1. Place Value, Addition, Subtraction
Use place value to add, subtract and round 6- and 7-digit numbers
Objectives
Day 1
Understand what each digit represents in 7-digit numbers Compare numbers up to 10 million.
Day 2
Add and subtract 1, 10, 100, 1000, 10,000, 100,000 and 1,000,000 to/from 7-digit numbers.
Day 3
Place 7-digit numbers on a number line and round to the nearest 10,000, 100,000 or 1,000,000.
Before teaching, be aware that:
On Day 1 children will need mini-whiteboards and pens. You will need a real or IWB dice.
On Day 2 children will need mini-whiteboards and pens. You may wish to use an IWB calculator’s constant function to repeatedly add, then subtract, 1, 10, 100, 1000, 10,000, 100,000 and 1,000,000 to/from 5,555,555.
On Day 3 children will need mini-whiteboards and pens.
Year 6

2. Place Value, Addition, Subtraction
Use place value to add, subtract and round 6- and 7-digit numbers
Starters
Day 1
Place value in 6-digit numbers (pre-requisite skills)
Day 2
Count on/back in 10s, 100s, 1000s and 10,000s from 5-digit numbers (pre-requisite skills)
Day 3
Add and subtract near multiples of 10, 100 and 1000 to/from 4-digit numbers (simmering 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

3. Place Value, Addition, Subtraction
Use place value to add, subtract and round 6- and 7-digit numbers
Starter
Place value in 6-digit numbers
Pre-requisite skills – to use this starter, drag this slide to the start of Day 1
Children use the digits 2, 3, 4, 5, 6 and 7 to make five 6-digit numbers and write them on their whiteboards. Ask children to circle a number where: the 6 is worth 60,000, the 3 is worth 3000, the 4 is worth 400, etc.
The first child to circle all five of their numbers is the winner.
Year 6

4. Place Value, Addition, Subtraction
Use place value to add, subtract and round 6- and 7-digit numbers
Starter
Count on/back in 10s, 100s, 1000s and 10,000s from 5-digit numbers
Pre-requisite skills – to use this starter, drag this slide to the start of Day 2
Working in pairs, children start by writing on their whiteboards: 45,378. They count on in 10s, recording each number until they have written five more numbers. Write 45,428. Was this the last number they wrote? If so they earn a point. Repeat counting back in 100s from 45,378, on in 1000s and on in 10,000s. Which pairs scored 4 points?
Year 6

5. Place Value, Addition, Subtraction
Use place value to add, subtract and round 6- and 7-digit numbers
Starter
Add and subtract near multiples of 10, 100 and 1000 to/from 4-digit numbers
Simmering skills – to use this starter, drag this slide to the start of Day 3
Write on the board 2357 and 4178 in one set, and 29, 51, 198, 203, 1997 in the second set. Explain that children choose a number in the first set and add or subtract a number from the second set. Challenge them to work in pairs to complete as many additions and subtractions as they can in 7 minutes. There are 20 possible calculations!
Year 6

6. Place Value, Addition, Subtraction
Use place value to add, subtract and round 6- and 7-digit numbers
Objectives
Day 1
Understand what each digit represents in 7-digit numbers Compare numbers up to 10 million.
Year 6

7. We will use commas to do this.
Day 1: Understand what each digit represents in 7-digit numbers; Compare numbers up to 10 million.
Commas or thin spaces (in print) are used to group digits in groups of three to help us to read big numbers.
We will use commas to do this.
4,351,468
Let’s read the part of the number that we can see: four hundred and sixty-eight
This digit tells us how many millions there are. Read the whole number: four million, three hundred and fifty-one thousand, four hundred and sixty-eight.
These digits tell us how many 1000s there are. Three hundred and fifty-one thousand, four hundred and sixty-eight.
Count on in 1s to write the next three numbers on your whiteboards:
4,351, ,351, ,351,471
Practise reading them out aloud with your partner.
Year 6

8. What is 2,743,561 – 40,000? Which digit will change?
Day 1: Understand what each digit represents in 7-digit numbers; Compare numbers up to 10 million.
2,743,561
Let’s read the last three digits, and then read the thousands, then the whole number.
What is 2,743,561 – 40,000? Which digit will change?
Now subtract 500.
What are we left with?
Now subtract 700,000.
What are we left with?
Now subtract 3001.
What are we left with?
2,000,060
two million and sixty
Year 6

