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# Maths Year 6 Autumn PV, Addition and Subtraction

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 value in 6-digit numbers (suggested as 2 days)

### Objectives

Understand place value in 6-digit numbers; add and subtract powers of 10
Unit 1: ID# 6113

National Curriculum
Num/PV (i) (iv)

Hamilton Objectives
4. Solve number and practical problems involving place value.

### Teaching and Group Activities for Understanding

Day 1 Teaching
Model writing 6-digit numbers dictated in words and show the place value of each digit using a place value chart. Add/subtract of powers of 10.
Group Activities
-- Select a digit from a 6-digit number and write its value. Repeat with other digits. Check by adding.
-- Eliminate digits from a 6-digit number, 1 or 2 at a time, using numbers based on a dice roll.
-- Write a 6-digit number and make it into 555,555 by adding/subtracting numbers of up to 6 digits.

Day 2 Teaching
Start with a 6-digit number and add/subtract 1s, 10s, 100s, 1000s, 10,000s and 100,000s. Add and subtract multiples of these powers of 10.
Group Activities
Use the in-depth problem-solving investigation ‘Activity Set A’ from NCETM.org.uk as today’s group activity.
Or, use these activities:
-- Write a 6-digit number and make it into 555,555 by adding or subtracting 1s, 10s, 100s, 1000s, 10,000s and 100,000s.
-- Make 999,999, by adding 1s, 10s, 100s, 1000s, 10,000s and 100,000s based on a dice roll. Repeat for subtraction to make 111,111.
-- ’Spend’ £999,999 by subtracting 6-digit numbers based on a dice roll. Make a million by adding two 6-digit numbers.

### You Will Need

• Vertical place value chart (see resources)
• Coloured pencils, sheets of plain paper
• 0–9 dice
• 6 packs of 10 digit cards, showing 0–9
• 1–6 dice

### Mental/Oral Maths Starters

Day 1
Order 5-digit numbers (pre-requisite skills)

Day 2
Count in steps of 1 though multiples of 100, 1000, 10,000 and 100,000 (pre-requisite skills)

### Procedural Fluency

Day 1
Write and complete place value number sentences (with extensions and challenges).

Day 2
Use place value and mental skills to practise 5- and 6-digit additions and subtractions.

### Mastery: Reasoning and Problem-Solving

• Sketch a line 0–1,000,000. Teacher marks a mystery number (e.g. 400,000). What number have I marked? Children ask questions to find the number. Repeat.
• What is the smallest number between 800,000 and 900,000 which has just four digits all the same and no zero?
• How many numbers between 100,000 and 200,000 contain exactly four 9s?
• Add 1, 10 or 100 each go. How many goes to turn 98,089 into 99,999?
• For a real-life problem, see final question (6) on day 1, practice sheet 2.

In-depth Investigation: Activity Set A
Choose an activity to explore PV in six-digit numbers. Activity Set A from ncetm.org.uk

### Extra Support

Pick 'n' Mix My Digits
Place value in 5-digit numbers; Adding and subtracting 1, 10, 100, 1000, 10,000

## Unit 2 Place 6-digit numbers on lines and round (suggested as 3 days)

### Objectives

Place 6-digit numbers on number lines; round to powers of 10
Unit 2: ID# 6121

National Curriculum
Num/PV (i) (ii)

Hamilton Objectives
1. Locate numbers up to 10 million on a landmarked line; use this to compare/ order numbers.
2. Round to ten, a hundred, a thousand, ten thousand, one hundred thousand or a million, as appropriate.

### Teaching and Group Activities for Understanding

Day 1 Teaching
Use digit cards to create 6 digit numbers; rearrange to make the largest and smallest numbers possible. Draw a 0–1,000,000 line and mark the multiples of 100,000. Place numbers on the line. Round 45,267 to the nearest 1000, 100 and 10, using different lines.
Group Activities
Use the in-depth problem-solving investigation ‘Nice or Nasty (Game 2, Nasty version)’ from NRICH as today’s group activity.
Or, use these activities:
-- Record numbers on a number line and write inequalities.

Day 2 Teaching
Look at the distance from London to Sydney and round 10,577 miles to nearest 1000, 100 and 10 miles, then draw a 1–100,000 number line and use this to round to nearest 1000, 100 and 10.
Group Activities
-- Research 5-digit numbers and mark them on a number line; round them to the nearest 1000 and 100 (Greater Depth to nearest 10 as well).

Day 3 Teaching
Sketch number lines and place 6-digit numbers on these. Round these numbers to the nearest 10, 100, 1000, 10,000 or 100,000.
Group Activities
-- Use number lines to determine place value and to round to the nearest 10, 100, 1000, 10,000 or 100,000.

