Short Blocks

Maths Year 5/6 Autumn Decimals

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 added value for Hamilton Friends and School Subscribers.

Unit 1 PV in 2- and 3-place decimal numbers (suggested as 3 days)

Objectives

Place value in 2- and 3-place decimal numbers
Unit 1: ID# 56230

Y5: Place value in numbers with 2 decimal places, place on a line and compare.
Y6: Place value in numbers with 2 decimal places, place on a line, compare and round.

National Curriculum
Y5: Dec/Fr (ix)
Mult-Div (vii)
Y6: Dec/Fr (vii)

Y5 Hamilton Objectives
19. Understand the effect of multiplying/dividing by 10, 100, 1000, including 1- and 2-place decimal answers.
29. Write decimal numbers as tenths and hundredths.
30. Locate 2-place decimal numbers on a line; round them to the nearest tenth or whole number.

Y6 Hamilton Objectives
28. Identify the place value of each digit in a number with up to 3 decimal places; multiply/divide numbers by 10, 100, 1000 giving answers with up to 3-decimal places.

Teaching and Group Activities for Understanding

Day 1
Look at the pattern of digits on a 10s, 1s, 0.1s and 0.01s place value chart. Make numbers with 2 decimal places by ringing and recombining a number in each row. Divide 3-digit numbers by 100.
Further Teaching with Y6
Make numbers with 3 decimal places by ringing and recombining numbers on a 10s, 1s, 0.1s, 0.01s and 0.001s place value chart.
Group Activities: T with Y6
Y5 -- Play a game using the place value grid to reinforce the value of different digits. Other children will ‘Zap’ digits in numbers with 2 decimal places, using a calculator.
Y6 -- Write place value additions, divide by 10 and 100 (numbers/answers with up to 3 decimal places; includes pre-teaching for Day 2). Other children will play I’m thinking of a number with 3dp place value additions/subtractions.

Day 2
Children hold four number cards either side of a large decimal point and move in response to ×/÷10, 100 and 1000 instructions.
Group Activities: T with Y5
Use the in-depth problem-solving investigation ‘Dicey Operations in Line’ from NRICH as today’s group activity.
Or, use these activities:
Y5 -- Use digit cards in place value grids to multiply and divide by 10 and 100 (up to 2 decimal places).
Y6 -- Create inputs and outputs for function machines, or play a reasoning game, to rehearse × 10, ÷ 10, × 100, ÷ 100, × 1000 or ÷ 1000.

Day 3
Use a 0–100 bead bar and 10-part counting stick to teach where numbers with 2 decimal places belong, between adjacent multiples of 1, on the number line.
Further Teaching with Y6
Place numbers with 3 decimal places on landmarked and empty number lines and round to nearest whole, tenth and hundredth.
Group Activities: T with Y6
Y5 -- Play one team against the other to place numbers with 2 decimal places on a line, trying to stop opponents getting numbers in between.
Y6 -- Order numbers with 3 decimal places, place on landmarked lines to check. Some children will also round numbers to the nearest whole and tenth.

You Will Need

  • Place value chart: 10s, 1s, 0.1s and 0.01s (see resources)
  • 100s, 10s, 1s, 0.1s and 0.01s Place value grids (see resources, enlarge to A3)
  • 100s, 10s, 1s, 0.1s, 0.01s and 0.001s Place value grids (see resources)
  • Additional activity sheets (see resources)
  • 1–6, 0-9 dice and calculators
  • Large number cards (1–7)
  • 0–9 digit cards (with extra 0s)
  • 100-bead bar and tags and counting stick
  • Mini-whiteboards and pens
  • Blank cards
  • 3–4 and 7–8 number lines with tenths marked drawn lengthways on a piece of flipchart paper

Short Mental Workouts

Day 1
Place value in 1-place decimal numbers

Day 2
Adding to the next whole

Day 3
Units of time

Procedural Fluency

Day 1
Y5: Complete place value number sentences.
Y6: Complete place value number sentences.

