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# Maths Year 4 Summer Decimals and Fractions

Each unit has everything you need to teach a set of related skills and concepts. 'Teaching for Understanding' provides whole-class teaching and fully differentiated adult-led group activities. ‘Problem-solving and Reasoning’ develops these skills, and includes questions to enable you to assess mastery. Practice sheets ensure procedural fluency. Extra support activities enable targeted work with children who are well below ARE.

‘UNIT PLAN’ gives you a text version of all parts of the unit to use in your school planning documentation. ‘DOWNLOAD ALL FILES’ gives you that unit plan plus all of associated documents.

## Unit 1 Introduction: 1- and 2-place decimals (suggested as 3 days)

### Objectives

Revise 1-place decimals; introduce 2-place decimals
Unit 1: ID# 4799

National Curriculum
Dec/Fr (ii) (v) (vii) (viii)

Hamilton Objectives
29. Find the effect of dividing a one- or two-digit number by 10 and 100, identifying the value of the digits in the answer as ones, tenths and hundredths.
26. Know that one-place decimal numbers represent ones and tenths.
28. Recognise and write decimal equivalents of any number of tenths.
27. Round decimals with one decimal place to the nearest whole number.

### Teaching and Group Activities for Understanding

Day 1 Teaching
Show a 0–10 landmarked line. Point to around 7.3. What number would be here? Call out numbers with one decimal place and ask children to place them on the line. Remind children that 0.1 is one tenth. So 7.3 is seven and three tenths, etc. Round each number to the nearest whole. Repeat with a new set of 1-place decimal numbers between 0 and 1.
Group Activities
Use the ‘Connect 3’ in-depth problem-solving investigation below as today’s group activity.
Or, use these activities:
-- Make a 2-digit number with one decimal place. Mark the number on a landmarked line, and circle the nearest whole.
-- Mark numbers with one decimal place between two whole numbers. Then round to the nearest whole.
-- Play a game, marking 1-place decimal numbers on empty 0–10 lines. Write numbers with one decimal place that round up and down to a given whole.

Day 2 Teaching
Using the ITP Moving digits, make 5. Click on ÷10. Agree that it is now worth a tenth of the value and has moved one place to the right. We need a zero before the decimal point to indicate no whole numbers. Click on ÷10 again. This 5 is now worth 5 hundredths, written 0.05, read as zero point zero five. Point out the 0 to show that there are no longer any tenths.
Group Activities
-- Use number cards on a place value grid to ×/÷ 1-digit numbers by 10/100.
-- Explore × and ÷ by 10 and 100 on a place value chart (100s to 0.01s).

Day 3 Teaching
Draw a large decimal point on the flipchart. Ask two children to stand on either side, holding large number cards 2 and 5 to show 2.5. Discuss what happens when you divide this by 10. Repeat, showing how we divide 2- and 3-digit numbers by 100 and 1-place decimals by 10 to get 2-place decimals. Play with a ×/ ÷ by 10/100 ‘function machine’.
Group Activities
-- Use the function machine with place value grids to multiply by 10 and 100 (numbers with one or two decimal numbers).
-- Use the function machine to support ×/÷ by 10 and by 100.

### You Will Need

• 0–10 landmarked line (see resources)
• Number cards 0–9 and extra zero cards
• Coloured pencils
• ITP: Moving digits
• Whiteboards and pens
• Place value grid (see resources),
• Place value chart (see resources)
• Calculators
• Large number cards 0–9
• Cardboard box with two slots
• Cards with ×10, ×100, ÷10 and ÷100
• Plain cards and pens

### Mental/Oral Starters

Suggested for Day 1
Convert mm to cm, and vice versa (simmering skills)

Day 2
Multiply numbers with one decimal place by 10 (pre-requisite skills)

Suggested for Day 3
Convert cm to m and vice versa (simmering skills)

### Procedural Fluency

Day 1
Place 1-place decimals on landmarked lines, round them to the nearest whole.

