1. Decimals and Fractions
Understand place value in numbers with three decimal places
Objectives
Day 1
Understand place value addition and subtraction of numbers with 3 decimal places.
Day 2
Multiply and divide by 10, 100 and 1000 (answers from 3 decimal places to 7-digit whole numbers).
Day 3
Round decimals to the nearest whole, tenth and hundredth.
Before teaching, be aware that:
On Day 1 children will need mini-whiteboards and pens. You may wish to use the ITP Moving digits (see resources).
On Day 2 children will need mini-whiteboards and pens.
On Day 3 children will need mini-whiteboards and pens. You may wish to use a real counting stick.
Year 6

2. Decimals and Fractions
Understand place value in numbers with three decimal places
Starters
Day 1
Count in steps of 0.01 and 0.1 from numbers with 2 decimal places (pre-requisite skills)
Day 2
Place value in numbers with 3 decimal places (pre-requisite skills)
Day 3
Place numbers with 2 decimal places on a line (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

3. Decimals and Fractions
Understand place value in numbers with three decimal places
Starter
Count in steps of 0.01 and 0.1 from numbers with 2 decimal places
Pre-requisite skills – to use this starter, drag this slide to the start of Day 1
Count around the class in steps of 0.01, starting at 5.45 to at least 6.2. Children shout multiples of 0.1 or 1 when they reach them. Repeat, this time counting back from 6.19 to Ensure you count through multiples of 0.1 and 1.
Year 6

4. Decimals and Fractions
Understand place value in numbers with three decimal places
Starter
Place value in numbers with 3 decimal places
Pre-requisite skills – to use this starter, drag this slide to the start of Day 2
Children play in pairs. They each write a 4-digit number with 3 decimal places, all digits different, no zeros, e.g They take it in turns to roll a 1–9 dice. If the digit matches one of the digits in their number, they subtract what the digit is worth, e.g. roll 8 so subtract The first to reach 0 wins.
Year 6

5. Decimals and Fractions
Understand place value in numbers with three decimal places
Starter
Place numbers with 2 decimal places on a line
Pre-requisite skills – to use this starter, drag this slide to the start of Day 3
Sketch a line from 0 to 1. Mark, but do not label, where 0.47 would be. I’m thinking of a number on this line. Suggest a number and I will tell you whether my number is greater or less than that number. Take a suggestion from each table. You can now ask me to mark on two different tenths, e.g. 0.1 and 0.2, to help you to guess my number. Which tenths do you think would be useful? Mark on the tenths children suggest (e.g. 0.4 and 0.5). Each group agrees an estimate and show the same time. The group with the closest estimate wins.
Year 6

6. Decimals and Fractions
Understand place value in numbers with three decimal places
Objectives
Day 1
Understand place value addition and subtraction of numbers with 3 decimal places.
Year 6

7. Day 1 Understand place value addition and subtraction of numbers with 3 decimal places.
4.735
What do the 7, 3 and 5 represent?
Subtract Write the answer on your whiteboards.
4 8
When subtracting 0.005, check that children write 4.73, not
Which is more, or 4.8? Why?
4.735 only has 7 tenths whereas 4.8 has 8 tenths. So, 4.8 is more even though has more digits.
Year 6

8. Day 1 Understand place value addition and subtraction of numbers with 3 decimal places.
4.735
What needs to be subtracted from to give 4.035?
What needs to be subtracted from to give 4.705?
Year 6

9. Day 1 Understand place value addition and subtraction of numbers with 3 decimal places.
Write at the top of your whiteboard.
4.7357
Add Write the new number on your whiteboard.
4.775
4.375
4.495
4.494
4.444
Subtract 0.4. Write the new number.
Add Write the new number.
Subtract Write the new number.
Today would be a great day to use a problem-solving investigation – The Size and Distance of the Planets – 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: Add and subtract 0.1s. 0.01s and 0.001s. Test predictions with a calculator.
ARE/GD: Add and subtract 0.1s. 0.01s and 0.001s from to make target numbers.
Subtract Write the new number.
What was your final number?
Did your neighbour get the same answer?
Year 6

10. 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 to add and subtract 0.1s, 0.01s and 0.001s.
Challenge
Year 6

11. Decimals and Fractions
Understand place value in numbers with three decimal places
Objectives
Day 2
Multiply and divide by 10, 100 and 1000 (answers from 3 decimal places to 7-digit whole numbers).
Year 6

