Maths Year 5/6 Spring PV, Addition and Subtraction

In the Spring term, it is likely you will begin to think about more formal SATs preparation for your Year 6s. While this revision will be driven by the specific needs of the children in your class, we hope to help by providing a set of SATs-style questions to accompany each Spring term unit: 'Y6 SATs Practice' is an additional 'Teaching & Group Activities' download.

Each unit still has everything you need to teach a set of related skills and concepts for the whole class: 'Teaching & Group Activities' provides a plan for whole-class teaching; a 'Slide Presentation' brings this teaching to life on the IWB. Fully-differentiated adult-led group activities follow, allowing for small-group personalised learning, where you may deal with children's 'Common Misconceptions'. Fluency can be rehearsed with our 'Practice Sheets', or learning checked with the 'Mastery Activity'. '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 the associated documents. These bulk downloads are only available to Hamilton Friends and School Subscribers.

Unit 1 Place value (suggested as 4 days)

Planning and Activities

Day 1 Teaching
Discuss how to write and say 6-digit numbers. Build numbers using place value chart. Generate 6-digit numbers by rolling a dice and create an inequality. Discuss how to write 7-digit numbers. Write a number between two 7-digit numbers.
Group Activities: T with Y5
Use the in-depth problem-solving investigation ‘Lost Digit’ as today’s group activity.
Or, use these activities:
Y5 -- Compare and use place value to subtract from 6-digit numbers; Use place value subtraction to ‘zap’ each digit in a 6-digit number.
Y6 -- Use dice rolls to construct and subtract from 7-digit numbers. Order 7-digit numbers with consecutive digits.

Day 2 Teaching
Use the Interactive Whiteboard calculator’s constant function to repeatedly add then subtract 1, 10, 100, 1000, 10,000 and 100,000 to 6-digit numbers. Check that children can cross the place value ‘boundaries’ when adding powers of ten.
Further Teaching with Y6
As above but beginning with 7-digit numbers.
Group Activities: T with Y6
Y5 -- Subtract and/ or add 1, 10, 100, 1000, 10,000 and 100,000 to 6-digit numbers.
Y6 -- 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 and 1,000,000.

Day 3 Teaching
Place 6-digit numbers on landmarked lines and round to the nearest 100,000, 1000 and 100.
Further Teaching with Y6
Place 7-digit numbers on lines and round to the nearest 1,000,000, 100,000 and 10,000.
Group Activities: T with Y6
Y5 -- Place 6-digit numbers on landmarked or empty lines; round to the nearest 100 and 1000.
Y6 -- 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 and 1,000,000.

Day 4 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: T with Y5
Y5 -- Use place value to add and subtract multiples and near multiples of 100 and 1000.
Y6 -- Choose pairs of numbers to add and subtract, using an ‘add/subtract and adjust’ strategy, including some decimals.

You Will Need

  • Vertical place value chart (see resources)
  • 1–6 and 0–9 dice
  • Calculators
  • Interactive whiteboard calculator
  • Landmarked lines (see resources)
  • Sticky notes
  • 0–9 digit cards
  • 250,000–260,000 landmarked lines with 1000s labelled (see resources)
  • Landmarked line from 2,000,000 to 3,000,000 (see resources)
  • Mental addition and subtraction activity sheets 1 and 2 (see resources)
  • SATs-style questions (see download)

Short Mental Workouts

Day 1
Double 2-digit numbers

Day 2
Count on/back in 10s, 100s, 1000s and 10,000s from 5-digit numbers

Day 3
Place value in 6-digit numbers

Day 4
Add and subtract near multiples of 10, 100 and 1000 to/from 4-digit numbers

Worksheets

Day 1
Y5: Write 6-digit numbers with digits of given values.
Write missing digits in numbers to create ascending/descending lists of 6-digit numbers.
Y6: Compare and order numbers, including use of > and <.

Day 2
Y5: Add and subtract 1, 10, 100, 1000, 10,000 and 100,000; preserve inequalities.
Y6: Use place value to add and subtract from large numbers.

Day 3
Y5: Place 6-digit numbers on lines and round to the nearest 100 or 1000.
Y6: Round numbers to the nearest 1,000,000, 100,000, 10,000 and 1,000.

Day 4
Y5: Add and subtract from 4- and 5-digit numbers:
- using place value;
- recognising near multiples of 100, 1000 and 10,000.
Y6: Add and subtract from whole numbers and decimals:
- using place value;
- recognising near multiples.

Mastery: Reasoning and Problem-Solving

Y5

  • True or false?
    10 more than 99,999 is 100,090.
    100 less than 202,020 is 201,920.
    199,009 add 1000 is 201,009.
    Add 10,000 to 105,432 five times to get 150,432.
  • Sketch a line between two multiples of 100,000. Mark the appropriate 10,000s. Choose an adjacent pair of numbers and mark the midpoint between them.
  • Write a number that rounds to 40,000 as the nearest 10,000 and to 35,000 as the nearest 1000.
  • Round 49,949 to the nearest:
    -- ten thousand
    -- thousand
    -- hundred
    -- ten
  • What is the smallest number between 800,000 and 900,000 which has just four digits all the same and no zero?

Y6

  • 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: Lost Digit
Children explore place value in 6-digit numbers through finding digit sums and ‘casting out nines’.

Extra Support

Y5: Back to the Start
Adding/ subtracting 1, 10, 100 and 1000 to/from 4-digit numbers (not crossing 10s, 100s or 1000s).

Line ‘em Up
Placing 4-digit numbers on landmarked lines.

Y6: 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 Negative numbers (suggested as 2 days)

Planning and Activities

Day 1 Teaching
Use negative numbers in the context of temperature. Using the ITP Thermometer, label some temperatures and calculate rises/falls in temperature.
Group Activities: T with Y5
Y5 -- Calculate rises and falls in temperature, drawing own vertical number lines or using a thermometer image.
Y6 -- Compare day and night temperatures across a 5-day period. Find temperature differences. Use a web-based resource to compare temperatures in different places around the world.

Day 2 Teaching
Display a table showing the temperatures recorded at a school weather station. Discuss the differences between temperatures. Find how much the temperature rose and fell during the day and night.
Further Teaching with Y6
Show a line from –20 to 20, with multiples of 5 labelled. Discuss contexts for negative numbers. Make up additions and subtractions with positive and negative answers.
Group Activities: T with Y6
Use the in-depth problem-solving investigation ‘Noughts and negatives’ as today’s group activity.
Or, use these activities:
Y5 -- Find pairs of temperatures with a difference of 10°C. One temperature must be above freezing and one below. Add and subtract numbers to/from -5 to give one answer >0 and one answer <0.
Y6 -- Investigate the difference between a positive and a negative number and two negative numbers.

You Will Need

  • ITP: Thermometer
  • 'Temperature' activity sheet (see resources)
  • –9°c to 9°C cards
  • 2 cut-out card arrows
  • Sticky-tack
  • PCs/laptops/tablets
  • Atlas
  • –20 to 20 number line with 0 and multiples of 5 labelled (see resources)
  • Calculators (optional)
  • SATs-style questions (see download)

Short Mental Workouts

Day 1
Pairs to 100

Day 2
Place negative and positive numbers on lines

Worksheets

Day 1
Y5 Order temperatures and calculate rises and falls in temperature.
Y6: Calculate temperature differences.

Day 2
Y5: Calculate differences on a bar chart of temperatures in a range of cities.
Y6: Add and subtract with negative numbers.

Mastery: Reasoning and Problem-Solving

Y5

  • Sketch a line –20 to +20. Mark 0. Teacher marks a mystery number (e.g. –8). What number have I marked? Children ask questions to guess. Repeat.
  • Count on in steps of 4 from –27. How many steps to reach or pass 20?
  • Count in steps of –5. Start at +3. How many steps to get to –42?
  • Order these temperatures, starting with the lowest: 12°C, –6°C, –11°C, 0°C, 27°C

Y6

  • 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

Y5: Out at Sea
Understanding negative numbers.

Y6: 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 Use of brackets in calculation (suggested as 2 days)

Planning and Activities

Day 1 Teaching
Write 4 + 3 × 12. Ask half the class to work from left to right and others work beginning with the 3, i.e. 3 × 12 + 4. Discuss different answers. Introduce the rules: Brackets, then multiplication/division, then addition/subtraction. Repeat with calculations 4 + 16 ÷ 2 and (4 + 16) ÷ 2.
Group Activities: T with Y6
Y5 -- Explore different orders of addition, multiplication and brackets.
Y6 -- Use three or more number cards 2–9 to create calculations; solve using correct order of operations.

Day 2 Teaching
Explore the order of operations using brackets, for example, (15 + 2) × 4 and 15 + (2 × 4). Discuss how putting the brackets in different places can alter the answer to a calculation. Write 12 + 8 ÷ 4 – 3. Children work in pairs to find the (only) correct answer (11), then other possibilities by using brackets.
Group Activities: T with Y5
Use the in-depth problem-solving investigation ‘All at 6s and 7s’ as today’s group activity.
Or, use these activities:
Y5 -- Use numbers 1, 2 and 3 with any operations/brackets, to make all numbers from 0 to 9. Use just the number 3 repeatedly with any operations/brackets, to make all numbers from 0 to 10.
Y6 -- Use just the number 3 repeatedly with any operations/brackets, to make all numbers from 0 to 10. Use numbers 6, 2, 3, 4 in sequence to make whole numbers.

Short Mental Workouts

Day 1
Mental division

Day 2
Find intervals using 24-hour clock

Worksheets

Day 1
Y5: Solve calculations, observing brackets and the correct order of operations.
Y6: Solve calculations, observing brackets and the correct order of operations.

Day 2
Y5: Place brackets to create correct number sentences.
Y6: Place brackets to create correct equalities.

