• Hamilton's Flexible Maths Blocks Explained Open our sample 'Year 5 Autumn Unit 1' to find out how the blocks of units work.

• Teacher support for Maths Hamilton has a range of additional reference and advice materials for Maths.

• Free Maths Resources on Hamilton Find out which Hamilton maths units you can access for free, including our new slide presentations.

Maths Year 3 Autumn Place Value and Money

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 Place 2-digit & 3-digit numbers on lines (suggested as 3 days)

Objectives

Revise placing 2-digit numbers on lines; place 3-digit numbers on lines
Unit 1: ID# 3119

National Curriculum
Num/PV (iii) (iv) (v)

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.
2. Estimate quantities and represent numbers in different ways.

Teaching and Group Activities for Understanding

Day 1 Teaching
Revise placing 2-digit numbers on a 0–100 landmarked line. Understand place value in 2-digit numbers and use this to place numbers on the line.
Group Activities
Use the in-depth problem-solving investigation ‘Reasoned Rounding’ from NRICH as today’s group activity.
Or, use these activities:
-- Mark 2-digit numbers on 0–100 lines.
-- Mark 2-digit numbers on lines and create inequality sentences. Also write numbers in between.

Day 2 Teaching
Use number lines 0–100, then 100–200 and then 0–1000.
Show on a beaded bar and use this to count by 10s. Children place given numbers on their own landmarked lines.
Group Activities
-- Mark 3-digit numbers on lines with accuracy. Compare.
-- Mark numbers on 0–100 grids and landmarked lines and check each other’s work.

Day 3 Teaching
Children use place value cards (or arrow cards) to create 3-digit numbers. Compare the numbers. Then write the numbers on a place value grid and use this to compare them. Which number has the most hundreds? The most tens? Children then order three 3-digit numbers.
Group Activities
-- Make greatest and least possible 3-digit numbers from 3 digits.
-- Whole class investigation looking at combinations of numbers possible using three digits.

You Will Need

• Beaded bars with tags
• A visible landmarked line (e.g. on IWB)
• 0–100 landmarked lines (see resources)
• 0–9 dice & 0-9 cards
• 0–1000 landmarked lines (see resources)
• Landmarked lines, preferably on A3 paper
• Post-it notes
• Number grids (see resources)
• Arrow or place value cards

Mental/Oral Maths Starters

Day 1
Place value in 2-digit numbers (pre-requisite skills)

Day 2
Count in 1s from 101 to 200 (pre-requisite skills)

Suggested for Day 3
Count on or back in 10s from any 2-digit or 1-digit number (simmering skills)

Procedural Fluency

Day 1
Mark numbers on number lines 1–100.

Day 2
Mark given numbers on lines 1–1000 / Identify numbers marked on number lines.

Day 3
Mark numbers on empty number lines. Write numbers in between two numbers.

Mastery: Reasoning and Problem-Solving

• Sketch a line 0–1000. Mark 500. Draw an arrow pointing to the position of 250. Ask: What number have I marked? Repeat with other positions on the line.
• True or false?
There are always four numbers between two multiples of 5.
There are always nine numbers between two multiples of 10.
The number just before a multiple of 10 always ends in 9.
• What number will be marked halfway between 125 and 151 on the number line?
• Can you identify the number halfway between 333 and 344?

In-depth Investigation: Reasoned Rounding
Which 10s number is your 2-digit number closest to? Reasoned Rounding from nrich.maths.org.

Extra Support

Bigger or Beaten
Partitioning and comparing 2-digit numbers

Unit 2 Understand PV in 3-digit numbers (suggested as 4 days)

Objectives

Develop understanding of place value in 3-digit numbers; add/subtract 1, 10, 100
Unit 2: ID# 3137

National Curriculum
Num/PV (ii) (v)

Hamilton Objectives
3. Understand place value in 3-digit numbers; add/subtract 1s, 10s or 100s without difficulty.
5. Solve number problems and practical problems involving place value.

Teaching and Group Activities for Understanding

Day 1 Teaching
Children use place value cards to create 3-digit numbers. They then change one card to change the number: turn 45 into 145, which card has changed? Then into 245, which card has changed now? Find ways to make place value additions with 100, 70, 3 and with 400, 50, 6.
Group Activities
-- Use digit cards to create 3-digit numbers and write place value additions. Order numbers.

Day 2 Teaching
Using place value cards, discuss what happens when you subtract different digits and write the corresponding place value subtractions, e.g. 456 – 6 = 450.
Group Activities
Use the ‘Round the Three Dice’ in-depth problem-solving investigation below as today’s group activity.
Or, use these activities:
-- Use a mobile keypad to create 3-digit numbers, ‘zap’ a digit to use 0 as a place holder.
-- Use a calculator to see the effect of zapping a digit using place value.

Day 3 Teaching
Children write 246. They add 1, making 247. Ask them to add 10 to 247. Repeat, adding 100 to 257. Each time, check they know which column changed. Look at adding numbers when two columns change.
Group Activities
-- Use calculators to see effects when adding 1, 10 and 100 to 3-digit numbers.
-- Use place value cards to add 1, 10 and 100 to 3-digit numbers, occasionally crossing a 10s barrier.

Day 4 Teaching
Children write a 3-digit number and then subtract 1. Which column changes? Repeat to subtract 10 and 100. Discuss when subtracting 1, 10, or 100 means that two or three columns change.
Group Activities
-- Whole class investigation subtracting and adding 1, 10 and 100 from/to 3-digit numbers.

