Maths Year 5/6 Summer Decimals, Addition and Subtraction

Day 1
Write 4.378. Discuss digit place value, saying both the fraction and the decimal. Play decimal number bingo to subtract the value of a digit from a 4-digit number with three decimal places. Show cans/jars with masses in grams. Convert the masses into kg. Convert millilitres to litres and kilometres to metres.
Group activities: T with Y5
Y5 -- Use digit cards on a place value grid to convert between km and m, l and ml.
Y5/6 -- Order weights in kg with different numbers of decimal places. Convert to grams to check.
Y6 -- Order numbers with one, two and three decimal places.

Day 2
Write ☐.☐☐☐ > ☐.☐☐☐. Place 0 to 9 cards to make it true. Write a number in between. Repeat with ☐.☐☐☐ < ☐.☐☐☐. Order numbers with three decimal places. Think of one number between each neighbouring pair of numbers: one with one decimal place, one with two decimal places and one with three decimal places. Enter 1 ÷ 3 on the calculator. Discuss rounding errors. Repeat with ÷ 4, ÷ 5 and ÷ 6.
Group activities: T with Y5
Use the in-depth problem-solving investigation ‘Guesstimate’ as today’s group activity.
Or, use these activities:
Y5 -- Play a number line game to practise ordering numbers with three decimal places.
-- Play a number line game to practise ordering numbers with one, two or three decimal places.
Y6 -- Investigate divisors 2 to 10 that will give rounding errors on the calculator.
-- Investigate divisors 2 to 20 that will give rounding errors on the calculator.

• Number cards 0–9,
• Cans and jars with weights (in grams) written on sticky notes
• Weights: 1g, 10g and 100g
• ‘Converting measurements’ (see resources)
• A3 paper
• Digit cards 0–9
• ‘Cat weights’ (see resources)
• Mini-whiteboards and pens
• ‘5 to 6 landmarked line’ (see resources)
• Calculators
• Interactive whiteboard calculator
• Coloured pencils
• ‘0 to 1 landmarked lines’ (see resources)
• ‘Number grid’ (see resources)

Day 1
Count on and back in steps of 0.002

Day 2
Round numbers with one or two decimal places to the nearest whole

Day 1
Y5 Convert between km and m, l and ml.
Y6 Convert between km and m, l and ml. Order weights, lengths and capacities

Day 2
Y5 Locate 1-, 2- and 3-place decimals on a number line; order smallest to largest.
Y6 Enter the key sequences into a calculator. Which calculations does the calculator get wrong?

Y5

• Write the value of each digit as a fraction:
  0.375
• Write the total of this addition as a decimal:
  6/1000 + 4/10 + 3/100
• Ali’s homework needs marking. Write the correct answers for those he has wrong. Explain any mistakes Ali is making.
  Write < or > or = between each pair of numbers:
  (a) 0.34 < 0.099
  (b) 1.075 > 1.08
  (c) 6.006 < 6.06
  (d) 5.264 > 5.27
  (e) 9.999 > 10.001

Y6

• Write the value of each digit as a fraction:
  3.726
• Write the total of this addition as a decimal:
  9/1000 + 3/10 + 7/100
• Sadi’s homework needs marking. Write the correct answers for any she has wrong. Explain any mistakes Sadi is making.
  Write < or > or = between each pair of numbers:
  (a) 0.27 < 0.088
  (b) 1.075 > 1.09
  (c) 3.003 < 3.03
  (d) 5.148 > 5.32

In-depth Investigation: Guesstimate
Children calculate the capacity of their classroom in litres.

Y5: Decimal divisions
Converting from cm to m and vice versa. Understanding place value in numbers with two decimal places.

Y6: Deduce the Decimal
Understanding place value in numbers with three decimal places.

Day 1
Write 23.46 and 23.64. Which is bigger? Demonstrate finding the difference using Frog. Children use Frog to calculate 23.32 – 19.67. Display a word problem for children to read and solve. A volunteer models their working.
Group activities: T with Y5
Y5/Y6 -- Write a number using four consecutive digits in the form □□.□□, e.g. 45.67. Reverse it and find the difference between the two numbers. Explain any pattern.

Day 2
Revise using counting up (Frog) to subtract numbers with different numbers of decimal places. Start by demonstrating how to use Frog to count up to find 6.24 – 4.5. Children then calculate 9.2 – 6.48. Then use Frog to help children solve a subtraction word problem.
Group activities: T with Y5
Y5 -- Find the difference between side lengths of rectangles where the lengths sometimes have a different number of decimal places (one or two).
Y5/6 -- Solve word problems requiring subtraction of numbers with different numbers of decimal places (one or two).
Y6 -- Use Frog to subtract numbers with three decimal places from numbers with one decimal place.

• Mini-whiteboards and pens
• ‘0 to 4m lines’ (see resources)
• Flipchart and pens
• ‘Subtracting decimals’ word problems (see resources)
• 1–9 digit cards

Day 1
Find the complement to the next whole

Day 2
Subtract any pair of 2-digit numbers mentally

Day 1
Y5/Y6 Use Frog (counting up) to subtract pairs of numbers, each with 2 decimal places.

Day 2
Y5 Solve word problems requiring subtraction of numbers with the same number (one or two) of decimal places.
Solve word problems requiring subtraction of numbers with one and two decimal places.
Y6 Solve word problems requiring subtraction of numbers with one and two decimal places.

