Integrated Math 1
Name
Introduction
Have you ever seen a child’s shape sorting toy? Some are in the shape of an animal and some are one side of a simple box. Your task is to design a toy like this.

What shapes are you going to include?

How much material will be required to actually produce your toy?
Part 1: Designing your toy
You need to create a design for a new shape sorting toy. The requirements are below:

The toy needs to include four pieces that are different shapes – a circle, a square, an equilateral triangle, and a shape of your choice should be chosen for the face (base). The shape that you choose can be any shape for which you can calculate the surface area. The shape could be a combination of shapes that are familiar to you. Ask your teacher if you need help thinking of another shape for the fourth piece.

Create accurate diagrams of each of the shapes you plan to use. Your diagrams should be the actual size. Label the dimensions of each shape. Each piece must be a minimum of 4 square inches or 25 square centimeters in area. (Decide whether you will use inches or centimeters and be consistent throughout this task.) This minimum area is very important since a toy that is too small could create a risk of the child choking.

When you create the pieces of this toy, make sure that one piece cannot fit through the opening intended for a different piece. For example, the circle should not fit through the opening for a square and the square should not fit through the opening for the circle. Explain how you know this is true for your toy.
Part 1 Due Date: (Either Apr. 25 or Apr. 26)
On the above date, you need to have completed the following:

A good copy of the calculations for the area of the face (base) of each part of your toy

An accurate diagram of each shape you are including for the face (base) of each part of your toy. This needs to be the final version of the 2D shapes. Use grid paper and ensure that each figure is outlined in ink. You may use a computer for this part, but it still needs to be the actual size.

A rough draft of the net diagrams for the 3D shapes (sketch and not yet to scale)

A rough draft of the surface area calculations for each part of your toy and

A rough draft of your explanation for the surface area calculations (if time).
Part 2: Determining the material needed
The company who will produce this toy likes your idea and is willing to go ahead with production. However, they want to determine the cost of production. The company has asked you for the amount of material required to produce each of your shapes.

Draw a net diagram of each of your shapes. Each diagram should be done in ink and should be labeled to indicate the actual dimensions. However, these do not need to be drawn in the actual size. The shapes you created in ‘Part 1’ are just one side of the object (the base). Each piece should be a right prism. So one piece will be a rectangular prism, one a triangular prism, etc.

How much material is needed for each of your shapes individually? How much is required altogether? Show your calculations.

Aside from the pieces that fit into the toy, what else might require additional material? Approximately how much would you need? Explain.
Reflection

Think about the toy you have designed. Is this an appropriate toy for a baby? Is it safe? Explain.
Construction

Using light weight cardboard or sturdy paper, create a model of your toy.