Day 2
Y5: Calculate outputs for ×10, ÷10, ×100 and ÷100 function machines.
Y6: Calculate outputs, for ×10, ÷10, ×100, ÷100, ×1000 and ÷1000 function machines.

Day 3
Y5: Place numbers with 1 or 2 decimal places on number lines. Use the number line to order numbers.
Y6: Place numbers with 3 decimal places on lines, then round to the nearest hundredth, tenth and whole.

Mastery: Reasoning and Problem-Solving

Y5

  • Divide 27,680 by 10 repeatedly until you get a number that is less than 100. Write that number.
  • Write the missing numbers.
    23.4 ÷ 10 = ☐
    ☐ × 100 = 34
    460 ÷ ☐ = 4.6
  • Draw a number line between 3 and 4. Mark these numbers in the correct places:
    3.5, 3.05, 3.55, 3.95, 3.42
  • True or false?
    4.05 comes after 4.5 on the number line.
    9.9 is greater than 9.09.

Y6

  • Draw a line from 9.99 to 10. Mark 9.995 and two other numbers, one more than 9.995 and one less.
  • Write the missing numbers in these sentences.
    4.351 × 10 = ☐
    ☐ × 100 = 39.2
    1.871 × ☐ = 1871
  • Write <, = or > between each pair of numbers.
3.4053.45
8.068.061
9.2019.219
0.0022/1000

In-depth Investigation: Dicey Operations in Line (adapt Game 6)
Roll a 0–9 dice four times to create a calculation in the form ☐☐☐☐ ÷ 10 or ☐☐☐☐ ÷ 100. Whoever has the answer closest to 555.5 or 55.55 wins. Dicey Operations in Line (adapt Game 6) from nrich.maths.org.

Extra Support

Y5: Moving Digits
Multiplying and dividing amounts of money by 10

Y6: Dastardly Decimals
Understanding place value in numbers with 2 decimal places

Unit 2 Count/add/subtract 0.1, 0.01, 0.001 (suggested as 2 days)

Objectives

Count in steps of/add/subtract 0.1, 0.01, 0.001
Unit 2: ID# 56246

Y5: Use place value to add/subtract 0.1, 0.01 and multiples of these.
Y6: Use place value to add/subtract 0.1, 0.01 and 0.001 and multiples of these.

National Curriculum
Y5: Dec/Fr (vii) (ix) (x)
Y6: Dec/Fr (vii)

Y5 Hamilton Objectives
29. Write decimal numbers as tenths, hundredths, thousandths, e.g. 0.71 as 71/100, 0.327 as 327/1000; relate thousandths to tenths and hundredths.
31. Add 2-place decimal numbers mentally or using column addition.

Y6 Hamilton Objectives
28. Identify the place value of each digit in a number with up to 3 decimal places; multiply/divide numbers by 10, 100, 1000 giving answers with up to 3-decimal places.

Teaching and Group Activities for Understanding

Day 1 Teaching
Count on and back in steps of 0.01, then 0.1 on a 0.01–1 grid.
Further Teaching with Y6
Fill in a row, column and last number on a partially complete 0.001–0.1 grid.
Group Activities: T with Y6
Y5 -- Play a game adding/subtracting 0.01 and 0.1 on a grid.
Y6 -- Count in steps of 0.001 and 0.01 to complete rows and columns in a part-complete 0.001–0.1 number grid.

Day 2 Teaching
Y5 children write 34.56 and Y6 write 34.567. They add multiples of 0.1 and 0.01 (and 0.001 for Y6) without crossing through a multiple of 0.1 or 1, e.g. not 34.67 + 0.05 or 34.23 – 0.4.
Group Activities: T with Y5
If children already have a secure grasp of decimal place value, use the in-depth problem-solving investigation ‘Sometimes We Lose Things’ from NRICH as today’s group activity.
Otherwise, use these activities:
Y5 -- Practise adding and subtracting multiples of 0.1 and 0.01, sometimes crossing ‘boundaries’.
Y6 -- Repeatedly add 0.001. Other children will make predictions, then add 0.007, 0.07 and 0.7 to pass targets.

