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# Maths Year 6 Autumn More PV, Addition, 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 Add, subtract & round 6-/7-digit numbers (suggested as 3 days)

### Objectives

Use place value to add, subtract and round 6- and 7-digit numbers
Unit 1: ID# 6421

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

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 and a thousand, ten thousand, one hundred thousand or a million, as appropriate.
3. Solve number and practical problems involving place value, rounding and negative numbers.

### Teaching and Group Activities for Understanding

Day 1 Teaching
Write on the board 4,351,468. Discuss the commas or spaces used to separate parts. Cover the first four digits. Read the number. Uncover the next three digits and read it. Uncover the final digit and read again. Repeat with other 7-digit numbers. Practise some ‘place value’ calculations, e.g. 2,743,561 – 40,000? Now subtract 500. Subtract 700,000. Subtract 3001. What’s left?
Write on the board ☐,☐☐☐,☐☐☐ > ☐,☐☐☐,☐☐☐. Roll a 0–9 dice and ask children where to place the digit. Explain that they are to try to make the first number greater than the second number. Repeat until all the spaces are filled.
Group Activities
Use the ‘Sometimes we lose things’ in-depth problem-solving investigation from NRICH as today’s group activity.
Or, use these activities:
- Use dice rolls to construct and subtract from 7-digit numbers.
- Order 7-digit numbers with consecutive digits.

Day 2 Teaching
Use the IWB calculator’s constant function to repeatedly add then subtract 1, 10, 100, 1000, 10,000, 100,000 and 1,000,000 to/from 5,555,555. Take care when crossing boundaries of powers of ten.
Group Activities
- Use dice rolls to add/subtract 1, 10, 100, 1000, 10,000, 100,000 or 1,000,000 from 5,000,000.
- Turn a 7-digit number into 5,555,555 by adding and subtracting multiples of 1, 10, 100, 1000, 10,000, 100,000.

Day 3 Teaching
Children mark halfway on a sketched 1,000,000 to 2,000,000 number line. Ask them to mark a number rounding to 1,000,000 and one rounding to 2,000,000.
Repeat for rounding to the nearest 100,000 between 2,500,000 and 2,600,000.
Repeat for rounding to the nearest 10,000 between 2,530,000 and 2,540,000.
Group Activities
- Mark numbers on a 2,000,000 to 3,000,000 landmarked line and round them.
- Round 7-digit numbers to the nearest 100, 1000, 10,000, 100,000

### You Will Need

• Whiteboards and pens
• 0–9 dice
• 1–6 dice
• IWB calculator
• calculators
• 0 to 100,000 landmarked lines (see resources)
• 2,000,000 to 3,000,000 landmarked lines (see resources)

### Mental/Oral Maths Starters

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

Day 2
Count on/back in 10s, 100s, 1000s and 10,000s from 5-digit numbers (pre-requisite skills)

Suggested for Day 3
Add and subtract near multiples of 10, 100 and 1000 to/from 4-digit numbers (simmering skills)

### Procedural Fluency

Day 1
Comparing and ordering numbers including use of > and <.

Day 2
Use place value to add and subtract from large numbers.

Day 3
Rounding numbers to the nearest 1,000,000, 100,000 and 10,000.

### Procedural Fluency

• Fill in the missing digits:
384,☐79 < 384,0☐9
1,0☐0,841 > 1,040,996
• Complete the place value subtractions.
(a) 1,249,541 – [_____] = 1,240,501
(b) 673,890 – [_____] = 70,090
(c) 2,951,159 – [_____] = 2,050,050
• Draw a line from 3,000,000 to 4,000,000. Mark the halfway point.
Mark two numbers that round to 3,000,000. Mark two numbers that round to 3,500,000 as the nearest 100,000.

In-depth Investigation: Sometimes We Lose Things
What would happen if we lost all the nines in our number system? Have a go at writing the numbers out in this way. Sometimes We Lose Things from nrich.maths.org.

### Extra Support

Dicey Decisions
Understanding place value in 4-digit and 5-digit numbers. Comparing 4-digit numbers and 5-digit numbers.

Zoom Zoom
Rounding 5-digit numbers to the nearest 100, 1000 and 10,000.

