Maths Year 6 Spring Measures and Data

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 available to friends and School Subscribers. These bulk downloads are added value for Hamilton Friends and School Subscribers.

Unit 1 Conversion: metric/imperial units; line graphs (suggested as 4 days)

Objectives

Conversion of units: metric and common imperial; conversion line graphs
Unit 1: ID# 6553

National Curriculum
Meas (i) (ii) (iii)
Data (i)

Hamilton Objectives
40. Use, read and write, and convert between, standard units including miles and kilometres, using decimal numbers with up to three places as appropriate.
41. Solve problems using standard units and convert between them.
47. Interpret and construct line graphs and use these to solve problems.

Teaching and Group Activities for Understanding

Day 1 Teaching
Show a 1kg weight. Write some weights in g and kg on cards. Put up a washing line, and order the weights along it. Repeat for capacities in ml/litres.
Group Activities
-- Play a game converting from grams to kilograms and vice versa (1 or 3 decimal places).
-- Convert from litres to millilitres and vice versa, including amounts with 2 decimal places.

Day 2 Teaching
Ask children to write some km distances as metres. Discuss km and miles. Say that 5 miles is about 8km. Find 10, 15, 50 miles in km. Show how to draw a line graph to show this relationship.
Group Activities
-- Plot a line graph with given axes; use this to find kilometre to mile equivalents and vice versa, including at intermediate points on the graph.

Day 3 Teaching
Discuss Imperial measures. Discuss some approximate conversions between pounds, ounces, kg, cm, inches etc.
Group Activities
-- Make connections between regularly-used imperial units and familiar objects and contexts. Relate to well-known metric equivalents, understanding that some of these are approximate.

Day 4 Teaching
Show a table of conversions from grams to ounces. Convert some weights from ounces to pounds and ounces. Draw two axes and label them kilograms and ounces. Then draw the conversion graph and discuss.
Group Activities
Use the in-depth problem-solving investigation ‘Weights in a line’ as today’s group activity.
Or, use these activities:
-- Draw a line graph to convert litres to pints and vice versa.
-- Draw a line graph to convert centimetres to inches.

You Will Need

  • 1kg weight, washing line, 14 pegs and cards
  • Activity sheet of Converting Metric Units (see resources)
  • Scissors
  • Range of labelled containers with capacities between 100ml and 2l, such as 250ml and 168ml (e.g., vinegar, soy sauce, chilli sauce bottles)
  • Squared background on the IWB
  • Graph paper and online mapping tool
  • Bag of 28g crisps, 30cm ruler and pint glass
  • A3 paper and tape measure
  • Table of approximate conversions of kg to pounds and ounces (see resources)
  • ITP: Measuring Scales
  • ITP: Measuring Cylinders

Mental/Oral Maths Starters

Day 1
Multiply and divide by 10, 100 and 1000 (pre-requisite skills)

Suggested for Day 2
Reading scales (weight) (simmering skills)

Suggested for Day 3
Reading scales (capacity) (simmering skills)

Suggested for Day 4
Reading scales (general) (simmering skills)

Procedural Fluency

Day 1
Convert from litres to millilitres to order capacities order.

Day 2
Use a line graph to convert from miles to km and vice versa.

Day 3
Use conversions between feet and inches to metres and centimetres to order children in terms of height.

Day 4
Draw a line graph to convert litres to pints and vice versa.
Draw a line graph to convert hand measurements in cm to inches.

Mastery: Reasoning and Problem-Solving

  • Write a familiar object that weighs:
    (a) 5 Kg
    (b) 1 pound
    (c) 100g
  • Write a familiar container that holds:
    (a) 1 pint
    (b) 5 ml
    (c) 2 gallons
  • True or false?
    10 lots of 100 grams are 10 kilograms.
    One tenth of a litre is 10ml.
    Half a pint is about 1/4 of a litre.
    You can weigh people in stones.
  • Use this fact: 5 miles = 8km
    15 miles is ? km
    ? miles is 4 km
    64 km is ? miles
    Roughly how many miles is 250 km?