12. We are going to multiply by 10 three times.
Day 2: Multiply and divide by 10, 100 and 1000 (answers from 3 decimal places to 7-digit whole numbers).
10,000s
1000s
100s
10s 1s
0.1s
1/10s
0.01s
1/100s
0.001s
1/1000s
5 6
We are going to multiply by 10 three times.
Year 6

13. We are going to multiply by 10 three times.
Day 2: Multiply and divide by 10, 100 and 1000 (answers from 3 decimal places to 7-digit whole numbers).
10,000s
1000s
100s
10s 1s
0.1s
1/10s
0.01s
1/100s
0.001s
1/1000s
We are going to multiply by 10 three times.
Year 6

14. We are going to multiply by 10 three times.
Day 2: Multiply and divide by 10, 100 and 1000 (answers from 3 decimal places to 7-digit whole numbers).
10,000s
1000s
100s
10s 1s
0.1s
1/10s
0.01s
1/100s
0.001s
1/1000s
What have we multiplied 56 by? What has happened to the digits? What was the digit 6 worth? And now? Why? And the digit 5?
We are going to multiply by 10 three times.
Year 6

15. We are going to multiply by 1000.
Day 2: Multiply and divide by 10, 100 and 1000 (answers from 3 decimal places to 7-digit whole numbers).
10,000s
1000s
100s
10s 1s
0.1s
1/10s
0.01s
1/100s
0.001s
1/1000s
5 6
We are going to multiply by 1000.
Year 6

16. We are going to multiply by 1000.
Day 2: Multiply and divide by 10, 100 and 1000 (answers from 3 decimal places to 7-digit whole numbers).
10,000s
1000s
100s
10s 1s
0.1s
1/10s
0.01s
1/100s
0.001s
1/1000s
5 6
We are going to multiply by 1000.
Year 6

17. We are going to multiply by 1000.
Day 2: Multiply and divide by 10, 100 and 1000 (answers from 3 decimal places to 7-digit whole numbers).
10,000s
1000s
100s
10s 1s
0.1s
1/10s
0.01s
1/100s
0.001s
1/1000s
5 6
We are going to multiply by 1000.
Year 6

18. What happened to the zero?
Day 2: Multiply and divide by 10, 100 and 1000 (answers from 3 decimal places to 7-digit whole numbers).
10,000s
1000s
100s
10s 1s
0.1s
1/10s
0.01s
1/100s
0.001s
1/1000s
What happened to the zero?
We’re going to divide 2340 by What will happen to the digits this time?
Year 6

19. Day 2: Multiply and divide by 10, 100 and 1000 (answers from 3 decimal places to 7-digit whole numbers).
10,000s
1000s
100s
10s 1s
0.1s
1/10s
0.01s
1/100s
0.001s
1/1000s
We’re going to divide 3457 by Write the answer on your whiteboard. Were you correct?
Year 6

20. Day 2: Multiply and divide by 10, 100 and 1000 (answers from 3 decimal places to 7-digit whole numbers).
10,000s
1000s
100s
10s 1s
0.1s
1/10s
0.01s
1/100s
0.001s
1/1000s
We’re going to multiply 4.52 by 100. Write the answer on your whiteboard. Were you correct?
Year 6

21. Day 2: Multiply and divide by 10, 100 and 1000 (answers from 3 decimal places to 7-digit whole numbers).
10,000s
1000s
100s
10s 1s
0.1s
1/10s
0.01s
1/100s
0.001s
1/1000s
We’re going to multiply 4.32 by Write the answer on your whiteboard. Were you correct?
Year 6

22. Day 2: Multiply and divide by 10, 100 and 1000 (answers from 3 decimal places to 7-digit whole numbers).
Draw a 1000s, 100s, 10s, 1s, 0.1s, 0.01s 0.001s grid on your whiteboard.
Write 7842, then the answer to 7842 ÷ 1000.
Now write and multiply by 1000.
432 × ÷ ÷ × 1000
Work with a partner to find the answer, discussing which way the digits will move, and by how many places.
Year 6

