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# Maths Year 5 Autumn 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. These bulk downloads are available to friends and School Subscribers. These bulk downloads are added value for Hamilton Friends and School Subscribers.

## Unit 1 Divide by 10/100; 2-place decimals (suggested as 2 days)

### Objectives

Multiply/divide by 10 and 100 to get decimals (2 decimal places)
Unit 1: ID# 5209

National Curriculum
Dec/Fr (ix) (x)

Hamilton Objectives
19. Understand the effect of multiplying/dividing by 10, 100, 1000, including 1- and 2-place decimal answers.
29. Write decimal numbers as tenths and hundredths.

### Teaching and Group Activities for Understanding

Day 1 Teaching
Use a place value chart of whole numbers, tenths and hundredths. Ask children to describe each row and show what happens if a digit is multiplied by 10 or 100. Suppose a digit is divided by 10? Make different numbers using the chart/place value\ additions.
Group Activities
-- ‘Zap’ digits in numbers with 2 decimal places, using a calculator.
-- Play a game using the place value grid to reinforce the value of different digits.

Day 2 Teaching
Write numbers in a 100s, 10s, 1s, 0.1s and 0.01s place value grid, multiply and divide by 10 and 100. Give 4 children number cards, e.g. 1, 2, 3, 4. They stand on either side of a large decimal point on the flipchart to show 12.34. They multiply their number by 10 and move accordingly. Do the class agree? Multiply by 10 again, then divide by 100. Repeat.
Group Activities
Use the in-depth problem-solving investigation ‘Dicey Operations in Line (adapt Game 6) from NRICH as today’s group activity.
Or, use these activities:
-- Use digit cards in place value grids to multiply and divide by 10 and 100 – up to 2 decimal places.

### You Will Need

• Place value chart (see resources)
• Calculators
• 100s, 10s, 1s, 0.1s and 0.01s place value grid (enlarge to A3)
• sets of 0–9 digit cards
• Large number cards (1–9)
• 1–6 dice

### Mental/Oral Maths Starters

Day 1
Place value in 1-place decimal numbers (pre-requisite skills)

Suggested for Day 2
Adding to the next whole number from a 1-place decimal number (simmering skills)

### Procedural Fluency

Day 1
Complete place value number sentences,
e.g. 1 + 0.5 + ☐ = 1.58.

Day 2
Work out the outputs for × 10, ÷ 10, × 100 and ÷ 100 function machines.

### Mastery: Reasoning and Problem-Solving

• Divide 27,680 by 10 repeatedly until you get a number that is less than 100. Write that number.
• Write the next two numbers in each sequence.
4650 465 ____ ____
2.953 29.55 ____ ____
9300 930 93 ____ ____
• Write the missing numbers.
23.4 ÷ 10 = ☐
☐ × 100 = 34
460 ÷ ☐ = 4.6

In-depth Investigation: Dicey Operations in Line (adapt Game 6)
Roll a 0 to 9 dice four times to create a calculation in the form ☐☐☐☐ ÷ 10 or ☐☐☐☐ ÷ 100. Whoever has the answer closest to 555.5 or 55.55 wins. Dicey Operations in Line (adapt Game 6) from nrich.maths.org.

### Extra Support

Moving Digits
Multiplying and dividing amounts of money by 10

## Unit 2 1- & 2-place decimals on a line; compare (suggested as 2 days)

### Objectives

Place decimals (1 and 2 decimal places) on a line
Compare
Unit 2: ID# 5227

National Curriculum
Dec/Fr (ix) (x)

Hamilton Objectives
19. Understand the effect of multiplying/dividing by 10, 100, 1000, including 1- and 2-place decimal answers.
29. Write decimal numbers as tenths and hundredths.
30. Locate 2-place decimal numbers on a line; round them to the nearest tenth or whole number.

### Teaching and Group Activities for Understanding

Day 1 Teaching
Use a 100 bead bar or line. Say that the ends are 0 and 1. Explain that each bead is one hundredth. Write 1/100 and 0.01. What is each group of 10 beads? Write 10/100, 1/10 and 0.1 on the board. Ask children to hang tags to show 0.1, 0.2, 0.3, 0.5, and 0.9. Show a counting stick and say the ends are 0 and 1. Children identify numbers in between. Then say the ends are 2 and 3. Count in steps of 0.1. Children write three numbers between 2.2 and 2.3. Order three examples.
Group Activities
-- Play one team against the other to place numbers with 2 decimal places on a line, trying to stop opponents getting numbers in between.
-- Use a number line to compare and order numbers with 1 and 2 decimal places.

