1. Decimals and Fractions
Revise 1-place decimals
Introduce 2-place decimals
Objectives
Day 1
Revise numbers with one decimal place Mark them on empty number lines and round them to the nearest whole.
Day 2
Introduce numbers with two decimal places on place value grids by multiplying and dividing single-digit numbers by 10 and 100 to give tenths, then hundredths.
Day 3
Multiply and divide 2-digit, then 3-digit numbers by 10 and 100 to give tenths and hundredths.
Before teaching, be aware that:
On Day 2 children will need mini-whiteboards and pens. You can use the Moving Digits ITP to show further examples of multiplying and dividing by 10 and 100
On Day 3 You can use a cardboard box with two openings as a Function Machine.
Year 4

2. Decimals and Fractions
Revise 1-place decimals
Introduce 2-place decimals
Starters
Day 1
Convert mm to cm, and vice versa (simmering skills)
Day 2
Multiply numbers with one decimal place by 10 (pre-requisite skills)
Day Convert cm to m and vice versa (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 4

3. Decimals and Fractions
Revise 1-place decimals
Introduce 2-place decimals
Starter
Convert mm to cm, and vice versa
Simmering skills – to use this starter, drag this slide to the start of Day 1
Children use a ruler to draw three lines of different lengths and label the lines with numbers 1–3. They measure each line, in cm, and write the three lengths on a separate piece of paper. They swap their lines with a partner and – using a ruler – they accurately measure their partner’s lines in mm. They share their measurements. Do their measurements in cm and mm match?
Year 4

4. Decimals and Fractions
Revise 1-place decimals
Introduce 2-place decimals
Starter
Multiply numbers with one decimal place by 10
Pre-requisite skills – to use this starter, drag this slide to the start of Day 2
Children write nine 2-digit numbers between 20 and 40 in a 3 × 3 grid.
If you have the number that is 10 times as big as 2.3, circle it.
What is 3.6 multiplied by 10?
What is the product of 10 and 2.8?
Repeat for other numbers between 2 and 4. The first person to circle all of their numbers wins.
Year 4

5. Decimals and Fractions
Revise 1-place decimals
Introduce 2-place decimals
Starter
Convert cm to m and vice versa
Simmering skills – to use this starter, drag this slide to the start of Day 3
Draw on the board a 3 × 2 grid. Fill the grid with six lengths in metres, e.g. 1.25m, 3.5m, 6.38m, 0.45m. Children draw a blank 3 × 2 grid on their whiteboards. They convert each of the lengths into cm and write the lengths in the corresponding boxes in their grid (125cm, 350cm, 638cm, 45cm). Repeat, this time writing measurements in cm. Children write them in metres. Include a few less than 1m, e.g. 75cm (0.75m).
Year 4

6. Decimals and Fractions
Revise 1-place decimals
Introduce 2-place decimals
Objectives
Day 1
Revise numbers with one decimal place Mark them on empty number lines and round them to the nearest whole.
Year 4

7. Day 1: Revise numbers with one decimal place; Mark them on empty number lines and round them to the nearest whole. 10 5 3 8 4 6 9 1 2 7
2.5
3.9
5.6
8.1
7.3
Talk to your neighbour. Where would 5.6, 2.5, 3.9 and 8.1 go on this line?
Which number would go here on this line? Remember each whole number can be split into tenths.
Let’s check…
7.3 or 7 and 3 tenths.
Year 4

8. 2.5 is halfway between 2 and 3 so it rounds up!
Day 1: Revise numbers with one decimal place; Mark them on empty number lines and round them to the nearest whole. 10 5 3 8 4 6 9 1 2 7
2.5
3.9
5.6
8.1
7.3
Which whole number is 7.3 closest to? Which whole number does it round to?
Agree with your neighbour what whole number the other numbers round to. Which ones round up and which round down?
It rounds down to 7!
2.5 is halfway between 2 and 3 so it rounds up!
Year 4

9. Day 1: Revise numbers with one decimal place; Mark them on empty number lines and round them to the nearest whole. 10 5 3 8 4 6 9 1 2 7
0.7
4.5
6.3
9.8
Talk to your neighbour. Where would 9.8, 4.5, 0.7 and 6.3 go on the line?
Agree with your neighbour what whole number each of these round to. Which ones round up and which round down?
Let’s check…
Today would be a great day to use a problem-solving investigation – Connect 3 – 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/ARE/GD: Make a 2-digit number with one decimal place. Mark the number on a landmarked line, and circle nearest whole number.
Year 4