Day 2
Multiply and divide numbers by 10 and 100. Find missing numbers that have been multiplied or divided by 10 or 100 to give the stated answer.

Day 3
Identify the input or output in function machines that multiply or divide by 10 or 100.

### Mastery: Reasoning and Problem-Solving

• 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 of these numbers by 10: 5.4 0.3 91.9 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.

In-depth Investigation: Connect 3
Children play a dice game on a 0–10 number line, aiming to get three numbers in a row.

### Extra Support

On your Mark
Placing 1/10s and 0.1s on landmarked lines

## Unit 2 Decimal/fraction equivalents, 10/100ths (suggested as 2 days)

### Objectives

Write decimal and fraction equivalents of tenths/hundredths
Unit 2: ID# 4813

National Curriculum
Dec/Fr (ii) (v) (vi) (vii) (ix)

Hamilton Objectives
28. Recognise and write decimal equivalents of any number of tenths or hundredths and decimal equivalents to 1⁄4, 1⁄2, 3⁄4.
31. Compare numbers with the same number of decimal places up to two decimal places.

### Teaching and Group Activities for Understanding

Day 1 Teaching
Display a blank 100 square. What fraction of the big square is one little square? ‘One hundredth’. Write 1⁄100 = 0.01. Shade the top row. Write this as a decimal fraction. Write 10⁄100 = 1⁄10 = 0.1. Shade 5⁄10. Write as 1⁄2 and 0.5. Shade other numbers of tenths, as needed, to show equivalence.
Group Activities
-- Match fraction and decimal cards to fraction pictures on a 100 square.

Day 2 Teaching
Display a place value chart. Write on a flipchart 5.89. Point to each digit and say what each represents. I can make this number with three numbers on the place value chart. Write 5 + 0.8 + 0.09. Repeat, to write other place value additions for 2-place decimal numbers using the place value chart. Circle just two numbers, to make, e.g. 0.84, 5.07, 1.3.
‘Zap’ digits by subtraction: 3.65 – 0.6 = ___, 3.65 – 0.05 = ___, 3.65 – 3 = ___ .
Group Activities
Use the ‘Target timings’ in-depth problem-solving investigation below as today’s group activity.
Or, use these activities:
-- Use place value to subtract from 2-place decimals.

### You Will Need

• 100 square (see resources)
• Mini-whiteboards and pens
• Fraction and decimal cards (3 sheets – see resources)
• Fraction pictures (5 sheets – see resources)
• Place value chart (see resources)
• Calculators
• ITP: Tell the Time

### Mental/Oral Starters

Suggested for Day 1
Round distances, e.g. 4.6cm to the nearest whole cm (simmering skills)

Suggested for Day 2
Read, then convert analogue times to digital (simmering skills)

### Procedural Fluency

Day 1
Write the fraction and equivalent decimal of the shaded part of 10 by 10 grids.

Day 2
Find answers for and missing numbers in decimal place value addition and subtractions.

### Mastery: Reasoning and Problem-Solving

• Write each fraction as a decimal. The first is done for you.
13⁄100 = 0.13
5⁄100 =
9⁄10 =
97⁄100 =
25⁄100 =
• Write the missing numbers:
4 + 0.1 + ☐ = 4.17
6 + ☐ + 0.03 = 6.33
7.87 = 0.8 + ☐ + ☐
0.09 + 0.2 + 4 = ☐
☐ + ☐ + ☐ = 13.31
• Use the digits 9, 3 and 1 to create a 2-place decimal number which is less than 1.5.

In-depth Investigation: Target Timings
Children add or subtract ones, tenths or hundredths to reach a target number. They use mathematical reasoning to choose the best strategies.

### Extra Support

Decimal Bingo
Multiplying and dividing by 10 (including numbers and answers with one decimal place)

## Unit 3 Compare, order 2-place decimal numbers (suggested as 2 days)

### Objectives

Compare and order 2-place decimal numbers
Unit 3: ID 4831

National Curriculum
Dec/Fr (ii) (v) (ix)

Hamilton Objectives
30. Count up and down in hundredths.
31. Compare numbers with the same number of decimal places up to two decimal places.
28. Recognise and write decimal equivalents of any number of tenths or hundredths and decimal equivalents to 1⁄4, 1⁄2, 3⁄4.