Day 2 Teaching
Write 24.37 and 24.73 in the 10s, 1s, 0.1s and 0.01s place value grid. Discuss which number is worth more. Repeat with 52.91 and 52.68; 45.09 and 45.9; 36.7 and 36.29. Children write each pair of numbers on their whiteboards with a > or < between to answer. Children then write 62,7, 62,38, 62,83, 62,07 in order from least to greatest.
Group Activities
Use the in-depth problem-solving investigation ‘Round the Dice Decimals 2’ from NRICH as today’s group activity.
Or, use these activities:
-- Look at numbers to 2 decimal places in the context of measuring length. Discuss the value of each digit and compare and order numbers.

### You Will Need

• 100 bead bar or 0–1 beaded line (see resources) & tags
• Counting stick
• 0–9 dice
• DIY type tape measure
• Place value grid (see resources)
• 0–9 cards

### Mental/Oral Maths Starters

Suggested for Day 1
Placing 5-digit numbers on a human number line (simmering skills)

Day 2
Count on in steps of 0.01 (pre-requisite skills)

### Procedural Fluency

Day 1
Place numbers with 1 to 2 decimal places on number lines. Use the number line to order these numbers.

Day 2
Compare, then order numbers with 1 to 2 decimal places.

### Mastery: Reasoning and Problem-Solving

• Draw a number line between 3 and 4. Mark these numbers in the correct places.
3.5, 3.05, 3.55, 3.95, 3.42
• True or false?
4.05 comes after 4.5 on the number line.
9.9 is greater than 9.09.
0.11 and 0.21 are adjacent numbers on a 0–1 line marked in hundredths.
• Write digits to make these statements correct.
4.☐5 > 4.5☐
0.9☐ < 0.☐9
10.☐1 = 10.5☐

In-depth Investigation: Round the Dice Decimals 2
Use three 1 to 6 dice to make all possible numbers with 1 and 2 decimal places. Round each of these numbers to the nearest tenth and/ or whole number. Round the Dice Decimals 2 from nrich.org.uk

### Extra Support

This unit has no separate Extra Support activities.

## Unit 3 Add/subtract multiples of 0.1/0.01 (suggested as 2 days)

### Objectives

Use place value to add/subtract 0.1, 0.01 and multiples of these

Unit 3: ID# 5233

National Curriculum
Dec/Fr (vi) (x)

Hamilton Objectives
29. Write decimal numbers as tenths, hundredths, thousandths, e.g. 0.71 as 71/100, 0.327 as 327/1000; relate thousandths to tenths and hundredths.

### Teaching and Group Activities for Understanding

Day 1 Teaching
Show a 0.01–1 grid. Count in steps of 0.01 from 0 to 0.23. Then from 0.35 to 0.45 and back. Children close their eyes and count from 0.65 to 0.75 and back. Ring one column. When we move down this grid, what do we add? Start at 0.05. Count down the grid in steps of 0.1. Repeat, counting back from 0.97. Children close their eyes and count from 0.43 to 0.93 and back.
Group Activities
-- Add 0.1 or 0.01, writing the answers in a blank 0.01–1 grid.
-- Add four numbers with 2 decimal places. Look for patterns in the answers.

Day 2 Teaching
Children write 34.56 on whiteboards. If we add 0.1, which digit will change? If we subtract 0.01, which digit will change? Children add 0.2 and write the new number under it. Add and subtract multiples of 0.1 or 0.01 without crossing multiples of 0.1 or 1.
Group Activities
Use the in-depth problem-solving investigation ‘Dicey Operations in Line (adapt Game 1)’ from NRICH as today’s group activity.
Or, use these activities:
-- Practise adding and subtracting multiples of 0.1 and 0.01.
-- Do every other question on the whole class practice, then work to add and subtract multiples of 0.1 and 0.01 which cross boundaries.

