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

• Go Deeper with Maths Investigations Our Investigations provide the materials to confidently teach problem solving & investigation skills.

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

# Maths Year 4 Autumn Place Value

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 3- and 4-digit numbers on a line (suggested as 2 days)

### Objectives

Place 3- and 4-digit numbers on a line
Unit 1: ID# 4111

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

Hamilton Objectives
1. Read, write and locate any 3-digit number on a landmarked line from 0-1000; use this to Locate 4-digit numbers on a landmarked line and use this to compare/order numbers.
1a. Use < and > signs when comparing numbers.

### Teaching and Group Activities for Understanding

Day 1 Teaching
2 children hold a washing line. Mark 1 end 0 and the other end 1000. Children place 3-digit numbers on the line, discussing which numbers to mark first to help us.
Group Activities
-- Ordering and placing 3-digit numbers on a number or washing line.
Day 2 Teaching
Display a landmarked 0-10,000 line and ask children to place 6000, 4500, 1250 and 9999 on the line. Then use a washing line to represent numbers 0 to 10,000. Ask children to place numbers on this line.
Group Activities
Use the in-depth problem-solving investigation ‘The Thousands Game’ from NRICH as today’s group activity.
Or, use these activities:
-- Place 4-digit numbers on 0-10,000 number lines and find numbers in between two 4-digit numbers.

### You Will Need

• Washing line, pegs
• Blank cards
• Landmarked lines 0-1000 & 0-10,000 (see resources)
• Unmarked lines 0-1000 & 0-10,000 (see resources)
• Number lines
• 0-1000 number lines

### Mental/Oral Maths Starters

Day 1
Place 2-digit numbers on an empty 0 to 100 line (pre-requisite skills)

Day 2
Count in 1s from 990 to 1100 and other 4-digit numbers (pre-requisite skills)

### Procedural Fluency

Day 1
Order 2-digit and 3-digit numbers and place them on 0-1000 landmarked and unmarked lines.

Day 2
Place 4-digit numbers on 0-10,000 number lines.
Compare and order 4-digit numbers.

### Mastery: Reasoning and Problem-Solving

• Sketch a line 0-10,000.
Mark 5,000.
Draw an arrow to 7500. What number have I marked?
Repeat with other 1000s and _500 numbers.
• Counting in 1s, work out what digits a and b stand for and write the next number in this sequence:
54aa, 54ab, 54b0, _____ .

In-depth Investigation: The Thousands Game
Explore the properties of 4-digt numbers. The Thousands Game from nrich.maths.org.

### Extra Support

Walk the Line
Placing 3-digit numbers on a 100 to 200 line, then a 0 to 1000 landmarked line

## Unit 2 Place value in 4-digit numbers (suggested as 3 days)

### Objectives

Understand place value in 4-digit numbers
Unit 2: ID# 4127

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

Hamilton Objectives
1. Understand the numbers of 1s, 10s, 100s, 1000s in a 4-digit number and the use of zero as a place holder.
3a. Use this understanding of place value to compare and order 3-digit and 4-digit numbers.

### Teaching and Group Activities for Understanding

Day 1 Teaching
Demonstrate that thousands can be added to a 3-digit number to create a 4-digit number. Use a vertical PV chart to select 1 number from each row to create 4-digit numbers. Show as additions.
Group Activities
-- Make 4-digit numbers and write them as place value additions.

Day 2 Teaching
Use a calculator to ‘zap’ one of the digits in a 4-digit number and record using place value subtractions: 3648 – 600 = 3048 etc.
Group Activities
-- Zap digits in 4-digit numbers using place value subtractions.

Day 3 Teaching
Play a game, using digit cards to create 4-digit numbers. Compare these numbers making explicit reference to the place value of the digits.
Group Activities
Use the ‘No Zero’ in-depth problem-solving investigation below as today’s group activity.
Or, use these activities:
--Compare 4-digit numbers using < and >. Order 4-digit numbers from least to greatest.

