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- CH 17|Overview & Teacher Resource Sheets
Student Resource Book |
Year 7 (4A)
Measurement & Geometry
Chapter 17 | Nets and 3D drawings
Overview & Teacher Resource Sheets
Rich tasks
- These tasks are problem solving open-ended questions that require students to be able to draw different views and nets of 3-D shapes. They can be given at the start of a topic and done as the students gain enough knowledge to complete them, inserted into a topic at an appropriate place or given as homework or extension.
- Container shops
- Eight cubes
- Box it
> More on "Rich tasks for this Chapter"...
1. Container shops
- You could start a lesson with Task 1 but it is best if students have first had some exposure to making isometric drawings, and views.
- Encourage students to make more than just the simplest model possible (cubes in a row with one cube in the second storey position is only the minimum to satisfy the requirement).
- You could make this task simpler by restricting the number of cubes used.
2. Eight cubes
- This task does have a finite number of answers. See the answer section for these. Although not open-ended it is a challenging task for students to find all the ways. Encourage students to explain how they might know when they have found all the ways.
3. Box it
- Encourage students to make something more interesting than a cuboid shaped box if you think they are capable.
- You could ask students to make a net and box for something specific that you brought into the classroom like an ornament, or for a group of small items to be packaged together, which when combined do not form a cuboid shape, such as 10 golf balls. This will require them to think creatively about the best way to arrange the items and to make a box that fits them.
Nets
- Match nets with 3-D shapes and vice versa.
Teaching ideas
Package it up (Getting started sheet 17)
This link displays the Getting started on page 277.
Dot 1 is a good introduction to nets. You could bring some interesting packaging to show. All of the packages shown can be made from a net but they would be awkward shapes and therefore wastage is higher than with a net for a cuboid.
Dot 2 could be done at this point or prior to Isometric drawing.
Will it or won’t it? (Teacher resource sheet 40)
This link displays some nets of cubes and open boxes with some that don’t fold to the correct shape. These can be printed and cut out. For each net in turn, ask a volunteer to predict if it will fold to a cube an open box or if it won’t fold to give a solid shape at all. Ask the class/group to stand up if they agree. Have a copy of each net already cut out. Hand it to the student who made the prediction to fold. Discuss how to predict accurately.
Teacher notes
- Students often find nets difficult. They may need to cut the net out and fold it for themselves. The nets for all of the questions are given in:
Printable Master - Activity 1 Question 1
Printable Master - Activity 1 Question 2
Printable Master - Activity 1 Question 3 - Encourage students as they fold nets to look at which edges join with which and then close their eyes and imagine it without looking.
- Before folding a net, encourage students to put the same mark on edges that they think will join up when the net is folded. Then they can check if they are correct when they fold the net.
- Encourage students to count the faces that the solid will have when the net is folded and the shape of the faces. This will help students decide which solid the net will fold to.
- When checking whether a net will fold to make a solid shape at all, encourage students to check the number of faces and that the edges that will join are the same length.
Isometric drawings
- Draw 3-D shapes on isometric paper.
> More on "Isometric drawings"...
Teaching ideas
- 3-D to 2-D (Teacher resource sheet 41)
This link displays Isometric paper which you can print out for students to use.
Ask for a volunteer to come and teach the rest of the class/group how to draw a cube. Ask another student to come and teach the class/group how to draw a solid you have displayed made from three or four cubes. You could show some more solids and ask for volunteers to draw them. If you divided the class/group in two you could award points for correct drawings or have a competition.Note: If you wanted students to draw on the viewable isometric paper, you would need to project onto a whiteboard or similar.
Teacher notes
- Isometric paper must be orientated the correct way. Encourage students to find a way of remembering which way is correct. Some of these ideas could be shared.
- Make students aware of the fact that isometric drawings can be made without isometric paper. They could practise doing this. The angles made with the horizontal must be 30°.
- Isometric drawings can be difficult for some students and they may need plenty of practice. These isometric drawing skills lead on to being able to make perspective drawings and so it is important that students grasp them well.
- Making 3-D models with straws and Plasticine is a good way to help students visualize where the edges, faces and vertices are when they can’t be seen.
Views
- Deduce the number of missing cubes and visualize the faces that can be seen on a 3-D shape depending on from where you look.
- Draw and recognise plan, front, side views of 3-D shapes.
Teaching ideas
- How many cubes? (Teacher resource sheet 42)
This link displays two drawn models that have hidden cubes when viewed from the front or the side. Ask students to write down how many cubes the shape has. Discuss why there is more than one correct answer. Initially it will be helpful to get students to make the models displayed. - Imagine
Ask students to:
Imagine that a magic potion has shrunk them and they are standing in front of a huge cube.
Would it be possible to stand so they could only see one face, two faces, three faces or more than three faces?
Sketch what they would see each time.
You could take students outside and get them to stand in front of a cuboid shaped building to illustrate.
- View it
Divide the class into groups and give each group a model made from five cubes (each one should be different). Tell each group which is the front of the model. Ask that group to look at the model from the front, the right side and the top and draw the view they see.
You may have to demonstrate a view first. The group then passes their drawings and the model to the next group and asks them to check it.
Teacher notes
- Encourage students to build the models if they have trouble visualizing them.
- This section is the precursor to the section in NZ Curriculum Mathematics Level 4B chapter 16 which asks students to build several different models given the same front, side or top view.
- Encourage students to think of themselves as having been shrunk by a magic potion when they look at the front, top or side. This encourages them to draw ONLY those faces directly in front of the view.
- Students may need the models in front of them when drawing the views.
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