### You Will Need

• 0.01–1 grid (see resources)
• Blank 0.01–1 grid and/or a completed 0.01 to 1 grid (see resources)
• Coins
• Whole class practice (see resources)

### Mental/Oral Maths Starters

Day 1
Multiply and divide by 10 and 100 (pre-requisite skills)

Suggested for Day 2
How much to the next pound? (simmering skills)

### Procedural Fluency

Day 1
Add/subtract 0.01/0.1 to fill in empty squares on a 0.01–1 grid.

Day 2
Add and subtract multiples of 0.1 and 0.01.

### Mastery: Reasoning and Problem-Solving

• How many times must I add 0.1 to 9.2 to reach 10?
How many times must I add 0.01 to 9.9 to reach 10?
• Find the answer to 3.42 + 0.2. Then find the answer to 3.42 + 0.02. Which answer is greater?
• Write the missing number in the bar chart:
 4.53 4.23 ?
• Write the number at each stage in this chain:
2.19 + 0.2 – 0.02 + 0.2 – 0.02 + 0.2 – 0.02 + 0.2 – 0.02.

In-depth Investigation: Dicey Operations in Line (adapt Game 1)
Create three multiples of 0.01 or 0.1; find their total. Whoever has the sum closest to 1 wins. Dicey Operations in Line (adapt Game 1) from nrich.maths.org.

### Extra Support

Decimal Pictures
Understanding place value in numbers with one decimal place and how we can write tenths as fractions or decimals

Teeny Decimals
Understanding place value in numbers with two decimal places and how we can write hundredths as fractions or decimals

## Unit 4 Subtract decimals with 1 or 2 places (suggested as 3 days)

### Objectives

Subtract decimals with 1 or 2 places
Unit 4: ID# 5261

National Curriculum
Dec/Fr (ix) (x)

Hamilton Objectives
32. Subtract 1- and 2-place decimal numbers by counting up: 6.2 – 3.5, 13.1 – 9.45.

### Teaching and Group Activities for Understanding

Day 1 Teaching
Use Maths Frog to calculate how much a mouse of 6.7 cm grows to reach 9cm. On an empty number line 6.7cm–9cm draw Frog’s hops: a hop of 0.3 to 7cm then a hop from 7cm to 9cm labelled 2cm. Repeat for other mice.
Group Activities
Use the ‘Talisman Squares’ in-depth problem-solving investigation below as today’s group activity.
Or, use these activities:
-- Use counting up (Frog) or counting back/place value to work out subtractions for numbers with 1 decimal place.
-- Use counting up (Frog) to work out subtractions for numbers with 1 decimal place.
Day 2 Teaching
Write 8 – 5.67. Show how Maths Frog can hop to 6 (hop of 0.33) then jump to 8 (jump of 2). Repeat to calculate other differences shown on a bar model and calculated using Maths Frog.
Group Activities
-- Use counting up (Frog) to work out subtractions for numbers with 2 decimal places.
-- Measure arm spans and heights, find the difference between the two.

Day 3 Teaching
Write 4.3 – 2.67 on the board. Draw a line from 2.67 to 4.3. Model using Maths Frog to find this difference. Subtract other pairs of numbers with 1 or 2 decimal places using counting up (Frog).
Group Activities
-- Subtract numbers with 2 decimal places.
-- Subtract numbers with different numbers of decimal places.

### You Will Need

• 1–9 dice
• Number cards 0–9, one set per pair
• Measuring tape
• Paper clips
• Subtract pairs of numbers with 1 or 2 decimal places (see resources)
• Subtract numbers with 2 decimal places from numbers with 1 decimal place (see resources)

### Mental/Oral Maths Starters

Suggested for Day 1
Double and halve two-digit numbers (simmering skills)

Day 2
Pairs to 100 (pre-requisite skills)

Day 3
Change from £1 (pre-requisite skills)

### Procedural Fluency

Day 1
Work out how much hamsters have grown (in cm, with 1 decimal place).

Day 2
Find differences between measurements (1 and 2 decimal places).

Day 3
Subtract pairs of numbers with 1 or 2 decimal places.

