Addition and Subtraction Column subtraction with 4 and

Addition and Subtraction Column subtraction with 4 - and 5 -digit numbers Word problems Objectives Day 1 Use decomposition to subtract pairs of 5 -digit numbers. Day 2 Use decomposition to subtract pairs of 5 -digit numbers. Day 3 Use decomposition to subtract pairs of 5 -digit numbers and 4 -digit numbers from 5 -digit numbers. Solve word problems. Day 4 Revise column addition and subtraction of 4 -digit and 5 -digit numbers. © hamilton-trust. org. uk 1 Year 5

Addition and Subtraction Column subtraction with 4 - and 5 -digit numbers Word problems Starters Day 1 Revise subtraction facts to 20 (pre-requisite skills) Day 2 Pairs to 100 (pre-requisite skills) Day 3 Count up to the next 1000 (pre-requisite skills) Day 4 Change from £ 1 (simmering skills) © hamilton-trust. org. uk 2 Year 5

Addition and Subtraction Column subtraction with 4 - and 5 -digit numbers Word problems Starter Revise subtraction facts to 20 © hamilton-trust. org. uk 3 Year 5

Addition and Subtraction Column subtraction with 4 - and 5 -digit numbers Word problems Starter Pairs to 100 © hamilton-trust. org. uk 4 Year 5

Addition and Subtraction Column subtraction with 4 - and 5 -digit numbers Word problems Starter Count up to the next 1000 © hamilton-trust. org. uk 5 Year 5

Addition and Subtraction Column subtraction with 4 - and 5 -digit numbers Word problems Starter Change from £ 1 © hamilton-trust. org. uk 6 Year 5

Addition and Subtraction Column subtraction with 4 - and 5 -digit numbers Word problems Objectives Day 1 Use decomposition to subtract pairs of 5 -digit numbers. © hamilton-trust. org. uk 7 Year 5

Day 1: Use decomposition to subtract pairs of 5 -digit numbers. Estimate the answer to 64, 783 – 35, 327. Let’s remind ourselves how to use both expanded and compact column subtraction (decomposition). First subtract the 1 s, then 100 s, then 1000 s, then 10, 000 s. 50, 000 60, 000 - 30, 000 20, 000 14, 000 4000 700 5000 300 9000 400 29, 456 70 80 20 50 Hint! Round each number to the nearest 10, 000. 13 3 7 6 5 6 -3 2 14 7 13 4 7 8 3 5 3 2 7 9 4 5 6 Does this answer seem about right? Yes, it’s just under 30, 000. © hamilton-trust. org. uk 8 Year 5

Day 1: Use decomposition to subtract pairs of 5 -digit numbers. Use either expanded or compact decomposition to work out 72, 846 – 47, 063. 60, 000 70, 000 - 40, 000 20, 000 12, 000 700 2000 800 7000 0 5000 700 25, 783 © hamilton-trust. org. uk 140 40 6 60 3 80 3 9 6 7 -4 2 12 2 7 5 7 8 0 7 14 4 6 6 3 8 3 Year 5

Day 1: Use decomposition to subtract pairs of 5 -digit numbers. Whole class investigation • Work in pairs to write a number with five consecutive digits, e. g. 98, 765. • Reverse the digits to make a new number and subtract the smaller from the larger, e. g. 98, 765 – 56, 789. • Repeat with other pairs of 5 -digit numbers with consecutive digits. • What do you find? © hamilton-trust. org. uk 10 Year 5

Challenge © hamilton-trust. org. uk 11 Year 5

Addition and Subtraction Column subtraction with 4 - and 5 -digit numbers Word problems Objectives Day 2 Use decomposition to subtract pairs of 5 -digit numbers. © hamilton-trust. org. uk 12 Year 5

Day 2: Use decomposition to subtract pairs of 5 -digit numbers. 86072 - 32537 Can you spot where a 10, 1000 or 10, 000 will have to be moved? 5000 1000 80, 000 6000 0 - 30, 000 2000 50, 000 3000 53, 535 © hamilton-trust. org. uk 60 70 30 30 12 2 7 5 13 The ‘top’ number has a zero so we will definitely have to move a 1000 to the 100 s column. A 10 will also need to be moved into the ones column as 2 is less than 7. 5 8 6 -3 2 5 3 10 0 5 5 6 12 7 2 3 7 3 5 Year 5