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: Rounding numbers with one decimal place Sheet 1, Parts A and B.
ARE: Rounding numbers with one decimal place Sheet 1, Parts B and C.
GD: Rounding numbers with one decimal place Sheet 1, Parts B and C.
Year 4

11. Decimals and Fractions
Revise 1-place decimals
Introduce 2-place decimals
Objectives
Day 2
Introduce numbers with two decimal places on place value grids by multiplying and dividing single-digit numbers by 10 and 100 to give tenths, then hundredths.
Year 4

12. Day 2: Introduce numbers with two decimal places on place value grids by multiplying and dividing single-digit numbers by 10 and 100 to give tenths, then hundredths. .
100s
10s 1s
0.1s
0.01s . 5 5
Let’s divide 5 by 10 on this place value grid.
What has happened? What is the value of the 5 now?
The 5 has moved one place to the right. It is worth a tenth of its previous value.
We need a zero before the decimal point to show that there are no longer any 1s. We read 0.5 as zero point five.
Year 4

13. Day 2: Introduce numbers with two decimal places on place value grids by multiplying and dividing single-digit numbers by 10 and 100 to give tenths, then hundredths. .
100s
10s 1s
0.1s
0.01s . 5 5
What will happen if we divide by 10 again?
What has happened? What is the value of the 5 now?
The 5 has moved one more place to the right. It is now worth 5 hundredths.
This is written 0.05, read as zero point zero five. It can also be written as 5/100.
Year 4

14. Day 2: Introduce numbers with two decimal places on place value grids by multiplying and dividing single-digit numbers by 10 and 100 to give tenths, then hundredths. .
100s
10s 1s
0.1s
0.01s . 5 5
What will happen if we multiply 0.05 by 100?
What has happened? What is the value of the 5 now?
The 5 has moved two places to the left. It is now worth 5 and there is no need for a zero before it.
Year 4

15. Day 2: Introduce numbers with two decimal places on place value grids by multiplying and dividing single-digit numbers by 10 and 100 to give tenths, then hundredths. .
What will happen if we divide this number by 100? Write the answer on your whiteboards.
100s
10s 1s
0.1s
0.01s . 7 7
Let’s check…
The 7 has moved two places to the right. Dividing by 100 is the same as dividing by 10, then dividing by 10 again!
Year 4

16. Day 2: Introduce numbers with two decimal places on place value grids by multiplying and dividing single-digit numbers by 10 and 100 to give tenths, then hundredths. .
100s
10s 1s
0.1s
0.01s . 7 7
What will happen if we multiply 0.07 by 10?
Let’s check…
The 7 has moved one place to the right.
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: Use number cards on a place value grid to × and ÷ 1-digit numbers by 10/100.
ARE/GD: Explore × and ÷ by 10 and 100 on a place value chart (100s to 0.01s).
Year 4

17. 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: Multiplying and dividing by 10 and 100 Sheet 1, use digit cards on a place value grid to support.
ARE: Multiplying and dividing by 10 and 100 Sheet 1, use calculators to check.
GD: Multiplying and dividing by 10 and 100 Sheet 1, use calculators to check.
Challenge
Year 4

18. Decimals and Fractions
Revise 1-place decimals
Introduce 2-place decimals
Objectives
Day 3
Multiply and divide 2-digit, then 3-digit numbers by 10 and 100 to give tenths and hundredths.
Year 4

19. Zero point two five NOT ‘zero point twenty-five’.
Day 3: Multiply and divide 2-digit, then 3-digit numbers by 10 and 100 to give tenths and hundredths.
Zero point two five NOT ‘zero point twenty-five’. 2 . 2 5 5
What will happen to the digit cards when we divide 2.5 by 10?
Let’s see..
The digits moved one place to the right. The decimal point didn’t move but we need a zero before it.
Year 4

20. Zero point six seven NOT ‘zero point sixty-seven’.
Day 3: Multiply and divide 2-digit, then 3-digit numbers by 10 and 100 to give tenths and hundredths.
Zero point six seven NOT ‘zero point sixty-seven’. 6 7 . 6 7
What will happen to the digit cards when we divide 67 by 100?
Let’s see..
The digits moved two place to the right.
Year 4

