1. Decimals and Fractions
Place value in decimals
Multiply/divide by 10 and 100
Rounding
Objectives
Day 1
Place value addition and subtraction of numbers with two decimal places.
Day 2
Multiply and divide by 10, 100 and 1000.
Day 3
Round decimals to the nearest whole and tenth.
Before teaching, be aware that:
On Day 1 children will need mini-whiteboards and pens. You may wish to us 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 5

2. Decimals and Fractions
Place value in decimals
Multiply/divide by 10 and 100
Rounding
Starters
Day 1
1-place decimals (pre-requisite skills)
Day 2
Adding to the next whole number from a 1-place decimal number (simmering skills)
Day 3
Difference between negative 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 5

3. Decimals and Fractions
Place value in decimals
Multiply/divide by 10 and 100
Rounding
Starter
1-place decimals
Pre-requisite skills – to use this starter, drag this slide to the start of Day 1
Place children in groups of 3 or 4. Ask each child to write, on their whiteboards, a number between 3 and 4 with one decimal place. On the count of 3, ask each group to put their whiteboards in ascending order. The group who manages to do this first wins 2 points!
Whose number has six tenths in it? Three tenths? Those groups can have a bonus point! Repeat.
Year 5

4. Decimals and Fractions
Place value in decimals
Multiply/divide by 10 and 100
Rounding
Starter
Adding to the next whole number from a 1-place decimal number
Simmering skills – to use this starter, drag this slide to the start of Day 2
Play ‘Ping-pong’. You call out a number with one decimal place, e.g Children answer with the complement to the next whole number, e.g Occasionally say ‘ping’ to which they reply ‘pong’, or ‘pong’ to which they reply ‘ping’!
Year 5

5. Decimals and Fractions
Place value in decimals
Multiply/divide by 10 and 100
Rounding
Starter
Difference between negative numbers
Simmering skills – to use this starter, drag this slide to the start of Day 3
Ask children to each write a number between 1 and 9. Score a point if I say two numbers with a difference of your chosen number, e.g. children write 5, you say −3 and 2. Repeat with several pairs of numbers then start a new game with children each choosing a new number.
Use a thermometer to help children visualise differences.
Year 5

6. Decimals and Fractions
Place value in decimals
Multiply/divide by 10 and 100
Rounding
Objectives
Day 1
Place value addition and subtraction of numbers with two decimal places.
Year 5

7. Day 1: Place value addition and subtraction of numbers with two decimal places.
What does the 3 represent?
What is the place value of this 7?
Write the answer to the addition on your whiteboards.
7.38 – 0.08
What does the 8 represent?
What is the place value of this 3?
Write the answer to the subtraction on your whiteboards.
Check that children write 7.3 not 7.30 as the answer. Explain that we only write 0 in the hundredths place when writing amounts of money, e.g. £7.30 (as long as it’s not holding that place for digits that follow, e.g ).
3 tenths is 30 hundredths. 3/10 = 30/100 So, 7.3 is 27 hundredths more than 7.03.
£7.30 is 27p more than £7.03.
The value of the 3 changes according to its place in the number.
How many hundredths is 0.3?
Year 5

8. Day 1: Place value addition and subtraction of numbers with two decimal places.
Write 4.56 at the top of your whiteboards.
Which digit is in the hundredths place?
And the tenths?
4.56
Add one hundredth. Write the answer underneath.
4.57
4.77
3.77
3.73
3.33
Add two tenths to the new number.
Subtract one whole.
Subtract four hundredths.
Subtract four tenths.
Hold up the new number you now have.
Year 5

9. Day 1: Place value addition and subtraction of numbers with two decimal places.
Write 8.34 at the top of your whiteboards.
Which digit is in the hundredths place?
And the tenths?
8.34
+ 0.3
8.64
8.44
8.55
8.6
7.5
8.7
-0.2
+ 0.11
+ 0.05
- 1.1
Today would be a great day to use the problem-solving investigation – Spiralling Decimals – (from NRICH) 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 on our website.
WT: Use place value to add and subtract in numbers with two decimal places, using a place value grid to support.
ARE/GD: Use place value to add and subtract in numbers with two decimal places.
+ 1.2
Hold up the new number you now have.
Year 5

10. 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: Children do the first 12 questions.
ARE: Children start at question 4 and do as many as they can.
GD: Children do questions 11 to 20 then the challenge.
Start at Add or subtract tenths and hundredths to make an addition and subtraction chain ending with the number 5.02.
Challenge
Challenge
Year 5

11. Decimals and Fractions
Place value in decimals
Multiply/divide by 10 and 100
Rounding
Objectives
Day 2
Multiply and divide by 10, 100 and 1000.
Year 5

12. What should we do to move the digits back to show the number 235?
Day 2: Multiply and divide by 10, 100 and 1000.
10,000s
1000s
100s
10s 1s
0.1s 1/10s
0.01s 1/100s
If this was a measurement in centimetres, how would we write this in metres?
What should we do to move the digits back to show the number 235?
Note that the digits move and the decimal point does NOT move.
Year 5

13. What should we do to move the digits back to show the number 235?
Day 2: Multiply and divide by 10, 100 and 1000.
10,000s
1000s
100s
10s 1s
0.1s 1/10s
0.01s 1/100s
What should we do to move the digits back to show the number 235?
2.35 x 100 = 235
So to convert from metres to cm we multiply the number by 100.
Year 5