Y5 & Y6

• Choose two numbers and find the difference between them:
  14.45 16.12 13.57 8.87
  Repeat this twice.
• Write the missing numbers.
  (a) 23.4 – ☐ = 18.67
  (b) 15.5 = ☐ + 8.78
  (c) 32.4 – 18.55 = ☐
• Find change from £100 when buying:
  -- chair £56.89
  -- table £75.37
  -- rug £20.08

In-depth Investigation: Use Day 1’s Group Activity
Find differences and explain patterns in answers.

Y5: Mini minuses
Using Frog to subtract numbers with one decimal place

Y6: Dream Shopping
Finding change from £100 using Frog (counting up)

Day 1
Write 45,782 + 52,476, 345.7 + 278.6, £24.78 + £52.69. Place children in groups of 3: one to calculate the answer to each addition. Talk through what is similar/different with the addition of 0.7 + 0.6 and the addition of 70p and 60p. Write 45.83m + 23.45m. Carefully talk through 0.8 + 0.4 to give 1.2m. Note how this is very similar to adding money.
Group activities: T with Y5
Y5 -- Explore the use of expanded and compact addition for adding decimals, noting similarities when adding measures and money.
Y5/Y6 -- Collaborate to find pairs of amounts of money with a total of £44.44 and pairs of lengths with a total of 33.3cm. Note the digit restrictions.
Y6 -- Consolidate addition of two or more numbers with different numbers of decimal places.

Day 2
Write 45,706 – 28,342 as an expanded vertical subtraction and a compact vertical subtraction. Solve together to revise these strategies. Next, write 42,567 – 21,348; 51,230 – 24,769; and 34,213 – 22,048. Ask children which they think will be the fastest to work out and why.
Group activities: T with Y5
Y5 -- Explore moves between columns in 4-digit subtractions.
-- Explore moves between columns in 5-digit subtractions.
Y6 -- Play the ‘Dicey operations’ strategy game: arrange digits to create a pair of 5-digit numbers, subtract, nearest to 10,000 wins.

Day 3
Write: 4005 – 3789; £10.00 – £7.46; 61,003 – 45,869. Children use counting up (Frog) to answer one of these, sharing strategies. Discuss how subtractions with lots of zeroes are probably best done with Frog, not column subtraction. Write subtractions on the board, children discuss how to solve each.
Further teaching with Y6
Explore how to use the calculator’s memory buttons (M+, M-, MR).
Group activities: T with Y6
Use the in-depth problem-solving investigation ‘Durer's magic square’ as today’s group activity.
Or, use these activities:
Y5 -- Explore the choice of methods available for subtraction by solving and creating calculations.
-- Justify your choice of methods available for subtraction; create and solve calculations.
Y6 -- Practise using the memory functions in multi-step calculations, including word problems.
-- Use the memory function to help solve a shopping-related multi-step calculation.

Day 4
Display multi-step word problems. Children read and discuss in pairs what they need to do with the numbers in the problems, then agree the necessary calculations.
Further teaching with Y6
Write this sequence of keys: 6 + 4 = M+ 4 + 2 = × MR = and ask children to decide what happens. Repeat with other sequences including division, e.g. 5 − 3 = M+ 6 + 4 ÷ MR =. Use the memory buttons to find (32 + 35) ÷ (42 + 19).
Group activities: T with Y6
Y5 -- Identify calculations necessary to solve ‘holiday’ word problems.
Y6 -- Discuss given calculator key sequences. Compare estimates of answers with actual answers.

• Mini-whiteboards and pens
• Flipchart and pens
• 0–9 dice
• Calculators
• Small blank cards
• ‘Using the memory function’ Sheet 2 (see Day 3 Practice Worksheets)
• ‘Holiday word problems’ Sheets 1 and 2 (see Day 4 Practice Worksheets)
• ‘Using the calculator’s memory’ Sheet 3 (see Day 4 Practice Worksheets)

Day 1
Adding near multiples of 1000

Day 2
Speedy subtraction facts

Day 3
Complements to 1000s

Day 4
Mental subtraction of 2-digit numbers

Day 1
Y5/Y6 Use column addition to add whole numbers, amounts of money and distances in metres.

Day 2
Y5/Y6 Use column subtraction to subtract 4-digit or 5-digit numbers.

Day 3
Y5 Choose to use column subtraction or counting up (Frog) to work out subtractions.
Y6 Practise using the memory functions in multi-step calculations, including word problems.

Day 4
Y5 Solve holiday word problems.
Y6 Practise using the memory functions by entering given sequences.

Y5

• Arrange the digits 1 to 9 to create an addition of three 3-digit amounts of money which add to as close to £1000 as possible. You may only use each digit once!
• Good mathematicians like us always try to choose the most efficient calculation strategy. Here are three additions. Which calculation strategy would you choose for each? Write a short explanation to tell me why, then go ahead and solve them…
  (a) 48.663 + 275.09 + 7707.9
  (b) £60,006 + £2998
  (c) 38,000 + 54,000
• This table shows the number of people living in various GB towns:
  town population
  Alnwick 8316
  Berwick 12,143
  Carrickfergus 39,215
  Droitwich 23,935
  What is the total of the numbers of people living in Carrickfergus and in Alnwick?
  Marie studied some towns, added their populations, then rounded her total to the nearest 1000. Her answer was 44,000. Which towns did she look at?

Y6
This unit has no separate problem-solving activities for Year 6.

In-depth Investigation: Durer's magic square
Children complete ‘Durer’s Magic Square’, then use it to create 2- or 3-digit numbers and find the difference between different pairs. Identify patterns.

Y5: Super 7000
Using compact column addition to add pairs of 4-digit numbers.

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