## Unit 2 Understand/calculate negative numbers (suggested as 2 days)

### Objectives

Understand negative numbers; perform calculations across 0
Unit 2: ID# 6427

National Curriculum
Num/PV (iii)

Hamilton Objectives
3. Use negative numbers in context, calculate intervals across zero.
4. Solve number and practical problems involving place value, rounding and negative numbers.

### Teaching and Group Activities for Understanding

Day 1 Teaching
Use negative numbers in the context of temperature. Launch ITP Thermometer, choose a range of −10 to 10. At what temperature might we get ice outside? Why? Agree that as water freezes at 0 degrees Celsius the temperature will be less than this, e.g. –1, –2, etc. Ask children to label some temperatures and calculate rises/falls in temperature.
Group Activities
-- Use a web-based resource to compare temperatures in different places around the world. Find temperature differences.
-- Compare day and night temperatures across a 5-day period. Find temperature differences.

Day 2 Teaching
Show a line from –20 to 20, with multiples of 5 labelled. This has positive/negative numbers. Numbers can be less than 0 (temperatures, a bank account overdrawn, or a depth below sea level).
Make up additions and subtractions with positive and negative answers: What do you think 5 subtract 6 is?
Group Activities
Use the ‘Noughts and Negatives’ in-depth problem-solving investigation below as today’s group activity.
Or, use this activity:
-- Investigate the difference between a positive and a negative number and two negative numbers.

### You Will Need

• ITP Thermometer: www.taw.org.uk/lic/itp/thermometer.html
• ‘Temperature’ sheet (see resources)
• PCs, laptops or tablets
• Atlas
• –20 to 20 number lines (see resources)
• Calculators (optional)

### Mental/Oral Maths Starters

Day 1
Place negative and positive numbers on lines (pre-requisite skills)

Suggested for Day 2

### Procedural Fluency

Day 1
Calculating rise and fall in temperatures.

Day 2
Adding and subtracting with negative numbers.
Solving problems with negative numbers.

### Mastery: Reasoning and Problem-Solving

• The temperature at 6pm is given first; then the fall during the night until 5am. Write the night temperatures for each weekday.
Monday: 5°C Falls 9°
Tuesday: 3°C Falls 8°
Wednesday: 8°C Falls 10°
Thursday: 3°C Falls 7°
Friday: 2°C Falls 3°
• On which night was the temperature lowest?
• On Saturday, the temperature fell 15° overnight to −6°C. What was the temperature at 6pm?
• On Sunday, the temperature was 13°C at 6pm and −5°C at 5am. How much did it fall overnight?

In-depth Investigation: Noughts and Negatives
Children play an adapted game of noughts and crosses, aiming to get negative number answers.

### Extra Support

Sea Level
The picture shows a lighthouse and many underwater creatures. If you know the markings on the lighthouse are 1m apart, can you work out the distances between some of the different creatures? Sea Level from nrich.maths.org.

## Unit 3 Strategies in mental & written calculation (suggested as 2 days)

### Objectives

Informal methods of mental and written calculation
Unit 3: ID# 6451

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.
4. Solve number and practical problems involving place value, rounding and negative numbers.

### Teaching and Group Activities for Understanding

Day 1 Teaching
Demonstrate how to use ‘add and adjust’ strategies to add ‘nearly numbers’, such as 4735 + 203, 4735 + 197, 4735 + 1995, 465 + 299, 4.65 + 2.99.
Repeat to ‘subtract and adjust’ for subtraction of nearly numbers, e.g. 4735 – 705, 4735 – 197, 4735 – 1995, 6.25 – 1.98, 4.21 – 3.02.
Group Activities

Day 2 Teaching
Show costs of activities. Ask children to estimate the total cost (e.g. rounding to the nearest pound). Model using column addition to find the exact cost, and then Frog to find the change from the £100 budget. Sketch a bar model to represent this.
Group Activities
-- Investigate totals and change for combinations of Activities for Year 6 Residential.

### You Will Need

• Whiteboards and pens
• ‘Mental addition and subtraction’ sheet (see resources)
• ‘Activities for Year 6 residential’ (see resources)
• 0–100 landmarked line’ (see resources)

### Mental/Oral Maths Starters

Day 1
Add to the next whole number from a 2-place decimal number (pre-requisite skills)

Suggested for Day 2
Round numbers with two decimal places to the nearest whole (simmering skills)

### Procedural Fluency

Day 1
Mental addition and subtraction worksheet practice.

