Maths Year 5/6 Summer Top-up Revision Menu

Day 1
Children list the factors of 24, then list common factors of 24 and 36, including the ‘Highest Common Factor’. Repeat for other factors, then common multiples, including the ‘Lowest Common Multiple’.
Group activities: T with Y5 or Y6
Y5 Use the ‘LCM Squares’ in-depth problem-solving investigation below as today’s group activity.
Or, use these activities:
-- Play card games to generate and investigate common multiples and common factors.
Y6 -- Play card games to generate and investigate lowest common multiples and highest common factors. Some children might play an online multiples and factors game.

Day 2
List prime numbers up to 20. Discuss how to efficiently tell if larger numbers are prime. List square numbers up to 100.
Group activities: T with Y6
Y5 -- Investigate which square numbers have a prime next-door neighbour.
Y6 -- Play a game to identify square, prime or composite numbers.

• Whiteboards and pens
• Number cards 0–12
• Internet access
• Flipchart and pen

Day 1
Times tables

Day 2
Order of operations

Day 1
Y5: Find common multiples and factors of given numbers.
Y6: Find common multiples and factors of given numbers.

Day 2
Y5: Identify prime and square numbers.
Y6: Identify prime and square numbers.

Y5

• Is the lowest common multiple of 6 and 4 smaller than the highest common factor of 30 and 45?
• Write common factors of 24 and 48.
  Write common multiples of 3 and 5 up to 60.
  Are any numbers in both sets?
• True or false?
  -- There are exactly four 2-digit, common multiples of 3 and 7.
  -- 4 and 5 are common factors of all 2-digit multiples of 10.
  -- 15 is a factor of 100.

Y6

• Which pair(s) of numbers under 25 have the largest number of common factors? What is the highest common factor?
• Write common multiples of 3 and 5 up to 60. What is the lowest common multiple?
  Use this information to find the lowest common multiple of 6 and 10.
• True or false?
  The lowest common multiple of two prime numbers, a and b is always a × b.
  The highest common factor of two multiples of 7 is always 7.

Y5 In-depth Investigation: LCM Squares
Children use trial and improvement to find the smallest possible total on a square of lowest common multiples.

Y5: Times Table Puzzler
Find multiples and factors

Day 1
Children reason about and calculate missing digits in short multiplications.
Further teaching with Y6
Revise long multiplication; discuss potential pitfalls and how to avoid them in today’s Top tips for tests.
Group activities: T with Y6
Y5 -- Write 3-digit by 1-digit multiplications; reason about and calculate the missing digits in missing-digit multiplications.
Y6 -- Multiply numbers by 16, 26, 36… using long multiplication (some children may use the grid method).

Day 2
Write the following problem on the board: Chloe chooses a number, multiplies it by 6, then adds 78. Her answer is 432. What number did she choose? Children discuss in pairs how they could go about solving this problem.
Further teaching with Y6
Revise long division in the context of a word problem. Share today’s Top tip for tests.
Group activities: T with Y6
Y5 Use the ‘Riveting reversals’ in-depth problem-solving investigation below as today’s group activity.
Or, use these activities:
-- Use inverse operations and short division to solve puzzles.
Y6 -- Divide numbers by 23, 25 or 24 writing remainders as decimals or fractions, as necessary

• Whiteboards and pens or paper to record
• Flipchart and pen
• Sticky notes
• Internet access

Day 1
Multiply multiples of 10 by multiples of 100

Day 2
Rockin’ remainders

Day 1
Y5: Short multiplication estimation and calculation: 3-digit x 1-digit, then 4-digit x 1-digit.
Y6: Practise short and long multiplication, including word problems.

Day 2
Y5: Short division practise and reasoning.
Y6: Practise short and long division, including word problems.

Y5

• Use short multiplication to find:
  53 × 7 = ☐
  3 × 879 = ☐
  246 × 8 = ☐
  5035 × 6 = ☐
  4 × 2907 × 4 = ☐
• Tom’s sister Millie has been alive for 254 weeks. How many days is this?
• Find:
  581 ÷ 7 = ☐
  3456 ÷ 5 = ☐
  5400 ÷ 9 = ☐
• A farmer is packing eggs. Each box holds six eggs. The farmer has 890 eggs to pack. How many boxes will the farmer fill?
• Ali has been alive for 2764 days. How many weeks is this?