### Teaching and Group Activities for Understanding

Day 1 Teaching
Use three number cards 0–9 to create the largest possible 2-place decimal number. Use the same cards to create the smallest possible 2-place decimal number. Then write these in order using the > sign.
Write on the board: ☐ .☐ ☐ > ☐ .☐ ☐. With the class, take cards one at a time and choose where to place them to make the number sentence work. Repeat for ☐ .☐ ☐ < ☐ .☐ ☐.
Group Activities
Use the ‘Decimal detective’ in-depth problem-solving investigation below as today’s group activity.
Or, use these activities:
-- Use digit cards on a place value grid to compare and order numbers with two decimal places.
-- Use digit cards to compare and order two, then three numbers, with two decimal places.

Day 2 Teaching
Show children a 100-bead bar: one end represents 0 and the other 1. Each bead represents one hundredth. Write 1⁄100 and 0.01. What does each group of 10 beads represent? Write 10⁄100, 1⁄10 and 0.1. Children then mark different tenths, and then 0.25 and 0.75. They then mark other numbers with two decimal places.
Group activities
-- Play a game, marking numbers with two decimal places on landmarked lines.
-- Use more than/less than clues to identify 2-place decimal numbers on landmarked lines.

### You Will Need

• Number cards 0–9 and large number cards 0–9
• Whiteboards and pens
• Place value grid (see resources)
• 100-bead bar and counting stick
• 0–1 landmarked number line (see resources)
• Red and blue felt tip pens
• Large sheet of paper, e.g. flipchart paper

### Mental/Oral Starters

Suggested for Day 1
Division facts for 6 times table (simmering skills)

Suggested for Day 2
Division facts for 9 times table (simmering skills)

### Procedural Fluency

Day 1
Compare, then order numbers with two decimal places. Children may use landmarked lines to help.

Day 2
Children place numbers with one or two decimal places on landmarked lines. They then order a set of given decimals between 0 and 2.

### Mastery: Reasoning and Problem-Solving

• Draw a line. Label one end 0 and the other end 1.
Mark the tenths as 0.1, 0.2, etc. Now mark these fractions as accurately as you can, using the decimal fraction, e.g. 0.29
-- 25⁄100
-- 33⁄100
-- 3⁄100
-- 51⁄100
-- 70⁄100
-- 3⁄4
• Write two decimal numbers between each pair:
(i) 1.4 and 1.5
(ii) 3.9 and 4
(iii) 2.75 and 2.8
(iv) 0.4 and 0.43

In-depth Investigation: Decimal Detective
Children use clues to find a number with two decimal places.

### Extra Support

Inbetweenies
Placing numbers with one decimal place on a 0–10 line, with only whole numbers marked.

## Unit 4 Add/subt 0.1s & 0.01s; measures problems (suggested as 3 days)

### Objectives

Add/subtract 0.1s & 0.01s; solve measures decimal problems
Unit 4: ID# 4861

National Curriculum
Dec/Fr (ii) (v) (ix) (x)

Hamilton Objectives
26. Know that one-place decimal numbers represent ones and tenths.
28. Recognise and write decimal equivalents of any number of tenths and decimal equivalent to 1/2 and 1/5.
31. Compare numbers with the same number of decimal places up to two decimal places.

### Teaching and Group Activities for Understanding

Day 1 Teaching
Today we’re going to use two familiar resources that both represent or show numbers from 0.01 to 1 – the bead bar and the 100 square. Use tags to mark the tenths on a bead bar; count along in tenths, then hundredths. Show a blank 100 square with just 0.01, 0.02, and 0.03 marked. Discuss what number will be at the end of the top row/ in the square under that/ in the bottom right corner. Mark other numbers on the square. What size steps are we counting in going down the grid?
Group Activities
-- Use counting on and back in tenths or hundredths to fill in missing adjacent numbers in a 0.01–1 square.
-- Fill in a row and column of a 0.01–1 square; identify the numbers in ‘crosses’ drawn on the 0.01–1 square.
-- Work backwards to identify starting numbers when adding/subtracting tenths and hundredths.

