Short Blocks

Maths Year 5 Autumn 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 Divide by 10/100; 2-place decimals (suggested as 2 days)

Objectives

Multiply/divide by 10 and 100 to get decimals (2 decimal places)
Place value additions
Unit 1: ID# 5209

National Curriculum
Dec/Fr (ix) (x)

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.

Teaching and Group Activities for Understanding

Day 1 Teaching
Use a place value chart of whole numbers, tenths and hundredths. Ask children to describe each row and show what happens if a digit is multiplied by 10 or 100. Suppose a digit is divided by 10? Make different numbers using the chart/place value\ additions.
Group Activities
-- ‘Zap’ digits in numbers with 2 decimal places, using a calculator.
-- Play a game using the place value grid to reinforce the value of different digits.

Day 2 Teaching
Write numbers in a 100s, 10s, 1s, 0.1s and 0.01s place value grid, multiply and divide by 10 and 100. Give 4 children number cards, e.g. 1, 2, 3, 4. They stand on either side of a large decimal point on the flipchart to show 12.34. They multiply their number by 10 and move accordingly. Do the class agree? Multiply by 10 again, then divide by 100. Repeat.
Group Activities
Use the in-depth problem-solving investigation ‘Dicey Operations in Line (adapt Game 6) from NRICH as today’s group activity.
Or, use these activities:
-- Use digit cards in place value grids to multiply and divide by 10 and 100 – up to 2 decimal places.

You Will Need

  • Place value chart (see resources)
  • Calculators
  • 100s, 10s, 1s, 0.1s and 0.01s place value grid (enlarge to A3)
  • sets of 0–9 digit cards
  • Large number cards (1–9)
  • 1–6 dice

Mental/Oral Maths Starters

Day 1
Place value in 1-place decimal numbers (pre-requisite skills)

Suggested for Day 2
Adding to the next whole number from a 1-place decimal number (simmering skills)

Procedural Fluency

Day 1
Complete place value number sentences,
e.g. 1 + 0.5 + ☐ = 1.58.

Day 2
Work out the outputs for × 10, ÷ 10, × 100 and ÷ 100 function machines.

Mastery: Reasoning and Problem-Solving

  • Divide 27,680 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 ____ ____
    2.953 29.55 ____ ____
    9300 930 93 ____ ____
  • Write the missing numbers.
    23.4 ÷ 10 = ☐
    ☐ × 100 = 34
    460 ÷ ☐ = 4.6


In-depth Investigation: Dicey Operations in Line (adapt Game 6)
Roll a 0 to 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

Moving Digits
Multiplying and dividing amounts of money by 10

Unit 2 1- & 2-place decimals on a line; compare (suggested as 2 days)

Objectives

Place decimals (1 and 2 decimal places) on a line
Compare
Unit 2: ID# 5227

National Curriculum
Dec/Fr (ix) (x)

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.

Teaching and Group Activities for Understanding

Day 1 Teaching
Use a 100 bead bar or line. Say that the ends are 0 and 1. Explain that each bead is one hundredth. Write 1/100 and 0.01. What is each group of 10 beads? Write 10/100, 1/10 and 0.1 on the board. Ask children to hang tags to show 0.1, 0.2, 0.3, 0.5, and 0.9. Show a counting stick and say the ends are 0 and 1. Children identify numbers in between. Then say the ends are 2 and 3. Count in steps of 0.1. Children write three numbers between 2.2 and 2.3. Order three examples.
Group Activities
-- Play one team against the other to place numbers with 2 decimal places on a line, trying to stop opponents getting numbers in between.
-- Use a number line to compare and order numbers with 1 and 2 decimal places.

Day 2 Teaching
Write 24.37 and 24.73 in the 10s, 1s, 0.1s and 0.01s place value grid. Discuss which number is worth more. Repeat with 52.91 and 52.68; 45.09 and 45.9; 36.7 and 36.29. Children write each pair of numbers on their whiteboards with a > or < between to answer. Children then write 62,7, 62,38, 62,83, 62,07 in order from least to greatest.
Group Activities
Use the in-depth problem-solving investigation ‘Round the Dice Decimals 2’ from NRICH as today’s group activity.
Or, use these activities:
-- Look at numbers to 2 decimal places in the context of measuring length. Discuss the value of each digit and compare and order numbers.

You Will Need

  • 100 bead bar or 0–1 beaded line (see resources) & tags
  • Counting stick
  • 0–9 dice
  • DIY type tape measure
  • Place value grid (see resources)
  • 0–9 cards

Mental/Oral Maths Starters

Suggested for Day 1
Placing 5-digit numbers on a human number line (simmering skills)

Day 2
Count on in steps of 0.01 (pre-requisite skills)

Procedural Fluency

Day 1
Place numbers with 1 to 2 decimal places on number lines. Use the number line to order these numbers.

Day 2
Compare, then order numbers with 1 to 2 decimal places.

Mastery: Reasoning and Problem-Solving

  • 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.
    0.11 and 0.21 are adjacent numbers on a 0–1 line marked in hundredths.
  • Write digits to make these statements correct.
    4.☐5 > 4.5☐
    0.9☐ < 0.☐9
    10.☐1 = 10.5☐


In-depth Investigation: Round the Dice Decimals 2
Use three 1 to 6 dice to make all possible numbers with 1 and 2 decimal places. Round each of these numbers to the nearest tenth and/ or whole number. Round the Dice Decimals 2 from nrich.org.uk

Extra Support

This unit has no separate Extra Support activities.

