Maths Year 6 Summer Revision

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.

Unit 1 Mental strategies; written multiplication (suggested as 4 days)

Objectives

Mental strategies; long/short multiplication
Unit 3: ID# 6037

National Curriculum
Add/Sub/Mult/Div
(i), (ii), (iii), (iv), (v)

Hamilton Objectives
9. Know all multiplication and division facts up to 12 x 12; identify common factors, common multiples, square numbers to 144 and prime numbers up to 20.
10. Multiply/divide whole numbers mentally, using facts to 12 × 12 and place value (e.g. 60 × 70); use facts to work with larger numbers.
11. Multiply 2-, 3 and 4-digit numbers by numbers up to 12 using short multiplication or another appropriate written method.
12. Multiply numbers with up to 4 digits by 2-digit numbers using formal long multiplication.
14. Perform divisions mentally within the range of tables facts; divide multiples of 10 and 100 (4500 ÷9) and use mental strategies such as halving (450 ÷20).
15. Interpret remainders as whole number remainders, fractions, including decimal fractions where equivalents are known or by rounding up or down.
16. Divide numbers with up to 4-digits by a number up to 12 using short division and giving an appropriate answer.
17. Divide numbers with up to 4 digits by 2-digit numbers using a formal written method of long division; give an appropriate answer.

Teaching and Group Activities for Understanding

Day 1 Teaching
Children list all the factors of 36. Take 1 pair of factors, e.g. 9 and 4. If we know 4 × 9 = 36, what is 4 × 90? 4 × 900? 4 × 9000? What is 36 ÷ 9? 360 ÷ 9? 360 ÷ 90? 3600 ÷ 9? Children use 1 other pair to generate a similar list of facts using place value. Children work out 2 × 456 and 10 × 456; then use to derive other facts, e.g. 4 × 456, 5 × 456, 20 × 456 and associated divisions. End by creating today’s ‘Top Tip for Tests’.
Group Activities
-- Find factors and common multiples. Apply strategies for mental multiplication and division.

Day 2 Teaching
Show a worked example of 24 × 2153. Children working towards ARE work out 20 × 2153 and 4 × 2153, then add. Rest of class look at worked example to spot error – untidy work has led to wrongly adding the ‘carry’ figures in the addition at the end. End by creating today’s ‘Top Tip for Tests’.
Group Activities
-- Round numbers to estimate products. Select an appropriate method for accurate written multiplication.
-- Select an appropriate method for accurate written multiplication.

Day 3 Teaching
Write 496 ÷ 3, 496 ÷ 6, 496 ÷ 12 and 896 ÷ 3. Children discuss which will have the smallest/biggest answer and why. Each quarter of the class work out 1 of the divisions using short division. A child from each group shows how they found the answer. Help to write each remainder as a fraction, simplifying where possible. End by creating today’s ‘Top Tip for Tests’.
Group Activities
-- Divide 3-digit and 4-digit numbers by a single digit, using short division.

Day 4 Teaching
Martin the florist is making up bunches of 15 roses. He has 1250 roses in stock. How many bunches can he make? Remind children that making a list of multiples of the divisor is helpful for long division. Record this as today’s ‘Top Tip for Tests’. Model long division. The answer to the calculation is 83 r 5, but what is the answer to the question? Repeat with another problem.
Group Activities
-- Use multiples of 15 to divide numbers between 150 and 1000 by 15.
-- Solve problems using long division. Decide how to handle remainders.

You Will Need

  • Mini-whiteboards and pens.
  • ‘Multiples, factors, multiplication and division’ (see resources).
  • ‘Long multiplication’ (example of an error for 24 x 2153) (see resources).
  • ‘Multiplication practice’ sheets 1 and 2 (see resources).
  • Flipchart and pens.
  • ‘Long division’ (see resources).
  • 1 to 9 digit cards.

Mental/Oral Starters

Day 1
Lowest common multiples and common factors (pre-requisite skills).

Day 2
8, 80, 800 and 8000 × and ÷ facts (pre-requisite skills).

Suggested for Day 3
Recognise prime numbers to at least 19 (simmering skills).

Suggested for Day 4
Square numbers to 144 (simmering skills).

Procedural Fluency

Day 1
Apply knowledge of multiples and factors to solve mental multiplication and divisions. Solve missing number problems and find products of 3 numbers.

Day 2
Use written multiplication (short and long), both in straight calculations and in contexts.

Day 3
Short division by 1-digit numbers, writing remainders as fractions.
Short division by 3 to 12, writing remainders as fractions and as decimals.

Day 4
Use long division, both in straight calculations and in context.
Divide 3-digit numbers by 13 and 14.