Use decomposition to subtract pairs of 5 -digit numbers. Use either expanded or compact decomposition to calculate 40, 178 – 35, 423 = 4755 We have 100 – 400 but don’t have any 1000 s that we can move! We first need to move 10, 000 from the 10, 000 s column… 9000 30, 000 1100 40, 000 0 100 70 8 - 30, 000 5000 400 20 3 0 4000 700 50 5 4755 © hamilton-trust. org. uk 14 9 3 10 4 0 -3 5 4 11 1 7 8 4 2 3 7 5 5 Year 5

Day 2: Use decomposition to subtract pairs of 5 -digit numbers. 30008 - 25783 Discuss what moves would be necessary for this subtraction. We would have to move a 10, 000 to the 1000 s, then a 1000 to the 100 s and then a 100 to the 10 s! When we have this many moves to make, using Frog (counting up) would probably be a less error-prone strategy! Frog is using the pair to 1000 to make the first hop. Where will Maths Frog hop to next? 217 30, 008 25, 783 26, 000 © hamilton-trust. org. uk 15 Year 5

Day 2: Use decomposition to subtract pairs of 5 -digit numbers. 30008 - 25783 Discuss what moves would be necessary for this subtraction. We would have to move a 10, 000 to the 1000 s, then a 1000 to the 100 s and then a 100 to the 10 s! When we have this many moves to make, using Frog (counting up) would probably be a less error-prone strategy! Frog is using the pair to 1000 to make the first hop. Where will Maths Frog hop to next? 4000 217 30, 000 30, 008 25, 783 26, 000 © hamilton-trust. org. uk 16 Year 5

Day 2: Use decomposition to subtract pairs of 5 -digit numbers. 30008 - 25783 Discuss what moves would be necessary for this subtraction. We would have to move a 10, 000 to the 1000 s, then a 1000 to the 100 s and then a 100 to the 10 s! When we have this many moves to make, using Frog (counting up) would probably be a less error-prone strategy! Frog is using the pair to 1000 to make the first hop. 30, 008 25, 783 Where will Maths – Frog hop to next? = 4225 Much quicker with Frog! 217 4000 30, 008 25, 783 26, 000 © hamilton-trust. org. uk 8 17 Year 5

Investigation: Adult Sheet © hamilton-trust. org. uk 18

Investigation: Child Sheet © hamilton-trust. org. uk 19

Challenge © hamilton-trust. org. uk 20 Year 5

Addition and Subtraction Column subtraction with 4 - and 5 -digit numbers Word problems Objectives Day 3 Use decomposition to subtract pairs of 5 -digit numbers and 4 -digit numbers from 5 -digit numbers. Solve word problems. © hamilton-trust. org. uk 21 Year 5

Day 3: Use decomposition to subtract pairs of 5 -digit numbers and 4 -digit numbers from 5 -digit numbers; Solve word problems. 45, 782 – 7356 = 38, 426 Write this as a vertical subtraction. What do you think we need to watch out for when setting it out? Calculate the answer and check with a partner. © hamilton-trust. org. uk 22 Year 5

Day 3: Use decomposition to subtract pairs of 5 -digit numbers and 4 -digit numbers from 5 -digit numbers; Solve word problems. 34, 784 people live in Oakville. 9784 of them are children. 14, 378 are pensioners. How many are adults? We didn’t need to know how many were pensioners; that was surplus information! Agree the necessary calculation with a partner. A number 37 bus driver drove 37, 806 miles last year. A number 48 bus driver drove 34, 928 miles. What is the difference between how far they drive? We didn’t need to know the bus numbers; that was surplus information! Agree the necessary calculation with a partner. How could we check our answers to these problems? © hamilton-trust. org. uk Check one answer using addition. 23 Would either calculation have been more straightforward with Frog? It’s always useful to check! Year 5

Challenge © hamilton-trust. org. uk 24 Year 5

Addition and Subtraction Column subtraction with 4 - and 5 -digit numbers Word problems Objectives Day 4 Revise column addition and subtraction of 4 -digit and 5 -digit numbers. © hamilton-trust. org. uk 25 Year 5