9. ☐,☐☐☐,☐☐☐ > ☐,☐☐☐,☐☐☐ Roll a 0–9 dice.
Day 1: Understand what each digit represents in 7-digit numbers; Compare numbers up to 10 million.
☐,☐☐☐,☐☐☐ > ☐,☐☐☐,☐☐☐
We are to going try to make the first number greater than the second number.
Where should we place the first digit rolled?
Roll a 0–9 dice.
Repeat until all the spaces are filled.
Half the class write the biggest number possible using the seven digits on the left.
Half the class write the smallest number possible using the seven digits on the right.
Today would be a great day to do Hamilton’s recommended investigation - Sometimes We Lose Things (from NRICH) - 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/ARE: Use dice rolls to construct and subtract from 7-digit numbers.
ARE/GD: Order 7-digit numbers with consecutive digits.
Now write a number in between these two 7-digit numbers.
Year 6

10. Challenge
The Practice Sheet on this slide is suitable for most children.
You can download differentiated PRACTICE WORKSHEETS from Hamilton’s website in this unit’s PROCEDURAL FLUENCY box.
WT: Compare and order trios of numbers including use of > and <.
ARE/GD: Compare and order sets of numbers including use of > and <.
Year 6

11. Place Value, Addition, Subtraction
Use place value to add, subtract and round 6- and 7-digit numbers
Objectives
Day 2
Add and subtract 1, 10, 100, 1000, 10,000, 100,000 and 1,000,000 to/from 7-digit numbers.
Year 6

12. Day 2: Add and subtract 1, 10, 100, 1000, 10,000, 100,000 and 1,000,000 to/from 7-digit numbers.
5,555,510
5,555,559
5,555,558
5,555,555
5,555,556
5,555,557
And the next number is? Write it on your whiteboard.
5,555,550
5,555,549
5,555,551
5,555,552
5,555,554
5,555,555
5,555,553
Read numbers as they appear on screen…
And the next number is? Write it on your whiteboard.
Year 6

13. Day 2: Add and subtract 1, 10, 100, 1000, 10,000, 100,000 and 1,000,000 to/from 7-digit numbers.
5,555,585
5,555,595
5,555,575
5,555,555
5,555,565
5,555,605
And the next number is? Write it on your whiteboard.
5,555,495
5,555,525
5,555,505
5,555,545
5,555,555
5,555,515
5,555,535
And the next number is? Write it on your whiteboard.
Year 6

14. Day 2: Add and subtract 1, 10, 100, 1000, 10,000, 100,000 and 1,000,000 to/from 7-digit numbers.
5,555,855
5,555,955
5,555,755
5,555,555
5,555,655
5,556,055
And the next number is? Write it on your whiteboard.
5,555,055
5,554,955
5,555,155
5,555,255
5,555,455
5,555,555
5,555,355
And the next number is? Write it on your whiteboard.
Year 6

15. Day 2: Add and subtract 1, 10, 100, 1000, 10,000, 100,000 and 1,000,000 to/from 7-digit numbers.
5,558,555
5,559,555
5,557,555
5,555,555
5,556,555
5,560,555
And the next number is? Write it on your whiteboard.
5,549,555
5,550,555
5,551,555
5,552,555
5,554,555
5,555,555
5,553,555
And the next number is? Write it on your whiteboard.
Year 6

16. Day 2: Add and subtract 1, 10, 100, 1000, 10,000, 100,000 and 1,000,000 to/from 7-digit numbers.
5,585,555
5,595,555
5,575,555
5,555,555
5,565,555
5,605,555
And the next number is? Write it on your whiteboard.
5,515,555
5,555,555
5,525,555
5,495,555
5,505,555
5,545,555
5,535,555
And the next number is? Write it on your whiteboard.
Year 6

17. Day 2: Add and subtract 1, 10, 100, 1000, 10,000, 100,000 and 1,000,000 to/from 7-digit numbers.
5,855,555
5,555,555
5,955,555
5,655,555
5,755,555
6,055,555
And the next number is? Write it on your whiteboard.
5,055,555
4,955,555
5,155,555
5,255,555
5,455,555
5,555,555
5,355,555
And the next number is? Write it on your whiteboard.
Year 6

