Place Value Place value in 5-digit and 6-digit numbers, place on lines, add and subtract using place value. Objectives Day 1 Understand place value in 5-digit numbers. Understand place value in 6-digit numbers. Day 2 Add and subtract 1s, 10s, 100s, 1000s and 10,000s. Add and subtract 1s, 10s, 100s, 1000s, 10,000s and 100,000s. Day 3 Place 5-digit numbers on a line. Compare pairs of numbers, using < and >. Place 6-digit numbers on a line. Compare pairs of numbers, using < and >. 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 an IWB calculator. Year 5/6

Place Value Place value in 5-digit and 6-digit numbers, place on lines, add and subtract using place value. Short Mental Workouts Day 1 Place value in 4-digit numbers Day 2 Count on and back in steps of 100 Day 3 Decimal pairs to 100 The short activities suggested here do not have to be done at the beginning of your maths lesson - they are suitable for doing at any time of the day to provide ongoing revision of important mental and oral skills. While there probably isn’t time during your maths lesson for these activities, it is crucial to regularly revisit the skills used. If you decide to use them – perhaps at the beginning of the day for ‘morning maths’, as you line up for lunch, or as a ‘brain-break’ during the afternoon - it might be useful to drag and drop the relevant slide or slides below to that day’s teaching. Year 5/6

Place value in 4-digit numbers Place value in 5-digit and 6-digit numbers, place on lines, add and subtract using place value. Short Mental Workout Place value in 4-digit numbers You can choose to drag this slide to the start of Day 1 Children use whiteboards and pens to write their answers. Call out instructions such as: Write a 4-digit number where: - the digit 4 is worth 4000. - the digit 2 is worth 20. - the digit 3 is worth 300. Year 5/6

Count on and back in steps of 100 Place Value Place value in 5-digit and 6-digit numbers, place on lines, add and subtract using place value. Short Mental Workout Count on and back in steps of 100 You can choose to drag this slide to the start of Day 2 Count together or around the class, on or back in steps of 100, from 3-digit and 4-digit starting numbers, e.g. 510, 843, 1474, 5079, 8226. If counting round the class, consider starting the count with Y5 children so that Y6 children say the larger numbers. Ensure the counts go far enough to cross place value ‘boundaries’, such as 1000s and 10,000s. Year 5/6

Place Value Place value in 5-digit and 6-digit numbers, place on lines, add and subtract using place value. Short Mental Workout Decimal pairs to 100 You can choose to drag this slide to the start of Day 3 Play ‘Ping Pong’, with children responding with complements to 100. Begin with 2-digit whole numbers, e.g. you say 75; children respond with 25, you say 41; children respond with 59, etc. then include some decimals, e.g. 62.3, 37.7, 20.8. Year 5/6

Place Value Place value in 5-digit and 6-digit numbers, place on lines, add and subtract using place value. Objectives Day 1 Understand place value in 5-digit numbers. Understand place value in 6-digit numbers. Year 5/6

I am going to read a number. Write the number on your whiteboard. Day 1: Understand place value in 5-digit numbers; Understand place value in 6-digit numbers. 23,456 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! 43,2611 Read the number 23,456. Read, but do not show, 43,261. Children write the number on their whiteboards. In this number, the 4 tells us how many ten thousands, and then the 3 tell us how many one thousands. Year 5/6

Write the 5-digit number these place value cards make. Day 1: Understand place value in 5-digit numbers; Understand place value in 6-digit numbers. Write the 5-digit number these place value cards make. Year 5/6

Write the 5-digit number these place value cards make. Day 1: Understand place value in 5-digit numbers; Understand place value in 6-digit numbers. Write the 5-digit number these place value cards make. Year 5/6

Write the 5-digit number these place value cards make. Day 1: Understand place value in 5-digit numbers; Understand place value in 6-digit numbers. Write the 5-digit number these place value cards make. Year 5/6

Write the 5-digit number these place value cards make. Day 1: Understand place value in 5-digit numbers; Understand place value in 6-digit numbers. Write the 5-digit number these place value cards make. Year 5/6

Subtract 3000. Which digit will change? Day 1: Understand place value in 5-digit numbers; Understand place value in 6-digit numbers. Write 43,561. 1 43,561 Subtract 3000. Which digit will change? 40,561 Now subtract 500. 40,061 Subtract 61. 40,000 Add 4. 40,004 Add 210. 40,214 Year 5/6

Write the 6-digit number these place value cards make. Day 1: Understand place value in 5-digit numbers; Understand place value in 6-digit numbers. Write the 6-digit number these place value cards make. This time we also have cards for hundreds of thousands! 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. Y5 WT: Identify the value of digits. ‘Zap’ digits using subtraction. Y5 ARE/GD: Add and subtract using place value. Y6 WT/ARE: ‘Zap’ digits using subtraction from a 6-digit number, one or two digits at a time, based on a dice roll. Y6 GD: Write a 6-digit number and make it into 555,555 by adding/subtracting two numbers of up to six digits. How could we ‘zap’ each digit in 723,456? Year 5/6

