# Maths activities

## Frogs

**Setting**: indoors or outdoors

**Equipment**: some large squares on the floor

**Staff**: one person to supervise

Ten people is ideal, but less or more is fine too. Divide the players into two clear teams of equal numbers (eg boys/girls, coloured tops etc).

The two teams face each other in a line, with one space between each person and one space between the two teams.

The aim is to swap the teams over. Players may move one at a time. Each player may either move forward one space into an empty space or they may jump over the player in front into an empty space (actually it may be easier to walk round!). If the space is not empty players cannot move.

This is a puzzle. The teams must work together to find out how to solve the puzzle.

If the teams cannot work it out, try again with fewer ‘frogs’ on each team.

Mathematically there is a relationship between the smallest number of moves needed to solve the puzzle and the number of frogs in each team. Practice with the puzzle until you are good enough to work out the rule.

## Outdoor Data

**Setting**: in the playground or in a sports hall

**Equipment**: laptop or graph calculator

**Staff**: one person to supervise

Use a graphical calculator (or a laptop) to log data from outdoor activities.

Set up interesting hypotheses, but take care to be sensitive to student sensibilities. For example there is no point saying boys are faster than girls – that is well known.

Set up comparisons eg:

- Boys compared to girls.
- Year 7 compared to year 8.
- Look for changes comparing a sequence of age groups eg Year 7, 8, 9 then 10.
- People who play for sports clubs compared to those who don’t.

With a graphing calculator, or suitable software on a laptop, charts can be drawn and suitable statistics calculated ‘in the field’. This will generate immediate discussion about the validity of the conclusions and a restatement of the hypothesis.

You could measure and chart the following:

### Fitness

A good measure of fitness is difference in pulse rate after exercise. A neat way of measuring this is to get students to count their pulse for 30 seconds, then run on the spot for 30 seconds, then measure their pulse again.

Take the difference between the two counts as an indicator of fitness.

### Speed

Use any running race of a known distance, eg 100 metres. Any athletics event can be used in the same way, eg jumping and throwing events.

### Voice projection

Students read out a list of numbers to a measuring team who move progressively further away. They note the last distance at which the number can be clearly heard. The measuring team consists of two students, one who is recording the distances (say moving back in ten metre intervals) and who has the same list of numbers as the student who is calling them out. The second member of the measuring team listen carefully at each point for the next number in the list.

Other physical prowess activities can be measured, such as maximum number or time to complete a given number of press-ups.

## Linking maths and sport

If you would like to set up an innovative and fun study support club that uses physical activity to link with, and reinforce, maths, download our free sports and maths miniguide.

## Papering

**Setting:** indoors

**Equipment:** paper and ruler or tape measure

**Staff:** one person to supervise

Split pupils into groups and give each group one sheet of A4 and a measuring tape/ruler.

Ask the groups to answer the following questions:

- How many pieces of A4 paper do you need to cover the floor of the room that you are in?
- How many would you need to cover the ceiling?
- How many would you need to cover the whole room including the windows, doors, and walls?
- What is the area of an A4 piece of paper in cm2?
- What is the total surface area of the room in a)cm2? b)m2?
- How many pieces of paper would you need to fill the room?

## Mind-bending maths!

**Setting**: anywhere

**Equipment:** 2 dice; a pack of cards

**Staff:** one person to supervise

### 1. Magic numbers

Follow the simple scripts (in italics) and you will astound your friends with your ‘telepathic’ ability.

There’s no magic involved – just maths!

*‘Throw two dice (don’t tell me their numbers).**Multiply the first number by 2 and then add 1.**Multiply by 5.**Add the number of the second dice.**Tell me your answer.’*

The mind reader now subtracts 5 and the digits tell him the numbers on the dice.

For example:

- The subject throws a 6 and a 3.
- 2 x 6 + 1 = 13
- 13 x 5 = 65
- 65 + 3 = 68

The subject tells the mind reader that the answer is 68.

The mind reader subtracts 5 and tells the subject that his dice scores were 6 and 3.

(This also works for the number of brothers and sisters you have or any two one digit numbers).

### 2. Magic card maths

*Choose a card from a pack**Add the next number up to it.**(Jack=11 Queen=12 King= 13)**Multiply by 5.**Using these suit codes:**clubs = 6,**diamonds = 7,**hearts = 8,**spades = 9*; a*dd the code to the answer**Tell me your answer.*

The mind reader now subtracts 5 and the first digit tells her the number of the card and the second the suit code.

For example: the seven of hearts is chosen

- 7 + 8 = 15
- 15 x 5 = 75
- 5 + 8 = 83

The mind reader now subtracts 5 to get 78. The card is the seven of hearts.

**Extension: **Use a formula to show how these tricks work.

Use a formula to show that the two methods are really exactly the same method.