Short Blocks

Maths Year 5 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. These bulk downloads are added value for Hamilton Friends and School Subscribers.

Unit 1 Place value in 3-place decimals (suggested as 3 days)

Objectives

Understanding place value in 3-place decimals
Unit 1: ID# 5743

National Curriculum
Fr (vii) (ix)

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, 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
Write on the board 3.33. Discuss what each 3 represents. Write it on a place value grid to check.
Split the class into two groups. For each team, write on the board ☐.☐☐. Using number cards 0–9, teams take turns to choose, and then place a card in their number. The aim is to make largest number possible, then the smallest number.
Group Activities
-- Complete a short investigation to revisit 2-place decimals.

Day 2 Teaching
Display a place value chart and labels. Discuss the new ‘thousandths’ label. Ask children what happens to the digit 5 as each number is multiplied or divided by 10. Circle a number on each line and record the total of the circled numbers. Repeat, this time missing out a number on one or more rows.
Group Activities
-- Write place value additions to match numbers with three decimal places.
-- Write place value additions to match numbers with three decimal places. Derive missing numbers.

Day 3 Teaching
Show a place value grid on the IWB. Write 6.426 and read it together. Give four children number cards, e.g. 1, 2, 3 and 4 to show 1.234. They stand either side of another child holding a large decimal point. Now multiply the number by 10 and children move accordingly. Repeat to multiply and divide by 10 or 100.
Group Activities
Use the in-depth problem-solving investigation ‘Greater Than or Less Than?’ from NRICH as today’s group activity.
Or, use these activities:
-- Move digit cards on a place value grid to ×/÷ by 10 and 100.
-- Multiply and divide a number by 10, 100 and 1000. Divide capacities in ml to convert to litres.

You Will Need

  • Number cards 0–9
  • Whiteboards and pens
  • Place value chart (see resources)
  • Place value chart labels (see resources)
  • Place value grid (see resources)
  • Large number cards 0–9
  • Flipchart and pens
  • Large sheets of paper

Mental/Oral Maths Starters

Day 1
Count in steps of 0.01 (pre-requisite skills)

Day 2
Count in steps of 0.001 (pre-requisite skills)

Day 3
Convert between m and cm (pre-requisite skills)

Procedural Fluency

Day 1
Compare order and round numbers with 2 decimal places.

Day 2
Complete place value partitioning additions for numbers with 3 decimal places, e.g. 1.58 + 0.005 = ☐

Day 3
Work out the outputs for ×10, ÷10, ×100, ÷100, ×1000 and ÷1000 function machines.

Mastery: Reasoning and Problem-Solving

  • Write the next numbers in each sequence.
    41, 4.1 ____ ____
    0.009, 0.09 ____ ____
    20, 2 ____ ____ ____
  • Divide 65 by 10 repeatedly until you get a number that is less than 0.1. Write that number.
  • True or false?
    4.3 ÷ 100 = 0.43
    109 = 1.009 × 100
    0.005 × 100 = 0.5
    71 ÷ 1000 = 0.0071
    164 = 0.164 × 1000
    804 ÷ 1000 = 0.084

In depth Investigation: Greater Than or Less Than?
Use numbers and symbols to make a number sentence correct. How many different ways can you find? Greater Than or Less Than? from nrich.maths.org.

Extra Support

Rainbow Additions
Understanding place value in numbers with two decimal places

Left, Right, Left, Right
Multiplying and dividing by 10 (numbers and answers to include numbers with 2 decimal places)

Unit 2 Compare and use 3-place decimals (suggested as 2 days)

Objectives

Compare and use decimals with 3-places, showing understanding
Unit 2: ID# 5749

National Curriculum
Fr (vii) (ix) (x)

Hamilton Objectives
29. Write decimal numbers as tenths and hundredths.
31. Add 2-place decimal numbers mentally or using column addition.

Teaching and Group Activities for Understanding

Day 1 Teaching
Write on the board 4.378. Ask children what each digit represents. Say both the fraction and the decimal: three tenths; zero point three. Use number cards 0–9 to play decimal number bingo to subtract the value of a digit from a 4-digit number with three decimal places. Show cans/jars with masses in grams. Convert the masses into kg. What does each digit after the decimal point represent? Show a 100g weight: Is this 0.001kg, 0.01kg or 0.1kg? Repeat for a 1g and a 10g weight. Convert millilitres to litres and kilometres to metres.
Group Activities

Use the ‘Guesstimate’ in-depth problem-solving investigation below as today’s group activity.
Or, use these activities:
-- Use digits cards on a place value grid to convert between km and m, l and ml.
-- Order masses in kg with different numbers of decimal places. Convert to grams to check.