18. Day 2: Add and subtract 1, 10, 100, 1000, 10,000, 100,000 and 1,000,000 to/from 7-digit numbers.
1,000,001
999,995
999,999
999,996
999,998
999,997
And the next number is? Write it on your whiteboard.
1,999,998
1,999,999
2,000,000
2,000,001
2,000,003
2,000,002
2,000,004
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 on our website.
WT: Turn a 7-digit number into 5,555,555 by adding and subtracting multiples of 1, 10, 100, 1000, 10,000, 100,000 and 1,000,000.
ARE/GD: Use dice rolls to add/subtract 1, 10, 100, 1000, 10,000, 100,000 or 1,000,000 from 5,000,000.
And the next number is? Write it on your whiteboard.
Year 6

19. Challenge
The Practice Sheet on this slide is suitable for most children.
You can download differentiated PRACTICE WORKSHEETS from Hamilton’s website in this unit’s PROCEDURAL FLUENCY box.
WT: Use place value to add and subtract from large numbers (not crossing boundaries).
ARE/GD: Use place value to add and subtract from large numbers (including crossing boundaries).
Year 6

20. Place Value, Addition, Subtraction
Use place value to add, subtract and round 6- and 7-digit numbers
Objectives
Day 3
Place 7-digit numbers on a number line and round to the nearest 10,000, 100,000 or 1,000,000.
Year 6

21. Day 3: Place 7-digit numbers on a number line and round to the nearest 10,000, 100,000 or 1,000,000.
Do you agree with your neighbour?
Sketch a number line from 1,000,000 to 2,000,000.
Mark the number that is halfway.
Check with your neighbour.
Now mark a number which rounds to 1,000,000 and one which rounds to 2,000,000 (rounding to the nearest 1,000,000).
Year 6

22. Day 3: Place 7-digit numbers on a number line and round to the nearest 10,000, 100,000 or 1,000,000.
Sketch a number line from 2,500,000 to 2,600,000.
Mark the number that is halfway.
Now mark a number which rounds to 2,500,000 and one which rounds to 2,600,000 (rounding to the nearest 100,000).
Sketch a number line from 2,530,000 to 2,540,000.
Mark the number that is halfway.
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 on our website.
WT/ARE: Mark numbers on a 2,000,000 to 3,000,000 landmarked line and round them.
ARE/GD: Round 7-digit numbers to the nearest 100, 1000, 10,000, 100,000 and 1,000,000.
Now mark a number which rounds to 2,530,000 and one which rounds to 2,5400,000 (rounding to the nearest 10,000).
Year 6

23. The Practice Sheet on this slide is suitable for most children.
You can download differentiated PRACTICE WORKSHEETS from Hamilton’s website in this unit’s PROCEDURAL FLUENCY box.
WT: Round numbers to the nearest 1,000,000, 100,000 and 10,000 (including multiples of 100 and 1000).
ARE/GD: Rounding numbers to the nearest 1,000,000, 100,000 and 10,000.
Challenge
Year 6

24. Place Value, Addition, Subtraction
Use place value to add, subtract and round 6- and 7-digit numbers
Objectives
Day 1
Understand what each digit represents in 7-digit numbers Compare numbers up to 10 million.
Day 2
Add and subtract 1, 10, 100, 1000, 10,000, 100,000 and 1,000,000 to/from 7-digit numbers.
Day 3
Place 7-digit numbers on a number line and round to the nearest 10,000, 100,000 or 1,000,000.
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

25. Problem solving and reasoning questions
Fill in the missing digits:
3 8 4, ☐ 7 9 < 3 8 4, 0 ☐ 9
1,0 ☐0, 841 > 1, 0 40,996
Complete the place value subtractions.
(a) 1,249,541 – = 1,240,501
(b) 673, – = 70,090
(c) 2,951,159 – = 2,050,050
Draw a line from 3,000,000 to 4,000,000.
Mark the midpoint.
Mark two numbers that round to 3,000,000.
Mark two numbers that round to 3,500,000 as the nearest 100,000.
Year 6