## Exploring Patterns that involve space and measurement

You need to work in a group of four for this learning experience. Two of your group will explore

In your group of four, you will need:

**Part 1**of the experience and two of your group will explore**Part 2**.In your group of four, you will need:

- ones/unit blocks;
- flip tiles;
- graph paper;
- your maths book; and
- a calculator.

*Imagine you are tracing the growth of a family of cubes. Cubes grow quite differently to humans. On the eve of a one year old cube’s 2nd birthday it goes to bed as a one year old cube but wakes up on the morning of its 2nd birthday a complete two year old cube. Similarly, on the eve of a two year old cube’s 3rd birthday it goes to bed as a two year old cube but wakes up on the morning of its 3rd birthday a complete three year old cube and so on. What are the patterns to this growth, if any, that will allow the parents of such cubes to plan for housing (space) and clothing (covering) their offspring? If so, what are these patterns that would be useful in making such predictions?*

Part 1: Growing Solids

Part 1: Growing Solids

Use either one or two centimetre cubes or multilink cubes to construct a series of “growing” cubes.

**Part 2: Growing Figures**

Use either square grid paper or square flip tiles to construct “growing” squares.

## Squares upon squares

Task Instruction

- What would case 100 look like? How many blocks would it have? How do you know?
- What does case 0 look like? How do you know?
- How many blocks would there be in case n? How do you know?

## Algebra Online Puzzle

**Find the value of each object in the puzzle by looking for mathematical relationships.**

The numbers represent the sum of the objects in each row or column.

The numbers represent the sum of the objects in each row or column.

## Always End With 1089

Add two number together and always end with 1089.

Here is How:

Here is How:

**Can you work out an algebraic formula to represent your thinking?**