Level 7 Mathematics – Measurement and Geometry

A Learning Sequence for Level 7 Mathematics –

Measurement and GeometryBritt Gow, 2017

Level 7 Mathematics –Measurement and Geometry

Using units of measurement

• Establish the formulas for areas of rectangles, triangles and parallelograms and use these in problem solving (VCMMG258)

• Calculate volumes of rectangular prisms(VCMMG259)

Shape

• Draw different views of prisms and solids formed from combinations of prisms (VCMMG260)

Location and transformation

• Describe translations, reflections in an axis, and rotations of multiples of 90° on the Cartesian plane using coordinates. Identify line and rotational symmetries (VCMMG261)

1. Draw a House Plan – 240 metres square

• This task is to assess your understanding of area, perimeter, scale and ratio.

• You are required to draw the plan of a house showing the dimensions, labelling the measurements and calculating the area of each room. Your plan should include a kitchen, living area, one or more bedrooms, a bathroom and laundry, at minimum.

• You have a budget of $240,000 and the estimated cost per metre squared is $1000.

• Each cm on the plan, represents 1 metre, so the scale is 1:100. Label the plan with a ratio of 1cm (plan) = 1m (actual) and each room should be of a reasonable and realistic size

2. Create an image with Tangram shapes

• Use the colored paper squares provided to fold, draw and cut out the seven tangram shapes.

• Create a picture using all seven pieces and paste them down onto another sheet of paper. Describe how each shape has been transformed (translation, reflection or rotation)?

• Label each shape with its dimensions (length, width, height of triangles and parallelogram) and calculate the area of each shape.

• Does the area of the original square match the total area of the seven shapes added together? Why or why not?

3. Annotated photograph of a prism

• Take a digital photograph of a rectangular prism – it could be a packing crate, microwave, refrigerator or similar three dimensional object.

• Using an annotation app (such as Skitch) show the length, width and height of the object and calculate the surface area and volume.

• Send the annotated image to me by email.

4. Make a scale model of a simple building

• Use a photograph of a simple building to estimate measurements and transfer these to an isometric drawing, using a 1:50 scale.

• Make a template of a net in paper and transfer this to cardboard.

• Cut and fold the cardboard into the 3D model building.

5. SA and Volume in Minecraft

• Show the YouTube video “Minecraft Maths – Surface Area and Volume” at https://www.youtube.com/watch?v=AgqAcTxiToE

• You may also like to use “Increasing Volume using Minecraft” at http://technomaths.edublogs.org/2015/05/24/year-8-increasing-volume-with-three-little-pigs/

• Ask students to create their name using Minecraft blocks, take a screenshot and then annotate the image, showing the total surface area and volume.