Maths Week 2

Four operations, prime numbers, factors, multiples and an

arithmetic test

Mental calculations By the end of year 5 pupils should be able to add and subtract numbers mentally with increasingly large numbers and multiply and divide numbers mentally drawing upon known facts.

For example, if I know 5 x 6 = 30I can work out that 50 x 6 = 300 or 5 x 600 = 3000.

A. Can add and subtract increasingly large numbers mentally. 1. Add the following calculations mentally using your knowledge of place value:

534 + 30 = 584 + 210 = 494 + 40 =

4,521 + 300 = 8,283 + 1,600 = 8,684 + 700 =

16,843 + 2,000 = 34,843 + 4,050 = 68,294 + 6,000 =

2. Subtract the following calculations mentally using your knowledge of place value: 8,342 – 200 = 5,934 – 4,600 = 4,235 – 500 =

74,294 – 3,000 = 63,364 – 2,100 = 95,284 – 8,000 =

3. Solve the following calculations by rounding to the nearest multiple of 10, 100 or 1000 first and then adjusting your answer:853 – 199 = 853 - 200 = 653 - 1 = 652 4,394 + 403

5,283 + 603 17,393 – 2,998

4,593 – 1,005 45,293 + 299

B. Can recall and use multiplication and division facts for all the times tables.

1. ____ x 8 = 72

2. 32 ÷ 4 =

3. Explain how you can use 12 x 7 = 84 to work out 14 x 7 = ?

C. Can multiply and divide mentally using known number facts.

1. 40 x 50 =

2. 420 ÷ 7 =

3. 0.9 x 8 =

4. Toy boxes hold 12 toys. How many are needed for 72 toys?

D. Can multiply and divide mentally using known number facts.

1. 40 x 50 =

2. 420 ÷ 7 =

3. 0.9 x 8 =

4. Toy boxes hold 12 toys. How many are needed for 72 toys?

E. Can multiply and divide whole numbers and decimals by 10, 100, 1000

1. 2.8 x 100 =

2. 7.2 x 1000 =

3. 782 ÷ _____ = 7.82

4. 0.6 x 10 x 10 =

5. A brick measures 21cm. How tall are 10 bricks, 100 bricks, 1000 bricks?

Remember these are mental calculations so no written methods!

AdditionBy the end of year 5 pupils should be able to add whole numbers with more than 4 digits, including using formal written methods (columnar addition)

Can add 3-digit and extend to 4-digit numbers using the formal column method.

1. 623 + 165 =

2. 1,267 + 3,872 =

3. What is the total of 2,931 + 634 = ?

4. 823 + 48 + 312 =

5. Find the sum of £428, £49 and £398.

What are the common mistakes

someone might make when

completing these questions?

SubtractionBy the end of year 5 pupils should be able to subtract whole numbers with more than 4 digits, including using formal written methods (columnar addition)

Can subtract 3-digit and extend to 4-digit numbers using the formal column method.

1. 537 - 125 =

2. 4897 - 3245 =

3. 808 - 369 =

4. 8323 - 1789 =

5. Subtract 2,347 from 6,838

6. What is the difference between £1,265 and £764?

What are the common mistakes

someone might make when

completing these questions?

Multiplication

2 6 5 0 4 1

By the end of year 5 pupils should be able to multiply numbers up to 4 digits by a one- or two-digit number using a formal written method including long multiplication for two digit numbers.

A. Can multiply up to 4-digit numbers by 1-digit numbers using short multiplication.

1. 837 x 4 =

2. 1,678 x 5 =

3. Seven people have each saved £2,365. How much do they have altogether?

B. Can multiply up to four-digit numbers by two-digit numbers using long multiplication

1. 927 x 15 =

2. 2,465 x 37 =

3. 1,983 x 64 =

4. 8,463 people attended a music concert. They each paid £26 for their ticket. How much did the tickets cost in total for everyone who attended the concert?

DivisionBy the end of year 5 pupils should be able to divide numbers up to 4 digits by a one-digit number using the formal written method of short division and interpret remainders appropriately for the context.

03

Division without remaindersDivision with remainders

03

= 51 5 7

Challenge

A. Can divide up to 4-digit numbers by 1-digit numbers using short division.

1. 844 ÷ 4 =

2. 345 ÷ 3 =

3. 6482 ÷ 2 =

4. 1865 ÷ 7 =

5. 8,562 ÷ 5 =

6. Hussain has collected 1,462 stamps. If he shares them equally

between 8 books, how many stamps will be in each book?

03

Remember to regroup any numbers that do not divide equally. We only have 3 in the hundreds column but we have 7 groups so we regroup the 3 into the tens column to make 36 tens.