### Mastery: Reasoning and Problem-Solving

• True or false?
1.5 – 0.75 is 3/4
6 – 3.38 > 2.5
When you subtract a number with 2 decimal places from a whole number, the answer must have 2 decimal places.
• Write the missing numbers.
4.65 – ☐ = 3.8
☐ + 2.43 = 4
8.17 – 4.4 = ☐

In-depth Investigation: Talisman Squares
Children explore patterns in a Talisman Square. They find differences between adjacent numbers on a 4 x 4 grid and then explore arrangements on a 3 x 3 grid.

### Extra Support

This unit has no separate Extra Support activities.

## Unit 5 Mixed numbers and fractions of amounts (suggested as 3 days)

### Objectives

Mixed numbers and fractions of amounts
Unit 5: ID# 5273

National Curriculum
Dec/Fr (iii) (xii)

Hamilton Objectives
25. Recognise mixed numbers and improper fractions and convert from one to the other, writing mathematical statements.
33. Solve problems involving fractions, using known equivalences to help.

### Teaching and Group Activities for Understanding

Day 1 Teaching
Divide 3 pizzas into quarters. Shade five quarters.. How much have I shaded? We say/write this as 5/4, an improper fraction, or 1 1/4 pizzas, a mixed number. Repeat with 10 quarters, 7 thirds and 3 2/3.
Group Activities
Use the in-depth problem-solving investigation ‘Balance of Halves’ from NRICH as today’s group activity.
Or, use these activities:
-- Identify improper fractions which are greater than 1 or 2.
-- Identify improper fractions which are greater than 2, 3, 4 or 5.

Day 2 Teaching
Count in 1/3s along counting stick, until 3 1/3s. What are three thirds? Label 3/3 and 1. Continue saying four thirds, five thirds until six thirds. What is this? Point to 12/3, 21/3. Children write different ways of writing these numbers. Ask children to show other improper fractions.
Group Activities
-- Roll a 1–9 dice to create improper fractions, write them as mixed numbers.
-- Draw diagrams to show improper fractions and mixed numbers.
-- Place improper fractions and mixed numbers on a number line.

Day 3 Teaching
Say that in a school of 105 children, 1/7 are in Reception. 2/7 are in Key Stage 1 and 4/7 are in Key Stage 2. Show a bar model diagram to show this. Model finding each of these fractions. Repeat for other examples.
Group Activities
-- Draw bar models to find unit, then non-unit fractions of amounts.

### You Will Need

• 1–9 dice
• Counting stick
• 2–9 cards
• Bar model pictures (see resources)
• Whole class practice (see practice sheets Day 3)

### Mental/Oral Maths Starters

Day 1
Count in 1/4s and 1/8s along a number line (pre-requisite skills)

Suggested for Day 2
Mental multiplication (simmering skills)

Day 3
Mental division (pre-requisite skills)

### Procedural Fluency

Day 1
Write improper fractions as mixed numbers and vice versa using images of pizzas.

Day 2
Convert improper fractions to mixed numbers and vice versa.
Write sequences of mixed numbers according to a given rule.

Day 3
Find non-unit fractions of amounts.

### Mastery: Reasoning and Problem-Solving

• Count in fifths from 0 to 10.
How many numbers have you said?
• How many thirds in three whole pizzas?
How many quarters in four whole pizzas?
What are 25 fifths equivalent to?
• Suggest missing numbers to make these sentences true:
☐/6 = 2 ¹/6
1 ☐/10 > ☐/10
☐/8 > 3 ¹/☐
• Find 3/4 of 148:
 148 1/4 1/4 1/4 1/4
• Find 5/8 of 256:
 256

In-depth Investigation: Balance of Halves
Can you hang weights in the right place to make the scale balance? Balance of Halves from nrich.maths.org.

### Extra Support

Do the Splits
Finding 1/4, 3/4, 1/3 and 2/3 of numbers

## Unit 6 Add/subtract equivalent fractions (suggested as 5 days)

### Objectives

Unit 6: ID# 5281

National Curriculum
Dec/Fr (i) (ii) (iv)

Hamilton Objectives
23. Identify, name and write equivalent fractions; reduce fractions to simplest form, including tenths to fifths, hundredths to tenths, e.g. 40/100 = 4/10 = 2/5.
24. Compare and order fractions where the denominators are multiples of the same number.
26. Add and subtract fractions where the denominators are multiples of the same number.