Day 2 Teaching
Write on the board ☐.☐☐☐ > ☐.☐☐☐. Use 0–9 cards. Take one. Where should we put this card to ensure that the sentence is true? Repeat until each box has a card. Children write a number in between on their whiteboards. Repeat with ☐.☐☐☐ < ☐.☐☐☐. Write numbers: 5.289, 5.974, 5.278 and 5.419. Children order the numbers on their whiteboards. Think of one number between each neighbouring pair of numbers: one with one decimal place, one with two decimal places and one with three decimal places.
Group Activities
-- Play an online game to order numbers with one and two decimal places.
-- Play a number line game to practise ordering numbers with three decimal places.
-- Choose numbers from a grid with one, two or three decimal places. Place the numbers on a number line, to try to get three in a row.

You Will Need

  • Number cards 0–9
  • Cans and jars with weights (in grams) written on sticky notes
  • Weights: 1g, 10g and 100g
  • ‘Converting measurements’ sheet (see resources)
  • A3 paper and coloured paper
  • ‘Cat weights’ sheet (see resources)
  • Whiteboards and pens
  • Additional activity sheets (see resources)

Mental/Oral Maths Starters

Day 1
Count on and back in steps of 0.002 (pre-requisite skills)

Day 2
Round numbers with two decimal places to the nearest whole (pre-requisite skills)

Procedural Fluency

Day 1
Convert between km and m, l and ml.

Day 2
Locate 1-, 2- and 3-place decimals on a number line; order smallest to largest.

Mastery: Reasoning and Problem-Solving

  • Write the value of each digit as a fraction:
    0.375
  • Write the total of this addition as a decimal:
    6/1000 + 4/10 + 3/100
  • Ali’s homework needs marking. Write the correct answers for those he has wrong. Explain any mistakes Ali is making.
    Write < or > or = between each pair of numbers:
    (a) 0.34 < 0.099
    (b) 1.075 > 1.08
    (c) 6.006 < 6.06
    (d) 5.264 > 5.27
    (e) 9.999 > 10.001

In depth Investigation: Guesstimate
Children work out the capacity of their classroom in litres.

Extra Support

Decimal divisions
Convert from cm to m and vice versa. Understand place value in numbers with two decimal places.

Unit 3 Subtract decimal numbers by counting up (suggested as 3 days)

Objectives

Subtract decimal numbers by counting up
Unit 4: ID# 5791

National Curriculum
Fr (x)
Add/Sub (i)

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

Teaching and Group Activities for Understanding

Day 1 Teaching
Write on the board 23.46 and 23.64. Which is bigger? Demonstrate finding the difference using Frog. Sketch a number line from 23.46 to 23.64. Frog hops first to? (23.5). How big is that hop? And the next? (Either 23.6 or 23.64). Add hops to find the difference. Children use Frog to calculate 23.32 – 19.67. They record the answer on their whiteboards. Display a word problem for children to read and solve. A volunteer models their working.
Group Activities
-- Whole class investigation: write a number using four consecutive digits in the form: ☐☐.☐☐, e.g. 45.67. Reverse it and find the difference between the two numbers. Explain any pattern.

Day 2 Teaching
Revise using counting up (Frog) to subtract numbers with different numbers of decimal places. Start by demonstrating how to use Frog to count up to do 6.24 – 4.5. Then use Frog to help children solve subtraction word problems.
Group Activities
-- Use a landmarked number line to find the difference in side lengths of rectangles, working towards calculating with a mix of 1- and 2-place decimal numbers.
-- Solve word problems requiring subtraction of numbers with different numbers (one or two) of decimal places.

Day 3 Teaching
Use the context of buying items for their rooms to find change from £100 for amounts such as £18.49. Model representing the word problem using a bar diagram, and then using Frog to perform the calculation. Repeat, modelling several.
Group Activities
-- Play games to practise finding totals and calculating change from £100.

You Will Need

  • Mini-whiteboards and pens
  • ‘0 to 4m lines’ (see resources)
  • Flipchart and pens
  • ‘Subtracting decimals’ word problems (see resources)
  • Number cards 0–9

Mental/Oral Maths Starters

Day 1
Find the complement to the next whole (pre-requisite skills)

Day 2
Find the change from £10 (pre-requisite skills)

Suggested for Day 3
Subtract any pair of 2-digit numbers mentally (simmering skills)

Procedural Fluency

Day 1
Use Frog (counting up) to subtract pairs of numbers, with one or two decimal places.

Day 2
-- Solve word problems requiring subtraction of numbers with the same number (one or two) of decimal places.
-- Solve word problems requiring subtraction of numbers with one and two decimal places.

Day 3
-- Find change from £100.
-- Find the difference between prices.

Mastery: Reasoning and Problem-Solving

  • Choose two numbers and find the difference between them:
    14.45 16.12 13.57 8.87
    Repeat this twice.
  • Write the missing numbers.
    (a) 23.4 – ☐ = 18.67
    (b) 15.5 = ☐ + 8.78
    (c) 32.4 – 18.55 = ☐
  • Find change from £100 when buying:
    -- chair £56.89
    -- table £75.37
    -- rug £20.08

In-depth Investigation
Use Day 1’s Group Activity as this unit’s investigation.

Extra Support

Mini minuses
Using Frog to subtract numbers with one decimal place