Day 2
Bank Holiday leisure costs, calculating total costs and change.

### Mastery: Reasoning and Problem-Solving

Subtract 1998 from 6565.
Invent another similar pair of calculations where the same thing occurs.
• Drinks are £2.99 each.
A bag of crisps is 49p.
Burgers are £4.99 each.
Find the total of two drinks, a burger and a bag of crisps.
Find the change from £20.
• Frog does three hops: 51p, £2 and £10 to find change from £50. How much was the item bought?
• Write the missing number in this bar model
 £100 £43.25 £9.65 £14 ?

In-depth Investigation: Activities for Year 6 Residential Weekend (the Group Activity from Day 2).

### Extra Support

Dream Shopping
Finding change from £100 using Frog (counting up)

## Unit 4 Use brackets and order of operations (suggested as 3 days)

### Objectives

Using brackets and order of operations in solving addition/subtraction problems
Unit 4: ID# 6473

National Curriculum

Hamilton Objectives
18. Perform mental calculations, including with mixed operations. Carry out calculations using knowledge of the order of operations and brackets.
8. Solve addition and subtraction multi-step problems in context, deciding which operations to use and why.

### Teaching and Group Activities for Understanding

Day 1 Teaching
Write 4 + 3 × 12. Ask half class to work from left to right and others work from right to left. Discuss different answers. Introduce the rules: Brackets, then multiplication/division, then addition/subtraction. Reiterate with 4 + 16 ÷ 2 and (4 + 16) ÷ 2.
Write on the board: 1. Brackets; 2. Multiplication/division; 3. Addition/subtraction.
Group Activities
-- Agree the order of operations for two given examples. Use four number cards 1–9 to create calculations then solve using the correct order of operations.
-- Use three number cards 1–9 to create calculations then solve using the correct order of operations.

Day 2 Teaching
Explore the order of operations using brackets, for example, 2 + 1 × 3 = 5 and (2 + 1) × 3 = 9. Discuss how putting the brackets in different places can alter the answer to a calculation. Write on the board 12 + 8 ÷ 4 – 2. Putting brackets in different places, how many different answers can you find?
Group Activities
-- Use only the numbers 1, 2 and 3 with any operations/brackets, to make numbers 0–9.
-- Use only the number 3 repeatedly with any operations/brackets, to make all numbers 0–10.
-- Use the numbers 6, 2, 3 and 4 in sequence to make whole numbers.

Day 3 Teaching
Write on the board 78 × 100 – 42 and 78 × (100 – 42). Remind the class that we find the answers to calculations in brackets first. Discuss why the answer to the second calculation is different. Display two word problems (see teaching download); use knowledge of the order of operations to solve.
Group Activities
Use the ‘All at 6s and 7s’ in-depth problem-solving investigation below as today’s group activity.
Or, use these activities:
-- Create and solve and multi-step word problems involving correct order of operations.

### You Will Need

• Whiteboards and pens (optional)
• Number cards 2–9

### Mental/Oral Maths Starters

Day 1
Practising order of operations (pre-requisite skills)

Suggested for Day 2
Mental division, answers as fractions (simmering skills)

Suggested for Day 3
Find intervals using 24-hour clock (simmering skills)

### Procedural Fluency

Day 1
Order of brackets and operations activity sheets.

Day 2
Identifying where brackets go in number sentences.

Day 3
Solving multi-step word problems with brackets.

### Mastery: Reasoning and Problem-Solving

• In relation to multi-part calculations, agree if these statements are true or false:
We leave the part in brackets until last.
It does not matter which order you do the parts of the calculation not in brackets.
We should always do the easiest parts of a calculation first.
12 + (3 × 4) gives the same answer if the brackets are removed.
• Put a pair of brackets in three different places in this calculation to give three different answers .
4 + 5 × 12 – 7 =
• Write a word problem involving the numbers 5, 6, and 12 and the answer 132. (Hint, you will need to use brackets in the final calculation.)

In-depth Investigation: All at 6s and 7s
Children try to make every number to at least 10 using 6, 7 and sometimes 2 and 3, and any operations.

### Extra Support

Order, Order!
Practising ordering calculations involving brackets, +, −, × and ÷