23. Day 2: Multiply and divide by 10, 100 and 1000 (answers from 3 decimal places to 7-digit whole numbers).
Clear your whiteboards and write 4578 in the middle. Multiply it by 10, writing the answer underneath, multiply by 10 again, writing the answer underneath, aligning the digits, and then by 10 again.
Repeat, this time dividing by 10 three times and writing the answers above. Make sure the align the digits, 1s above 1s, 10s above 10s etc.
Look at the pattern of digits. What is × 100? × 1000? 457,800 ÷ 1000?
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: Sequentially multiply and divide a number by powers of 10 to arrive back at the starting number.
GD: Divide four numbers by 100 and 1000, then order. Repeat for multiplying by 100 and 1000.
Year 6

24. The Practice Sheet on this slide and the next are suitable for most children. Choose the sheet(s) most appropriate for your class.
You can download differentiated PRACTICE WORKSHEETS from Hamilton’s website in this unit’s PROCEDURAL FLUENCY box.
WT/ARE: Multiply and divide masses/weights in kilograms by powers of 10. (Sheet 1).
ARE/GD: Identify functions (×/÷ 10, 100 and 100) (Sheet 2).
Year 6

25. The Practice Sheet on this slide and the next are suitable for most children. Choose the sheet(s) most appropriate for your class.
You can download differentiated PRACTICE WORKSHEETS from Hamilton’s website in this unit’s PROCEDURAL FLUENCY box.
WT/ARE: Multiply and divide masses/weights in kilograms by powers of 10 (Sheet 1).
ARE/GD: Identify functions (×/÷ 10, 100 and 100) (Sheet 2).
Year 6

26. Decimals and Fractions
Understand place value in numbers with three decimal places
Objectives
Day 3
Round decimals to the nearest whole, tenth and hundredth.
Year 6

27. Day 3: Round decimals to the nearest whole, tenth and hundredth.2
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
2.9 3
Write a number that goes between 2.3 and 2.4.
Sketch a line from 2.3 to 2.4 and mark on your number.
You have written different numbers, but which whole number are they all closest to?
Show your line if your number is closer to 2.3. Do the rest of the class agree?
Show your line if your number is closer to 2.4. Do the rest of the class agree?
So, they all round to 2.
Remember that numbers ending in 5 round up so 2.35 rounds up to 2.4.
Year 6

28. Day 3: Round decimals to the nearest whole, tenth and hundredth.
0kg
1kg
2kg
3kg
1.499kg
2.125kg
1.752kg
Discuss where to mark 1.499kg, 1.752kg, 2.125kg on the line and which whole numbers of kilograms they round to.
Year 6

29. Day 3: Round decimals to the nearest whole, tenth and hundredth.
1.7kg
1.8kg
1.752kg
Discuss where to mark 1.752kg, on the line. Round 1.752kg to the nearest tenth of a kilogram.
Year 6

30. Day 3: Round decimals to the nearest whole, tenth and hundredth.
1.75kg
1.76kg
1.752kg
Discuss where to mark 1.752kg, on the line. Round 1.752kg to the nearest hundredth of a kilogram.
Year 6

31. HINT! Remember that numbers ending in 5 round up.
Day 3: Round decimals to the nearest whole, tenth and hundredth.
Sketch a line between 2.1kg and 2.2kg, marking on 2.125kg, then ring the closest tenth.
2.125kg rounds to 2.1kg
Now sketch a line between 2.12kg and 2.13kg, marking on 2.125kg, then ring the closest hundredth.
2.125kg rounds to 2.13kg
HINT! Remember that numbers ending in 5 round up.
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: Round numbers with 3 decimal places to the nearest whole kilogram.
ARE/GD: Generate, then round numbers with 3 decimal places to the nearest whole, tenth and hundredth.
Year 6

32. 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: Mark numbers with 1, 2 and 3 decimal places on lines and round to the nearest whole.
ARE/GD: Mark numbers with 1, 2 and 3 decimal places on lines and round to the nearest whole, tenth and hundredth.
Year 6

33. Decimals and Fractions
Understand place value in numbers with three decimal places
Objectives
Day 1
Understand place value addition and subtraction of numbers with 3 decimal places.
Day 2
Multiply and divide by 10, 100 and 1000 (answers from 3 decimal places to 7-digit whole numbers).
Day 3
Round decimals to the nearest whole, tenth and hundredth.
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

34. Problem solving and reasoning questions
Identify the value of the ‘4’ in the following numbers:
(a) 3.407
(b) 4.821
(c) 0.043
(d) 5.104
48,739
How many times must Dan multiply by 10 to get 48,000?
What number is one hundred times smaller than 0.4?
Write three numbers, two with 3 digits and one with four digits, that round to 4 as the nearest whole number.
Year 6