Can interpret remainders in context as fractions, decimals or by rounding

1. Write the remainder for 51 ÷ 4 as a decimal. 2. Write the remainder for 136 ÷ 9 as a fraction. 3. 4 glasses can fit into one container. There are 29 glasses in total. How many containers will be needed? Explain your reasoning. 4. True or False?

123 ÷ 5 = 24.3Explain your answer.

Challenge

03

= 51 5 7

Problem solvingBy the end of year 5 pupils should be able to solve addition,

subtraction, multiplication and division multi-step problems in contexts, deciding which operations and methods to use and why.

A. Can solve multi-step problems involving addition and subtraction, deciding which operation to use

1. A train has 172 people travelling on it. At the first stop 47 people get off and 13 more people get on, at the next stop another 38 people get off. How many people are on the train?

2. A supermarket has 2,355 loaves of bread at the start of the day. During the day, 657 loaves are sold, and a further 489 loaves are delivered. How many loaves of bread are there at the end of the day?

3. Ruby has 55 litres of petrol in her car and her petrol tank is full. On a journey to Wales, she uses 30 litres of petrol. She then travels to a fairground and uses a further 1,250ml of petrol. How much petrol will she have to put back in to fill the tank?

4) Sarah buys one piece of cod and four portions of chips.What is the total cost of her order?

5) Louise takes her three children to the zoo.What is the total cost of their tickets?

6) Sam has 37 trading cards, Lucy has 62 and Joe has 39.They put their cards together and then share them equally.How many cards do they each now have?

7) Susan has collected 18 conkers, Jane has collected 21, Maddie has 9 and Cole has 16.They put their collections together and then share them equally.How many does each person get?

Multiples and factorsA. Can identify multiples and factors

1. Write all the factors for 36.

2. True or False? The number 21 and the number 49 have the same number of factors. Explain how you know.

3. Complete the following table (YES or NO):

Prime NumbersCan establish whether a number up to 100 is prime

1. Which of these numbers is a prime number? 72 73 74 75 2. Tick the correct box for each number:

3. True or False? 99 is a prime number. Explain your answer.

Can recall prime numbers up to 19

1. Explain why the number 2 is a prime number.

2. Tick the correct box for each number:3. True or False? The first four prime numbers add up to 16. Explain your answer.

Arithmetic test

The arithmetic test is going to be 6 questions which you should complete within 6 minutes.

Record your results each week.

12 x 5 =

8 x 11 =

3,456 – 457 =

5 . Tickets for a cricket match cost £10.50 for children and £15.40 for adults. How much will it cost for 4 children and 1 adult?

6. Use each digit once to make the largest number you can. Write down the number in words.

1

2

3

4

AnswersMental calculations

1) 534 + 30 = 564 584 + 210 = 794 494 + 40 = 534 4,521 + 300 = 7821 8,283 + 1,600 = 9883 8,684 + 700 = 1638416,843 + 2,000 = 18843 34,843 + 4,050 = 38893 68,294 + 6,000 = 74294

2) 8,342 – 200 = 8142 5,934 – 4,600 = 1334 4,235 – 500 = 373574,294 – 3,000 = 71294 63,364 – 2,100 = 61264 95,284 – 8,000 = 87284

3. Solve the following calculations by rounding to the nearest multiple of 10, 100 or 1000 first and then adjusting your answer:You may have used a different method to me but as long as the answer is correct you can have a tick!

853 – 199 = 853 - 200 = 653 - 1 = 652 4,394 + 403 = 4394 + 400 = 4794 + 3 = 4797

5,283 + 603 = 5283 + 600 = 5883 + 3 = 5886 17,393 – 2,998 = 17393 - 3000 = 14393 + 2 = 14395

4,593 – 1,005 = 4593 - 1000 = 3593 - 5 = 3588 45,293 + 299 = 45293 + 300 = 45593 - 1 = 45592

Multiplication and Division 1. __9__ x 8 = 722. 32 ÷ 4 = 8 3. Explain how you can use 12 x 7 = 84 to work out 14 x 7 = ? 84 + (2 x 7) = 84 + 14 = 98 1. 40 x 50 = 2000 2. 420 ÷ 7 = 603. 0.9 x 8 = 7.24. Toy boxes hold 12 toys. How many are needed for 72 toys? ? x 12 = 72 ? = 6

Addition using written method

1. 623 + 165 = 7882. 1,267 + 3,872 = 51393. What is the total of 2,931 + 634 = 35654. 823 + 48 + 312 = 11835. Find the sum of £428, £49 and £398. £875 - did you remember the £ symbol?

