# Welcome Back for Term 2!

Image Source

This term we will be studying Measurement and Geometry.

Year 7 Maths (JacPlus Chapter 9 – Measurement and Chapter 5 – Geometry)

By the end of this term I hope you will be able to:

• Use appropriate units of measurement
• Calculate the perimeter of 2D shapes
• Calculate the area of triangles, quadrilaterals and composite shapes.
• Identify types of polygons (different triangles and quadrilaterals)
• Estimate, measure and draw angles between 0 and 360 degrees.
• Identify the properties of parallel and perpendicular lines and the angles that form between them.
• Calculate the missing angles in polygons, knowing that the internal angles of a triangle add to 180 degrees.
• Recognise various transformations (translations, reflections, rotations and dilations)

Year 8 Maths (JacPlus Chapter 7 – Congruence and Chapter 10 – Measurement)

By the end of this term I hope you will be able to:

• Use and convert units of measurement for perimeter, area and volume
• Calculate the area of various quadrilaterals.
• Calculate the area and perimeter of circles.
• Calculate the volume of various prisms using formulae.
• Identify congruent shapes
• Transform various shapes (translate, dilate, rotate and reflect).
• Solve geometric problems using congruence.
• Work out problems around different time zones using the 24 hour clock.

# Euler’s Formula

Learning Intention: Students will investigate Euler’s rule that describes the relationship between the number of faces, the number of edges and the number of vertices of 3D objects.

Success Criteria: Students will create 3D shapes using toothpicks and jelly-lollies to represent edges and vertices. They will then count and record in a table the faces, edges and vertices of the shapes and investigate Euler’s Rule.

Today we are going to learn more about 3D shapes and investigate a special relationship between the number of vertices, edges and faces of such shapes. Create the following shapes using toothpicks and jubes:

1. tetrahedron
2. triangular prism
3. square base pyramid
4. cube
5. pentagonal pyramid
6. pentagonal prism
7. hexagonal pyramid
8. hexagonal prism

Now draw a table with six columns that records the name of the polyhedron, the name of the base shape, the number of sides on the base shape, the number of faces, number of vertices and number of edges. Complete the table for each of the 8 shapes listed above. Now see if you can work out any relationship between the values in your table.

# Surface Area and Volume of Prisms

Image Source – Hexagonal prisms at the Giant’s Causeway in Ireland.

Firstly, what is a prism? A prism is a 3D shape that has cross-sections parallel to the base faces the same. Prisms are named for their base, so a prism with a triangular base is called a triangular prism (like a Toblerone package) and one with a pentagonal base is called a pentagonal prism. To work out the surface area of a prism, you need to calculate the area of each face and add them together. To calculate the volume of a prism, you need to work out the area of the base and multiply by the height of the prism ( the distance between congruent faces).