Day 4: Revise column addition and subtraction of 4 -digit and 5 -digit numbers. 30, 000 4000 700 80 2 - 10, 000 8000 300 40 6 Discuss in pairs how many place value moves they think will be necessary to work out the answer. 3 4 7 8 2 -1 8 3 4 6 Let’s work through both subtractions. Were you right about the number of moves? © hamilton-trust. org. uk 26 Year 5

Day 4: Revise column addition and subtraction of 4 -digit and 5 -digit numbers. 70, 000 8000 200 60 3 - 40, 000 3000 700 20 9 Discuss in pairs how many place value moves they think will be necessary to work out the answer. 7 8 2 6 3 -4 3 7 2 9 Choose expanded or compact subtraction to calculate the answer. Were you right about the number of moves? © hamilton-trust. org. uk 27 Year 5

Day 4: Revise column addition and subtraction of 4 -digit and 5 -digit numbers. 80, 000 5000 200 30 9 - 40, 000 7000 800 40 2 Discuss in pairs how many place value moves they think will be necessary to work out the answer. 8 5 2 3 9 -4 7 8 4 2 Choose expanded or compact subtraction to work out the answer. Were you right about the number of moves? © hamilton-trust. org. uk 28 Year 5

Day 4: Revise column addition and subtraction of 4 -digit and 5 -digit numbers. Here’s a challenge… Can you write a subtraction that will need 4 moves? ! What are we looking for to check the number of moves? Today we are going to need to add as well as subtract. Work out 46, 089 + 23, 666 to remind yourself. © hamilton-trust. org. uk 29 Year 5

Day 4: Revise column addition and subtraction of 4 -digit and 5 -digit numbers. Whole class investigation • Write a 5 -digit number. Reverse the digits and write the new number. • Subtract the smaller from the larger. • Reverse the digits of the answer and add it to the new number, e. g. . . • Now reverse the digits and add, i. e. add 22, 968 and 86, 922. • Start with a new number 5 -digit number. What happens? Does this always happen? © hamilton-trust. org. uk 30 Year 5

Addition and Subtraction Column subtraction with 4 - and 5 -digit numbers Word problems Well Done! You’ve completed this unit. Objectives Day 1 Use decomposition to subtract pairs of 5 -digit numbers. Day 2 Use decomposition to subtract pairs of 5 -digit numbers. Day 3 Use decomposition to subtract pairs of 5 -digit numbers and 4 -digit numbers from 5 -digit numbers. Solve word problems. Day 4 Revise column addition and subtraction of 4 -digit and 5 -digit numbers. © hamilton-trust. org. uk 31 Year 5

Problem solving and reasoning questions Use just the digits 4 and 5 to create a 5 -digit – 5 -digit subtraction to give an answer with at least two 9 s. Can you get 9091? What is the smallest answer you can get? What is the largest? Explain why it would be sensible to choose different methods to solve (a) and (b) below. (a) 67, 493 – 21, 561 (b) 50, 005 – 44, 878 Find the missing numbers in this subtraction: 12★62 – 9 3 � 8 31 1▲ © hamilton-trust. org. uk 32 Year 5

Problem solving and reasoning questions answers Use just the digits 4 and 5 to create a 5 -digit – 5 -digit subtraction to give an answer with at least two 9 s. e. g. 55, 544 – 44, 555. Other answers are possible; the key is to have 4 s in the first number in the same place as 5 s in the second. Can you get 9091? 54, 545 – 45, 454. What is the smallest answer you can get? 55, 555 – 55, 554 = 1. What is the largest? 55, 555 – 44, 444 = 11, 111. (b) 50, 005 – 44, 878 5127. Since 50, 005 is just over 50, 000 this can be solved by counting up (Frog) from 44, 878. Find the missing numbers in this subtraction: 5 12 1 2 4 6 2 – 9 3 4 8 3 1 1 4 Note the need to decompose the 60. Explain why it would be sensible to choose different methods to solve (a) and (b) below. (a) 67, 493 – 21, 561 45, 932. Probably best by column subtraction, since neither number is close to 10, 000 s and exchanges between columns are needed. © hamilton-trust. org. uk 33 Year 5