Place Value, Addition, Subtraction Understand place value in 6-digit numbers Add and subtract powers of 10 Objectives Day 1 Solve number and practical problems involving place value. Add/subtract powers of 10. Day 2 Solve number and practical problems involving place value. Add/subtract multiples of 1s, 10s, 100s, 1000s, 10,000s and 100,000s. Before teaching, be aware that: On Day 1 children will need mini-whiteboards and pens. On Day 2 children will need mini-whiteboards and pens. You will need six packs of 0 to 9 digit cards. Year 6

Place Value, Addition, Subtraction Understand place value in 6-digit numbers Add and subtract powers of 10 Starters Day 1 Order 5-digit numbers (pre-requisite skills) Day 2 Count in steps of 1 though multiples of 100, 1000, 10,000 and 100,000 (pre- requisite skills) Choose starters that suit your class by dragging and dropping the relevant slide or slides below to the start of the teaching for each day. Year 6

Place Value, Addition, Subtraction Understand place value in 6-digit numbers Add and subtract powers of 10 Starter Order 5-digit numbers Pre-requisite skills – to use this starter, drag this slide to the start of Day 1 Ask each child to write a number between 40,000 and 50,000 on their whiteboards. Children work in groups to put their whiteboards in ascending order. Fastest group wins! Repeat with different ranges. Year 6

Place Value, Addition, Subtraction Understand place value in 6-digit numbers Add and subtract powers of 10 Starter Count in steps of 1 though multiples of 100, 1000, 10,000 and 100,000 Pre-requisite skills – to use this starter, drag this slide to the start of Day ? Write the following numbers on the board: 478,597, 367,497, 839,998, 299,995. Children copy them and write the next 5 numbers after each. Year 6

Place Value, Addition, Subtraction Understand place value in 6-digit numbers Add and subtract powers of 10 Objectives Day 1 Solve number and practical problems involving place value. Add/subtract powers of 10. Year 6

I am going to read a number. Write the number on your whiteboard. Day 1: Solve number and practical problems involving place value; Add/subtract powers of 10. 723,456 The comma helps us to read the number: the digits before the comma tell us how many 1000s there are. I am going to read a number. Write the number on your whiteboard. Make sure the comma doesn’t look like a decimal point! 543,2611 Read the number 723,456. Read, but do not show, 543,261. Children write the number on their whiteboards. In this number, the 5 tells us how many hundred thousands there are, the 4 tells us how many ten thousands, and then the 3 how many one thousands. Year 6

Write the 6-digit number these place value cards make. Day 1: Solve number and practical problems involving place value; Add/subtract powers of 10. Write the 6-digit number these place value cards make. Year 6

Write the 6-digit number these place value cards make. Day 1: Solve number and practical problems involving place value; Add/subtract powers of 10. Write the 6-digit number these place value cards make. Year 6

Write the 6-digit number these place value cards make. Day 1: Solve number and practical problems involving place value; Add/subtract powers of 10. Write the 6-digit number these place value cards make. Year 6

Day 1: Solve number and practical problems involving place value; Add/subtract powers of 10. Write 543,261. 1 543,261 Subtract 40,000. Which digit will change? 503,261 Now subtract 200. 503,061 Subtract 61. 503,000 Add 4. 503,004 Add 210. 503,214 Children can now go on to do differentiated GROUP ACTIVITIES. You can find Hamilton’s group activities in this unit’s TEACHING AND GROUP ACTIVITIES download. WT: Select a digit from a 6-digit number and write its value. Repeat with other digits. Check by adding. ARE: Eliminate digits shown from a 6-digit number, 1 or 2 at a time, using numbers based on a dice roll. GD: Write a 6-digit number and make it into 555,555 by adding/subtracting numbers of up to 6 digits. How we could we ‘zap’ each digit? 723,456 Year 6

The Practice Sheet on this slide is suitable for most children. Differentiated PRACTICE WORKSHEETS are available on Hamilton’s website in this unit’s PROCEDURAL FLUENCY box. WT: Place value number sentences Sheet 1. ARE: Place value number sentences Sheet 2 (above). GD: Place value number sentences Sheet 3. Challenge Year 6

Place Value, Addition, Subtraction Understand place value in 6-digit numbers Add and subtract powers of 10 Objectives Day 2 Solve number and practical problems involving place value. Add/subtract multiples of 1s, 10s, 100s, 1000s, 10,000s and 100,000s. Year 6

What number is 1 more? Write it. Day 2: Solve number and practical problems involving place value; Add/subtract multiples of 1s, 10s, 100s, 1000s, 10,000s and 100,000s. 345,462 1 What number is 1 more? Write it. 345,463 10 more? 345,472 100 more? 345,562 1000 more? 346,462 10,000 more? 355,462 Year 6

What number is 1 less? Write it. Day 2: Solve number and practical problems involving place value; Add/subtract multiples of 1s, 10s, 100s, 1000s, 10,000s and 100,000s. 345,462 1 What number is 1 less? Write it. 345,461 10 less? 345,452 100 less? 345,362 1000 less? 344,462 10,000 less? 335,462 Year 6