21. One point four nine NOT ‘one point forty-nine’.
Day 3: Multiply and divide 2-digit, then 3-digit numbers by 10 and 100 to give tenths and hundredths.
One point four nine NOT ‘one point forty-nine’. 1 1 4 . 9 4 9
What will happen to the digit cards when we divide 14.9 by 10?
Let’s see...
The digits moved one place to the right.
Year 4

22. What will happen to the digit cards when we multiply 2.38 by 10?
Day 3: Multiply and divide 2-digit, then 3-digit numbers by 10 and 100 to give tenths and hundredths. 2 3 2 . 3 8 8
What will happen to the digit cards when we multiply 2.38 by 10?
Let’s see..
The digits moved one place to the left.
Year 4

23. What will happen to the digit cards when we multiply 2.38 by 100?
Day 3: Multiply and divide 2-digit, then 3-digit numbers by 10 and 100 to give tenths and hundredths. 2 3 2 8 . 3 8
What will happen to the digit cards when we multiply 2.38 by 100?
Let’s see...
The digits moved two places to the left.
Year 4

24. The function machine divides by 100!
Day 3: Multiply and divide 2-digit, then 3-digit numbers by 10 and 100 to give tenths and hundredths.
÷ 100
732 36 52 4
0.36
7.32
0.04
0.52
The function machine divides by 100!
Can you predict the answer when the numbers go through the machine?
Year 4

25. How can we reverse the function?
Day 3: Multiply and divide 2-digit, then 3-digit numbers by 10 and 100 to give tenths and hundredths.
342 6 63
0.06
3.42
× 100
÷ 100
0.63
How can we reverse the function?
Predict what number will come out each time.
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 the function machine with place value grids to × by 10 and by 100 (numbers with one and two decimal places).
ARE/GD: Use the function machine to support × and ÷ by 10 and by 100.
We can multiply by 100! 25
Year 4
Year 3

26. 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: Multiplying and dividing by 10 and 100 Sheet 1.
ARE: Multiplying and dividing by 10 and 100 Sheet 2.
GD: Multiplying and dividing by 10 and 100 Sheet 2.
Challenge
Year 4

27. Decimals and Fractions
Revise 1-place decimals
Introduce 2-place decimals
Well Done! You’ve completed this unit.
Objectives
Day 1
Revise numbers with one decimal place Mark them on empty number lines and round them to the nearest whole.
Day 2
Introduce numbers with two decimal places on place value grids by multiplying and dividing single-digit numbers by 10 and 100 to give tenths, then hundredths.
Day 3
Multiply and divide 2-digit, then 3-digit numbers by 10 and 100 to give tenths and hundredths.
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 4

28. Problem solving and reasoning questions
Write these numbers in order, smallest to largest.
0.3, 1, 0.9, 1.1, 0.1, 1.2, 0.5
Write the smallest and largest 1-place decimal numbers which both round to 5 as the nearest whole number.
Divide each number by 10.
• * 0.3
• * 15.6
Write the four numbers in order, smallest to largest.
Write each fraction as a decimal number:
• sixty-five hundredths
• five hundredths
• four tenths
• eleven hundredths
Now write the four numbers in order, smallest to largest.
Year 4

29. Problem solving and reasoning: Answers
Write these numbers in order, smallest to largest.
0.3, 1, 0.9, 1.1, 0.1, 1.2, , 0.3, 0.5, 0.9, 1, 1.1, 1.2
Some may put the 1 first or last because ‘it doesn’t have a decimal’ or ‘It has least digits’.
Write the smallest and largest 1-place decimal numbers which both round to 5 as the nearest whole number. 4.5 and 5.4 respectively. Some may give 4.6 for the lowest forgetting that 4.5 (halfway between 4 and 5) rounds up or give 5.5 for the highest (which should round to 6).
Divide each number by 10.
• *
• *
The digits move one placed to the right across the decimal point; in the first 2 numbers this means an additional 0 is needed to ‘hold’ the 1s place. Some children may mistakenly insert an extra 0 in the latter 2 numbers
Write the four numbers in order, smallest to largest. 0.3, 5.4, 15.6, 91.9
Write each fraction as a decimal number:
• sixty-five hundredths 0.65
• five hundredths
• four tenths 0.4
• eleven hundredths
Now write the four numbers in order, smallest to largest. 0.05, 0.11, 0.4, 0.65.
A common error is to put 0.4 first, this is usually due to misreading decimals such as 0.11 and 0.65 as ‘zero point eleven’ and ‘zero point sixty five’ respectively and thinking they are larger than 0.4
Year 4