There are 6 people in a room.

Prove that there is a group of at least 3 people who:

(a) know each other; or

(b) don't know each other.

Here's the solution, in video form:

Came across this question when working with a teacher who's never taught Decision Maths at A Level before. It's a bit of a stinker, and the explanation of the solution takes some doing, too.

Here's the solution, in video form:

There are 6 people in a room.

Prove that there is a group of at least 3 people who:

(a) know each other; or

(b) don't know each other.

Here's the solution, in video form:

Topics:
A Level,
D1,
Decision Maths,
Graph Theory,
Video

I haven't been using the Fruit Machine site I posted about anywhere near enough with my classes lately.

But I'm going to use it today with Year 8, as a bingo activity for converting decimals and fractions to percentages.

I'm going to try this using 4x4 answer grids, in teams, and give team points for correct answers as well as a bumper bonus for getting a line first, but you can of course do it however you like, and doesn't need to exclusively be a bingo activity.

But I'm going to use it today with Year 8, as a bingo activity for converting decimals and fractions to percentages.

I'm going to try this using 4x4 answer grids, in teams, and give team points for correct answers as well as a bumper bonus for getting a line first, but you can of course do it however you like, and doesn't need to exclusively be a bingo activity.

Topics:
Bingo,
Decimal Conversions,
Decimals,
Fraction Conversions,
Fractions,
Fruit Machine,
Games,
Grade D,
Grade E,
Level 5,
Level 6,
Percentage Conversions,
Percentages

There was a part of one of the Royal Institute's Maths lectures a few years ago based around this.

On 15th January 1995, just 2 months after the National Lottery began, 133 people had to share the jackpot and won "only" £120,000 each. This SMART Board Notebook file is about why so many people picked that particular set of six numbers, and why the human brain isn't so good about at making random selections.

It doesn't focus on any particular skill that's on the National Curriculum.

It's just interesting.

You could make it a bit more exciting by holding a draw to see how well the students do with the "random" numbers they pick.

**Being Random and The National Lottery**

On 15th January 1995, just 2 months after the National Lottery began, 133 people had to share the jackpot and won "only" £120,000 each. This SMART Board Notebook file is about why so many people picked that particular set of six numbers, and why the human brain isn't so good about at making random selections.

It doesn't focus on any particular skill that's on the National Curriculum.

It's just interesting.

You could make it a bit more exciting by holding a draw to see how well the students do with the "random" numbers they pick.

I've just been looking for some Probability investigations I can use with my Y7 classes whom I only see once a week, and found a pretty good set on the TES Resources website. I think I'll need to revise it a bit as the instructions are a bit wordy for a lot of my kids, but it looks like a nice activity.

I will aim to post up my extra bits and pieces for it here.

You need to be registered on the website to access it, but that's pretty straightforward to do. Here is the link:

**KS3 Maths Investigations**

Contents:

I will aim to post up my extra bits and pieces for it here.

You need to be registered on the website to access it, but that's pretty straightforward to do. Here is the link:

Contents:

- Square Rectangles (Area & Perimeter)
- Pocket Money (Handling Data)
- Consecutive Numbers (Positive & Negative Numbers)
- Polyominoes (Compound Shapes)
- Easy Winnings (Probability)
- Sequences

Topics:
2D Shapes,
Applications of Maths,
Area,
Data Collection,
Data Handling,
Functional Skills,
Investigations,
Negative Numbers,
Number,
Perimeter,
Probability,
Sequences,
Shapes,
Statistics

This is a very simple game that took me quite a long time to make; it would have been a lot easier if Microsoft Powerpoint had the ability to make an action button that takes you to a random slide.

Students simply guesstimate the percentage of the circle shaded, and then click to see the answer. Click on a red, amber or green button to be taken to another question.

The idea is simply to give students an idea of what percentages look like. I'll be playing it throwing a soft ball to whichever student I want to answer. I may well throw in a timed element too - see how much they can score in 2 minutes.

I'm sure it would make a good starter for any class who respond to this sort of activity.

What's The Percentage?

Students simply guesstimate the percentage of the circle shaded, and then click to see the answer. Click on a red, amber or green button to be taken to another question.

The idea is simply to give students an idea of what percentages look like. I'll be playing it throwing a soft ball to whichever student I want to answer. I may well throw in a timed element too - see how much they can score in 2 minutes.

I'm sure it would make a good starter for any class who respond to this sort of activity.

What's The Percentage?

Topics:
Arithmetic,
Estimating,
Games,
Grade F,
Grade G,
Level 3,
Level 4,
Number,
Percentages,
Plenaries,
Proportion,
Starters

This is an excellent video from the equally excellent TED site.

Art Benjamin squares some (very large) numbers in his head and explains how he breaks the problem down in his head. The way he does it links to how (x+y)^{2} is multiplied out. At a lower level you can show what he's doing using the grid method.