Day 2 Teaching
Display the 0.01–1 square. Count in steps of 0.01 from 0.3 to 0.4, then back, then in steps of 0.1 from 0.05 to 0.95 and back. Write 0.35 + 0.4 and model, using the 0.01–1 square: start at 0.35, count on 0.4. Which digit changes? Repeat for 0.35 – 0.04 and 0.35 – 0.4.
Group Activities
Use the ‘Decimals in a row’ in-depth problem-solving investigation below as today’s group activity.
Or, use these activities:
-- Play a game adding and subtracting hundredths on a completed or blank 0.01–1 square.

Day 3 Teaching
Write: A snail has crawled 2.34m. It crawls 4cm more. How far has it crawled now? What calculation do we need to do? Which digit will change when we add 4cm? Why? Establish that 4cm is the same as 4/100 of a metre or 0.04m. Write the number sentence: 2.34m + 4cm = 2.38cm. Repeat with another word problem to add a multiple of 10cm.
Group Activities
-- Convert distances in m to cm, or vice versa, to help solve measures problems.
-- Solving measurement problems, recognise which digit will change when a number of m or cm is added.

### You Will Need

• 100-bead bar and tags
• 0.01–1 square (blank - see resources)
• 0.01–1 square (completed - see resources)
• Counting stick
• Flipchart and pens
• Whiteboards and pens
• 0–9 dice and 1–6 dice
• Counters
• Snail journeys (see resources)
• Measurement problems (see resources)

### Mental/Oral Starters

Suggested for Day 1
How many ml in a litre, mm in a cm, g in a kg? (simmering skills)

Day 2
Count up and down in steps of 0.01 through multiples of 0.1 and 1 (pre-requisite skills)

Day 3
Write lengths between 3m and 4m, then put in order (pre-requisite skills)

### Procedural Fluency

Day 1
Fill in missing numbers in rows and columns in a 0.01–1 square.
Fill in missing numbers on sections of the 0.01–1 square.

Day 2
Use a 0.01–1 square to help to add/subtract multiples of 0.01 and 0.1.
Add/subtract multiples of 0.01 and 0.1, first using the 0.01–1 square, then adding to/subtracting from numbers >1.

Day 3
Convert cm to metres; use in a problem-solving context.
Answer measurement word problems involving cm to metre conversions.

### Mastery: Reasoning and Problem-Solving

• Write the missing numbers in each sequence:
4.55, 4.56, 4.57, ☐, ☐, ☐, ☐
1.05, 1.04, 1.03, 1.02, ☐, ☐, ☐, ☐
5.45, 5.46, 5.47, ☐, ☐, ☐, ☐
9.56, 9.66, 9.76, ☐, ☐, ☐, ☐
• Add 0.01 five times to each number.
-- 4.87
-- 3.07
-- 7.98
• The height of four trees is shown. Each tree grows 45cm. Write their new heights.
(a) Poplar: 29.5m
(b) Willow: 25.3m
(c) Aspen: 11.6m
(d) Cedar: 6.8m

In-depth Investigation: Decimals in a Row
Play a dice game on a 0.01–1 square, aiming to get four numbers in any row or column.

### Extra Support

Tiny Hops
Counting on and back in 0.1s; adding/subtracting tenths, e.g. 1.8 + 0.4.

## Unit 5 Equivalent fractions; fraction problems (suggested as 3 days)

### Objectives

Equivalent fractions; solve fraction problems
Unit 5: ID# 4871

National Curriculum
Dec/Fr (i) (iii) (v) (x)

Hamilton Objectives
23. Write the equivalent fraction for fractions with given denominators or numerators.
28. Recognise and write decimal equivalents of any number of tenths and decimal equivalents to 1/2, 1/5, etc.
24. Use times tables to find unit and non-unit fractions of amounts, e.g. 1/6 of 48, 3/8 of 64.
32. Solve simple measure/money problems involving fractions.