### You Will Need

• 4-digit place value grid (see resources)
• Whiteboards and pens
• 0-9 number cards
• Calculators
• Place value cards (1000s, 100s, 10s, 1s)

### Mental/Oral Maths Starters

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

Day 2
Count on and back in steps of 100 from 0 to at least 5000 (pre-requisite skills)

Suggested for Day 3
Write amounts in £ and p (simmering skills)

### Procedural Fluency

Day 1
Use number cards to make as many 4-digit numbers as possible.

Day 2
Zap digits in 4-digit numbers.

Day 3
Complete inequalities using < and >.

### Mastery: Reasoning and Problem-Solving

• Which 4-digit numbers can be made using exactly 3 place value counters of different colours (or 3 PV objects – little cubes, rods, squares, big cubes)?
• How many times must 99 be added to take 1009 over 2000?
• How many numbers between 4000 and 5000 contain two 5s? (E.g. 4505.)
• What must be added to …
1020 to make 2000?
9601 to make 9999?
190 to make 1000?

In-depth Investigation: No Zero
Children investigate how many numbers between one and ten thousand have a zero. They use their understanding of place value in numbers with up to 4-digits.

### Extra Support

Digit Do-it
Partitioning 3-digit numbers, and combining 100s, 10s and 1s to make 3-digit numbers

## Unit 3 Place value additions: 4-digit numbers (suggested as 3 days)

### Objectives

Add/subtract 1s, 10s, 100s and 1000s to/from 4-digit numbers
Unit 3: ID# 4133

National Curriculum
Num/PV (ii) (iv) (v) (vi)

Hamilton Objectives
3. Understand the numbers of 1s, 10s, 100s, 1000s in a 4-digit number and the use of zero as a place holder.
6. Add or subtract multiples of 1, 10, 100, and 1000.
4. Count in 1000s.

### Teaching and Group Activities for Understanding

Day 1 Teaching
Children write 4-digit numbers from spoken. Then count in 1000s from 5595 to 9555. Bridge 10,000 showing what happens. Repeat. Count in 1s from 5595 to 6001.
Group Activities
-- Add or subtract 1 or 1000 to 5555 until you get to 10000 or 1000.
-- Add or subtract 1 or 1000 to a 4-digit number to try and get to a secret target number.

Day 2 Teaching
Children write 4-digit numbers with a 0 in the 10s or 100s place. They use a PV grid and add/subtract 10s sometimes changing the 100s digit.
Group Activities
Use the ‘Magic Chains’ in-depth problem-solving investigation below as today’s group activity.
Or, use these activities:
- -Add and subtract 10 to find 4-digit numbers.
-- Make calculation chains, adding and subtracting 1000, 100, 10 or 1.

Day 3 Teaching
Children add and subtract 100s from 4-digit numbers where the total goes over a multiple of 1000.
Group Activities
-- Repeatedly add or subtract 100 to 4-digit numbers.

### You Will Need

• Whiteboards
• Coins
• Pieces of paper
• A blank dice labelled +1, -1, +10, -10, +1000, -1000

### Mental/Oral Maths Starters

Day 1
Count on and back 1s from any 4-digit numbers (pre-requisite skills)

Day 2
Count on and back in steps of 10 from 3-digit numbers (pre-requisite skills)

Suggested for Day 3
Count in steps of 25 from 0 to at least 2000 (simmering skills)

### Procedural Fluency

Day 1
Correct calculations involving adding and subtracting 1 and 1000.

Day 2
Add and subtract 10 to and from 4-digit numbers.

Day 3
Add and subtract 100 to and from 4-digit numbers.

### Mastery: Reasoning and Problem-Solving

• Use digits 1 and 2 only. How many 4-digit numbers can you create?
• Write the missing digits in this sequence of numbers:
4865, 48☐5, 4☐85, 48☐5, 4☐☐5
• True or false?
If you start with a 4-digit number and subtract 10 nine times, you will always have to change the hundreds digit.

