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# Maths Year 3 Spring 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 Partition 3-digit numbers; place on a line (suggested as 5 days)

### Objectives

Place 3-digit numbers on a line; partition into 1s, 10s 100s
Unit 1: ID# 3533

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

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.
3. Understand place value in 3-digit numbers; add/subtract 1, 10, 100 without difficulty.

### Teaching and Group Activities for Understanding

Day 1 Teaching
Discuss how we mark 2-digit numbers on a line 0–100. Then mark 275 on a line 200–300. Discuss halfway, and where 275 goes. Repeat, marking numbers on a 400–500 line.
Group Activities
-- Create a game placing hidden 3-digit numbers between hundreds on a landmarked line.
-- Mark 3-digit numbers on landmarked lines.

Day 2 Teaching
Review the top tips written yesterday. Model how to think about half and quarter to help place 3-digit numbers on a 0–1000 line.
Group Activities
-- Place 3-digit numbers on 0–1000 landmarked lines.
-- Make and use a 0–1000 number line.
-- Play a game to find mystery numbers string ‘number line’.

Day 3 Teaching
Play the Nasty Game. Show a place value grid (100s, 10s and 1s). Write different numbers on the grid, discussing their place value.
Group Activities
-- Play the ‘Nasty Game’ to make and compare 3-digit numbers.

Day 4 Teaching
Compare and order numbers using the place value grid. Discuss which digit to look at when the hundreds digit is the same. Find 3-digit numbers which fall between two given 3-digit numbers.
Group Activities
-- Order numbers using number lines and place value.
-- Find numbers between pairs of 3-digit numbers.
-- Ask questions to determine a mystery 3-digit number.

Day 5 Teaching
Challenge children to write the largest 3-digit number using digits 0–9 only once each. Repeat for other target numbers.
Group activities
Use the in-depth problem-solving investigation ‘Counter Place Value’ as today’s group activity.
Or, use this activity.
-- Investigate making 3-digit numbers with given criteria.

### You Will Need

• Mini-whiteboards and pens
• Blank landmarked line (see resources)
• Sticky notes
• ‘Placing 3-digit numbers on a landmarked line’ sheet (see resources)
• Pot containing a range of 3-digit numbers on cards
• ‘0–1000 landmarked lines’ sheet (see resources)
• Strips of paper, counters and felt tip pens
• Place value cards
• String and pegs
• 0–9 cards and sticky tack
• 2- and 3-player Nasty Game sheets (see resources)

### Mental/Oral Maths Starters

Day 1
Place 2-digit numbers on a 0–100 line (pre-requisite skills)

Day 2
Place value in 3-digit numbers (pre-requisite skills)

Suggested for Day 3
Tell the time to the nearest 5 mins (simmering skills)

Day 4
Compare pairs of 3-digit numbers (pre-requisite skills)

Suggested for Day 5
Round 2- and 3-digit numbers to nearest 10 (simmering skills)

### Procedural Fluency

Day 1
Place 3-digit numbers between hundreds on a number line.

Day 2
Place 3-digit numbers on a number line.

Day 3
Make and order 2- or 3-digit numbers using a range of starting digits.

Day 4
Order a series of 3-digit numbers. Find numbers between pairs of 3-digit numbers.

Day 5
Place value challenge: create 3-digit numbers according to given criteria.

### Mastery: Reasoning and Problem-Solving

• Sketch a 0–1000 line.
Mark 500.
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:
(i) 652
(ii) 591
(iii) 905

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 the combinations.

### Extra Support

In-betweenies
Placing numbers on a 0 to 100 landmarked line

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

## Unit 2 Understand x 100 and ÷ 100 as inverses (suggested as 3 days)

### Objectives

Understand multiplying and dividing by 10 and 100 (3-digit numbers) as inverse operations
Unit 2: ID# 3539

National Curriculum
Num/PV (iv) (v)

Hamilton Objectives
2. Estimate quantities and represent numbers in different ways.
3. Understand place value in 3-digit numbers; add/subtract 1, 10, 100 without difficulty.
5. Solve number problems and practical problems involving place value.

### Teaching and Group Activities for Understanding

Day 1 Teaching
Children copy a place value grid from the board to their whiteboards. They use digit cards to show 30 on it. Demonstrate multiplying by 10 and dividing by 10. Repeat to multiply 25 by 10 and to divide 270 by 10. Continue with other examples.
Group Activities
-- Create 2-digit numbers and multiply and divide them by 10. Record these calculations.
-- Challenge others to guess the starting number by giving the answer to × 10 questions.

Day 2 Teaching
Children write 4 on a place value grid on their whiteboards, they show 4 × 10 then 4 × 100. Point out that the digits are shifting two places to the left when we multiply by 100. Repeat with 7 × 10 and 7 × 100. Then divide by 100.
Group Activities
-- Play a divide by 10 and multiply by 10 card game.

