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A bit tricky!

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maths numeracy starter mathematics math topics teacher

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Advanced Lesson Starters and Online Activities

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A list of advanced Maths lesson starter activities and interactive exercises for students.

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Topics: Starter | Combinations | Probability

How did you use this starter? Can you suggest how teachers could present or develop this resource? Do you have any comments? It is always useful to receive feedback and helps make this free resource even more useful for Maths teachers anywhere in the world.
to enter your comments.

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Topics: Starter | Combinations | Probability How did you use this starter? Can you suggest how teachers could present or develop this resource? Do you have any comments? It is always useful to receive feedback and helps make this free resource even more useful for Maths teachers anywhere in the world.

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A Maths Starter of The Day

Topics: Starter | Probability

How did you use this starter? Can you suggest how teachers could present or develop this resource? Do you have any comments? It is always useful to receive feedback and helps make this free resource even more useful for Maths teachers anywhere in the world.
Click here to enter your comments.

If you don't have the time to provide feedback we'd really appreciate it if you could give this page a score! We are constantly improving and adding to these starters so it would be really helpful to know which ones are most useful. Simply click on a button below:

This starter has scored a mean of 3.1 out of 5 based on 302 votes.

Answers

Note to teacher: Doing this activity once with a class helps students develop strategies. It is only when they do this activity a second time that they will have the opportunity to practise those strategies. That is when the learning is consolidated. Click the button above to regenerate another version of this starter from random numbers.

Teacher, do your students have access to computers?
Do they have iPads or Laptops in Lessons?

Whether your students each have a TabletPC, a Surface or a Mac, this activity lends itself to eLearning (Engaged Learning).

Here a concise URL for a version of this page without the comments.
Transum.org/go/?Start=May19
Here is the URL which will take them to a related student activity.

Extension

Striped Sheep

The wool on each of these sheep is of two different colours.

What is the probability of two sheep being picked at random sharing a wool colour?

Your access to the majority of the Transum resources continues to be free but you can help support the continued growth of the website by doing your Amazon shopping using the links on this page. Below is an Amazon search box and some items chosen and recommended by Transum Mathematics to get you started.

Have you read Craig's book yet?

Craig Barton must surely be the voice of Mathematics teachers in the UK. His wonderful podcasts interviewing the industry experts have culminated in this wonderful book. As Craig says: "I genuinely believe I have never taught mathematics better, and my students have never learned more. I just wish I had known all of this twelve years ago..." more...

"How I wish I'd taught maths' is an extraordinary and important book. Part guide to research, part memoir, part survival handbook, it's a wonderfully accessible guide to the latest research on teaching mathematics, presented in a disarmingly honest and readable way. I know of no other book that presents as much usable research evidence on the dos and don'ts of mathematics teaching in such a clear and practical way. No matter how long you have been doing it, if you teach mathematics-from primary school to university-this book is for you." Dylan Wiliam, Emeritus Professor of Educational Assessment, UCL.

Casio Classwiz Calculator

There is currently a lot of talk about this new calculator being the best in its price range for use in the Maths classroom. The new ClassWiz features a high-resolution display making it easier to view numerical formulas and symbols but it isn't a graphical calculator as such (it has the capacity to draw graphs on your smart phone or tablet, via a scannable QR code and an app).

As well as basic spreadsheet mode and an equation solving feature you also get the ability to solve quadratic, cubic or quartic polynomial inequalities and the answer is given just as it should be written down, using the correct inequality symbols!

This calculator has a high-performance processor and twice the memory of previous models ensuring speedy operation and superior computational power. more...

Curriculum Reference

More Sheepish Activities

How accurately could you estimate the number of sheep in a field without counting them? If there were only five sheep in the field your estimate would probably be very accurate but if there were fifty how close do you think your estimate might be? In the first case your estimate would have probably been perfect while in the second case you are unlikely to get it absolutely correct. What is the cut off number, between five and fifty where your estimate starts to become less accurate?

There is a sheep counting activity here on the Transum website. Try your skills and work to improve them. What strategies could you use?

Have you ever tried herding sheep? Not easy is it? The online herding sheep activity is much easier than real life herding and has proved to be a great introduction to loci.

Here is a sheepish mathematical birthday card which can be downloaded and printed.

Finally, for the more advanced, there's a sheep-themed exam style question for you to try.

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Topics: Starter | Probability How did you use this starter? Can you suggest how teachers could present or develop this resource? Do you have any comments? It is always useful to receive feedback and helps make this free resource even more useful for Maths teachers anywhere in the world.

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How many different ways can 4 people stand in line for the bus stop?

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A Mathematics Lesson Starter Of The Day

Topics: Starter | Combinations | Investigations | Probability

How did you use this starter? Can you suggest how teachers could present or develop this resource? Do you have any comments? It is always useful to receive feedback and helps make this free resource even more useful for Maths teachers anywhere in the world.
Click here to enter your comments.

