Short Blocks

# Maths Year 6 Summer Maths Around Us

Each unit has everything you need to teach a set of related skills and concepts.

First time using Hamilton Maths?

The PowerPoint incorporates step-by-step teaching, key questions, an in-depth mastery investigation, problem-solving and reasoning questions - in short, everything you need to get started.

All the other resources are there to support as-and-when required. Explore at your leisure - and remember that we are always here to answer your questions.

## Unit 1 Measuring ourselves and around us (suggested as 5 days)

### Objectives

Measuring ourselves and what’s around us
Unit 1: ID# 6803

National Curriculum
PV (i) (iv),
Rat/Pr (iii),
Meas (i) (ii),
Stats (i) (ii)

Hamilton Objectives
4. Solve number and practical problems involving place value, rounding and negative numbers.
19. Use estimation to check answers and determine an appropriate degree of accuracy; round answers to multiplications and divisions to a specified degree of accuracy.
20. Solve problems involving all four operations.
34. Solve problems involving similar shapes where the scale factor is known or can be found.
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 converting between them.
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
55. Begin to reason mathematically making simple generalisations, using mathematical language and making connections between mathematical ideas.

### Planning and Activities

Day 1 Teaching
Explain that the cubit was an early unit of measurement used in Egypt around 5000 years ago. This is the distance from the elbow to the fingertip. Can you see any problems they might have had with this unit of measurement? Agree that it was not a ‘standard’ unit. Describe digit, span, palm, hand, foot, yard and arm span.
Group Activities
-- Find body measurements and find relationships between them.
-- Draw a scatter graph of arm spans and heights. Find the mean measurements of digits, palms, spans and cubits in the group.

Day 2 Teaching
Explain that Fermi estimates involves making fast, rough estimates using quantities which are difficult or impossible to measure directly. How many hairs do you think are on your head? What might be a sensible way to find out? Agree that it would take a long time to count them all, but an estimate can be made by finding how many are in a smaller area, and then multiplying by the number of areas.
Group Activities
-- Make a range of ‘Fermi’ estimates – approximate calculations of large numbers - such as the numbers of hairs on your head.

Day 3 Teaching
How many blades of grass do you think might be in the school field? Could we split up and count them all between us? Explain how ecologists make a quadrat (sampling frame), count what is inside, move it to different places and find an average. How many insects do you think might be on our field?
Group Activities
-- Make a Fermi estimate of the number of blades of grass on the school field and numbers of insects/daisies visible on it. Decide what size quadrats to use and calculate the area of the field.

Day 4 Teaching
Show children how to take their pulse. Children run for 30 seconds then retake their pulse. Repeat after running for 1 minute, 2 minutes, and then finally for 3 minutes. Show children how to draw a line graph of the results.
Group Activities
-- Construct and interpret line graphs to investigate the effect of different forms of exercise on heart rate.

Day 5 Teaching
The astrolabe was possibly invented in Greece either by Hipparchus, a 2nd century BCE astronomer, or Apollonius of Perga, a 3rd century BCE mathematician. We are going to make an astrolabe to measure the heights of trees and buildings. Show children one you prepared earlier. Show children how it works.
Group Activities
-- Make an astrolabe and use it to work out the height of the school building, trees or other tall structures.

### You Will Need

• Tape measure, ruler and graph paper
• Flipchart and pens
• ‘Relationships between body measurements’ (see resources)
• ‘Making estimates of large numbers’ (see resources)
• Calculators, metre sticks and trundle wheels
• Card strips and sticky tape to make quadrats (sampling squares)
• Clipboards, stopwatch and whistle
• ‘Making an astrolabe’ (see resources)
• ‘Astrolabe images’ (see resources)
• Protractor, string, card and tape
• Modelling clay and 30m measuring tape
• cm² paper

### Mental/Oral Maths Starters

Suggested for Day 1
Pairs with a total of 1 metre (simmering skills)

Day 2
Order numbers to 1 million (pre-requisite skills)

Day 3
Thousands and millions (pre-requisite skills)

Day 4
Estimate 1 minute (pre-requisite skills)

Day 5
Estimate angles (pre-requisite skills)

### Worksheets

Day 1
N/A

Day 2
N/A

Day 3
Work with a partner to estimate how many blades of grass each sheep has eaten.

Day 4
N/A

Day 5
N/A

### Mastery: Reasoning and Problem-Solving

This unit has no separate problem-solving activities or investigations.

### Extra Support

This unit has no separate Extra Support activities.

## Unit 2 Tesselation & other shape patterns (suggested as 3 days)

### Objectives

Tessellation and other shape patterns
Unit 2: ID# 6823

National Curriculum
PofS (i)

Hamilton Objectives
49. Draw 2-D shapes, using given dimensions and angles. Understand terms parallel and perpendicular.

