# 206. Seek a number pattern

So I’m all ready to teach a lesson recapping number patterns from the basics for a lower ability group … then a visitor to the Department arrives and asks if it’s okay if they observe my lesson. They’ve been told that there is usually something ‘off the wall’ happening in my room. Thanks … I think!

Well, I’m not one to disappoint. A little fun with the starter perhaps? The sun is shining and I’ve got whiteboards and chalk …

We’ve all seen fence panel number patterns. Here is a fence:

What can you see?

We discussed the pattern linking number of posts and spacers. We then represented the fence in colour coded symbols (yes, we have chalk in more than one colour!) and annotated it.

The class were then sent off to find their own patterns. They found repeating patterns and made notes on their whiteboards. Once they were happy with their work they could chalk it out.

This group looked at number of slats on a bench with number of benches.

They represented each bench as an ‘L’ and each slat with an ‘o’.

They worked out:
No of benches x 6 = No of slats

Other groups looked at number of windows & number of classrooms and number of benches & number of picnic tables.

We then went back to our quiet number pattern work in the classroom.

This task is easily adaptable for many aspects of number, including ratio and proportion.

# 125. View from … Pensthorpe

The Sandpit is currently in Norfolk and on a daytrip to Pensthorpe. In the ‘Wild Rootz’ adventure playground there is a bridge – except it’s not.

It’s a damped ‘see-saw’, which you can run up and down. This is great fun – people run from one end to the other and try to reach the end before it goes down, with a bump.

However, you can also use the principle of moments to try and balance the bridge. It took a bit of running up and down and fine tuning (bouncing), but we got the bridge balanced with five members of the family, age range: 84, weight range: wouldn’t be polite to say.

If you know somewhere near you, with a similar piece of equipment, this would be a brilliant way to demonstrate moments with a Sixth Form class. Obviously the calculations would be slightly out, due to the effect of the dampers, but it’s still fun – and a lot safer than piling a whole class on a see-saw.

# 80. Sunshine and constructions

Here is a quick consolidation/revision/application task for constructions, which involves very little preparation. If the sun isn’t shining you could always adapt this for indoors.

Equipment
Chunky chalk (look in your local pound shop)
String
Straight edge and tape measure or just a metre stick
Usual classroom textbook/notes

A company has sketched out a set of new signs and it is your job to accurately draw them without a protractor. The task is differentiated by sign design.

Sign 1
Made from a rectangle and two equilateral triangles.

Sign 2
Same as sign 1, but with a border of constant width

Sign 3
Made from a rectangle, an equilateral triangle and a right angled isosceles triangle.

Sign 4
Same as sign 3, with a border of constant width.

Skills used:
Constructing an equilateral triangle (1,2,3,4)
Constructing the locus of a moving point (2,4)
Bisecting an angle (3,4)
Constructing a perpendicular bisector (optional in all cases)

Activity
Once the signs are allocated, each group must present a plan to the teacher on how they will draw it. They may use their notes, textbooks and smartphones (if your school allows this).

When the groups are outside, they can easily increase their understanding by moving on to the next design or developing their own arrows.

Examples of work

Health Warning!
These signs, when viewed from the end, can look rather like rockets. All I will say is:
rockets + construction arcs + pink chalk + teenager boys’ level of humour= ….

# 32. SimCon: one set of cards, four games

This activity started as a simple card game to assess if pupils knew the difference between Similarity and Congruence. It’s grown into four tasks appropriate for small groups or whole classes, whether it is sunny or rainy.

Aim
To identify when simple shapes are similar and when they are congruent.

Equipment
Two identical sets of cards, either playing card size or A3/4. The cards can be downloaded in pdf or Word format here.

Mini-whiteboards (optional)
Chalk (optional)

Game 1: Snap
Using a set of playing cards, pairs or small groups of pupils play snap. Usual rules apply, with a twist. Instead of shouting ‘Snap’, you shout ‘Similar’ or ‘Congruent’. If you get it right, you win the cards. If you get it wrong, your opponent gets the cards.

Game 2: Find a …
Each pupil is given a card. The teacher says ‘Congruent’ and they must find a partner who is congruent to them. The teacher checks the pairs.

The pupils swap cards with their partner and the game restarts. The teacher continues to say congruent or similar until everyone has tried out a variety of shapes.

Game 3: Quiet cards
The teacher has two stacks of shuffled A4 cards at the front and the pupils have whiteboards. The teacher holds up two cards and the pupils secretly write down ‘Similar’, ‘Congruent’ or ‘Neither’. The class then share their results.

Variation: If a pupil gets it wrong, their whiteboard is taken away. The winner is the last pupil with a whiteboard.

Game 4: Loud cards
This works on a similar principle to quiet cards, except you are outside and louder.

Using chalk, allocate an area for each of the three answers. When the teacher holds up a pair of cards the pupils walk* to the correct answer. Pupils can be eliminated in a similar way to Game 4.

*Disclaimer: You know they are going to be running to their answers.

# 14. JDs Tree Diagram

My friend JD came up with this visual way of explaining tree diagrams. I’m reproducing it here with permission (Thanks!). It helps if you have a school uniform with a tie and jumper, however this could easily be done with coats and hats.

Set Up
You need 6 volunteers, dressed as listed:
1. (No jumper, no tie) x 2
2. (No jumper, tie) x 2
3. Jumper, tie
4. Jumper, no tie

(This can be adapted for listing multiple outcomes too)

Activity
Draw a V shape on the ground.
Explain that in the morning you have choices when you get dressed. Each branch represents a choice.
Choice 1: Do you put your tie on or not?
Get a student wearing a tie to stand at the end of one branch and one without a tie to stand at the end of the other

Draw a V from each student.
Choice 2: Do you put your jumper on or not?
Get the class to decide who stands where

Discussion
If all the choices are equally likely, what is the probability of getting in trouble with your teacher over uniform?
Can you prove this by looking at the probabilities of the individual events?
What would happen if the outcomes were not equally likely?

It’s a good idea to try and take a picture of what this looks like to display in class. You could also annotate it with fractions and overall probabilities.

# 3. Class Averages

This is my favourite activity for introducing different measures of average. You can do this in a corridor or outside, no special equipment required.

Set Up
Line up the class in height order

Range
Ask the shortest and tallest students to stand back to back. The difference in height is the range.

Median
Tell the first and last student to make a half turn. Ask the second and second to last student to make a half turn. Repeat until only one or two students are facing forward.
One pupil = median height.
Two pupils = halfway between their heights is the median.

Mean
Imagine everyone is the same height. Tell the students to try to be the same height by bending knees or standing on tiptoes. Explain the mean is about sharing out equally.

Mode
Ask students to put themselves into groups of the same height. The biggest group is the mode.

This activity links a numerical calculation with a physical activity, which makes it more memorable.