### Teaching and Group Activities for Understanding

Day 1 Teaching
Show a fraction wall. Children find fractions equivalent to 1/4. Children write fractions not on the wall which are equal to 1/4. Write 3/12 and explain it is more simply written as 1/4. This is called writing the fraction in its simplest form. Call out other fractions for children to write in simplest form.
Group Activities
-- Use two cards to make a fraction and simplify.

Day 2 Teaching
Which is greater, 3/5 or 7/10? Model comparing fractions with related denominators using ITP Fractions: two bars - 1/10s and 1/5s. Click to highlight 3/5 and 7/10. Repeat to compare other fractions.
Group Activities
-- Write lots of fractions equivalent to 1/2, then say whether fractions are less than 1/2, then greater or less than 1/3.
-- Compare fractions with unrelated denominators by writing them as fractions with the same denominator.

Day 3 Teaching
Write 3/8 and 1/4. Which is greater? Model comparing by writing both as eighths. Write 3/8 > 2/8. Repeat with 2/5 and 3/10. Order 5/6, 2/3, 7/12 by writing them as twelfths.
Group Activities
Use the ‘Fraction Pictures’ in-depth problem-solving investigation below as today’s group activity.
Or, use these activities:
-- Order groups of fractions with related denominators by writing them as fractions with the same denominator.

Day 4 Teaching
Model adding fractions with related denominators. Write 1/2 + 3/4 and model how we can add these fractions by making them both quarters. Repeat to show 2/3 + 1/6 and 1/2 + 5/8.
Group Activities
Use the ‘Oddly Friendly Fractions’ in-depth problem-solving investigation below as today’s group activity.
Or, use these activities:
-- Add unit fractions with related denominators.
-- Identify and add pairs of fractions with a total greater than, and with a total less than 1.

Day 5 Teaching
Write: 3/4 – 1/2, 7/10 – 2/5, 3/4 – 3/8. Show how we write each pair as same type of fraction. This is because each pair is the same fraction family.
Group Activities
-- Subtract fractions with related denominators.
-- Subtract fractions with unrelated denominators.

### You Will Need

• Fraction wall (see resources)
• Mini-whiteboards and pens
• 1–12 cards
• ITP: Fractions
• Flipchart and pen
• Comparing and ordering fractions sheet (see resources)
• Adding fractions sheet (see resources)
• Cards 1–16

### Mental/Oral Maths Starters

Day 1
Divisibility by 2, 3, and 5 (pre-requisite skills)

Day 2
Factors (pre-requisite skills)

Day 3
Count in 1/4s and 1/8s along a number line (pre-requisite skills)

Day 4
Improper fractions (pre-requisite skills)

Suggested for Day 5

or
Times tables (simmering skills)

### Procedural Fluency

Day 1
None for this day

Day 2
Children compare pairs of fractions by first writing them with the same denominator.

Day 3
Compare and order fractions (2 versions: one for Working at ARE/greater depth and one for working towards ARE.
Day 4
Add pairs of fractions, first with a total of less than 1, then with a total of more than 1.

Day 5
Subtract pairs of related fractions

### Mastery: Reasoning and Problem-Solving

• Write three fractions equivalent to 20/25.
Look at the pattern in the denominators.
Then write three fractions equivalent to 7/21 and do the same.
What can you predict about the pattern in the denominators of fractions equivalent to 3/4?
• Write the missing numbers to make each sentence true.
?/6 = 8/24
4/? < 5/?
?/6 > 7/10
• How many times must I add 1/5 to 1/10 to get a total over 1?
• Mystery fractions.
Fraction A is half fraction B
Fraction B is added to 6/8 to give one whole.
Write fractions A and B in their simplest forms.

In-depth Investigation 1: Fraction Pictures
Children use knowledge of equivalent fractions to work out what fraction each shape is as part of the whole picture, and which shapes are the same size.

In-depth Investigation 2: Oddly Friendly Fractions
Children explore patterns when adding fractions. They create fractions with related denominators and then add these, turning improper fractions into mixed numbers.

### Extra Support

Fraction Families
Finding equivalent fractions to 1/2, 1/3 and 1/4

Pete’s Pies