### You Will Need

• 0–9 cards
• 0–1,000,000 landmarked line (see resources)
• Plain or squared paper

### Mental/Oral Maths Starters

Day 1
Place value in 6-digit numbers (pre-requisite skills)

Day 2
Ordering 6-digit numbers (pre-requisite skills)

Suggested for Day 3
Count on/back in 25s from 4-digit numbers (simmering skills)
or
Multiplication and division facts (simmering skills)

### Procedural Fluency

Day 1
Mark data onto a 0–1,000,000 number line.

Day 2
Round 5-digit numbers.

Day 3
Round population numbers of UK cities to the nearest 10, 100, 1000, 10,000, 100,000.

### Mastery: Reasoning and Problem-Solving

• Round 124,949 to nearest 10, 100, 1000 and 10,000.
• How many numbers round to 550,000 as the nearest 10,000 and to 555,000 as the nearest 1000?
• Sketch a line from 680,000 to 690,000. Mark the 1000s. Write two consecutive numbers between each pair of marks – one must round up to the nearest 1000 and the other down to the nearest 1000. Say the numbers aloud.
• My answer has six digits. Four of the digits are identical and the other two are both 9. It rounds to 560,000 as the nearest 10,000. Write two different possible answers.

In-depth Investigation: Nice or Nasty (Game 2, Nasty Version)
Whoever makes the smaller six-digit number wins. Invent your own scoring system. Nice or Nasty (Game 2, Nasty Version) from nrich.maths.org.

### Extra Support

Ring and ring and rounding!
Place 4-digit numbers on a line and round to the nearest 10, 100 and 1000.

## Unit 3 Column addition and estimation (suggested as 2 days)

### Objectives

Use column addition to add numbers with up to 5 digits; estimate totals
Unit 3: ID# 6131

National Curriculum

Hamilton Objectives
6. Consolidate: Add several large numbers using written addition, including ‘piles of numbers’ with different numbers of digits.

### Teaching and Group Activities for Understanding

Day 1 Teaching
Write pairs of 5-digit numbers on the board. Discuss which has the largest answer. The smallest? Discuss how rounding can give approximations then use column addition to solve. Remember to leave a blank row above the answer for any extra numbers (‘carry’ digits). Children then use digits 0–9 to create two 5-digit numbers and find the total.
Group activities
-- Experiment with adding three numbers and/or aiming for answers that meet given criteria.

Day 2 Teaching
Write the addition 73,274 + 52,638 on the board. Ask children to estimate the total. Ask which columns will come to more than 10? Use column addition to solve. Ask children to come up with a 5-digit addition that will involve 4 ‘carries’. Then add numbers with different numbers of digits.
Group activities
Use the ‘Giant Domino Addition’ in-depth problem-solving investigation below as today’s group activity.
Or, use these activities:
-- Use given digits to find pairs of 5-digit numbers that sum to 100,000 and 150,000.
-- Use given digits to find pairs of 5-digit numbers that sum to 121,212.
-- Use pairs of numbers which have a sum of 9 to create pairs of 5-digit numbers; use this to find 5-digit numbers with a sum of 100,000.

### You Will Need

• Place value chart (see resources)
• Mini-whiteboards and pens
• Interactive class whiteboard
• IWB calculator
• Counters

### Mental/Oral Maths Starters

Day 1

Suggested for day 2
Roman numerals game to consolidate idea of carrying (simmering skills)

### Procedural Fluency

Day 1
Practise column addition with 5 and 6 digits.

Day 2
Use addition in a science experiment.
Practise column addition with 4–6 digits and 3 or 4 numbers.

### Mastery: Reasoning and Problem-Solving

• Write the missing digits in this sum:
3 4 7 1 9 + ☐ 6 5 ☐ ☐ = 7 ☐ ☐ 0 8
• Write an addition where the two 5-digit numbers add to 55,555. Neither number has a 0, and you must use 6, 7, 8 and 9 as digits; you can also use other digits!
• Write a 5-digit plus 4-digit addition where every column adds to more than 10.

Children follow a logic to convert arrangements of dominoes to numbers, and then perform a giant addition. They then create their own domino additions and explore addition patterns.

Colossal Column

## Unit 4 Column subtraction and estimation (suggested as 2 days)

### Objectives

Use decomposition to subtract numbers with up to 5 digits
Unit 4: ID# 6143

National Curriculum

Hamilton Objectives
7. Consolidate: Subtract large numbers using decomposition or counting up if appropriate.

### Teaching and Group Activities for Understanding

Day 1 Teaching
Draw 4,562 – 2,638 on the board as a compact decomposition. Carefully talk though each stage. Revise using column subtraction to subtract other pairs of 5-digit numbers.
Group Activities
-- Discuss when to count up (‘Frog’) and when to do column subtraction. Model and practise the method.
-- Practise subtracting a 4 or 5-digit number from a 5-digit number.
-- Practise subtracting 5-digit numbers from 5-digit numbers with speed and accuracy.