Subtraction using written method

1. 537 - 125 = 4122. 4897 - 3245 = 16523. 808 - 369 = 4394. 8323 - 1789 = 65345. Subtract 2,347 from 6,838 44916. What is the difference between £1,265 and £764? £501 - did you remember the £ symbol?

A. Can multiply up to 4-digit numbers by 1-digit numbers using short multiplication. 1. 837 x 4 = 33482. 1,678 x 5 = 83903. Seven people have each saved £2,365. How much do they have altogether? £16555

B. Can multiply up to four-digit numbers by two-digit numbers using long multiplication 1. 927 x 15 = 13905 2. 2,465 x 37 = 91205 3. 1,983 x 64 = 1269124. 8,463 people attended a music concert. They each paid £26 for their ticket. How much did the tickets cost in total for everyone who attended the concert? £220,038

Division 1. 844 ÷ 4 = 2112. 345 ÷ 3 = 1323. 6482 ÷ 2 = 32414. 1865 ÷ 7 = 266 r35. 8,562 ÷ 5 = 1712 r26. Hussain has collected 1,462 stamps. If he shares them equally between 8 books, how many stamps will be in each book? 182 r6

Challenge1. Write the remainder for 51 ÷ 4 as a decimal. 12.75 2. Write the remainder for 136 ÷ 9 as a fraction. 15 1/9 3. 4 glasses can fit into one container. There are 29 glasses in total. How many containers will be needed? Explain your reasoning. 4 x 7 = 28 and 4 x 8 = 32. All glasses need to fit in so you will need 8 containers as 7 will fit too few glasses. 4. True or False?

123 ÷ 5 = 24.3Explain your answer. False. The answer as a remainder is 24 r3 = 24 ⅗. ⅗ as a decimal is 0.6 so the answer would be 24.6

Problem solving1. A train has 172 people travelling on it. At the first stop 47 people get off and 13 more people get on, at the next stop another 38 people get off. How many people are on the train? 172 - 47 = 125, 125 + 13 = 138, 138 - 38 = 100 2. A supermarket has 2,355 loaves of bread at the start of the day. During the day, 657 loaves are sold, and a further 489 loaves are delivered. How many loaves of bread are there at the end of the day? 2355 - 657 = 1698, 1698 + 489 = 21873. Ruby has 55 litres of petrol in her car and her petrol tank is full. On a journey to Wales, she uses 30 litres of petrol. She then travels to a fairground and uses a further 1,250ml of petrol. How much petrol will she have to put back in to fill the tank? 55 - 30 = 25, 25 - 12.5 = 12.5, 12.5 + ? = 55, ? = 42.5 or 30 + 12.5 = 42.5.

4) Sarah buys one piece of cod and four portions of chips.What is the total cost of her order? 3.85 + (4 x 1.35) = 3.85 + 5.4 = 9.25 £9.25

5) Louise takes her three children to the zoo.What is the total cost of their tickets?

1. 9.25 + (3 x 6.85) = 9.25 + 20.55 = 29.8 £29.80

6) Sam has 37 trading cards, Lucy has 62 and Joe has 39.They put their cards together and then share them equally.How many cards do they each now have?

1. 37 + 62 + 39 = 138, 138 ÷ 3 = 46

7) Susan has collected 18 conkers, Jane has collected 21, Maddie has 9 and Cole has 16.They put their collections together and then share them equally.How many does each person get?

2. 18 + 21 + 9 + 16 = 64, 64 ÷ 4 = 16

46

93

4 2

67

2

Can identify multiples and factors

1. Write all the factors for 36.1, 2, 3, 4, 6, 12, 18, 36

2. True or False? The number 21 and the number 49 have the same number of factors. Explain how you know. True because they both have 2 factor pairs. 21 - 1, 3, 7, 21 and 49 - 1,, 7, 7, 49

3. Complete the following table (YES or NO):

Can establish whether a number up to 100 is prime

1. Which of these numbers is a prime number? 72 73 74 75 2. Tick the correct box for each number:

3. True or False? 99 is a prime number. Explain your answer.No 99 is not a prime number because it has more factors than 1 and 99. 1, 3, 9, 11, 33, 99

Explain why the number 2 is a prime number. Because it only has 1 and 2 as its factors.

Tick the correct box for each number:

3. True or False? The first four prime numbers add up to 16. Explain your answer. False because 1, 2, 3, 5 = 11.

12 x 5 =

8 x 11 =

3,456 – 457 =

5 . Tickets for a cricket match cost £10.50 for children and £15.40 for adults. How much will it cost for 4 children and 1 adult?

6. Use each digit once to make the largest number you can. Write down the number in words.

1

2

3

4

60

35

88

2999

£57.40

87641 = Eighty seven thousand, six hundred and forty-one