Short Blocks

Maths Year 3/4 Spring Decimals and Money

Each unit has everything you need to teach a set of related skills and concepts.

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The PowerPoint incorporates step-by-step teaching, key questions, an in-depth mastery investigation, problem-solving and reasoning questions - in short, everything you need to get started.

All the other resources are there to support as-and-when required. Explore at your leisure - and remember that we are always here to answer your questions.

Unit 1 x and ÷ with money and 1-place decimals (suggested as 3 days)

Objectives

x and ÷ with Money and 1-Place Decimals
Unit 3: ID# 34444

Y3: Multiply and divide by 10 and 100 including with money.
Y4: Divide numbers by 10 to give tenths (one place decimal). Multiply 1-place decimals to give whole numbers; Multiply and divide by 10 and 100 (one place decimals).

National Curriculum
Y3: Num/PV (ii); Mult/Div (iii)
Y4: Dec/Fr (vii)

Y3 Hamilton Objectives
18. Multiply 2-digit numbers by 10 or 1-digit numbers by 100; divide multiples of 10 or 100 by 10 or 100. Understand the effect of x or ÷ by 10 or 100.

Y4 Hamilton Objectives
26. Know that one-place decimal numbers represent ones and tenths.
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.

Planning and Activities

Day 1 Teaching
Model multiplying and dividing by 10 using a place value grid.
Further Teaching with Y4
Divide by 10 to give tenths using decimal place value grid.
Group Activities: T with Y4
Y3 -- Create 2-digit numbers and multiply and divide them by 10. Record these calculations. Some children challenge others to guess a starting number by giving the answer to × 10 questions.
Y4 -- Move digit cards on a place value grid to divide 2-digit numbers by 10. Write a generalisation.

Day 2 Teaching
Model multiplying and dividing by 10 and 100 using a place value grid.
Further Teaching with Y4
Multiply 1 place decimals by 10, moving digits across the decimal point. Use function machine to x10 and ÷10.
Group Activities: T with Y3
Use the in-depth problem-solving investigation ‘Testing 10s’ as today’s group activity.
Or, use these activities:
Y3 -- Play a divide and multiply card game.
Y4 -- Use a function machine or play bingo to practise multiplying and dividing numbers by 10.

Day 3 Teaching
Model multiplying and dividing by 10 and 100 (one-place decimals) using ITP ‘Moving digits’.
Further Teaching with Y3
Multiplying and dividing by 10 and 100 using money.
Group Activities: T with Y3
Y3 -- Multiply and divide shop prices by 10 and 100.
Y4 -- Find different routes through a maze (× 10, ÷ 10, × 100, ÷ 100) where the same number will come out exactly as it was entered.

You Will Need

  • 100s, 10s 1s place value grid (see resources)
  • 10s, 1s, 0.1s place value grid (see resources)
  • Cardboard box with two slots
  • Sticky notes labelled ÷ 10 and × 10
  • ÷ and × card game function cards and number cards (see resources)
  • ‘Party bag toy shop’ sheet (see resources)
  • Money place value grid (see resources)
  • ‘Multiplying by 10 and 100’ sheets 1 and 2 (see resources)
  • ITP: ‘Moving digits
  • Real money
  • ‘Multiplication and division maze’ (see resources)

Short Mental Workouts

Day 1
Division facts for 10 times table

Day 2
Division facts for 5 times table

Day 3
£ and p notation

Procedural Fluency

Day 1
Y3: Multiply and divide by 10.
Y4: Divide by 10 with decimals.

Day 2
Y3: Multiply and divide by 10 and 100.
Y4: Multiply and divide by 10 with decimals.

Day 3
Y3: Multiply and divide money by 10 and 100.
Y4: Multiply and divide by 10 and 100 with decimals.

Mastery: Reasoning and Problem-Solving

Y3

  • Describe in words what happens to a number when we multiply by 10. Now explain why it happens. You may draw a picture if it helps.
  • Write the missing numbers:
    (a) ☐ × 10 = 550
    (b) 100 × 39 = ☐
    (c) ☐ ÷ 10 = 60
    (d) 17 × ☐ = 170
    (e) 500 ÷ ☐ = 5
    (f) ☐ × 10 = 990
  • Write the result number in each chain:
    5 × 100 ÷ 10 × 10 ÷ 100 = ?
    300 ÷ 10 ÷ 10 × 10 × 10 = ?
    40 × 10 ÷ 100 × 10 = ?
    Invent your own chain where you finish with the starting number.
  • Write the missing numbers
    £3.40 × 10 = ☐ ☐ ÷ 10 = £5.50
    100 × 9p = ☐ £7 ÷ ☐ = 7p

Y4

  • Complete each sentence:
    3.4 × 10 = ☐ 65 ÷ 10 = ☐
    ☐ ÷ 10 = 12.3 ☐ × 10 = 81
  • Write the value of one tenth of each number:
    57 84 6 13
  • Use this fact 56 = 7 × 8 to find the answer to each calculation:
    7 × 80 7 × 0.8 7 × 800 560 ÷ 8

In-depth Investigation: Testing 10s
Children multiply (Y3) or divide (Y4) numbers by 10, carry out a given procedure and look for patterns in their answer.

