Short Blocks

Maths Year 4 Summer Decimals and Fractions (B)

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 added value for Hamilton Friends and School Subscribers.

Unit 1 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 Maths 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 2 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 Maths 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)