Keep going until you pass 245,900! Keep going until you pass 256,000! Day 2: Solve number and practical problems involving place value; Add/subtract multiples of 1s, 10s, 100s, 1000s, 10,000s and 100,000s. Work in groups. Write 245,865, then pass to the next person to add 10, writing the answer underneath. Keep going until you pass 245,900! Work in groups. Write 245,865, then pass to the next person to add 100, writing the answer underneath. Keep going until you pass 256,000! Year 6

Day 2: Solve number and practical problems involving place value; Add/subtract multiples of 1s, 10s, 100s, 1000s, 10,000s and 100,000s. 6 children are going to make a counting machine. Now they are going to keep adding 1. First they show the number 478,695. Check that they are doing this correctly! 6 different children are going to make a counting machine. Now they are going to keep adding 10. First they show the number 478,695. Check that they are doing this correctly! Ask 6 children to make a counting machine. Each child has a pack of 0–9 cards. Ask them to each choose a card to make the number 478,695 and then add 1 repeatedly until they reach 478,701. The rest of the class check. Repeat with 6 new children adding 10 from 478,695 until they reach 478,725. Call out instructions such as + 200,000, – 40,000. The children with the cards work together to make the new number. The rest of the class check. Today would be a great day to use a problem-solving investigation – Activity Set A (from NCETM) – as the group activity, which you can find in this unit’s IN-DEPTH INVESTIGATION box on Hamilton’s website. Alternatively, children can now go on to do differentiated GROUP ACTIVITIES. You can find Hamilton’s group activities in this unit’s TEACHING AND GROUP ACTIVITIES download. WT: Write a 6-digit number and make it into 555,555 by adding or subtracting 1s, 10s, 100s, 1000s, 10,000s and 100,000s. ARE: Make 999,999, by adding 1s, 10s, 100s, 1000s, 10,000s and 100,000s based on a dice roll. Repeat for subtraction to make 111,111. GD: ‘Spend’ £999,999 by subtracting 6-digit numbers based on a dice roll. Make a million by adding two 6-digit numbers. Add 200,000! Add 60! Subtract 5000! Subtract 40,000! Year 6

The Practice Sheet on this slide is suitable for most children. Differentiated PRACTICE WORKSHEETS are available on Hamilton’s website in this unit’s PROCEDURAL FLUENCY box. WT/ARE/GD: Use place value and mental skills to practise 5- and 6-digit additions and subtractions. Challenge Year 6

Place Value, Addition, Subtraction Understand place value in 6-digit numbers Add and subtract powers of 10 Well Done! You’ve completed this unit. Objectives Day 1 Solve number and practical problems involving place value. Add/subtract powers of 10. Day 2 Solve number and practical problems involving place value. Add/subtract multiples of 1s, 10s, 100s, 1000s, 10,000s and 100,000s. You can now use the Mastery: Reasoning and Problem-Solving questions to assess children’s success across this unit. Go to the next slide. Year 6

Problem solving and reasoning questions Sketch a line 0-1,000,000 Teacher marks a mystery number (e.g. 400,000). What number have I marked? Children ask questions to guess. Repeat. What is the smallest number between 800,000 and 900,000 which has just four digits all the same and no zero? How many numbers between 100,000 and 200,000 contain exactly four 9s? Add 1, 10 or 100 each go. How many goes to turn 98,089 into 99,999? Year 6

Problem solving and reasoning answers Sketch a line 0-1,000,000. Teacher marks a mystery number (e.g. 400,000). What number have I marked? Children ask questions to guess. Repeat. What strategies do children use to identify the numbers marked? e.g. locating 500,000 as halfway along the line and other significant markers such as 250,000 and 750,000. Do children make the connection that 400,000 is getting towards halfway, the equivalent of 40 on a 0-100 line? Note that although in earlier years children may have completed a similar exercise with numbers to 1000 or 10,000, some may find the larger numbers intimidating so ensure lots of practice correctly reading and writing 6-digit numbers. Some numbers may sound large, e.g. 10,000 but are, within the context of a 0-1,000,000 line, relatively small. 10,000 is the equivalent of just 1 on a 0-100 line! What is the smallest number between 800,000 and 900,000 which has just four digits all the same and no zero? 811,112 Most children will realise that the number has four 1s but may put them in different places, e.g. 821,111. How many numbers between 100,000 and 200,000 contain exactly four 9s? 45 The four 9s can occupy the 5 remaining places in 5 different ways: 199,99_ 199,9_9 199,_99 19_,999 1_9,999 The remaining digit can be any one of the digits 0-8, i.e. 9 choices, so there are 9 x 5 = 45 possible answers. Look for how systematically children set about this task, for example listing every possibility where the 9s are in the last 4 places. Add 1, 10 or 100 each go. How many goes to turn 98,089 into 99,999? 20 goes. Quickest will be to add 100s, then a final 10, the sequence is:  98,089 98,189 98,289 98,389 98,489 98,589 98,689 98,789 98,889 98,989 99,089 99,189 99,289 99,389 99,489 99,589 99,689 99,789 99,889 99,989 19 x 100 added 99,999 + 10 Year 6