In-depth Investigation: Magic Chains
Children use their knowledge of inverse operations to quickly work out a sequence of calculations.

### Extra Support

Flipping Fun
Place value in 3-digit numbers
Adding and subtracting 1, 10 and 100

## Unit 4 Deepen understanding of place value (suggested as 2 days)

### Objectives

Use place value grid
Write place value additions and subtractions

Unit 4: ID# 4139

National Curriculum
Num/PV (ii) (vi) (viii)

Hamilton Objectives
3. Understand the numbers of 1s, 10s, 100s, 1000s in a 4-digit number and the use of zero as a place holder.
6. Add or subtract multiples of 1, 10, 100, 1000.

### Teaching and Group Activities for Understanding

Day 1 Teaching
Children draw a PV grid on their boards and write 3036. They add 200 and record the addition. Then subtract 30, recording this.
Group Activities
-- Do place value additions and subtractions with 4-digit numbers, changing 1, 2 or 3 digits at a time.
Day 2 Teaching
Display Place Value Mystery, explain that children need to use place value addition or subtraction to fill in the missing number and function in the chain.
Group Activities
Use the in-depth problem-solving investigation ‘Nice or Nasty’ from NRICH as today’s group activity.
Or, use these activities:
-- Find missing numbers in place value additions and subtractions.

### You Will Need

• Whiteboards
• Place value cards
• Place Value Mystery 1, 2 and 3 (see resources)
• Post-it notes
• Place Value Mystery blank sheets (see resources)

### Mental/Oral Maths Starters

Day 1
Place value in 4-digit numbers (pre-requisite skills)

Day 2
Compare pairs of 4-digit numbers (pre-requisite skills)

### Procedural Fluency

Day 1
Solve mystery place value additions and subtractions.

Day 2
Solve place value additions and subtractions with missing numbers.

### Mastery: Reasoning and Problem-Solving

• Write the missing numbers:
[____] + 4040 = 9099
6166 – [____] = 6001
• Draw a place value grid. Use digits 9 and 0 (you must use at least one of both) to create the largest and smallest 4-digit numbers possible. Use the same digits to write two numbers in between.
• What is the largest possible 4-digit number whose digits add to 10? It must not contain a 0 and no two digits are the same. What is the smallest possible number like this?

In-depth Investigation: Nice or Nasty
Choose a game to explore PV in 4-digit numbers. Will you be nice or nasty to your opponent?! Nice or Nasty from nrich.maths.org.

### Extra Support

The Number Thief
Place value in 3-digit-numbers

## Unit 5 Add/subtract powers of 10, nos > 1000 (suggested as 3 days)

### Objectives

Add and subtract multiples of 1, 10, 100, 1000
Unit 5: ID# 4153

National Curriculum
Num/PV (ii) (iv) (viii)

Hamilton Objectives
3. Understand the numbers of 1s, 10s, 100s, 1000s in a 4-digit number and the use of zero as a place holder.
6. Add or subtract multiples of 1, 10, 100, 1000.

### Teaching and Group Activities for Understanding

Day 1 Teaching
Children write 4-digit numbers from dictation. Instruct them to add/subtract multiples of 10, 100 and 1000 and read out answer.
Group Activities
-- Roll a dice to add multiples of 1, 10, 100 and 1000 to 4-digit numbers. Add 10s and 100s in the context of centenaries and birthdays.

Day 2 Teaching
Take away multiples of 10, 100 and 1000 from a 4-digit number.
Group Activities
Use the ‘Tell the Teacher’ in-depth problem-solving investigation below as today’s group activity.
Or, use these activities:
-- Roll a dice to subtract multiples of 10 or 100 from 4-digit numbers. Use addition and subtraction to change digits in 4-digit numbers.