### Planning and Activities

Day 1 Teaching
Show Escher examples of tessellation. Cut out a shape from one side of a card square. If I stick this shape in the same orientation on the opposite side, the new shape will still tessellate. Repeat, this time cutting out a shape from a different side and sticking it to the opposite side. Now we have an interesting shape which will still tessellate. Discuss where tessellations might be used.
Group Activities
-- Explore tessellating combinations of regular shapes to make tiling patterns (semi-regular tessellations). Adapt a square to make a unique tessellating design.

Day 2 Teaching
Introduce the term fractal. Draw a vertical line, and then two lines at 60° to each other, each two thirds in length of the original, at the top of the original line. Keep repeating this process. What sort of shape is emerging?
Group Activities
-- Choose one of two fractals to create. Investigate fractals via the internet.

Day 3 Teaching
Draw a large square and divide it into 16 equal squares. Draw two arcs in the 1st square. Copy it into the next square (translation). If we carry on doing this, what will the final pattern look like? Repeat, this time reflecting the design.
Group Activities
-- Choose a design and make different patterns, using translations, rotations and reflections.

### You Will Need

• ‘Tessellating using regular shapes’ (see resources) preferably copied onto card so that children can draw around the shape (if not, children will require lots of copies of the shapes to stick and colour)
• ‘Fractal 1’ and ‘Fractal 2’ instruction sheets (see resources)
• ‘Translations, rotations and reflections’ (see resources)
• Card square, scissors, tape and glue
• Coloured pencils
• Internet access
• Rulers and cm² paper

### Mental/Oral Maths Starters

Day 1
2-D shape (pre-requisite skills)

Suggested for Day 2
Mental calculation (simmering skills)

Suggested for Day 3
Symmetry (simmering skills)

### Worksheets

This unit has no separate practice sheets.

### Mastery: Reasoning and Problem-Solving

This unit has no separate problem-solving activities or investigations.

### Extra Support

This unit has no separate Extra Support activities.

## Unit 3 Ratios in nature and art (suggested as 2 days)

### Objectives

Ratios in nature and art
Unit 3: ID# 6829

National Curriculum
PV (ii)
Fr (ix) Rat/Pr (i)
Alg (ii)
Meas (i)
Stats (ii)

Hamilton Objectives
19. Use estimation to check answers and determine an appropriate degree of accuracy. Round answers to multiplications and divisions to a specified degree of accuracy.
35. Solve problems involving simple ratios, using tables facts and knowledge of fractions and multiples, e.g. 2 eggs for every 250g of flour.
39.Generate, describe and continue linear sequences.
40. Use, read and write, and convert between, standard units including miles and kilometres, using decimal numbers with up to three places as appropriate.
48. Find and interpret the mean (average) of several quantities.

### Planning and Activities

Day 1 Teaching
Children sketch a rectangle on their whiteboards, measure each side and divide the longer side by the shorter side, using a calculator to help. List each answer. When large groups of people are asked to do this, a pattern emerges where many answers are between 1.5 and 1.75. How many of you drew rectangles in this range?
The Golden Section is a special ratio approximately equal to 1 to 1.618. Rectangles with this ratio are thought to look ‘right’ and are often used in art and architecture.
Group Activities
-- Draw a natural spiral. Record the length of each square in the spiral and find that the lengths are the numbers in the Fibonacci Sequence.
-- Calculate the ratios between neighbouring terms in the Fibonacci Sequence and find that they tend towards the Golden Section ratio.

Day 2 Teaching
Bend your middle finger and measure the longest, middle and shortest bones. Children use a calculator to divide the length of the longest bone by the middle bone, and the middle bone by the shortest bone. What do you notice? They should find an answer of approximately 1.6, the Golden section. Discuss why this might not exactly be the case. Explain how artists use proportions like this in their paintings.
Group Activities
-- Find pairs of body measurements with the ratio of the Golden section.

### You Will Need

• Mini whiteboards and pens
• Rulers, calculators and debit/credit card
• Internet access
• ‘Drawing a natural spiral’ (see resources)
• Compasses, cm² paper and graph paper
• ‘Golden measurements’ (see resources)
• Tape measures

### Mental/Oral Maths Starters

Day 1
Ratios (pre-requisite skills)

Day 2
Round decimal answers on a calculator (pre-requisite skills)

### Worksheets

This unit has no separate practice sheets.

### Mastery: Reasoning and Problem-Solving

This unit has no separate problem-solving activities or investigations.

### Extra Support

This unit has no separate Extra Support activities.