Place Value Addition Subtraction Understand place value in

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 1 s, 100 s, 1000 s, 10, 000 s and 100, 000 s. © hamilton-trust. org. uk 1 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, 10, 000 and 100, 000 (prerequisite skills) © hamilton-trust. org. uk 2 Year 6

Place Value, Addition, Subtraction Understand place value in 6 -digit numbers Add and subtract powers of 10 Starter Order 5 -digit numbers © hamilton-trust. org. uk 3 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, 10, 000 and 100, 000 © hamilton-trust. org. uk 4 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. © hamilton-trust. org. uk 5 Year 6

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 1000 s there are. Make sure the comma doesn’t look like a decimal point! I am going to read a number. Write the number on your whiteboard. 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. 543, 2611 © hamilton-trust. org. uk 6 Year 6

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. © hamilton-trust. org. uk 7 Year 6

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. © hamilton-trust. org. uk 8 Year 6

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. © hamilton-trust. org. uk 9 Year 6

Day 1: Solve number and practical problems involving place value; Add/subtract powers of 10. Write 543, 261 Subtract 40, 000. Which digit will change? 503, 261 503, 061 Now subtract 200. 1 503, 000 Subtract 61. 503, 004 Add 4. Add 210. How we could we ‘zap’ each digit? 723, 456 © hamilton-trust. org. uk 503, 214 10 Year 6

Challenge © hamilton-trust. org. uk 11 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 1 s, 100 s, 1000 s, 10, 000 s and 100, 000 s. © hamilton-trust. org. uk 12 Year 6

Day 2: Solve number and practical problems involving place value; Add/subtract multiples of 1 s, 100 s, 1000 s, 10, 000 s and 100, 000 s. 345, 462 What number is 1 more? Write it. © hamilton-trust. org. uk 345, 463 10 more? 345, 472 100 more? 1 345, 562 1000 more? 346, 462 10, 000 more? 355, 462 13 Year 6

Day 2: Solve number and practical problems involving place value; Add/subtract multiples of 1 s, 100 s, 1000 s, 10, 000 s and 100, 000 s. 345, 462 What number is 1 less? Write it. © hamilton-trust. org. uk 345, 461 10 less? 345, 452 100 less? 1 345, 362 1000 less? 344, 462 10, 000 less? 335, 462 14 Year 6

Day 2: Solve number and practical problems involving place value; Add/subtract multiples of 1 s, 100 s, 1000 s, 10, 000 s and 100, 000 s. 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! © hamilton-trust. org. uk 15 Year 6

Day 2: Solve number and practical problems involving place value; Add/subtract multiples of 1 s, 100 s, 1000 s, 10, 000 s and 100, 000 s. 6 children are going to make a counting machine. First they show the number 478, 695. 6 different children are going to make a counting machine. First they show the number 478, 695. Now they are going to keep adding 1. Check that they are doing this correctly! Now they are going to keep adding 10. Check that they are doing this correctly! Add 200, 000! Add 60! Subtract 40, 000! © hamilton-trust. org. uk 16 Subtract 5000! Year 6

Challenge © hamilton-trust. org. uk 17 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 1 s, 100 s, 1000 s, 10, 000 s and 100, 000 s. © hamilton-trust. org. uk 18 Year 6

Problem solving and reasoning questions Sketch a line 0 -1, 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 9 s? Add 1, 10 or 100 each go. How many goes to turn 98, 089 into 99, 999? © hamilton-trust. org. uk 19 Year 6

Problem solving and reasoning answers Sketch a line 0 -1, 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 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 1 s but may put them in different places, e. g. 821, 111. How many numbers between 100, 000 and 200, 000 contain exactly four 9 s? 45 The four 9 s 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 9 s 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 100 s, then a final 10, the sequence is: 98, 089 98, 989 99, 889 98, 189 98, 289 99, 089 99, 189 99, 989 19 x 100 added © hamilton-trust. org. uk 98, 389 98, 489 99, 289 99, 389 99, 999 + 10 20 98, 589 99, 489 98, 689 99, 589 98, 789 99, 689 98, 889 99, 789 Year 6