You Will Need

  • 0.01–1 grid (see resources)
  • Part-completed 0.001–0.1 grid (see resources)
  • Blank 0.01–1 grid and/or a completed 0.01–1 grid (see resources)
  • Coins and counters
  • Mini-whiteboards and pens
  • Additional activity sheets (see resources)
  • Flipchart and pens
  • Counting stick
  • Sticky notes

Short Mental Workouts

Day 1
Multiply and divide by 10 and 100

Day 2
Ordering numbers with decimal places

Procedural Fluency

Day 1
Y5: Add or subtract 0.01 or 0.1 to fill in empty squares on a 0.01–1 grid, or sections of a grid.
Y6: Use a 0.001–0.1 grid to add and subtract 0.001 and 0.01.
Fill in empty squares on sections of a 0.001–0.1 grid .

Day 2
Y5 Add and subtract multiples of 0.1 and 0.01.
Y6 Add and subtract multiples of 0.1, 0.01 or 0.001.

Mastery: Reasoning and Problem-Solving

Y5

  • Find the answer to 3.42 + 0.2. Then find the answer to 3.42 + 0.02. Which answer is greater?
  • How many times must I add 0.1 to 9.2 to reach 10?
    How many times must I add 0.01 to 9.9 to reach 10?
  • Write the number at each stage in this chain:
    2.19 + 0.2 – 0.02 + 0.2 – 0.02 + 0.2 – 0.02 + 0.2 – 0.02.
    What do you notice about the answer?

Y6

  • Write the missing numbers to complete this section of the 0.001–0.1 grid:
0.049
0.068
0.079
0.087
  • What must be added to 0.089 to make 0.09? To make 0.9? To make 9?
  • True or false?
    3.452 – 0.003 = 3.449
    0.002 + 1.009 = 0.11
    2.985 + 0.005 = 2.99
    0.019 > 0.091

In-depth Investigation: Sometimes We Lose Things
What would happen if we lost all the nines in our number system? Children's understanding of the place value system is put to the test. Sometimes We Lose Things from nrich.maths.org.

Extra Support

Y5
Decimal Pictures

Understanding place value in numbers with 1 decimal place and how we can write tenths as fractions or decimals

Teeny Decimals
Understanding place value in numbers with 2 decimal places and how we can write hundredths as fractions or decimals

Y6
All the 3s

Understanding place value in numbers with 2 decimal places; adding and subtracting multiples of 0.1 and 0.01 (not crossing 1s or 0.1s)

Unit 3 Place value in decimals (suggested as 2 days)

Objectives

Place value in decimals
Unit 3: ID# 56254

Y5: Place value in numbers with two decimal places
Y6: Place value in numbers with three decimal places

National Curriculum
Y5: Dec/Fr (vii) (ix)
Y6: Dec/Fr (vii)

Y5 Hamilton Objectives
19. Understand the effect of multiplying or dividing by 10, 100, 1000, including answers with one and two decimal places.
29. Write decimal numbers as tenths and hundredths, e.g. 0.71 as 71/100.

Y6 Hamilton Objectives
28. Identify the place value of each digit in a number with up to three decimal places. Multiply/divide numbers by 10, 100, 1000 giving answers with up to three decimal places.

Teaching and Group Activities for Understanding

Day 1 Teaching
Use place value to add and subtract from numbers with two decimal places.
Further Teaching with Y6
Use place value to add and subtract from numbers with three decimal places.
Group Activities: T with Y6
Use the in-depth problem-solving investigation ‘Dicey Operations in Line’ from NRICH as today’s group activity.
Or, use these activities:
Y5 -- Use place value to add and subtract in numbers with two decimal places.
Y6 -- Add and subtract tenths, hundredths and thousandths. Test predictions and make target numbers.