Day 3 Teaching
Show a function machine (see resources). Children think what is happening inside the machine. Use the machine to multiply by 10 or 100, and then to ‘undo’ this by dividing by 10 or 100. Use the machine to demonstrate these inverse operations.
Group Activities
Use the in-depth problem-solving investigation ‘Lost Logic’ as today’s group activity.
Or, use this activity.
-- Use function machines to multiply and divide in single and double steps through inversion.

### You Will Need

• Place value grid (see resources)
• Mini-whiteboards and pens
• Interactive Whiteboard calculator
• 0–9 digit cards
• Place value grid (see resources)
• ÷ and x card game function cards and number cards (see resources)
• Additional activity sheets (see resources)

### Mental/Oral Maths Starters

Day 1
Division facts for 10 times table (pre-requisite skills)

Suggested for Day 2
Division facts for 5 times table (simmering skills)

Suggested for Day 3
Doubling and halving (simmering skills)

### Procedural Fluency

Day 1
Multiply and divide numbers by 10.

Day 2
Multiply and divide by 100. Find the missing number or function.

Day 3
Complete the function machines that include single and double steps.

### Mastery: Reasoning and Problem-Solving

• 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 end up with the number you started.

In-depth Investigation: Lost Logic
Children use their knowledge of inverse operations to solve a logic problem.

### Extra Support

Treasure or Trap
Multiplying and dividing by 10

## Unit 3 Understand PV in money; x 10 and ÷ 10 (suggested as 2 days)

### Objectives

Understand place value in money; multiply and divide by 10 and 100
Unit 3: ID# 3547

National Curriculum
Num/PV (ii) (v)
Meas (iii)

Hamilton Objectives
2. Estimate quantities and represent numbers in different ways.
5. Solve number problems and practical problems involving place value.
32. Use both £ and p in practical contexts.

### Teaching and Group Activities for Understanding

Day 1 Teaching
Use mock or Interactive Whiteboard coins to show £2.40 and £2.04. Explain that the zero in £2.40 shows that are no pennies, and the zero in £2.04 shows that there are no 10ps. Which is more money, £2.04 or £2.40? Model adding and subtracting amounts of money. Play the ‘Nasty Game’ to make the smallest and largest amounts of money.
Group Activities
-- Play the ‘Nasty Game’, making 3-digit numbers with money.
-- Solve and create word problems for addition and subtraction with 3-digit amounts of money.

Day 2 Teaching
Show pictures of priced toys (see resources). Children work out how much it would cost to buy 10 whistles at 34p each. Model writing 34p in a money place value grid and moving the digits to the left to multiply by 10. Repeat for other toys.
Group Activities
-- Multiply and divide shop prices by 10 and 100.

### You Will Need

• Large mock or Interactive Whiteboard coins
• 0–9 cards, additional 0 cards
• ‘Nasty Game’ board sheet 1–3 (see resources)
• Mini-whiteboards and pens
• Place value grid (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)
• Real money

### Mental/Oral Maths Starters

Day 1
Write amounts of money in pounds and pence (pre-requisite skills)

Suggested for Day 2
Division facts for 2 times table (simmering skills)

### Procedural Fluency

Day 1
Order, add and subtract money using place value.

Day 2
Multiply and divide money by 10 and 100.

### Mastery: Reasoning and Problem-Solving

• Write these numbers in figures:
(i) Two hundred and five.
(ii) Six hundred and sixty.
(iii) Nine hundred and ninety-one.
(iv) Three hundred and three.
• Write these amounts in figures:
(i) Four pounds and thirty pence.
(ii) Six pounds and seven pence.
(iii) Ten pounds and eleven pence.
• Write the missing numbers
£3.40 × 10 = ☐
☐ ÷ 10 = £5.50
100 × 9p = ☐
£7 ÷ ☐ = 7p

In-depth Investigation
No investigative activity with this unit.

### Extra Support

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

## Unit 4 Represent 3-digit numbers in diff ways (suggested as 3 days)

### Objectives

Represent 3-digit numbers in many different ways; round numbers to 10 and 100
Unit 4: ID# 3557

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

Hamilton Objectives
2. Estimate quantities and represent numbers in different ways.
5. Solve number problems and practical problems involving place value.
6. Round to the nearest ten and hundred, e.g. 34 to nearest 10 is 30, 276 to nearest hundred is 300.

### Teaching and Group Activities for Understanding

Day 1 Teaching
Click on 700, 80 and 5 in arrowcards from www.ictgames.com . Show how to create 3-digit numbers using arrow cards. Then use Diennes and coins from www.topmarks.co.uk. Select HTU with Dienes and model making 3-digit numbers.
Group Activities
-- Understand and create pictorial representations of 3-digit numbers.
-- Make and compare 3-digit numbers.
-- Subtract 100s, 10s and 1s from a 3-digit starting number.

