Short Blocks

Maths Year 6 Spring Decimals and Fractions (A)

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 Place value in 3-place decimals (suggested as 3 days)

Objectives

Understand place value in numbers with three decimal places
Unit 1: ID# 6619

National Curriculum
Fr (vii) (x)

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
Write 4.735 and ask children what the 7, 3 and 5 represent. Agree they are tenths, hundredths, thousandths. Show this on a place value grid. After subtracting 0.005, check that they write 4.73 not 4.730. Emphasize that we only write 0 in thousandths place if there are digits after this. Children add and subtract multiples of 0.1, 0.01 and 0.001.
Group Activities
Use the in-depth problem-solving investigation ‘The Size and Distance of the Planets’ from UC Berkeley as today’s group activity.
Or, use these activities:
-- Add and subtract 0.1s. 0.01s and 0.001s, using a calculator to test predictions.
-- Add and subtract 0.1s. 0.01s and 0.001s from 3.457 to make target numbers.

Day 2 Teaching
Launch the ITP ‘Moving digits’. Use the cards to show 56. Click to multiply by 10 three times, saying multiply by 10, 100, 1000. Discuss how much we have multiplied by and what the effect on the digits is. Discuss the effect of dividing 2340 by 1000. Then multiply and divide other numbers by 10, 100 and 1000, monitoring the effect on the digits.
Group Activities
-- Sequentially multiply and divide a number by powers of 10 to arrive back at the starting number.
-- Divide four numbers by 100 and 1000, then order. Repeat for multiplying by 100 and 1000.

Day 3 Teaching
Show children a counting stick for 2–3. Count from 2 to 3 in steps of 0.1. Children draw a line 2.3–2.4 and mark a number with 2 decimal places. What does this round to? Repeat, for numbers with 3 decimal places.
Group Activities
-- Round numbers with 3 decimal places to the nearest whole kilogram.
-- Generate, then round numbers with 3 decimal places to the nearest whole, tenth and hundredth.

You Will Need

  • ITP: Moving digits
  • Place value addition and subtraction (see resources)
  • Mini-whiteboards and pens
  • Calculators
  • Flipchart and pens
  • 0–9 digit cards
  • Counting stick
  • Dartboard rounding from www.topmarks.co.uk

Mental/Oral Maths Starters

Day 1
Count in steps of 0.01 and 0.1 from numbers with 2 decimal places (pre-requisite skills)

Day 2
Place value in numbers with 3 decimal places (pre-requisite skills)

Day 3
Place numbers with 2 decimal places on a line (pre-requisite skills)

Procedural Fluency

Day 1
Use place value to add and subtract 0.1s, 0.01s and 0.001s.

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

Day 3
Mark numbers with 1, 2 and 3 decimal places on lines and round to the nearest whole.
Mark numbers with 1, 2 and 3 decimal places on lines and round to the nearest whole, tenth and hundredth.

Mastery: Reasoning and Problem-Solving

  • 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 0.4?
  • Write three numbers, two with 3 digits and one with 4 digits, that round to 4 as the nearest whole number.


In-depth Investigation: The Size and Distance of the Planets
Children will manipulate big numbers to investigate the relative size and distance between planets. The Size and Distance of the Planets from cse.ssl.berkeley.edu.

Extra Support

Deduce the Decimal
Understanding place value in numbers with 3 decimal places

Moving Digits
Multiplying and dividing by 10, 100 and 1000

Unit 2 Add numbers with up to 3 decimal places (suggested as 2 days)

Objectives

Add numbers with up to three decimal places
Unit 2: ID# 6637

National Curriculum
Fr (vii)
Meas (i)

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

Teaching and Group Activities for Understanding

Day 1 Teaching
Children use written addition to work out 4.72 + 3.45. They round each number to the nearest whole to check if the answer seems reasonable. Ensure that children understand that 0.7 + 0.4 = 1.1, not 0.11. Write 45.7 + 3.45 and show how we line up the decimal point to help add place values.
Group Activities
Use the in-depth problem-solving investigation ‘Decimal pyramids’ as today’s group activity.
Or, use these activities:
-- Add pairs of distances (with 2 decimal places and 1 decimal place) to find totals which round to 6m, 7m, 8m, 9m and 10m.
-- Add pairs of weights (with 2 decimal places and 3 decimal places) to find totals under 7kg.

Day 2 Teaching
Use Dartboard rounding and choose kilograms. Discuss which pair might have a total near 20kg. Take suggestions and click to round to the nearest kg to confirm. Work through some additions, talking through adding 0.001s, writing in any ‘carried’ amounts as necessary.
Group Activities
-- Use an online activity to practise adding towards a given total.
-- Use digit cards to create additions with a given target total.