Y6

• Complete each multiplication using a different method.
  (i) 4530 × 23
  (ii) 399 × 25
  (iii) 476 × 6
• True or false?
  - 28 × 4345 is the same as 7 × 4345 plus double 8690.
  - 1448 × 24 is the same as 36200 – 1448.
  - 258 × 32 gives the same product as 8 × 258 doubled twice.
• Which of the following divisions gives the greatest answer?
  3750 ÷ 24
  2223 ÷ 18
  2944 ÷ 21

Y5 In-depth Investigation: Riveting reversals
Multiply 4-digit numbers with consecutive digits by a 1-digit number; reverse the 4-digit number and repeat. Find the difference between the two answers.

Y5: Complete Day 1 group activity, using 2-digit by 1-digit multiplications
Reason about and calculate missing digits in multiplications.

Day 1
Children write fractions as the same type (having the same denominator), in order to compare them.
Further teaching with Y6
Shade different numbers of squares and rows on a blank 100-square. Children work in groups of three: one writes the fraction(s) shaded (simplifying where possible), another writes the decimal and the third writes the percentage shaded. Share ‘Top Tip for Tests’.
Group activities: T with Y6
Y5 -- Children write as many non-unit fractions as they can that are >1/2, <1/3, then >1/4, or between 1/2 and 3/4.
Y6 -- Place equivalent fractions, decimals and percentages on a large 0–1 line. Use this to compare fractions and decimals or fractions and percentages.

• Mini-whiteboards and pens
• ‘Blank 1-100 grid (see resources)
• ‘Fraction wall up to twelfths’ (see resources)
• A3 paper
• Strips of flipchart paper/ border roll
• Different coloured marker pens

Day 1
Simplify fractions

Day 1
Y5: Write <, = or > between pairs of fractions.
Y6: Find equivalent fractions, decimals and percentages. Compare and order fractions, decimals and percentages.

Y5

Compare these pairs of fractions using <, > or =
3/4 9/12
6/11 3/5
1/6 2/10
5/8 6/11

Write a fraction between each of these pairs:
2/3 4/5
4/10 2/7
5/8 8/12

Y6
Write the missing decimal numbers to make each sentence true. Some can have more than one answer!
☐ = 4¹/2
☐ = 5³/4
13/100 > ☐
7/10 < ☐
☐ = 2/5

Y5 In-depth Investigation: Use the Group Activity as this unit’s investigation.

Y5: Decimal pictures
Find equivalent fractions and decimals (halves, quarters and tenths).

Day 1
Display a pie chart showing proportions of different types of tree in a wood. Discuss what it shows, relating proportions of the chart to fractions of amounts.
Group activities: T with Y6
Y5 -- Sketch pie charts to represent chosen numbers of coloured counters. Some children will use clues from a pie chart to determine the number of each colour counter.
Y6 -- Interpret data about favourite ice-creams presented on pie charts; create a pie chart. Other children draw a pie chart according to given percentages and fractions of coloured doors.

Day 2
Discuss what an average is. Explain that the mean is one type of average. A sprinter ran 100m in times of 12s, 15s, 13s, and 16s; then calculated her mean time to be 18s. Does this sound right? Children add the four times and divide by 4 to find her mean time. Challenge children to write three different numbers with a mean of 10.
Group activities: T with Y5 or Y6
Y5 Use the ‘Mean Score’ in-depth problem-solving investigation below as today’s group activity.
Or, use these activities:
-- Find the mean height of towers of cubes. Other children find mean shoe size, then investigate other numbers with the same mean.
Y6 -- Manipulate data to create given mean values. Some children calculate the mean of a data set.

• Whiteboards and pens
• Flipchart and pens
• Pots of blue, red, yellow and green counters
• ‘Blank pie chart’ (see resources)
• Coloured pencils
• Cubes
• ‘Find a mean’ Day 2 Sheet 2 (see Practice Worksheets)
• Number cards 0–9

Day 1
Find non-unit fractions of amounts

Day 2
Add five numbers together

Day 1
Y5: Sketch and interpret simple pie charts.
Y6: Interpret bar and pie charts.

Day 2
Y5: Find the mean of up to 5 amounts.
Y6: Find a mean; solve problems involving finding a mean.

Y5 & Y6
What is the children’s mean height?
Alfie: 138cm
Baz: 153cm
Charmaine: 143cm
Dot: 166cm
Which of the children is closest to the mean height?

The friends have these amounts of money in their purses.
Jo: £5.50
Tim: £12
Sam: £4.60
Jill: £6.40
Fred: £8
Ann: £5.50
What is the mean amount that they have?
Which children have less than the mean?

Y5 In-depth Investigation: Mean Score
Children design a dice so that the mean score is 5.

Y5: Adapt Day 1’s Working towards ARE group activity so that children are using 16 counters.

