Activity 1: Toothpicks

- Copy the design below with cotton tips:
- How many triangles in each shape?
- What is the number of toothpicks needed to make each shape?
- How many diagonals in each shape?
- What question could have been asked to get a number pattern like 1, 1, 2, 2, 3, 3, … from the design?

Activity 2: Picture Frames

Look at the squares below. The first three have been done for you. In your maths books, complete up to square 6 and complete the table below.

Look at the squares below. The first three have been done for you. In your maths books, complete up to square 6 and complete the table below.

Activity 3: Toothpicks 2

Construct a table similar to the table in the activity 2 (picture frames) to record your information.

Ask: Would your partner be able to predict the number of toothpicks for any shape position using your rule? Why?

- Write a rule to say how the number of toothpicks changes with each new shape.
- In your own words, write a rule which connects the position number of the shape to the number of toothpicks.
- Exchange rules with a partner and use their rule to find the number of toothpicks in the next few shapes. Ask: Did the rule work? Use the toothpick pattern to explain why their rule works.

Ask: Would your partner be able to predict the number of toothpicks for any shape position using your rule? Why?

A group of eight adults and two children want to cross a river. Their boat can hold just one adult or up to two children, but not an adult and a child together. Everyone can row the boat. What is the minimum number of one-way trips needed for all to cross the river?

Create your own grid to test other early finishers

## Extension - Fibonacci and Phi

Follow the link HERE and watch the video that links the number Phi to the fibonacci sequence. Investigate this phenomenon and create a informative video or lesson that describes it.