Day 2 Teaching
Split the class into two teams. Use a set of large 0–9 cards and ask each team to generate 3-digit numbers, looking for a winner whose number is biggest / smallest/ closest to 555, etc.
Group Activities
-- Make 3-digit numbers to place on a 1–1000 number line.
-- Identify 3-digit numbers that are higher, lower or in-between other numbers on a 1–1000 number line.

Day 3 Teaching
Two children hold number cards 600 and 700 at either end of the room. A third child stands where 684 might be on an imaginary line from 600 and 700, keeping the number secret. Children discuss in groups what the number might be. Round the number to nearest 10. Repeat.
Group Activities
Use the in-depth problem-solving investigation ‘Guess my number’ as today’s group activity.
Or, use this activity.
-- Round 3-digit numbers to the nearest 10 and 100.

### You Will Need

• Internet access, mini-whiteboards and pens
• Base 10 equipment (e.g. Dienes)
• ‘Place value’ sheet (see resources)
• Place value cards
• Online dice 0–9 (or use a ten-sided dice) and tablets
• Set of 0–9 digit cards, sticky tack
• 0–1000 landmarked line (see resources)
• Sets of 3-digit number cards
• ‘Round to the nearest 10 and 100’ sheet (see resources)

### Mental/Oral Maths Starters

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

Suggested for Day 2
Multiply and divide by 10 (simmering skills)

Suggested for Day 3
Ordering Months of the year (simmering skills)

### Procedural Fluency

Day 1
Understand and create pictorial representations of 3-digit numbers.

Day 2
Make 3-digit numbers and order them.

Day 3
Round 3-digit numbers to the nearest 100 and 10.

### Mastery: Reasoning and Problem-Solving

• Use drawings or equipment to represent 562 in three different ways.
• Write the missing numbers:
529 – ☐ = 509
406 + ☐ = 446
801 – ☐ = 1
418 – ☐ = 400
990 + ☐ = 999
302 + ☐ = 302
• Write two numbers which round to 300 as the nearest 100. One must be less than 300, and one must be more.
• Write two numbers that round to 120 as the nearest 10. One must be less than 120, and one must be more.
• Round 448 to the nearest 10. Round the same number to the nearest 100.

In-depth Investigation: Guess my Number
Children use their knowledge of 3-digit numbers, rounding, and properties of numbers to work out a mystery number.

### Extra Support

Picture the Number
Understanding place value in 3-digit numbers; Beginning to compare 3-digit numbers

Tag to 200
Placing numbers between 100 and 200 on a 0 to 200 beaded line

## Unit 5 PV in money; add/subtract amounts (suggested as 2 days)

### Objectives

Represent place value in money; add and subtract amounts using place value
Unit 5: ID# 3571

National Curriculum
Num/PV (iv) (vi)
Meas (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
Remind children how we write amounts in pounds and pence, using a place value grid on the board. Ask children to write an amount in-between two given values and then order the amounts from smallest to largest.
Group Activities
-- Investigation: Work out how many amounts of money from £1 to £10 have the digit 9.

Day 2 Teaching
Use IWB £1, 10p and 1p coins to make £3.65. If I bought something for 60p, how much would I have left? Children write the subtraction on their whiteboards: £3.65 – 60p = £3. Repeat to show other additions and subtractions using place value.
Group Activities
-- Add and subtract multiples of 10p to and from given prices.
-- Making £10.00 challenge: make three amounts using rolls of a dice and add them to make a price closest to £10.00.
-- Count up and back in steps of 10p.

### You Will Need

• Mini-whiteboards and pens
• Calculators
• ‘Adding and subtracting money’ sheet (see resources)
• ‘Adding and subtracting’ sheet (see resources)
• Money place value grid (see resources)
• £1, 10p and 1p coins and dice

### Mental/Oral Maths Starters

Suggested for Day 1
Measure a line in cm (simmering skills)

Suggested for Day 2
Count in steps of 20 (simmering skills)

### Procedural Fluency

Day 1
Find amounts ‘in-between’ two prices.

Day 2
Add and subtract £1s, 10ps and 1ps.

### Mastery: Reasoning and Problem-Solving

• What is the smallest number of coins you can use to give me:
£2.31
£1.09
£4.40?
• Write these amounts on a place value grid. Then add 50p to each one.
(i) Three pounds and sixteen pence.
(ii) Five pounds and fifty pence.
(iii) Two pounds and two pence.
• What do I subtract from six pounds sixty-one pence to get five pounds ninety pence?

In-depth Investigation
Use the Group activity on Day 1.

### Extra Support

This unit has no separate Extra Support activities.