Day 2 Teaching
Use the place value grid on the Moving digits ITP to show the effect of multiplying and dividing by 10, 100 and 1000. (Y5: two decimal places; Y6: three decimal places.)
Group Activities: T with Y5
Y5 -- Investigate routes through a grid (× and ÷ by 10, 100 or 1000) with a range of outcomes.
Y6 -- Multiply and divide a number by powers of 10. Some children will also order the resulting products and dividends.

You Will Need

  • Whiteboards and pens
  • ‘Place value grid 10–0.01’ (see resources)
  • Number cards 0–9
  • Flipchart and pens
  • A4 paper
  • ‘Place value addition and subtraction’ (see resources)
  • Calculators
  • ITP: Moving digits (see resources)
  • ‘Multiplying and dividing by 10 and 100’ grid (see resources)
  • ‘Place value grid’ (see resources)

Short Mental Workouts

Day 1
Ordering decimals

Day 2
Ordering 24-hour times

Procedural Fluency

Day 1
Y5: Place value additions and subtraction; add and subtract 0.1 and 0.01 and multiples of 1, 0.1 and 0.01.
Y6: Use place value to add and subtract various combinations of tenths, hundredths and thousandths.

Day 2
Y5: Multiply and divide by 10 and 100, or by 10, 100 and 1000.
Y6: Multiply and divide masses/weights in kilograms by powers of 10. Identify functions (×/÷ 10, 100 and 100).

Mastery: Reasoning and Problem-Solving

Y5

  • Divide 47,310 by 10 repeatedly until you get a number that is less than 100. Write that number.
  • Write the next two numbers in each sequence.
    4650, 465, ____, ____
    2.955, 29.55, ____, ____
    9300, 930, 93, ____, ____
  • True or false?
    4030 ÷ 100 = 43
    1.09 × 100 = 190
    0.09 × 10 = 0.9
    7000 ÷ 1000 = 0.7
  • Write the missing numbers
    23.4 ÷ 10 = 
     × 100 = 34
    460 ÷  = 4.6

Y6

  • Identify the value of the ‘4’ in the following numbers:
    (a) 3.407
    (b) 4.821
    (c) 0.043
    (d) 5.104
    (e) 48,739
  • How many times must Dan multiply 0.048 by 10 to get 48,000?
  • What number is one hundred times smaller than 2.4?

In-depth Investigation: Dicey Operations in Line (adapt Game 1)
Create three multiples of 0.01 or 0.1; find their total. Whoever has the sum closest to 1 wins. Dicey Operations in Line (adapt Game 1) from nrich.maths.org.

Extra Support

Y5
Left or Right?

Multiplying numbers with one decimal place by 10 and dividing 2-digit whole numbers by 10

or

Left, Left or Right, Right?
Understanding place value in numbers with two decimal places; beginning to multiply numbers with two decimal places by 100 and dividing 3-digit numbers by 100

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

Moving Digits
Multiplying and dividing by 10, 100 and 1000

Unit 4 Rounding and adding decimals (suggested as 3 days)

Objectives

Rounding and adding decimals
Unit 4: ID# 56258

Y5: numbers with two decimal places: rounding and column addition.
Y6: numbers with three decimal places: rounding and column addition.

National Curriculum
Y5: Dec/Fr (viii) (x)
Y6: Dec/Fr (x), Meas (i)

Y5 Hamilton Objectives
29. Write decimal numbers as tenths and hundredths.
30. Locate numbers with two decimal places on a line; round them to the nearest tenth or whole number.
31. Add numbers with two decimal places mentally or using column addition.

Y6 Hamilton Objectives
30. Add several decimal numbers using mental or written addition.

Teaching and Group Activities for Understanding

Day 1 Teaching
Use the counting stick to show how we can round numbers with one decimal place to the nearest whole and numbers with two decimal places to the nearest tenth. Draw lines and discuss where to place masses with three decimal places, round to nearest whole, 0.1kg and 0.01kg.
Group Activities: T with Y5
Y5 -- Explore rounding numbers with two decimals places, marked on number lines. Some children will do so by playing ‘Rounding Bingo’.
Y6 -- Generate, then round numbers with three decimal places to the nearest whole, tenth and hundredth. Some children will round to the nearest kilogram.