You Will Need

  • Mini-whiteboards and pens
  • Flipchart and pens
  • Dartboard rounding at www.topmarks.co.uk
  • 2–9 digit cards (1 set per pair)

Mental/Oral Maths Starters

Day 1
Round numbers with 2 decimal places to the nearest whole and to the nearest tenth (pre-requisite skills)

Suggested for Day 2
Difference between positive and negative numbers (simmering skills)

Procedural Fluency

Day 1
Find pairs of distances with a total of less than 7m [mix of 2 decimal places (dp) and 1dp].
Add pairs of decimals (2 dp + 2 dp, 3dp + 3dp, 3dp + 2 dp)

Day 2
Find pairs of distances, weights and capacities within given ranges.

Mastery: Reasoning and Problem-Solving

  • 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?
  • Write the missing digits in this calculation:
    ☐.6☐8 + 26.☐56 = ☐1.39☐


In-depth Investigation: Decimal Pyramids
Children add numbers with 3 decimal places to give a number with 2 decimal places. They add numbers with 2 decimal places to give a number with 1 decimal place. They then add numbers with 1 decimal place to give a whole number.

Extra Support

Pyramid Pile-up
Adding decimals to complete a pyramid

Unit 3 Multiply/divide 2-place decimal numbers (suggested as 2 days)

Objectives

Multiply and divide numbers with up to two decimal places
Unit 3: ID# 6653

National Curriculum
Fr (viii) (ix)

Hamilton Objectives
32. Multiply numbers such as 4.7 and 0.06 by whole numbers.

Teaching and Group Activities for Understanding

Day 1 Teaching
Use ITP 'Number dials' to show the 6 times table. Then click to select 0.6, hiding numbers in the outside boxes. Reveal the first few. Discuss what children notice. Each answer is 1/10 of answer for the 6 times table. Use this to multiply and divide decimal numbers, e.g. 4.2 ÷ 6, 4 × 0.06, 1.8 ÷ 6, 0.48 ÷ 6 etc.
Group Activities
-- Derive 0.8 times table up to 10 x 0.8; peer-quiz on divisions using these tables. Repeat for the 0.08, 0.7 and 0.07 times tables.
-- Use tables knowledge to write corresponding multiplications and divisions.

Day 2 Teaching
Write 4 × 3.6 on the board and ask children to discuss how they could work this out. Draw out working out 4 × 3 and 4 × 0.6. Write 4 × 3.6 = (4 × 3) + (4 × 0.6) on the board. Repeat for 3 × 0.47.
Group Activities
-- Use this activity as this unit’s in-depth problem-solving investigation:
-- Use the digits 0, 3, 4, 5 and 6 to create and answer as many different multiplications as they can of the form ☐ x ☐.☐ and ☐ x 0.☐☐.

You Will Need

  • ITP: Number dials
  • Flipchart and pens
  • Mini-whiteboards and pens
  • Sets of number cards 0, 3, 4, 5, and 6

Mental/Oral Maths Starters

Day 1
Double and halve numbers with 1 decimal place (pre-requisite skills)

Day 2
Times tables (pre-requisite skills)

Or

Day 2
Division facts (pre-requisite skills)

Procedural Fluency

Day 1
Use place value and tables facts to mentally multiply decimals, e.g. 3 × 0.4 and 3 × 0.04, and divide decimals e.g. 4.5 ÷ 5 and 0.45 ÷ 5.

Day 2
Use partitioning to mentally multiply numbers with 1 decimal place, e.g. 3 × 4.6.
Use partitioning to mentally multiply numbers with 1 decimal place and 2 decimal places, e.g. 3 × 4.6 and 3 × 0.46.

Mastery: Reasoning and Problem-Solving

  • Write the first six facts in the 0.5 times table.
    1 × 0.5 = 0.5
    2 × 0.5 =
    etc.
  • What is 4.5 divided by 0.5?
  • A metal tag is 0.7cm long.
    How many tags can be cut from a strip of metal 6.3cm long?
    How many tags could be cut from a strip of metal 70cm long?
  • Use partitioning to find 28 × 6. Now explain how to multiply 2.8 by 6. Finally, write the answer to 0.28 × 6 without doing any further multiplication.

In-depth Investigation
Use the Group Activity from Day 2.

Extra Support

Adapt Day 2’s Group Activity to practise multiplications of the form: ☐ x 0. ☐, then ☐ x ☐.☐, e.g. 3 x 0.6; 4 x 3.5.