In-depth Investigation: Weights in a Line
Children use systematic working to calculate the number of possibilities of making weights using just two set weights; then look for patterns using line graphs.

Extra Support

Decimals Measure Up
Converting kilograms to grams and vice versa; Converting litres to millilitres and vice versa

Unit 2 Time intervals, timetables, 24-hour clock (suggested as 2 days)

Objectives

Calculate time intervals; use and interpret time tables; 24 hour clock
Unit 2: ID# 6563

National Curriculum
Meas (i)

Hamilton Objectives
45. Use 12 and 24-hour clocks including analogue with Roman numerals; calculate time intervals; use timetables.

Teaching and Group Activities for Understanding

Day 1 Teaching
Revise the 24-hour clock, converting from am and pm times to the 24-hour clock. Find differences between times that children have written, demonstrating how to count up along a time line.
Group Activities
-- Interpret a TV schedule to find a number of programmes with a total duration of less than nine hours.
-- Using a TV guide, calculate programme duration. Investigate the amount of TV time devoted to news.

Day 2 Teaching
Display the timetable of trains from Thurso (see resources). Discuss how we can work out how long particular parts of the journey take. Count up to calculate time intervals.
Group Activities
Use the in-depth problem-solving investigation ‘5 on the clock’ from NRICH as today’s group activity.
Or, use these activities:
-- Read a train timetable and draw timeline jottings to help work out time intervals.
-- Read a train timetable. Find journeys between 1 and 2 hours, then between 2 and 3 hours.

You Will Need

  • Mini-whiteboards and pens
  • TV guide for the week with times written using the 24-hour clock
  • Thurso to Penzance train timetable (see resources)
  • Reading timetables activity sheet (see resources)
  • Penzance to Exeter train timetable (see resources)

Mastery: Reasoning and Problem-Solving

  • Here is the time each child goes to sleep. Find out what time they each wake up if the first two sleep 9 hours and the second two sleep 9.5 hours.
    Amit: asleep at 22:00
    Anja: asleep at 21:45
    Sunil: asleep at 21:55
    Asha: asleep at 22:30
  • Which of these times would not change if you were using the 24-hour clock?
    3 o’clock in the morning
    Quarter to 2 after lunch
    Midnight
    Twenty past midday.
    6pm
  • Write any that will change using the 24-hour clock.

In-depth Investigation: 5 on the Clock
On a digital clock showing 24-hour time, over a whole day, how many times does a 5 appear? Is it the same number for a 12-hour clock over a whole day? 5 on the Clock from nrich.maths.org.

Extra Support

Time to Time
Converting times from am/pm to the 24-hour clock and vice versa; Beginning to say how long to next hour

Unit 3 Pie-charts; find the mean of a data set (suggested as 4 days)

Objectives

Construct and interpret pie charts; find the mean of a data set
Unit 3: ID# 6571

National Curriculum
Data (i) (ii)

Hamilton Objectives
47. Interpret and construct pie charts and line graphs and use these to solve problems.
48. Find and interpret the mean (average) of several quantities.

Teaching and Group Activities for Understanding

Day 1 Teaching
Show 2 pie charts with results of favourite sports surveys. Explain what a pie chart is. Discuss how we interpret these, asking questions, e.g., Which is the most popular sport for children from school A? School B?
Group Activities
-- Interpret pie charts showing the way children come to school.
-- Interpret pie charts to determine which matches bowls of different coloured counters.

Day 2 Teaching
Show a table of how difficult 12 children find each times-table. Discuss how to show this in a pie chart. We need to work out the size of each segment by finding the number of children as a fraction of the whole.
Group Activities
-- Construct a pie chart with 6 segments based on the TV preferences of 6 children.
-- Construct a pie chart to show the proportions of ingredients in different cereals.