Day 2 Teaching
Write 34,782 – 17,257, 34,782 – 7257, 34,782 – 782. Ask children to set them out on their whiteboards. Discuss how they did this. Did they ensure that 1s are under 1s, 10s under 10s, 100s under 100s and so on? Estimate and then solve using column subtraction. Compare estimates.
Group Activities
Use the in-depth problem-solving investigation ‘Dicey Operations’ from NRICH as today’s group activity.
Or, use these activities:
-- Study worked column subtractions to identify missing digits.
-- Subtract a 4 or 5-digit number from a 5-digit number.

### You Will Need

• Mini-whiteboards and pens
• Place value charts (optional)
• 0–9 cards
• Sticky notes
• Counters
• Pot

### Mental/Oral Maths Starters

Day 1
Subtractions facts (pre-requisite skills)

Suggested for Day 2
Mental subtraction of 2-digit numbers (simmering skills)

### Procedural Fluency

Day 1
Subtract pairs of 4 or 5-digit numbers.

Day 2
Complete population puzzle: ‘Alphabet Archipelago‘.

### Mastery: Reasoning and Problem-Solving

• How many times must 33,217 be subtracted from 100,000 to leave a number less than itself? What is the number left?
• What are the missing digits here?
5 ☐ 8 1 3
- 9 3 ☐ ☐
☐ 5 ☐ 6 5
• What is the easiest way to subtract 28,560 from 90,600?
• Use two different methods to subtract 28,560 from 90,600. Which method would you choose? Can you explain why?

In-depth Investigation: Dicey Operations
Choose an appropriate method to solve subtraction problems with five-digit numbers. Dicey Operations from nrich.maths.org.

### Extra Support

This unit has no separate Extra Support activities.

## Unit 5 Mental and written calculation strategies (suggested as 4 days)

### Objectives

Choose and use mental and written strategies to add/subtract including with money
Unit 5: ID# 6151

National Curriculum

Hamilton Objectives
5. Consolidate: Add and subtract mentally with confidence, where numbers are < 100 or it relies upon simple addition/subtraction and place value.
8. Solve addition/subtraction multi-step problems in context, deciding which operations to use and why.

### Teaching and Group Activities for Understanding

Day 1 Teaching
Add two or three prices under £20. Then draw an empty number line and use Frog to find change from £50. Repeat this, using a bar model to show the change from £100. Repeat for three prices between £20 and £30.
Group Activities
-- From an array of given items, find totals that would give change from £50 or £100. Amount/speed of solutions expected can be differentiated.

Day 2 Teaching
Draw empty number lines and use Frog to find the difference between two amounts of money between £100 and £500. Repeat this several times, estimating first.
Group Activities
-- Carry out 4-digit and 5-digit subtractions using ‘Frog’.

Day 3 Teaching
Write a series of subtractions on the board. Children choose whether to use counting up (Frog) or column subtraction (decomposition) to work out given calculations.
Group Activities
-- Work out change when using specified notes/coins. Discuss whether to use Frog or decomposition and complete the calculations.

Day 4 Teaching
Write a series of prices of aquarium fish on board. Children decide which to buy, up to £70, using mental strategies for summing different amounts and calculating change.
Group Activities
Use the ‘Nine AGAIN’ in-depth problem-solving investigation below as today’s group activity.
Or, use these activities:
-- Calculate the costs of different combinations of aquarium fish and the change from given amounts.

### You Will Need

• Jotters for working out
• ‘Whole class practice’ (see resources)
• Money – real coins, pretend notes
• ‘Choosing a method of Subtraction’ (see resources)
• Timer/stop clock
• Aquatic centre (see resources)
• 0–9 digit cards
• ITP: Tell the Time

### Mental/Oral Maths Starters

Day 1
Bonds to £1: number facts (pre-requisite skills)

Suggested for Day 2
Pieces of cheese: successive subtraction with weights to 3-digit decimals (simmering skills)

Day 3
Change from £20: 4-digit mental subtraction (pre-requisite skills)

Suggested for Day 4
24-hour clock: 4-digit mental subtraction (simmering skills)

### Procedural Fluency

Day 1
Work out totals and calculating change: ‘Shopping in Town’.

Day 2
Work out the cheapest place to buy new athletics gear by finding the difference.

Day 3
Choose methods of subtraction.

Day 4
Use subtraction to choose an aquarium and fish to suit different budgets.

### Mastery: Reasoning and Problem-Solving

• Subtract 17,835 from £18,009 in two different ways. Explain which method you thought was most efficient and why.
• Write three prices which total £100. None can be an exact number of pounds and the numbers of pence are not multiples of 5p.
• True or false?
-- Buying 3 things each less than £30, and each priced at a number of pounds and 99p, will result in 3p and some pounds change from £100.
-- £5 can be made in more than one way using exactly 7 coins.
-- Three amounts totalling £10 can be written without any being more than £3.40.
• When estimating how much change we will get, is it better to round up to the next pound than down to the previous pound? Give a reason for your answer.

In-depth Investigation: Nine AGAIN
Children subtract 5-digit numbers and look for patterns in the digital roots.

### Extra Support

Phone a frog
Using counting up (Frog) to calculate change from £100.