### Teaching and Group Activities for Understanding

Day 1 Teaching
Show a 0–2 line marked in eighths. Children count along the line in eighths. Remind children to say the equivalent fractions: one quarter, one half and three quarters. Count to 2. Repeat with a line marked in sixths, noting equivalent thirds. Repeat with a line marked in fifths. Repeat with a line marked in steps of 0.1. Again, note equivalents. Finally show a 0–1 line marked in 0.01s with 0.1s labelled. Mark on 1/4, 1/2, 3/4 above the line and the equivalent decimals under the line (0.25, 0.5, 0.75).
Group Activities
-- Use a fraction wall to find pairs of equivalent fractions.
-- Make large equivalent fraction and decimal lines for tenths, eighths and twelfths for an interactive classroom display.

Day 2 Teaching
Write: 36 ÷ 3, 1/10 of 120, 45 ÷ 5, 1/3 of 36, 120 ÷ 10, 1/5 of 45. Children discuss which questions have the same answers and why, e.g. Dividing by 5 and finding a 1/5 give the same answer. Sketch a bar model diagram to show how we find 1/5, 2/5, 3/5, etc. of £45. Repeat to find thirds of 36, then tenths of 120.
Group Activities
Use the ‘Fancy fraction answers’ in-depth problem-solving investigation below as today’s group activity.
Or, use these activities:
-- Use a bar model to find non-unit fifths of multiples of 5.
-- Use knowledge of factors to write non-unit fraction facts about 24, 48 and 72.

Day 3 Teaching
Write a word problem (see teaching document). Children read it and discuss in pairs how to solve it. Take feedback. Make a sketch of the cake or draw a bar model to help. Agree we find 1/8 of 32, then multiply by 3 to find 3/8. This comes to 4/8 altogether, so half of 32 buttons are left. Repeat with a second problem
Group Activities
-- Solve fraction word problems, using bar models to help.

### You Will Need

• 0–2 line marked in eighths (see resources)
• 0–2 line marked in sixths (see resources)
• 0–2 line marked in tenths (see resources)
• additional activity sheets (see resources)
• Scissors
• Large strips of paper
• Rulers
• Coloured felt tip pens
• Whiteboards and pens
• Flipchart

### Mental/Oral Starters

Day 1
Count in steps of 1/4, saying equivalent halves (pre-requisite skills)

Day 2
Find unit fractions of amounts (pre-requisite skills)

Day 3
Division facts for the 8 times table (pre-requisite skills)

### Procedural Fluency

Day 1
Identify equivalent fractions for 1/8s and 1/6s, and equivalent decimals for 1/10s on 0-1 number lines.
Identify equivalent fractions for 1/8s and 1/12s on 0-1 number lines. Derive equivalent fractions and decimals for tenths and fifths.

Day 2
Use fact webs to find tenths, then sixths of numbers.
Find unit fractions, then related non-unit fractions of amounts within times tables.

Day 3
Solve fraction problems, finding unit and non-unit fractions of amounts.

### Mastery: Reasoning and Problem-Solving

• Always true, sometimes true or false?
One quarter is one point two five.
A number of tenths can be written as an equivalent number of hundredths.
A number of hundredths can be written as a number of tenths.
0.34 > 4/10
98/100 + 0.02 = 1
1.25 – 0.2 = 1.5
• Find these fractions of £300:
(i) 1/5
(ii) 1/10
(iii) 1/20
• Write the number of tenths and twentieths which equal 2/5.
• Estimate which is larger:
2/3 of 999
2/5 of 500 or
1/4 of 1000
Write your estimate. Work out each one to check if you were correct.

In-depth Investigation: Fancy Fraction Answers
Children find non-unit fractions of multiples and look for patterns.

### Extra Support

Fraction Experiment
Finding 1/3, 1/4, and 3/4 of amounts (whole number answers)