Direct Link

Direct Link

Topics:
Arithmetic,
Brackets,
Expanding Brackets,
Fun,
Grid Method,
Multiplication,
Number,
Quadratic Expressions,
Square Numbers,
Talks,
Video

I'm trying this as a way to introduce the idea that there is a rule that will tell you the __position__ of the median in a list of numbers. I'm going to use it as a SMARTBoard resource and give the first page out as a worksheet. Tomorrow I'm going to use it as a starter but it could make a plenary exercise at the end of an introductory lesson on the median.

Finding the median:

PDF Worksheet | SMART Notebook file

Finding the median:

PDF Worksheet | SMART Notebook file

Topics:
Averages,
Data Handling,
Grade E,
Grade F,
Level 4,
Level 5,
Median,
Plenaries,
SMART Board,
Starters,
Statistics,
Worksheets

We've been doing linear graphs with our Year 8 group. I don't want to make a big thing of being able to draw linear graphs without a table at this stage, but I do want them to notice that the numbers in the equation reappear as features of the line they draw.

My first attempt at this lesson left them a bit lost - I left it too open ended and they didn't really know what they were working towards. I also didn't have any values in the tables for the equation, and most of them weren't confident enough to come up with their own values.

I've now done a new worksheet on a SMART Notebook file, and exported it to PDF for printing/those of you not using SMARTBoards. It leads them through the process much more closely so tomorrow I shouldn't be swamped with students who don't get it, and I can focus on the (hopefully) smaller number who need my assistance.

There is actually*no mention* of the words 'gradient' or 'y-intercept' in the worksheet but I *will* certainly mention those terms to selected students, and possibly the whole class if they seem happy enough.

Linear graphs - introducing gradient and y-intercept (without actually mentioning those words):

PDF Worksheets | SMART Notebook file

My first attempt at this lesson left them a bit lost - I left it too open ended and they didn't really know what they were working towards. I also didn't have any values in the tables for the equation, and most of them weren't confident enough to come up with their own values.

I've now done a new worksheet on a SMART Notebook file, and exported it to PDF for printing/those of you not using SMARTBoards. It leads them through the process much more closely so tomorrow I shouldn't be swamped with students who don't get it, and I can focus on the (hopefully) smaller number who need my assistance.

There is actually

Linear graphs - introducing gradient and y-intercept (without actually mentioning those words):

PDF Worksheets | SMART Notebook file

Topics:
Algebra,
Grade C,
Grade D,
Grade E,
Gradient,
Graphs,
Level 5,
Level 6,
Level 7,
Linear Graphs,
SMART Board,
Straight Line Graphs,
Worksheets,
y-intercept

Something my top set Year 9 class struggled with when I presented it to them the other day. Hopefully this should fix it.

Backwards Mean Questions

__Learning Objective:__ To be able to work backwards in problems when you are given the mean and have to work out other values.

This powerpoint file shows you how to work out the following problems:

__Example 1 (“Missing Value”): __

Jessica goes fishing. She catches 5 fish.

Their mean weight is 1.6 kg.

The weights of the first 4 fish (in kg) are:

1.5, 1.2, 0.9, 1.9

**What is the weight of the fifth fish?**

__Example 2 (“New Mean”):__

Mohibullah is taking some exams.

After his first 4 exams, his mean score is 79%.

In his fifth exam, he scores 64%.

**What is his new mean score?**

Backwards Mean Questions

This powerpoint file shows you how to work out the following problems:

Jessica goes fishing. She catches 5 fish.

Their mean weight is 1.6 kg.

The weights of the first 4 fish (in kg) are:

1.5, 1.2, 0.9, 1.9

Mohibullah is taking some exams.

After his first 4 exams, his mean score is 79%.

In his fifth exam, he scores 64%.

Topics:
Averages,
Backwards Problems,
Data Handling,
Grade C,
Grade D,
Level 6,
Level 7,
Mean,
Powerpoint,
Statistics

I'm going to use this in the coming couple of weeks with my Year 9 and 10 classes. I hope it explains finding averages from frequency tables quite well.

Averages from Frequency Tables

__Learning objectives:__

ALL: Understand a method for finding the mode and median from a frequency table [L5] [E]

MOST: Find the median from a frequency table without converting the table to a list [L5] [D]

SOME: Work out a quick way to find the mean from a frequency table [L6] [D]

Averages from Frequency Tables

ALL: Understand a method for finding the mode and median from a frequency table [L5] [E]

MOST: Find the median from a frequency table without converting the table to a list [L5] [D]

SOME: Work out a quick way to find the mean from a frequency table [L6] [D]

Topics:
Averages,
Data Handling,
Frequency,
Frequency Tables,
Grade C,
Grade D,
Grade E,
Level 5,
Level 6,
Level 7,
Mean,
Median,
Mode,
Powerpoint,
Statistics

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