Day 2 Teaching
Write on the board 4.56 + 2.37. Ask children to round each number to the nearest whole and add to estimate the total. Demonstrate, using expanded and compact addition. Show incorrect layout of 45.7 + 3.45. Emphasise correct alignment of decimal points.
Further Teaching with Y6
Demonstrate column addition of kilograms and kilometres with three decimal points, in word problems.
Group Activities: T with Y6
Use the ‘Four of the best’ in-depth problem-solving investigation below as today’s group activity.
Or, use these activities:
Y5 -- Use expanded and compact layouts to add pairs of numbers with one then two decimal places. Identify missing digits in additions of 3-digit numbers with two decimal places.
Y6 -- Add pairs of distances (1 or 2dp) or pairs of weights (2 or 3dp).

Day 3 Teaching
Show a table of shot put results and explain that the total of two shot put throws for each thrower was used to find the winner. Children round the lengths of each throw to estimate who won, and then add two and three decimal numbers to find out.
Further Teaching with Y6
Use weights taken from Dartboard rounding. Discuss which pair might have a total near 20kg. Accurately find totals using column addition.
Group Activities:
Y5 -- Explore and investigate column addition of numbers with two decimal places.
Y6 -- Use estimation to help adding towards a given total.

You Will Need

  • Counting stick
  • Whiteboards and pens
  • Number cards 0–9
  • ‘Adding decimals’ (see resources)
  • Sticky notes
  • Flipchart and pens
  • ‘Table of shot put results’ (see resources)
  • ‘Estimating totals: Weight’ Sheets 1 and 2 (see resources)

Short Mental Workouts

Day 1
Place numbers with two decimal places on a line

Day 2
Place value additions and subtractions

Day 3
Multiply and divide by 10, 100 and 1000

Procedural Fluency

Day 1
Y5: Place numbers with two decimal places on a 0–1 line. Round them to the nearest tenth and whole.
Y6: Mark numbers with one, two and three decimal places on lines and round to the nearest whole, tenth and hundredth.

Day 2
Y5: Round to estimate totals. Written addition of numbers with one then two decimal places.
Y6: Find pairs of distances with a total of less than 7m (mix of one and two decimal places). Add pairs of decimals (mix of one, two and three decimal places).

Day 3
Y5: Add two lengths with two decimal places. Add three distances with two decimal places.
Y6: Find pairs of distances, masses and capacities within given ranges.

Mastery: Reasoning and Problem-Solving

Y5

  • Sometimes/ Always/ Never… ‘If you add two numbers, each with two decimal places, the answer also has two decimal places.’
  • Jamie added 6.77 to a number and his answer was 20. What number did he start with?
  • Write the missing digits:
    4.9☐ + ☐.78 = 8.☐6
  • Ali’s homework might need correcting. Correct any wrong answers and explain what he did wrong.
    a) 2.75 + 5.95 = 7.60
    b) 3.42 + 5.57 = 8.99
    c) 4.83 + 1.93 = 5.76
    d) 2.47 + 68.5 = 93.2

Y6

  • Add 3.21 and 32.1
    Add 4.32 and 43.2
    Add 5.43 and 54.3
    Before doing the addition, can you predict the answer to 6.54 and 65.4? Explain any patterns you are using.
  • Write the missing digits in this calculation:
    ☐.6☐8 + 26.☐56 = ☐1.39☐

In-depth Investigation: Four of the Best
Children use an incomplete magic square to explore patterns in the addition of four numbers.

Extra Support

Y5: Decimals on a 0–3 Number Line
Marking decimals and fractions on a 0–3 number line, and practising counting forwards and backwards in tenths

Y6: Pyramid Pile-up
Adding decimals to complete a pyramid