# Powers and roots

This collection of resources supports the teaching of powers and roots in secondary mathematics.

Here are some favourite activities selected by the NRICH team.

- Sticky Numbers Can you arrange the numbers 1 to 17 in a row so that each adjacent pair adds up to a square number?
- Generating Triples Sets of integers like 3, 4, 5 are called Pythagorean Triples, because they could be the lengths of the sides of a right-angled triangle. Can you find any more?
- Power Countdown In this twist on the well-known Countdown numbers game, use your knowledge of Powers and Roots to make a target.

These are just a few of the activities on Powers and Roots that you can find on the NRICH curriculum pages.

The activities below, taken from the STEM Learning website, complement the NRICH activities above.

### Powers and Roots

__Powe rs and Roots Pack One__

**Smile worksheet 2019** (pdf page 11) shows a set of twelve cards for a card sort where students need to pair up the cards and find an unknown.

__Powers and Roots Pack Two __

**Smile worksheet 2020** (pdf page 8) shows a set of twelve cards for a card sort where students need to pair up the cards and find an unknown. The highest power is three.

**Smile 1684** (pdf page 30) is an investigation into the remainders of power series when divided by ten. The investigation then introduces remainders when divided by seven.

**Smile 1637** (pdf page 34) is an investigation into the relationship between other positive integer powers and the difference between square numbers.

### Pythagoras' Theorem

This document has four ideas for investigating Pythagorean Triples and brief ideas for solutions. They are found at the end of page two and on page three.

The first investigation shows how the addition of recipricals of consecutive odd or consecutive even numbers leads to the smaller two numbers of a Pythagorean Triple.

The next three investigations look at the factors and product of numbers in Pythagorean Triples.

### Indices

This resource contains two interactive Excel files providing an introduction to indices, both positive and negative and also zero.

Students can explore products and quotients involving indices and evaluate numbers with fractional indices (positive and negative).

### Pythagoras' Theorem

This document has four ideas for investigating Pythagorean Triples and brief ideas for solutions. They are found at the end of page two and on page three.

The first investigation shows how the addition of recipricals of consecutive odd or consecutive even numbers leads to the smaller two numbers of a Pythagorean Triple.

The next three investigations look at the factors and product of numbers in Pythagorean Triples.

### Indices

This resource contains two interactive Excel files providing an introduction to indices, both positive and negative and also zero.

Students can explore products and quotients involving indices and evaluate numbers with fractional indices (positive and negative).

### Arthur Benjamin: the Magic of Fibonacci Numbers

This short video deals with the sum of the squares of Fibonacci Numbers. It may be viewed from about 1min 20sec. The explanation is clear and may be used with students to conclude the investigation.