# Mini Set Activity Examples

## Here are some activities to try with your Mini Sets to give you a place to start.

Click on the picture of the Mini Set you have to see the activities.

### Mini Set 1

This set contains 20 equilateral triangles and 12 regular pentagons.

##### Fractions

- Make an equilateral triangle that is 1/9 yellow, 1/3 green and 5/9 purple.
- Now make an equilateral triangle that is 1/4 purple, 1/4 green, 3/16 orange and 5/16 yellow.

Notes:

In these problems, the student must first realize that he needs 9 and 16 triangles, respectively, to make each figure. (A multiple of 9 or 16 would also work, but this impossible due to the size of the set)

Answers:

##### Puzzle

Make a closed object out of all the 12 pentagons in your box such that any two adjacent tiles have different colors.

Answers:

The object in question is called a *dodecahedron. *There 4 solutions two this problem, and the two in each row are mirror images of one another.

### Mini Set 2

This set contains 4 equilateral triangles, 4 rectangles, 12 squares, and 12 scalene right triangles.

##### Fractions

- Make a square that is 1/3 green, 1/3 yellow, and 1/3 orange.
- Now make an equilateral triangle that is 1/2 purple, 1/3 green, and 1/6 yellow.

Notes:

In the first problem, the student must first realize that she needs to make a square using a number of tiles that is divisible by 3. The only tiles available to her for making this larger square are the small square tiles. So she needs to use a number of them that is (a) a perfect square (b) divisible by 3. The only number that fits the bill is 9.

In the second problem, the student needs to understand that the equilateral triangle has to be made of 6 “equal” parts.

Answers:

##### Puzzle

How many different equilateral triangular prisms can you make using the tiles in your set?

Answers:

As the base of the prism, you can use either a larger equilateral triangle made of two scalene right triangles, or the smaller equilateral triangles.

If you use the larger triangle, only one prism is possible:

If you use the small triangular tile as the base of your prism, there are many possibilities possible depending on how many “stories” your prism has. In fact, it would be a good exercise to ask the students how many different heights are possible. The shortest prism would have only one “story” worth of square faces as its side walls. The tallest one will have 4 “stories” worth of side walls: 1 tall rectangular “story” plus 3 square “stories”

The best way to enumerate the possibilities is to stay organized. A prism can have 0, 1, 2, or 3 square stories. For each of these 4 possibilities, there are 2 possibilities for a rectangular story: to have one or not to have one. So the total number of possible heights is 4 ×2 -1= 7. Why do we subtract 1? Because it’s impossible to have a prism with 0 stories!

5 of the 7 solutions are shown below:

Let the student figure out what variations are missing. Hint: how many prisms are possible with 3 square stories?

### Mini Set 3

This set contains 8 rectangles, 12 isosceles right triangles, and 12 scalene right triangles.

##### Fractions

- Make a square that is 1/4 purple, 3/8 yellow, and 3/8 green.
- Make an equilateral triangle that is 1/3 purple, 1/2 green, and 1/6 orange.

Notes:

In the first problem, the student must first realize that he needs to make a square using a number of tiles that is divisible by 8. The only tiles available to him for making this larger square are the isosceles triangle tiles. He will need to use 8 of them to make a square

In the second problem, the student needs to understand that the equilateral triangle has to be made of 6 “equal” parts.

Answers:

##### Puzzle

How many different equilateral triangular prisms can you make using the tiles in your set?

Answers:

The base of the prism must be made of two scalene right triangles.

The variations are formed by the types of side walls the prism has. We can have square walls made of 4 isosceles triangles per wall. We can also have walls made of rectangles, with a 1 or 2 “stories” worth of rectangles. Or we can have a combination of rectangles and squares.

The best way to enumerate the possibilities is to stay organized. A prism can have 0, 1, or 2 rectangular stories. For each of these 3 possibilities, there are 2 possibilities for a square story: to have one or not to have one. So the total number of possible heights is 3 ×2 -1= 5. Why do we subtract 1? Because it’s impossible to have a prism with 0 stories!

The solutions are shown below: