# Insides and Outsides

### Shaping It

##### Stage: 1 and 2 Challenge Level:

These pictures were made by starting with a square, finding the half-way point on each side and joining those points up. You could investigate your own starting shape.

### Torn Shapes

##### Stage: 2 Challenge Level:

These rectangles have been torn. How many squares did each one have inside it before it was ripped?

### Area and Perimeter

##### Stage: 2 Challenge Level:

What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.

##### Stage: 2 Challenge Level:

How can you arrange the 5 cubes so that you need the smallest number of Brush Loads of paint to cover them? Try with other numbers of cubes as well.

### Next Size Up

##### Stage: 2 Challenge Level:

The challenge for you is to make a string of six (or more!) graded cubes.

### Making Boxes

##### Stage: 2 Challenge Level:

Cut differently-sized square corners from a square piece of paper to make boxes without lids. Do they all have the same volume?

### Numerically Equal

##### Stage: 2 Challenge Level:

Can you draw a square in which the perimeter is numerically equal to the area?

### More Transformations on a Pegboard

##### Stage: 2 Challenge Level:

Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.

### Fitted

##### Stage: 2 Challenge Level:

Nine squares with side lengths 1, 4, 7, 8, 9, 10, 14, 15, and 18 cm can be fitted together to form a rectangle. What are the dimensions of the rectangle?

### Cover the Tray

##### Stage: 2 Challenge Level:

These practical challenges are all about making a 'tray' and covering it with paper.

### Ribbon Squares

##### Stage: 2 Challenge Level:

What is the largest 'ribbon square' you can make? And the smallest? How many different squares can you make altogether?