Mastery: Reasoning and Problem-Solving

  • Write the correct symbol (<, > or =) in each box to make the statements correct:
    12 x 12 ☐ 14 x 10
    80 ÷ 20 ☐ 90 ÷ 30
    240 ÷ 6 ☐ 270 ÷ 9
    800 x 5 ☐ 70 x 50
  • Sophia has the digit cards 6, 7 and 5. She makes a 2-digit number and a 1-digit number. She multiplies them together. Her answer is a multiple of 10. What could Sophia’s multiplication be?
  • A farmer is packing eggs in boxes of 6. She has 980 eggs to pack. How many boxes can the farmer fill using 980 eggs? How many boxes will she need to hold all 980 eggs?
  • Shaula calculates 1252 ÷ 14. She says, ‘There’s no remainder in the answer!’ Do you agree with her?

Extra Support

This unit has no separate Extra Support activities.

Unit 2 Mental multiplication & division; ratio (suggested as 2 days)

Objectives

Mental multiplication and division and ratio
Unit 5: ID# 6047

National Curriculum
Fr (viii)
Rat/Pr (i), (iii)

Hamilton Objectives
32. Multiply numbers such as 4.7 and 0.06 by whole numbers.
34. Solve problems involving similar shapes where the scale factor is known or can be found.
35. Solve problems involving simple ratios, using tables facts and knowledge of fractions and multiples, e.g. 2 eggs for every 250g of flour.

Teaching and Group Activities for Understanding

Day 1 Teaching
Children to list all the factors of 42. Take 1 pair of factors, e.g. 6 and 7. If we know 6 × 7 = 42, what is 6 × 0.7? 6 × 0.07? What is 24 ÷ 6? 2.4 ÷ 6? 0.24 ÷ 6? Children use factors 3 and 12 to generate a similar list of facts, beginning 3 x 12 = 36. Children find 3 × 425, then use this to work out 3 × 42.5 and 4.25, then find 126 ÷ 6 and use to work out 12.6 ÷ 6 and 1.26 ÷ 6. Share ‘Top Tip for Tests’.
Group Activities
-- Use number facts and place value to multiply and divide decimals.
-- Use facts and place value to multiply numbers with 3 decimal places.

Day 2 Teaching
Draw a rectangle measuring 40cm by 20cm. Label the length of the longer side. The ratio of the longer side to the shorter side of this rectangle is 2 to 1. Children write length of shorter side answers on w/bs. Measure to check. Children draw a rectangle with same ratio of sides. Repeat for 20cm by 30cm rectangle. Share ‘Top Tip for Tests’.
Group Activities
-- Draw sets of rectangles with given ratios of side lengths.

You Will Need

  • ‘Multiplying and dividing decimals by whole numbers’ (see resources)
  • Mini-whiteboards and pens

Mental/Oral Starters

Suggested for Day 1
Simplify fractions (simmering skills)

Day 2
Adapting recipes (pre-requisite skills)

Procedural Fluency

Day 1
Practise using known facts and place value to multiply, divide and find in missing numbers.

Day 2
Identify missing sides of rectangles with given ratios, and work out measurements of scaled drawings.

Mastery: Reasoning and Problem-Solving

  • Kate knows that 136 × 31 = 4216. Explain how she can use this information to solve these calculations:
    137 × 31
    136 x 3.1
    1.36 x 31
    421.6 ÷ 136
  • Steph saves £1.20 per week. How many weeks before she can buy a pair of trainers costing £48?
  • Shopping for her birthday party, Amie buys a pack of 24 cans of lemonade for £10.80. What is the cost of each can?
  • The height of an adult can be estimated by measuring their head length then multiplying that length by 8. Flo’s dad has a head length of 22.5cm. What is his approximate height?
    Flo’s mum is 1.64m tall. What is her approximate head length?
  • The Blackpool Tower is 160 metres tall and 31 metres wide at its base. Ally makes a scale model of the tower. Her model is 32 centimetres tall. How wide is the base of her model?
  • A square of side length a has an area = 16cm². Another square, of side length b, has an area = 100cm². What is the ratio of their side lengths, a : b?

Extra Support

This unit has no separate Extra Support activities.

Unit 3 Fractions, decimals and percentages (suggested as 2 days)

Objectives

Fractions, decimals and percentages
Unit 6: ID# 6053

National Curriculum
Fr (xi)
Rat/Pr (ii)

Hamilton Objectives
23. Identify simple fraction/ decimal/ percentage equivalents: 1/2 = 0.5 = 50%, 1/4 = 0.25 = 25%, 3/4 = 0.75 = 75%, 1/3 = 0.33 = 33%.
33. Calculate simple percentages of whole numbers and solve problems involving use of percentages for comparisons.

Teaching and Group Activities for Understanding

Day 1 Teaching
Display a blank 100 square. Shade 1 square, write as a fraction, decimal and percentage of whole square. Shade different numbers of rows and squares. Children work in 3s: 1st writes the fraction(s) shaded (simplifying as much as possible), 2nd writes the decimal and 3rd writes the percentage shaded. Use to compare fractions and decimals or fractions and percentages. Share ‘Top Tip for Tests’.
Group Activities
-- Whole class activity: Place equivalent fractions, decimals and percentages on a large 0 to 1 line. Use to compare fractions and decimals or fractions and percentages.

Day 2 Teaching
Ask children to find 10%, 1%, 50% of £248. Discuss how they did this. They quickly think of and list other percentages they could easily find now that they know these percentages, e.g. 5%, 25%, 75%, 90%, 19%, 21% etc. Share today’s ‘Top Tip for Tests’. Play ‘I’d prefer…’ Ask such questions as: Would you prefer 10% of £180 or 20% of £200? Share ‘Top Tip for Tests’.
Group Activities
-- Calculate fractions and percentages of amounts, e.g. lengths, weights and amounts of money.
-- Calculate percentages of amounts, e.g. lengths and amounts of money.

You Will Need

  • ‘Blank 100 square’ (see resources).
  • ‘Finding fractions and percentages’ (see resources).
  • Strips of flipchart paper and different coloured marker pens.
  • Percentage fraction chains from www.topmarks.co.uk
  • Mini-whiteboards and pens

Mental/Oral Starters

Day 1
Compare decimals with different numbers of places (pre-requisite skills)

Suggested for Day 2
Find non-unit fractions of amounts (simmering skills)

Procedural Fluency

Day 1
Find equivalent fractions, decimals and percentages. Compare and order fractions, decimals and percentages.

Day 2
Find fractions and percentages of numbers, measures and amounts of money. Solve problems.

Mastery: Reasoning and Problem-Solving

  • Write these numbers in order, starting with the smallest:
    7/10, 0.6, 2/5, 50/100
  • Write a fraction which is greater than 0.4 and less than 0.5.
  • Write a decimal which is greater than 5/8 and less than 6/8.
  • What percentage of this grid is shaded?
########
##
####
##########
  • Emilia scores 40 out of 70 in a test. Jay scores 55% in the same test. Who has the higher score? Explain how you know.
  • Write these numbers in order, starting with the smallest:
    0.43, 3/4, 34%, 4/3, 3.4

Extra Support

This unit has no separate Extra Support activities.

Unit 4 Understanding and calculating fractions (suggested as 2 days)

Objectives

Understanding and calculating fractions
Unit 7: ID# 6067

National Curriculum
Fr (iii), (iv), (v)

Hamilton Objectives
22. Use knowledge of equivalence to compare and order fractions and to add and subtract fractions and mixed numbers.
25. Understand that if 2 numbers less than 1 are multiplied, the answer is smaller than either of them.
26. Multiply simple pairs of proper fractions, writing the answer in its simplest form.
27. Divide proper fractions by whole numbers, recognising that 3/4 ÷ by 2 is equivalent to 3/4 x 1/2.

Teaching and Group Activities for Understanding

Day 1 Teaching
Show the ‘Grid of fractions’. Divide the class into 4 teams. Each group choose a pair of fractions to add, they say the total and if correct ring the 2 fractions in their chosen colour. Then each group choose a pair of fractions to subtract. Continue alternating adding and subtracting until 1 group has 4 fractions ringed in a line in any direction.
Group Activities
-- Use equivalence to add and subtract fractions less than 1.
-- Use equivalence to add and subtract fractions, including mixed numbers.

Day 2 Teaching
Write 1/2 x 3/4 on the board. We multiply the numerators and then multiply the denominators (to give an answer of 3/8). This is today’s ‘Top Tip’. Demonstrate that this is the case by sketching a pizza on the board, shading 3/4 and asking children how much is half of the shaded section (3/8). Repeat for 3/4 x 1/2 to show the answer is the same. Draw a pizza divided into quarters. Shade 3/4 and then divide each of the shaded quarters into 2 parts. Point out that 3/4 ÷ 2 is the same as 1/2 × 3/4.
Group Activities
-- Multiply pairs of fractions. Divide fractions by whole numbers.

You Will Need

  • ‘Grid of fractions’ (see resources)
  • ‘Adding and subtracting fractions’ (see resources)
  • ‘Fraction wall’ (see resources)
  • ‘Multiplying and dividing fractions’ (see resources)
  • Mini-whiteboards and pens

Mental/Oral Starters

Day 1
Compare fractions (pre-requisite skills)

Suggested for Day 2
Equivalents fractions and decimals (simmering skills)

Procedural Fluency

Day 1
Add and subtract fractions and mixed numbers: related denominators.

Day 2
Multiply pairs of fractions, both in and out of context. Divide fractions by whole numbers, in and out of context.

Mastery: Reasoning and Problem-Solving

  • A book has 276 pages. Annie has read 1/6 of the book. How many pages are left for Annie to read?
  • This is a diagram of an orchard. It shows the fractions of the orchard planted with apples and plums.

Plums 1/4
Apples
2/3
Pears
  • The remaining area is planted with pears. What fraction is this
  • Poppy calculates 3/4 + 2/5 = 5/9. Do you agree with her?
  • Find the missing numbers in these calculations:
    4/10 x 2 = ☐/5
    9/6 ÷ ☐ = 1/2
    3/4 - 2/5 = ☐

Extra Support

This unit has no separate Extra Support activities.