14. So to convert from centimetres to metres we divide the number by 100.
Day 2: Multiply and divide by 10, 100 and 1000.
10,000s
1000s
100s
10s 1s
0.1s 1/10s
0.01s 1/100s
How do I get 235 back to 2.35?
235 ÷ 100 = 2.35
So to convert from centimetres to metres we divide the number by 100.
Year 5

15. Day 2: Multiply and divide by 10, 100 and 1000.
10,000s
1000s
100s
10s 1s
0.1s 1/10s
0.01s 1/100s
0 0
What if 235 was the measurement in metres, and we wanted to convert it to cm?
What happens to each digit? What is the place value of the 2, the 3, the 5 in 23,500?
Year 5

16. Day 2: Multiply and divide by 10, 100 and 1000.
10,000s
1000s
100s
10s 1s
0.1s 1/10s
0.01s 1/100s
This is an amount in pennies. Write this amount in pounds on your whiteboards.
What did you need to do?
4299 ÷ 100 = 42.99
Year 5

17. Day 2: Multiply and divide by 10, 100 and 1000.
10,000s
1000s
100s
10s 1s
0.1s 1/10s
0.01s 1/100s
What if this was a distance in centimetres and I wanted to write it in millimetres?
What did you need to do?
4299 x 10 = 42,990
Year 5

18. This is an amount in millimetres. Write it in centimetres.
Day 2: Multiply and divide by 10, 100 and 1000.
10,000s
1000s
100s
10s 1s
0.1s 1/10s
0.01s 1/100s
This is an amount in millimetres. Write it in centimetres.
What did you need to do?
4299 ÷ 10 = 429.9
Year 5

19. Day 2: Multiply and divide by 10, 100 and 1000.
Sketch your own 1000s, 100s, 10s, 1s, 0.1s and 0.01s place value grid.
Write 7840 in it.
Divide 7840 by How many places will the digits need to move?
1000s
100s
10s 1s
0.1s 1/10s
0.01s 1/100s
Where has the zero gone?
Year 5

20. Day 2: Multiply and divide by 10, 100 and 1000.
Sketch your own 1000s, 100s, 10s, 1s, 0.1s and 0.01s place value grid.
Write 6.45 in it.
Multiply 6.45 by How many places will the digits need to move?
1000s
100s
10s 1s
0.1s 1/10s
0.01s 1/100s
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: Explore place value changes when multiplying and dividing by 10 and 100.
ARE/GD: Explore decimal place value when multiplying and dividing by 10, 100 and 1000.
Year 5

21. 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: Multiply and divide by 10 and 100.
ARE/GD: Multiply and divide by 10, 100 and 1000.
Challenge
Year 5

22. Decimals and Fractions
Place value in decimals
Multiply/divide by 10 and 100
Rounding
Objectives
Day 3
Round decimals to the nearest whole and tenth.
Year 5

23. If we are rounding 2.3 to the nearest whole number, 2.3 rounds to 2.
Day 3: Round decimals to the nearest whole and tenth. 2
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
2.9 3
What about 2.5? What multiple of ten would you round 25 to? So, we round 2.5 up to…
Is 2.3 nearer to 2 or 3?
If we are rounding 2.3 to the nearest whole number, 2.3 rounds to 2.
Year 5

24. Write a number that goes between 2.3 and 2.4.
Day 3: Round decimals to the nearest whole and tenth. 2
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
2.9 3
You've written different numbers but which whole number are they all closest to?
Write a number that goes between 2.3 and 2.4.
So, they all round to 2.
Sketch a line from 2.3 to 2.4 and mark on a number with two decimal places.
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 you agree?
Think of another number with two decimal places that rounds to 2.
Year 5

25. Day 3: Round decimals to the nearest whole and tenth.2
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
2.9 3
You've written different numbers but which whole number are they all closest to? So, they all round to...
Write a number that goes between 2.8 and 2.9.
Sketch a line from 2.8 to 2.9 and mark on a number with two decimal places.
Show your line if your number is closer to 2.8. Do the rest of the class agree?
Show your line if your number is closer to 2.9. Do the rest of the class agree?
Think of another number with two decimal places that rounds to 3.
Year 5

26. Day 3: Round decimals to the nearest whole and tenth.
Write a number less than 6 with two decimal places that rounds up to 6.
What is the smallest number with two decimal places that rounds up to 10?
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: Explore rounding 2-place decimals marked on number lines.
ARE/GD: Explore rounding 2-place decimals while playing Bingo.
Year 5

27. 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 decimals to the nearest whole number.
ARE/GD: Round decimals to the nearest tenth and whole number.
Year 5

28. Decimals and Fractions
Place value in decimals
Multiply/divide by 10 and 100
Rounding
Well Done! You’ve completed this unit.
Objectives
Day 1
Place value addition and subtraction of numbers with two decimal places.
Day 2
Multiply and divide by 10, 100 and 1000.
Day 3
Round decimals to the nearest whole and tenth.
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 5

29. Problem solving and reasoning questions
Divide 47,310 by 10 repeatedly until you get a number that is less than Write that number.
Write the next two numbers in each sequence.
____ ____
____ ____
43, ____ ____
True or false?
4030 ÷ 100 = x 100 = 190
0.09 x 10 = ÷ 1000 = 0.7
Rounding to nearest tenth. Tick (a) or (b)
(a) > 20 (b) > 20.1
Rounding to nearest whole number
(a) > 21 (b) > 20
Year 5