiplication tables Calculate 56 ÷ 7.
- divide within multiplication tables Calculate 40 ÷ 5.
- divide within multiplication tables Calculate 36 ÷ 4.
- identify hundreds, tens and ones How many hundreds, tens and ones are in 605?
- identify hundreds, tens and ones How many hundreds, tens and ones are in 482?
- identify place value In 73,084, what is the value of the digit 8?
- identify place value In 40,625, what is the value of the digit 4?
- identify place value What is the value of the digit 6 in 6305?
- identify place value What is the value of the digit 8 in 4827?
- interpret approximate equality Explain what 70,184 ≈ 70,000 means.
- interpret approximate equality Explain what 58,235 ≈ 58,000 means.
- interpret the division symbol Calculate 30 ÷ 5.
- interpret the division symbol Calculate 24 ÷ 4.
- multiply by a multiple of a power of ten Calculate 408 × 200 without a calculator.
- multiply by a multiple of a power of ten Calculate 324 × 300 without a calculator.
- multiply up to three digits by one digit Calculate 407 × 6.
- multiply up to three digits by one digit Calculate 236 × 4.
- operation precedence Calculate 72 + 8 × 5.
- operation precedence Calculate 48 + 6 × 7.
- read a large numeral Read 9,800,700 in words.
- read a large numeral Read 4,305,018 in words.
- read a numeral Read 73,084 in words.
- read a numeral Read 40,625 in words.
- read a numeral Write 6305 in words.
- read a numeral Write 4827 in words.
- read a numeral Write 605 in words.
- read a numeral Write 482 in words.
- recall a multiplication fact Calculate 9 × 6 mentally.
- recall a multiplication fact Calculate 7 × 8 mentally.
- represent a five-digit number Represent 73,084 in expanded form.
- represent a five-digit number Represent 40,625 in expanded form.
- represent a four-digit number Express 6305 in expanded form.
- represent a four-digit number Express 4827 in expanded form.
- represent a three-digit number Write 482 in expanded form.
- represent a three-digit number Write 605 in expanded form.
- round to the nearest hundred Round 70,184 to the nearest hundred.
- round to the nearest hundred Round 58,235 to the nearest hundred.
- round to the nearest ten Round 70,184 to the nearest ten.
- round to the nearest ten Round 58,235 to the nearest ten.
- round to the nearest thousand Round 70,184 to the nearest thousand.
- round to the nearest thousand Round 58,235 to the nearest thousand.
- subtract three-digit numbers Calculate 802 − 367.
- subtract three-digit numbers Calculate 643 − 285.
- subtract with a four-digit algorithm Calculate 8002 − 3567.
- subtract with a four-digit algorithm Calculate 6243 − 2785.
- test a one-digit factor Is 8 a factor of 936?
- test a one-digit factor Is 6 a factor of 425?
- whole-number division Calculate 7,392 ÷ 6.
- whole-number division Calculate 6,552 ÷ 7.
- whole-number multiplication Calculate 7,128 × 4.
- whole-number multiplication Calculate 4,805 × 6.
- whole-number multiplication Calculate 625 × 34.
- whole-number multiplication Calculate 407 × 52.
- write a large numeral Write “nine million eight hundred thousand seven hundred” in numerals.
- write a large numeral Write “four million three hundred and five thousand and eighteen” in numerals.
- write a numeral Write “seventy-three thousand and eighty-four” in numerals.
- write a numeral Write “forty thousand six hundred and twenty-five” in numerals.
- write a numeral Write “six thousand three hundred five” in numerals.
- write a numeral Write “four thousand eight hundred twenty-seven” in numerals.
- write a numeral Write “six hundred five” in numerals.
- write a numeral Write “four hundred eighty-two” in numerals.
All the problem patterns → · the revision list
The 33 problem patterns
All 33 patterns, one to a page — the 19 behind Primary 5 and 6 word problems, and the skills the younger years are built on. The bar model, how to spot it in the question, and the mistake children make. A booklet you can print. Free.
A PDF, and a note when new solutions go up.