Extra Support

Y3: Treasure or Trap
Multiplying and dividing by 10

Zeros Matter
Writing amounts of money in pounds and pence, including amounts with 0 in the 10ps or 1ps column

Y4: Moving Digits
Multiplying and dividing by 10 (whole number answers)

Digit Dance
Multiplying and dividing by 10 (including numbers and answers with one decimal place)

Unit 2 Decimals and money on a line (suggested as 3 days)

Objectives

Decimals and Money on a Line
Unit 4: ID# 34460

Y3: Placing and ordering 3-digit numbers and money on a number line; rounding them to the nearest 10.
Y4: Placing and ordering 1-place decimals on a line and rounding.

National Curriculum
Y3: PV (iii)
Y4: Fr (viii) (ix)

Y3 Hamilton Objectives
1. Read, write and locate any 3-digit number on a landmarked line from 0–1000 and use this to order and compare numbers.
6. Round to the nearest ten and hundred.

Y4 Hamilton Objectives
26. Know that one-place decimal numbers represent ones and tenths.
27. Round decimals with one decimal place to the nearest whole number.

Planning and Activities

Day 1 Teaching
Model placing numbers on a number line and rounding.
Further Teaching with Y4
Relate one place decimals to cm and mm, and round decimals.
Group Activities: T with Y3
Y3 -- Locate 3-digit numbers on landmarked lines.
Y4 -- Position 1-place decimals accurately on landmarked 0–10 lines and round to the nearest whole. Some children will measure items less than 10cm to the nearest mm.

Day 2 Teaching
Order decimals on a number line.
Further Teaching with Y3
Order money on a number line and round to the nearest pound.
Group Activities: T with Y3
Y3 -- Create amounts of money using number cards and round to the nearest pound.
Y4 -- Position 1-place decimals accurately on number lines; some children will round to the nearest whole.

Day 3 Teaching
Compare decimal numbers using a number line.
Further Teaching with Y3
Compare and order amounts money using a number line.
Group Activities: T with Y4
Use the in-depth problem-solving investigation ‘Counter Place Value’ as today’s group activity.
Or, use these activities:
Y3 -- Investigation: How many amounts of money from £1 to £10 have the digit 9?
Y4 -- Roll a dice to make numbers with 1 decimal place. Play ‘Higher or lower’ using the rolled digits. Some children write 1-place decimal numbers in a given range then order the group of numbers.

You Will Need

  • Rulers marked in cm and mm
  • Blank landmarked line (see resources)
  • Small sticky notes
  • ‘Placing 3-digit numbers on a landmarked line’ sheet (see resources)
  • Items less than 10cm long
  • 0–9 digit cards
  • 0–10 lines (see resources)
  • Blank cards
  • £0 to £10 number line (see resources)
  • 1–6 and 0–9 dice
  • Squared paper
  • Calculators

Short Mental Workouts

Day 1
Place 2-digit numbers on a 0–100 line

Day 2
Count on and back in 1s and 10s

Day 3
Tell the time to the nearest 5 minutes

Procedural Fluency

Day 1
Y3: Place 3-digit numbers between hundreds.
Y4: Place decimals on lines.

Day 2
Y3: Place money on a line.
Y4: More placing decimals on lines.

Day 3
Y3: Find ‘in between’ amounts.
Y4: Compare numbers with 1 decimal place.

Mastery: Reasoning and Problem-Solving

Y3

  • Sketch a 0–1000 line. Mark 500. Now mark 350, 700 and 990. How can you demonstrate that you have marked these accurately?
  • True or false?
    - Between any pair of next-door multiples of 100, there are always 98 whole numbers.
    - The middle of a 500–1000 line is 800.
    - There are ten numbers ending in 3 between 300 and 400.
    - The digit 0 is used 18 times between 600 and 700.
  • Write numbers to make the sentences true:
    100 < ☐ < 110
    304 > ☐ > 302
    999 > ☐ > 888
    0 < 101 < ☐
    459 < ☐ < 461
  • Write the value of the 5 digit in these numbers:
    652
    591
    905

Y4

  • Write each number as a decimal:
    (i) One and four tenths
    (ii) 6/10
    (iii) 102/10
    (iv) One half
    (v) One fifth
  • Billy measured his mobile phone. These were its dimensions:
    Length: 12cm and 8mm
    Width: 64mm
    Thickness: 8mm.
    Write these as numbers of centimetres, with a decimal place if necessary.
  • Write <, > or = between each pair of numbers:
    4.5 5.4
    0.6 1/2
    7.1 7.8
    0.3 3/10
    2/5 0.5

In-depth Investigation: Counter place value
Children place counters on a place value grid to make 3-digit numbers and then use logic to ensure they have made all combinations.
Y3 make whole numbers.
Y4 make numbers with 1 decimal place.

Extra Support

Y3: In-betweenies
Placing numbers on a 0–100 landmarked line

Make the number
Knowing the value of each digit in 3-digit numbers

Y4: Decimals are a snip
Understanding place value in numbers with 1 decimal place and how we can write tenths as fractions or decimals