Day 3 Teaching
Ask children what ‘average’ means. There are different ways of finding an average. Work together to find the mean length (letter count) of a set of six names. Explore the effect of adding another name to the set (more letters than the current mean), using a calculator to find the answer.
Group Activities
-- Calculate the mean length of classmates’ names.
-- Find mean number of words per line for a page in two different books.

Day 4 Teaching
Show children a table of numbers of texts (see resources) sent on one typical day by children in Y7. Children find the average. Compare with numbers of texts send by children in Y10.
Group activities
Use the in-depth problem-solving investigation ‘Mean score’ as today’s group activity.
Or, use this activity:
-- Use understanding of how to calculate the mean to find different averages within a small group: heights, name lengths, ages etc.

You Will Need

  • ‘Pie charts’ (see resources)
  • ‘Interpreting pie charts’ sheet (see resources)
  • Two bowls, red, blue, green and yellow counters
  • ‘Pie charts showing numbers of counters’ sheet (see resources)
  • Paper and coloured pencils
  • ‘Drawing pie charts’ sheets (see resources)
  • Flipchart and different coloured pens
  • Cereal packets, calculators, compasses and protractors
  • Copies of 2 pages, each from a different book
  • ‘Tables of numbers of texts sent’ sheet (see resources)
  • Measuring tapes

Mental/Oral Maths Starters

Day 1
Angles round a point (pre-requisite skills)

Day 2
Add 5 numbers together (pre-requisite skills)

Suggested for Day 3
Kilometres to miles (simmering skills)

Suggested for Day 4
Parts of circles (simmering skills)

Procedural Fluency

Day 1
Answer questions about pie charts to show the way 36 Y2 children come to school compared with 24 Y6 children.

Day 2
Draw a pie chart of excuses for homework not being handed in.

Day 3
Find the mean of numbers rolled on a dice

Day 4
Find the mean of values in tables and bar graphs.

Mastery: Reasoning and Problem-Solving

  • Match each data set (i–v) to the best way of displaying it (a, b or c).
    (a) Line graph
    (b) Bar chart
    (c) Pie chart

    (i) Favourite songs chosen by Y6 from a list of 8 songs
    (ii) Converting pints to litres
    (iii) Hours of homework done each week by children in Y6
    (iv) Matching pounds (£) against US dollars ($)
    (v) Votes for the nation’s favourite animal from a list of 10
  • 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 average amount that they have?
    Which children have less than the average?


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

Extra Support

Interpreting Pie Charts
If you haven’t done it already, complete the Practice sheet from Day 1.

Unit 4 Calculate areas of different shapes (suggested as 3 days)

Objectives

Calculate areas of triangles, parallelograms and rectilinear shapes
Unit 4: ID# 6577

National Curriculum
Meas (iv) (v) (vi)

Hamilton Objectives
42. Measure areas and perimeters; understand that area is a measurement of covering and is measured in square units, and perimeter is a length, measured in mm, cm, m or km; recognise that shapes with the same area can have different perimeters and vice versa.
43. Calculate the area of parallelograms and triangles.

Teaching and Group Activities for Understanding

Day 1 Teaching
Draw right-angled triangles and discuss how to find their areas by considering each as half of a rectangle. Demonstrate that this works for any triangle. Conclude area = half base × height.
Group Activities
-- Find the areas of rectangles and then divide these to find the areas of triangles.
-- Generalise how to find the area of right-angled triangles. Test with other types of triangle.

Day 2 Teaching
Show a set of quadrilaterals and identify parallelograms. Demonstrate how to find the area by dividing into 2 triangles and a rectangle. Find areas and derive formula after the activity.
Group Activities
-- Derive a formula for finding the area of a parallelogram.

Day 3 Teaching
Revise finding areas and perimeters of rectilinear shapes. Show some shapes with the same perimeter. Demonstrate that these have different areas. Can you approximate the area of a bedroom floor? The area of a village? The surface area of a little finger nail? One side of a sticky note?
Group Activities
Use the in-depth problem-solving investigation ‘Through the window’ from NRICH as today’s group activity.
Or, use this activity:
-- Use investigative strategies to find the dimensions of a rectangle of specified area. Investigate compound shapes.