Day 1
Say co-ordinates of an image on a grid before and after reflection and translation. Identify a diagonal mirror line.
Group activities: T with Y5 or Y6
Y5/Y6 -- Place and transform an ‘L’ shape on a co-ordinate grid. Give instructions to the rest of the group to make their shapes finish in the same position.

Day 2
Identify missing vertices of polygons drawn on grids.
Group activities: T with Y6
Y5 Use the in-depth problem-solving investigation ‘Treasure Hunt’ from NRICH as today’s group activity.
Or, use these activities:
-- Plot polygons on a 1st quadrant co-ordinate grid. Can their partner replicate it when given the co-ordinates?
Y6 -- Draw polygons according to instructions, work out co-ordinates of a missing vertex.

• Whiteboards and pens
• ‘Transformations’ Sheets 1 to 4 (see resources)
• ‘Reflections and Translations Sets A and B’ Sheets 1 to 4 (see resources)
• ‘L-shaped’ pieces of card
• Coloured pencils
• ‘Co-ordinate grid’ Sheets 1 to 4 (see resources)
• Squared paper or ‘1st quadrant co-ordinate grid’ (see resources)
• ‘4-quadrant co-ordinate grid’ (see resources)
• Flipchart and pens

Day 1
Find lines of symmetry

Day 2
Parts of circles and describing regular and irregular polygons

Day 1
Y5: Drawing and describing reflections and translations in the first quadrant.
Y6: Drawing and describing reflections and translations in all four quadrants.

Day 2
Y5: Plot co-ordinates to draw polygons in the first quadrant.
Y6: Plot co-ordinates to draw polygons in all four quadrants; identify missing vertices.

Y5

• List the first quadrant coordinates of a hexagon with two lines of symmetry
• A square has vertices at (3,1) and (7,1). What are the co-ordinates of its two other vertices?
• Draw a kite in the first quadrant
  - reflect it in the y-axis
  - translate the original shape squares to the right and 3 squares down.
  What are the coordinates of the three shapes?

Y6

• A triangle is translated so that it has moved 3 squares up the grid and 7 squares to the right. Its co-ordinates are now: (3,1) (7,2) and (0,5) Draw it in its original position.
• (0,0) (5,0) (5,5) (0,5) are the vertices of a shape. When it is reflected in the x-axis, 2 pairs of co-ordinates do not change. Why not? Sketch it to explain.

Y5 In-depth Investigation: Treasure Hunt
Can children find and explain a reliable strategy for choosing co-ordinates that will locate the treasure in the minimum number of guesses? Treasure Hunt from nrich.maths.org.

Y5: Walk then Fly
Plot points in the first quadrant

Day 1
Show a cuboid (3 × 4 × 3) made from 36 centimetre cubes. Ask how many cubes are in each layer, how many layers, and so how many cubes are in the whole cuboid. Use the formula – length × width × height, or l × w × h for short, to find the volume. Sketch a 6 × 4 × 5 cuboid, labelling each side in metres. Children calculate its volume in m³.
Group activities: T with Y5 or Y6
Use one of the in-depth problem-solving investigations for this unit ‘Roomy boxes’ or ‘Queued Cubes’ – as today’s group activity.
Or, use these activities:
Y5 -- Make one layer of a cuboid, find the volume given a number of layers. Some children sketch cuboids, calculate their volumes; calculate the length of a missing edge in a cuboid of known volume.
Y6 -- Sketch cuboids; calculate their volumes. Calculate the length of a missing edge in a cuboid of known volume.
-- Investigate the different cuboids that can be made with a volume of 48cm3.

• 100 centimetre (1cm3) cubes
• Whiteboards and pens
• ‘Isometric paper’ (see resources)

Day 1
Multiply three numbers together

Day 1
Y5: Calculate volume of cuboids, first with cubes sketched, then without.
Y6: Calculate volume of cuboids. Reason about missing dimensions, given two dimensions and the volume.

Y5/ Y6

• What is the difference in volume between cuboids measuring 4 × 3 × 10cm and 5 × 5 × 5cm?
• List the possible edge lengths (whole numbers of centimetres) of a cuboid with volume 100cm3.

In-depth investigation: Roomy boxes
Children cut squares from a square piece of paper, fold up the sides to form an open cuboid and find out which size will hold the most 1cm3 cubes.
OR
Queued Cubes
Children apply a combination of knowledge of 3-D shape, area and volume to solve a problem that introduces surface area.

(Whichever investigation the children did not do in the Spring Term)

Y5: Revisit Hidden Volumes
Find the volumes of cuboids.