The Practice Sheet on this slide is suitable for most Y5 children. Differentiated PRACTICE WORKSHEETS are available on Hamilton’s website in this unit’s PROCEDURAL FLUENCY box. Y5 WT: Place value additions and subtractions Sheet 1. Y6 ARE/GD: Place value additions and subtractions Sheet 2. Year 5/6

The Practice Sheet on this slide is suitable for most Y6 children. Differentiated PRACTICE WORKSHEETS are available on Hamilton’s website in this unit’s PROCEDURAL FLUENCY box. WT: Place value additions and subtractions Sheet 3. ARE/GD: Y6 Place value additions and subtractions Sheet 4. Challenge Year 5/6

Place Value Place value in 5-digit and 6-digit numbers, place on lines, add and subtract using place value. Objectives Day 2 Add and subtract 1s, 10s, 100s, 1000s and 10,000s. Add and subtract 1s, 10s, 100s, 1000s, 10,000s and 100,000s. Year 5/6

Day 2: Add and subtract 1s, 10s, 100s, 1000s and 10,000s; Add and subtract 1s, 10s, 100s, 1000s, 10,000s and 100,000s. Let’s count in steps of 100. 636 736 836 936 1036 1136 1236 1336 1436 1536 1636 2423 2523 2623 2723 2823 2923 3023 3123 3223 3323 3423 8514 8614 8714 8814 8914 9014 9114 9214 9314 9314 9414 Year 5/6

What number is 1 more? Write it. Day 2: Add and subtract 1s, 10s, 100s, 1000s and 10,000s; Add and subtract 1s, 10s, 100s, 1000s, 10,000s and 100,000s. 45,462 1 What number is 1 more? Write it. 45,463 10 more? 45,472 100 more? 45,562 1000 more? 46,462 10,000 more? 55,462 Year 5/6

What number is 1 less? Write it. Day 2: Add and subtract 1s, 10s, 100s, 1000s and 10,000s; Add and subtract 1s, 10s, 100s, 1000s, 10,000s and 100,000s. 36,478 1 What number is 1 less? Write it. 36,477 10 less? 36,468 100 less? 36,378 1000 less? 35,478 10,000 less? 26,478 Year 5/6

Day 2: Add and subtract 1s, 10s, 100s, 1000s and 10,000s; Add and subtract 1s, 10s, 100s, 1000s, 10,000s and 100,000s. I am going to enter 30,567 into a calculator. We will add or subtract multiples of 10,000, 1000, 100, 10 and 1 to make all the digits the same (4), so the new number will be 44,444. 30,567 44,444 How can we make the first digit change to 4? What do we need to add? How can we make the third digit change to 4? What do we need to subtract? Y5 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: Work out what to add and subtract, one step at a time, to make 55,555 from a starting number. ARE/GD: Start with 11,111. Play a dice game, using place value addition to get as close to 99,999 as possible. How can we make the second digit change to 4? What do we need to add? How can we make the last digit change to 4? What do we need to subtract? How can we make the fourth digit change to 4? What do we need to subtract? Year 5/6

The Practice Sheet on this slide is suitable for most Y5 children. Differentiated PRACTICE WORKSHEETS are available on Hamilton’s website in this unit’s PROCEDURAL FLUENCY box. WT: Adding and subtracting 1, 10, 100, 1000 and 10,000 Sheet 1. ARE/GD: Adding and subtracting 1, 10, 100, 1000 and 10,000 Sheet 2. Challenge Year 5/6

Day 2: Add and subtract 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! Further teaching with Year 6. 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 other children 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 other children check. Y6 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: Work out what to add and subtract, one step at a time, to make 555,555 from a starting number. ARE/GD: Start with 111,111. Play a dice game aiming to get as close to 999,999 as possible. Add 200,000! Add 60! Subtract 5000! Subtract 40,000! Year 5/6

The Practice Sheet on this slide is suitable for most Y6 children. Differentiated PRACTICE WORKSHEETS are available on Hamilton’s website in this unit’s PROCEDURAL FLUENCY box. WT: Adding and subtracting 1s, 10s, 100s, 1000s, 10,000s and 100,000s Sheet 3. ARE/GD: Adding and subtracting 1s, 10s, 100s, 1000s, 10,000s and 100,000s Sheet 4. Challenge Year 5/6

Place Value Place value in 5-digit and 6-digit numbers, place on lines, add and subtract using place value. Objectives Day 3 Place 5-digit numbers on a line. Compare pairs of numbers, using < and >. Place 6-digit numbers on a line. Compare pairs of numbers, using < and >. Year 5/6

Day 3: Place 5-digit numbers on a line Day 3: Place 5-digit numbers on a line. Compare pairs of numbers, using < and >. Place 6-digit numbers on a line. Compare pairs of numbers, using < and >. , 9 3 2 5 1 Where shall we put this digit to make the largest 5-digit number we can? Where do the three numbers belong on this landmarked line? Use these digits to write largest and the smallest possible numbers. Ask Y5 children to indicate roughly where each of the three numbers written above belongs on the line, between which 10,000s, and which multiple of 10,000 is closer. Y5 children come up and mark them. Do the rest of the class agree? Year 5/6