Day 3 Teaching
Give instructions: Think of a 4-digit number, write it down. Add 400, subtract 50, add 70, subtract 200, subtract 20, subtract 200, add 5. Write down your answer on the other side of your whiteboard. Children show whiteboards. Repeat.
Group Activities
-- Create adding and subtracting chains using inverse operations.

• 1-6 dice
• 0-9 dice
• Calculators
• A3 paper
• Whiteboards

### Mental/Oral Maths Starters

Day 1
Count on/back in steps of 100 (pre-requisite skills)

Day 2
Count/back in steps of 10 (pre-requisite skills)

Suggested for Day 3
6 times table (simmering skills)

### Procedural Fluency

Day 1
Count on and back in 10s, 100s or 1000s.

Day 2
Complete sequences adding and subtracting multiples of 10, 100 and 1000.
Find missing numbers in subtraction grids.

Day 3
Find missing multiples of 10, 100 and 1000 in additions and subtractions.

### Mastery: Reasoning and Problem-Solving

• Complete this sequence by adding 30 each time.
2467, ______, ______,
______, 2587
• What needs to be subtracted from 3987 to get 2345?
• Do 3 identical subtractions to get from 3265 to 2365.
What number are you subtracting?
• Write the missing digits:
6☐56 + 134 = 70☐0

In-depth Investigation: Tell the Teacher
Children consider whether given calculations are harder or easier and work out a scoring system.

### Extra Support

Tens Chains
Adding and subtracting 10s to and from 3-digit numbers

## Unit 6 Use place value in calculations (suggested as 2 days)

### Objectives

Revise place value in 4-digit numbers and use place value in calculations
Unit 6: ID# 4159

National Curriculum
Num/PV (vi) (v) (viii)

Hamilton Objectives
1. Read, write and locate any 3-digit number on a landmarked line from 0-1000; use this to Locate 4-digit numbers on a landmarked line and use this to compare/order numbers.
6. Add or subtract multiples of 1, 10, 100, 1000

### Teaching and Group Activities for Understanding

Day 1 Teaching
Ask children to draw lines and mark numbers. Discuss numbers at the beginning and end of lines and how it is possible to zoom in on a number line.
Group Activities
Use the ‘Round the Four Dice’ in-depth problem-solving investigation below as today’s group activity.
Or, use these activities:
-- Mark 4-digit numbers on a landmarked line between the relevant multiples of 100 or 10.
Day 2 Teaching
Write 4375; children subtract 305 recording on w/bs. Children explain why this is a ‘no work’ calculation. Repeat. Children add 202 to 4375, recording on w/bs. Subtract 1002. Repeat with other numbers.
Group Activities
-- Use place value to identify which number has been added/subtracted to/from 4-digit numbers.
-- Make number chains by adding and subtracting a series of numbers to and from a 4-digit number.

### You Will Need

• Whiteboards
• Pieces of paper

### Mental/Oral Maths Starters

Day 1
Place 3-digit numbers on an empty number line (pre-requisite skills)

Day 2
Order 4-digit numbers (pre-requisite skills)

### Procedural Fluency

Day 1
Locate 4-digit numbers on a number line.
Identify which 4-digit numbers are marked on a landmarked number line.

Day 2
Use place value to add and subtract with 4-digit numbers.

### Mastery: Reasoning and Problem-Solving

• Mark 8650 accurately on an 8000 to 9000 line.
• If a number line has 2500 as its halfway mark, what thousands numbers could be at the beginning and end of the line?
• You need to draw a line with these numbers marked: 100, 2600, 3850, and 4500. What are sensible numbers to have at the beginning and end of your line?
• 904 is added to a number. The total is 3006. What is the number?

In-depth Investigation: Round the Four Dice
Explore 4-digit combinations; round to the nearest 1000, 100 and 10. Round the Four Dice from nrich.maths.org.

### Extra Support

Round the Clock
Using place value to add and subtract

100s Neighbours
Placing 3-digit numbers on landmarked lines