If you don't have the time to provide feedback we'd really appreciate it if you could give this page a score! We are constantly improving and adding to these starters so it would be really helpful to know which ones are most useful. Simply click on a button below:

This starter has scored a mean of 3.3 out of 5 based on 444 votes.

Answers

Teacher, do your students have access to computers?
Do they have iPads or Laptops in Lessons?

Whether your students each have a TabletPC, a Surface or a Mac, this activity lends itself to eLearning (Engaged Learning).

Here a concise URL for a version of this page without the comments.
Transum.org/go/?Start=March12
Here is the URL which will take them to the Systematic Listing activity.
Transum.org/go/?to=Listing

Extension activities

Here is a solution to this problem with at least one mistake.
Can you spot the mistake(s)?

In how many ways can 5, 10 or 100 people stand in line?

In how many different ways can the letters in the word Transum be arranged?

In how many different ways can the letters in the word Google be arranged?

Extension Answers

Curriculum Reference

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Topics: Starter | Combinations | Investigations | Probability How did you use this starter? Can you suggest how teachers could present or develop this resource? Do you have any comments? It is always useful to receive feedback and helps make this free resource even more useful for Maths teachers anywhere in the world.

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Marbles and Chance - Simple introduction

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Marbles and Chance - Simple introduction

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http://splash.abc.net.au/home#!/media/2119341/what-are-the-chances-

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Many events can't be predicted with total certainty. The best we can say is how likely they are to happen, using the idea of probability.

Tossing a Coin

When a coin is tossed, there are two possible outcomes:

Heads (H) or
Tails (T)

Also:

the probability of the coin landing H is ½

the probability of the coin landing T is ½

Throwing Dice

When a single die is thrown, there are six possible outcomes: 1, 2, 3, 4, 5, 6.

The probability of any one of them is

Probability

In general:

Probability of an event happening = Number of ways it can happen Total number of outcomes

Example: the chances of rolling a "4" with a die

Number of ways it can happen: 1 (there is only 1 face with a "4" on it)

Total number of outcomes: 6 (there are 6 faces altogether)

Example: there are 5 marbles in a bag: 4 are blue, and 1 is red. What is the probability that a blue marble gets picked?

Number of ways it can happen: 4 (there are 4 blues)

Total number of outcomes: 5 (there are 5 marbles in total)

Probability Line

We can show probability on a Probability Line:

Probability is always between 0 and 1

Probability is Just a Guide

Probability does not tell us exactly what will happen, it is just a guide

Example: toss a coin 100 times, how many Heads will come up?

Probability says that heads have a ½ chance, so we can expect 50 Heads.

But when we actually try it we might get 48 heads, or 55 heads ... or anything really, but in most cases it will be a number near 50.

Learn more at Probability Index.

Words

Some words have special meaning in Probability:

Experiment: a repeatable procedure with a set of possible results.

Example: Throwing dice

We can throw the dice again and again, so it is repeatable.

The set of possible results from any single throw is {1, 2, 3, 4, 5, 6}

Outcome: A possible result.

Example: "6" is one of the outcomes of a throw of a die.

Trial: A single performance of an experiment.

Example: I conducted a coin toss experiment. After 4 trials I got these results:

Three trials had the outcome "Head", and one trial had the outcome "Tail"

Sample Space: all the possible outcomes of an experiment.

Example: choosing a card from a deck

There are 52 cards in a deck (not including Jokers)

So the Sample Space is all 52 possible cards: {Ace of Hearts, 2 of Hearts, etc... }

The Sample Space is made up of Sample Points:

Sample Point: just one of the possible outcomes

Example: Deck of Cards

the 5 of Clubs is a sample point

the King of Hearts is a sample point

"King" is not a sample point. There are 4 Kings, so that is 4 different sample points.

Example: Throwing dice

There are 6 different sample points in that sample space.

Event: one or more outcomes of an experiment

Example Events:

An event can be just one outcome:

Getting a Tail when tossing a coin

Rolling a "5"

An event can include more than one outcome:

Choosing a "King" from a deck of cards (any of the 4 Kings)

Rolling an "even number" (2, 4 or 6)

Hey, let's use those words, so you get used to them:

Example: Alex wants to see how many times a "double" comes up when throwing 2 dice.

The Sample Space is all possible Outcomes (36 Sample Points):

The Event Alex is looking for is a "double", where both dice have the same number. It is made up of these 6 Sample Points:

{1,1} {2,2} {3,3} {4,4} {5,5} and {6,6}

These are Alex's Results:

After 100 Trials, Alex has 19 "double" Events ... is that close to what you would expect?

700, 701, 702, 1475, 1476, 1477, 2175, 2176, 2177, 2178

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Math explained in easy language, plus puzzles, games, quizzes, worksheets and a forum. For K-12 kids, teachers and parents.

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The BEST resource out there about Chance and Probability

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The BEST resource out there about Chance and Probability

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Specifically type in: http://splash.abc.net.au/home#!/topic/494566/chance-and-probability