Day 3: Place 5-digit numbers on a line Day 3: Place 5-digit numbers on a line. Compare pairs of numbers, using < and >. Place 6-digit numbers on a line. Compare pairs of numbers, using < and >. , , 3 4 8 7 2 5 Y5: Where shall we put this digit to make the largest 5-digit number we can? Y6 You’re trying to make the largest 6-digit number. Y5: Where do the three numbers belong on this landmarked line? Use these digits to write largest and the smallest possible numbers. Year 5/6

Y6: Where do the three numbers belong on this landmarked line? Day 3: Place 5-digit numbers on a line. Compare pairs of numbers, using < and >. Place 6-digit numbers on a line. Compare pairs of numbers, using < and >. , , 3 4 8 7 2 5 Y6: Where do the three numbers belong on this landmarked line? Ask Y6 children to say roughly where each of the 3 numbers belongs on the line – between which 100,000s. Y6 children come up and mark them. Today’s GROUP ACTIVITY is a whole class activity. You can find more details in the unit’s TEACHING AND GROUP ACTIVITIES download. Y5/Y6 WT/ARE/GD: Use digit cards to make a pair of numbers, compare and place on a line. Year 5/6

The Practice Sheet on this slide is suitable for most Y5 children. Differentiated PRACTICE WORKSHEETS are available on Hamilton’s website in this unit’s PROCEDURAL FLUENCY box. WT/ARE: Comparing 5-digit numbers Sheet 1. GD: Ordering 5-digit numbers Sheet 2. Year 5/6

The Practice Sheet on this slide is suitable for most Y6 children. Differentiated PRACTICE WORKSHEETS are available on Hamilton’s website in this unit’s PROCEDURAL FLUENCY box. WT: Comparing numbers up to 1 million Sheet 3. ARE/GD: Comparing numbers up to 1 million Sheet 4. Working at ARE complete questions 1 to 14. Greater Depth complete all questions. Challenge Year 5/6

Well Done! You’ve completed this unit. Place Value Place value in 5-digit and 6-digit numbers, place on lines, add and subtract using place value. Well Done! You’ve completed this unit. Objectives Day 1 Understand place value in 5-digit numbers. Understand place value in 6-digit numbers. Day 2 Add and subtract 1s, 10s, 100s, 1000s and 10,000s. Add and subtract 1s, 10s, 100s, 1000s, 10,000s and 100,000s. Day 3 Place 5-digit numbers on a line. Compare pairs of numbers, using < and >. Place 6-digit numbers on a line. Compare pairs of numbers, using < and >. Year 5/6

Problem solving and reasoning questions Year 5 Sketch a line 0–100,000. Teacher marks a mystery number (e.g. 5000). What number have I marked? Children ask questions to find the number, e.g. Is it 6000? Repeat. How many numbers between 19,000 and 20,000 contain just one zero? Add 1, 10 or 100 each go. How many goes to turn 98,089 into 99,999? Year 5/6

Problem solving and reasoning answers Year 5 Sketch a line 0–100,000. Teacher marks a mystery number (e.g. 5000). What number have I marked? Children ask questions to find the number, e.g. Is it 6000? Repeat. What strategies do children use to identify the numbers marked? e.g. locating 50,000 as halfway along the line and other significant markers such as 25,000 and 75,000. 5000 is relatively close to 0, the equivalent of 5 on a 0-100 line. Do children make that connection? Note that although in earlier years children may have completed a similar exercise with numbers to 1000, some may find the larger numbers intimidating so ensure lots of practice correctly reading and writing 5-digit numbers. How many numbers between 19,000 and 20,000 contain just one zero? 243.   All of the decade numbers 19,110 – 19,190 (9) and similar for subsequent 100s, so 81 in total where the 1s digit is the only zero. Numbers 19,101 – 19,109 (9) where the 10s is the only zero and similar for subsequent 100s, so again 81 where the 10s digit is the only zero. Finally, any number beginning 190 without a further zero in the final 2 digits, another 81 numbers 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) +10 = 99,999 Year 5/6

Problem solving and reasoning questions Year 6 Sketch a line 0–1,000,000. Mark a mystery number (e.g. 400,000). What number have I marked? Children ask questions to find the number, e.g. Is it 350,000? Repeat. What is the smallest number between 800,000 and 900,000 which has just four digits all the same (no zeros allowed)? 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 5/6

Problem solving and reasoning answers Year 6 Sketch a line 0–1,000,000. Mark a mystery number (e.g. 400,000). What number have I marked? Children ask questions to find the number, e.g. Is it 350,000? 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. 400,000 is getting towards halfway, the equivalent of 40 on a 0-100 line. Do children make that connection? 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 (no zeros allowed)? 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? 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) +10 = 99,999 Year 5/6