You Will Need

• Place value cards (arrow cards)
• 0–9 cards
• Copy of a mobile keypad layout (see resources)
• Calculators
• Whiteboards
• Missing numbers sheet (see resources)
• Place value cards: 1s, 10s, 100s. One set per three children

Mental/Oral Maths Starters

Day 1
Place value in 3-digit numbers (pre-requisite skills)

Day 2
Compare pairs of 3-digit numbers, using > and < (pre-requisite skills)

Day 3
Count on and back in 1s from a 3-digit number (pre-requisite skills)

Day 4
Count on and back in 10s from a 3-digit number (pre-requisite skills)

Procedural Fluency

Day 1
Use place value additions to create greater numbers, including crossing 10s and 100s barriers.

Day 2
‘Zap’ different digits in 3-digit numbers using place value subtractions.

Day 3
Add 1, 10 and 100 to 3-digit numbers, sometimes crossing a 10s or 100s barrier.

Day 4
Subtract 1, 10 and 100 from 3-digit numbers, sometimes crossing a 10s or 100s barrier.

Mastery: Reasoning and Problem-Solving

• How many different 3-digit numbers can you create using place value equipment if you are only allowed to use six objects (squares, rods or cubes)?
• ☐ + 108 = 148
238 – ☐ = 38
☐ + 40 = 846
• Add sequences of 1s, 10s, and 100s: 473 + 1 – 10 + 100. Use different starting numbers. Look for patterns.

In-depth Investigation: Round the Three Dice
Which 100s number is your 3-digit number closest to? Round the Three Dice from nrich.maths.org.

Extra Support

Spider Sums
Adding 10s to 2-digit numbers (answers less than 100); Subtracting 10s from 2-digit numbers

Unit 3 Place value in money: add/subtract (suggested as 3 days)

Objectives

Develop understanding of place value in money; use to add and subtract
Unit 3: ID# 3163

National Curriculum
Num/PV (iv) (vi)
Measures (iii)

Hamilton Objectives
2. Estimate quantities and represent numbers in different ways.
5. Solve number problems and practical problems involving place value.
32. Add and subtract amounts of money; use both £ and p in practical contexts.

Teaching and Group Activities for Understanding

Day 1 Teaching
Show 3 large pound coins, a 50p coin and a 2p coin (or IWB coins). How much money is here? How can we write it? Revise how we write this as £3.52. Rehearse writing amounts of money.
Group Activities
Use the ‘Three Coins’ in-depth problem-solving investigation below as today’s group activity.
Or, use these activities:
-- Identify a given amount of money and write it in £ and p notation.
-- Identify two coins from given clues.

Day 2 Teaching
Display the Money place value grid (see resources). Remind children how to write amounts in £ and p. Write amounts including those containing 0 on the PV grid. Compare the amounts using symbols.
Group Activities
Use the ‘Money Bags’ in-depth problem-solving investigation below as today’s group activity.
Or, use these activities:
- -Identify amounts written in words and lay these out on PV grids. -- Compare two amounts and write inequality sentences.
-- Use coins to make different amounts of money and write corresponding inequality sentences.

Day 3 Teaching
Play the ‘Nasty Game’ and record place value additions such as £2 + 30p + 5p, £2.05 + 30p, etc. Check all possibilities. Ensure children are confident in writing amounts such as £2.05 and do not write this as £2.5. Ask children to write subtraction sentences for same amount.
Group Activities
-- Solve word problems involving place value additions and subtractions of money.
-- Solve missing number problems based on money place value additions and subtractions.

You Will Need

• Large or IWB coins and £5 note
• ‘Writing amounts using £ and p’ (see resources)
• Real coins: pounds, 10ps and 1ps
• Money place value grids (see resources)
• Place value grid to show on the IWB
• ‘Writing & comparing amounts of money’ (see resources)
• Real coins: pounds, 10s and 1ps
• 1–6 dice with numbers not dots
• 0–9 cards
• Additional activity sheets (see resources)

Mental/Oral Maths Starters

Suggested for Day 1
Place value in 3-digit numbers (simmering skills)

Suggested for Day 2
Count in 10s between 100 and 200 using 101–200 square (simmering skills)

Day 3
Three coin guesses (pre-requisite skills)

Procedural Fluency

Day 1
Choose cards, e.g. £4, 30p and 2p and write the total amounts. Children write the amounts shown in purses containing coins: £1s, 10ps and 1ps.

Day 2
Write amounts on money place value grids and then write inequality sentences to compare two amounts.

Day 3
Solve word problems and explore a challenge. Use a money place value chart to create and compare amounts.

Mastery: Reasoning and Problem-Solving

• Jo has more than £1.50 and less than £2. She has three coins, all different. None are brown. How much could she have?
• £2 – ☐ = £1.55
☐ + £1.23 = £2.30
£4 + ☐ = £4.51
£6.02 – ☐ = £5.00
• Jo took three 10ps from her mum’s purse. Her little brother took 5p. Her mum had £3.35 left.
How much did she have before the children took the money?
• What is £1.11 less than £10?

In-depth Investigation 1: Three Coins
Using exactly three coins, children work out how many amounts can be made between £1 and £2.
In-depth Investigation 2: Money Bags
Children use their knowledge of counting in 10s to solve a problem involving money.

Extra Support

Coin Count Up
Writing amounts of money in pounds and pence

Money Matters
Adding and subtracting £1, 10p and 1p (not crossing boundaries)