Short Blocks

Maths Year 6 Spring Measures

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 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 2 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 6cm x 6cm x 6cm cube is chopped in half three times (see download for diagram).
Find the volume of each cuboid after each of the three cuts and write the lengths of their edges.


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.