Mastery: Reasoning and Problem-Solving

Y5 and Y6

  • 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

Y5 and Y6: Order, Order!
Practising ordering calculations involving brackets, +, −, × and ÷.

Unit 4 Addition and subtraction (suggested as 5 days)

Planning and Activities

Day 1 Teaching
Use Frog to work out how far cyclists have to go before cycling 4000 miles across America. Model using frog to calculate 100,000 – 76,459.
Group Activities: T with Y5
Y5 -- Practise counting up to find a difference between 4-digit numbers and 10,000 by completing an investigation.
Y6 -- Practise counting up to find a difference between 5-digit numbers and 100,000 by completing an investigation.

Day 2 Teaching
Round to find an estimate; use column addition to add pairs of 5-digit numbers. Find pairs of numbers which add to 40,000. What do the pairs have in common?
Further Teaching with Y6
Use column addition to add a 4-digit number to a 5-digit number, then find the difference between the total and 100,000.
Group Activities: T with Y6
Y5 -- Work out the mystery digits in 4- or 5-digit column additions.
Y6 -- Work out mystery digits in a range of column additions.

Day 3 Teaching
Use column subtraction to subtract 5-digit numbers, predict numbers of moves, add to check.
Further Teaching with Y6
Discuss how to lay out 61,638 – 4271 and 61,638 – 742, subtract.
Group Activities: T with Y6
Y5 -- Work out mystery digits in 4- or 5-digit column subtractions.
Y6 -- Work out mystery digits in a range of column subtractions.

Day 4 Teaching
Display priced items on the board. Use Frog to find how much change we would have from £100 to buy a chosen item. Calculate a total of two items, then the change from £100.
Group Activities: T with Y5
Y5/Y6 -- Find money totals and change from £100 (or £50, or £200).

Day 5 Teaching
Draw a diagram on the board showing differences between amounts. Use Frog to find which pairs of amounts have which differences.
Group Activities: T with Y5
Use the in-depth problem-solving investigation ‘Pence and pounds reversed’ as today’s group activity.
Or, use these activities:
Y5 -- Explore money differences using Frog.
Y6 -- Investigation involving 4-digit and 5-digit subtractions of money using Frog.

You Will Need

  • 6, 7, 8 and 9 digit cards
  • Sticky notes
  • ‘Room makeover’ sheet (see resources)
  • Number cards 4–9
  • SATs-style questions (see download)

Short Mental Workouts

Day 1
Pairs to 1000

Day 2
Rounding whole numbers to the nearest 1000

Day 3
Add pairs of 2-digit numbers

Day 4
Bonds to £1

Day 5
Subtract pairs of 2-digit numbers

Worksheets

Day 1
Y5: Use Frog to count up from 4-digit numbers to multiples of 1000.
Y6: Use Frog to count up from 5-digit numbers to multiples of 10,000.

Day 2
Y5: Add pairs of 4- or 5-digit numbers; find the difference between the total and 10,000 or 100,000.
Y6: Add to find new scores; calculate how many to reach 100,000.

Day 3
Y5: Use column subtraction to subtract 3-, 4- and 5-digit numbers from 5-digit numbers.
Y6: Use column subtraction to subtract pairs of 5-digit numbers.

Day 4
Y5: Find the change from £50 and £100, then find totals and the change from £100.
Y6: Calculate totals and calculating change: ‘Shopping in Town’.

Day 5
Y5: Estimate, then find the difference between amounts of money.
Y6: Calculate the cheapest place to buy new athletics gear by finding the difference.

Mastery: Reasoning and Problem-Solving

Y5

  • Use just digits 4 and 5 to create a 5-digit – 5-digit subtraction to give an answer with at least two 9s.
    -- Can you get 9091?
    -- What is the smallest answer you can get?
    -- What is the largest?
  • Explain why it would be sensible to choose different methods to solve (a) and (b) below.
    (a) 67,493 – 21,561
    (b) 50,005 – 44,878
  • Find the missing numbers in this subtraction:
    1 2 ☐ 6 2 – 9 3 ☐ 8 = 3 1 1 ☐

Y6

  • Add 1998 to 2569.
    Subtract 1998 from 6565.
    Invent another pair of calculations where the same thing occurs (an addition and a subtraction of the same 4-digit number, resulting in the same answer).
  • -- Drinks cost £2.99 each.
    -- An apple is 49p.
    -- Wraps are £4.99 each.
    Find the total of two drinks, a wrap and an apple.
    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: Pence and pounds reversed
Children find patterns in the differences when pounds and pence are reversed.

Extra Support

Y5: Hop to 100s, and Beyond
Using counting up (Frog) to subtract numbers either side of a multiple of 100, e.g. 304 - 297, then 304 – 267.

Y6: Phone a Frog
Using counting up (Frog) to calculate change from £100.

Jump to Millennia
Using counting up (Frog) to subtract 4-digit numbers from multiples of 1000 (e.g. 4000 - 2586), or when the larger number has zeros (e.g. 4002 - 3987, 4020 - 3987, 4200 - 3987).