You Will Need

  • Squared background on Interactive Whiteboard
  • Area of triangles sheet (see resources)
  • cm2 paper
  • A set of quadrilaterals on squared paper (see resources)
  • Scissors
  • Perimeter and area at https://web.archive.org

Mental/Oral Maths Starters

Day 1
Area of rectangles (pre-requisite skills)

Suggested for Day 2
Times table bingo (simmering skills)

Suggested for Day 3
Perimeters of rectangles (simmering skills)

Procedural Fluency

Day 1
Find the area of triangles and a compound shape made from triangles and a rectangle.

Day 2
Find areas of parallelograms.

Day 3
Draw rectangles with the same perimeter, but different areas.

Mastery: Reasoning and Problem-Solving

  • Find the area of the triangle (see download). The perpendicular height = 6cm and the base = 5cm
  • What is the area of the shape (see download)? The total length = 12cm and the base of the triangle is half the length of the rectangle. The triangle has two equal sides.
  • Draw two rectilinear shapes, one L-shaped and one T-shaped, with equal areas but different perimeters.

In-depth Investigation: Through the Window
The local DIY shop calculates the price of its windows according to the area of glass and the length of frame used. Can you work out how they arrived at these prices? Through the Window from nrich.org.uk.

Extra Support

Folding Areas
Finding areas of rectangles and triangles

Unit 5 Calculate volumes of cubes/cuboids (suggested as 2 days)

Objectives

Calculate volumes of cubes and cuboids
Unit 5: ID# 6599

National Curriculum
Meas (vii)

Hamilton Objectives
44. Calculate, estimate and compare volume of cubes and cuboids using standard units, cm³, m³, mm³ and km³.

Teaching and Group Activities for Understanding

Day 1 Teaching
Show children a cuboid made from 60 centimetre cubes (4 × 5 × 3). Discuss its volume, i.e. the number of cubes in it. Show how we can count or calculate. Derive the formula. Find the volume of a cube 7 by 4 by 5 metres.
Show children a (200ml+) measuring cylinder with 100ml of coloured water in it. Drop 100 centimetre cubes into it. What is the new water level? 200ml! Discuss what this means. 1ml of water and 1cm3 take up the same amount of space! They have the same volume.
Group Activities
-- Find the volume of cubes of given dimensions.
-- Experiment to make/sketch cuboids with a volume of 24cm3, then 36cm3. Check that all possibilities have been found.

Day 2 Teaching
Show children a cuboid made from 2 by 3 by 5 multilink cubes. Calculate volume as 30. Discuss how 2, 3 and 5 are the prime factors of 30. This is the smallest cube that can be made using the prime factors of a number.
Group Activities
Use the ‘Queued cubes’ in-depth problem-solving investigation as today’s group activity.
Or, use this activity:
-- Explore creating cubes with dimensions which are prime numbers.

You Will Need

  • Centimetre cubes
  • measuring cylinder
  • 100ml coloured water
  • Finding volumes of cuboids sheet (see resources)
  • Flipchart and pens
  • Multilink (or centimetre cubes)

Mental/Oral Maths Starters

Day 1
Multiply 3 numbers together (pre-requisite skills)

Suggested as an alternative for Day 1
Recognise years written using Roman numerals (simmering skills)

Day 2
Factors (pre-requisite skills)

Procedural Fluency

Day 1
Find volumes of cubes and cuboids.

Day 2
Work out the missing lengths of sides of cuboids, given the lengths of two dimensions and the volume.

Mastery: Reasoning and Problem-Solving

A cube is chopped in half three times. Find the volume of each cuboid and write the length of their edges (see download).


In-depth Investigation: Queued Cubes
Children apply a combination of knowledge of 3-D shape, area and volume to solve a problem that introduces surface area.