Unit 3 Add/subtract multiples of 0.1/0.01 (suggested as 2 days)

Objectives

Use place value to add/subtract 0.1, 0.01 and multiples of these

Unit 3: ID# 5233

National Curriculum
Dec/Fr (vi) (x)

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.

Teaching and Group Activities for Understanding

Day 1 Teaching
Show a 0.01–1 grid. Count in steps of 0.01 from 0 to 0.23. Then from 0.35 to 0.45 and back. Children close their eyes and count from 0.65 to 0.75 and back. Ring one column. When we move down this grid, what do we add? Start at 0.05. Count down the grid in steps of 0.1. Repeat, counting back from 0.97. Children close their eyes and count from 0.43 to 0.93 and back.
Group Activities
-- Add 0.1 or 0.01, writing the answers in a blank 0.01–1 grid.
-- Add four numbers with 2 decimal places. Look for patterns in the answers.

Day 2 Teaching
Children write 34.56 on whiteboards. If we add 0.1, which digit will change? If we subtract 0.01, which digit will change? Children add 0.2 and write the new number under it. Add and subtract multiples of 0.1 or 0.01 without crossing multiples of 0.1 or 1.
Group Activities
Use the in-depth problem-solving investigation ‘Dicey Operations in Line (adapt Game 1)’ from NRICH as today’s group activity.
Or, use these activities:
-- Practise adding and subtracting multiples of 0.1 and 0.01.
-- Do every other question on the whole class practice, then work to add and subtract multiples of 0.1 and 0.01 which cross boundaries.

You Will Need

  • 0.01–1 grid (see resources)
  • Blank 0.01–1 grid and/or a completed 0.01 to 1 grid (see resources)
  • Coins
  • Whole class practice (see resources)

Procedural Fluency

Day 1
Add/subtract 0.01/0.1 to fill in empty squares on a 0.01–1 grid.

Day 2
Add and subtract multiples of 0.1 and 0.01.

Mastery: Reasoning and Problem-Solving

  • 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?
  • Find the answer to 3.42 + 0.2. Then find the answer to 3.42 + 0.02. Which answer is greater?
  • Write the missing number in the bar chart:
4.53
4.23?
  • 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?

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

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

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

Unit 4 Subtract decimals with 1 or 2 places (suggested as 3 days)

Objectives

Subtract decimals with 1 or 2 places
Unit 4: ID# 5261

National Curriculum
Dec/Fr (ix) (x)

Hamilton Objectives
32. Subtract 1- and 2-place decimal numbers by counting up: 6.2 – 3.5, 13.1 – 9.45.

Teaching and Group Activities for Understanding

Day 1 Teaching
Use Maths Frog to calculate how much a mouse of 6.7 cm grows to reach 9cm. On an empty number line 6.7cm–9cm draw Frog’s hops: a hop of 0.3 to 7cm then a hop from 7cm to 9cm labelled 2cm. Repeat for other mice.
Group Activities
Use the ‘Talisman Squares’ in-depth problem-solving investigation below as today’s group activity.
Or, use these activities:
-- Use counting up (Frog) or counting back/place value to work out subtractions for numbers with 1 decimal place.
-- Use counting up (Frog) to work out subtractions for numbers with 1 decimal place.
Day 2 Teaching
Write 8 – 5.67. Show how Maths Frog can hop to 6 (hop of 0.33) then jump to 8 (jump of 2). Repeat to calculate other differences shown on a bar model and calculated using Maths Frog.
Group Activities
-- Use counting up (Frog) to work out subtractions for numbers with 2 decimal places.
-- Measure arm spans and heights, find the difference between the two.

Day 3 Teaching
Write 4.3 – 2.67 on the board. Draw a line from 2.67 to 4.3. Model using Maths Frog to find this difference. Subtract other pairs of numbers with 1 or 2 decimal places using counting up (Frog).
Group Activities
-- Subtract numbers with 2 decimal places.
-- Subtract numbers with different numbers of decimal places.

You Will Need

  • 1–9 dice
  • Number cards 0–9, one set per pair
  • Measuring tape
  • Paper clips
  • Subtract pairs of numbers with 1 or 2 decimal places (see resources)
  • Subtract numbers with 2 decimal places from numbers with 1 decimal place (see resources)

Mental/Oral Maths Starters

Suggested for Day 1
Double and halve two-digit numbers (simmering skills)

Day 2
Pairs to 100 (pre-requisite skills)

Day 3
Change from £1 (pre-requisite skills)

Procedural Fluency

Day 1
Work out how much hamsters have grown (in cm, with 1 decimal place).

Day 2
Find differences between measurements (1 and 2 decimal places).

Day 3
Subtract pairs of numbers with 1 or 2 decimal places.

Mastery: Reasoning and Problem-Solving

  • Choose how to subtract 3.45 from 6. Explain your choice of method. Check your answer using addition.
  • True or false?
    1.5 – 0.75 is 3/4
    6 – 3.38 > 2.5
    When you subtract a number with 2 decimal places from a whole number, the answer must have 2 decimal places.
  • Write the missing numbers.
    4.65 – ☐ = 3.8
    ☐ + 2.43 = 4
    8.17 – 4.4 = ☐


In-depth Investigation: Talisman Squares
Children explore patterns in a Talisman Square. They find differences between adjacent numbers on a 4 x 4 grid and then explore arrangements on a 3 x 3 grid.

Extra Support

This unit has no separate Extra Support activities.