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- Work with organised lists Sample spaces and probability (review)
- Complete and use Venn diagrams (review)
- Construct and interpret plans and elevations (review)
- Use data to compare distributions (review)
- Interpreting scatter diagrams (review)

For higher-attaining pupils:

- Use the product rule for counting

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Here are some related resources in alphabetical order. Some may only be appropriate for high-attaining learners while others will be useful for those in need of support. Click anywhere in the grey area to access the resource.

- Venn Worksheet A collection of worksheets all related to the regions in Venn diagrams and the set notation describing them (answers included)
- Drawing 3D Objects Draw two-dimensional representations of three-dimensional objects on an isometric dotty grid.
- Graph Paper Flexible graph paper which can be printed or projected onto a white board as an effective visual aid.
- Hi-Low Predictions A version of the Play Your Cards Right TV show. Calculate the probabilities of cards being higher or lower.
- Net or Not Drag the nets into the corresponding panels to show whether they would fold to form a cube.
- Cube Face Meetings Visualise the cubes formed by the nets and paint the three faces meeting at a vertex.
- Cubical Net Challenge Find all the ways of painting the faces of cubes using only two colours.
- Coloured Cube 3D Colour in the remaining faces of the nets of the cubes to match the rotating three-dimensional picture.
- Predictive Survey An eight question survey collecting data for an amazing probability experiment.
- Cartoon Scatter Graph Place the cartoon characters on the scatter graph according to their height and age.
- Estimating Correlation Practise the skill of estimating the correlation of data on a scatter graph in this self marking exercise.
- Correlation Arrange the given statements in groups to show the type of correlation they have.
- Snail Race Projectable Twelve snails have a race based on the sum of two dice. This is the teachers' version of the race simulation.
- Plans and Elevations Interpret plans and elevations of three dimensional shapes.
- Human Scatter Graphs Pupils move to positions in the room according to their data relative to the walls as axes.
- Venn Totals Practise reading and creating Venn diagrams containing two and three sets and the number of elements in those sets.
- Dice Bingo Choose your own numbers for your bingo card. The caller uses two dice and adds the numbers together.
- Frequency Trees Use a frequency tree to show two or more events and the number of times they occurred.
- Venn Paint Video Here is a demonstration of how to illustrate union, intersection and complement of sets as they appear in Venn diagrams.
- Tree Diagrams Video Tree diagrams can be really helpful showing combinations of two or more events in order to calculate probabilities.
- Venn Paint Flood fill the regions of the Venn diagrams according to the given statements.
- Tree Diagrams Calculate the probability of independent and dependent combined events using tree diagrams.
- Plotting Scatter Graphs Plot scatter graphs from data representing a number of different everyday situations.
- Conditional Probability Find the probability of one event happening given that another event has already happened.

Here are some exam-style questions on this topic:

- "
*Ben measured the length and the width of each of 10 sea shells of the same type. The results are shown below.*" ... more - "
*The number of visitors to a cycle track and the number of drinks sold by a cafĂ© at the location are recorded in the table below.*" ... more - "
*The midnight train to Georgia is not the most reliable. The probability that the train will be late on any day is 0.35*" ... more - "
*180 pupils had some homework to do for the following day.*" ... more - "
*On centimetre squared or graph paper draw the front elevation, side elevation and plan view of this house using a scale of 1:100.*" ... more - "
*The scatter graph shows the maximum temperature (*" ... more^{o}C) and the number of bowls of soup sold at a sandwich shop on twelve randomly selected days last year. - "
*Carol has two fair 5-sided spinners. One spinner is pink and the other is green.*" ... more - "
*In the Bubbleless Bandits free-diving club, members practice breath-holding techniques as part of their routine.*" ... more - "
*The diagram shows the plan, front elevation and side elevation of a solid shape, drawn on a centimetre grid.*" ... more - "
*A driving test has two sections, practical(p) and theory(t). One day everyone who took the test passed at least one section. 77% passed the practical section and 81% passed the theory section.*" ... more - "
*The 37th Wolverhampton Sea Scouts make a game for a fund raising event.*" ... more - "
*The scatter graph gives information about the marks earned in a Statistic exam and a Mathematics exam by each of 13 students.*" ... more - "
*The Venn diagram represents a collection of 40 books on sale in an online store.*" ... more - "
*46 adults and 52 children visit a bowling alley.*" ... more - "
*At an international conference there were 300 delegates from both the northern and southern hemispheres. Each delegate wore a t-shirt in one of three different colours:*" ... more - "
*Sumville has three newspapers: The Chronicle, The Express and Moon, and The Scribe.*" ... more - "
*900 professional footballers were surveyed with the following results*" ... more - "
*Julie chooses a cake from a yellow box on a shelf. The box contains two chocolate cakes and three plain cakes. She eats the cake and chooses another one from the box. The tree diagram below represents the situation with the four possible outcomes where C stands for chocolate cake and P for plain cake.*" ... more - "
*In a survey of insect life near a stream, a student collected data about the number of different insect species \((y)\) that were found at different distances \((x)\) in metres from the stream.*" ... more - "
*The table below shows the scores for 12 students on two Mathematic exam papers. For the first paper calculators were allowed and for the second paper they were not.*" ... more - "
*Mathsland's national currency comes in denominations of 1 unit, 5 units, 10 units and 50 units. Sofya places this collection of these coins in her purse then, without looking, takes out two coins at random, one after the other.*" ... more

Here are some Advanced Starters on this statement:

**Bertrand's Box Paradox**

Bertrand's box paradox is a paradox of elementary probability theory, first posed by Joseph Bertrand in 1889 more**Other Child's Gender**

What is the probability that the other child is also a boy? more**Singers and Dancers**

What fraction of the singers and dancers are both singers and dancers? more**Tri-Junction**

A real life situation that can be analysed with the use of a tree diagram. more**Two Pots**

Use tree diagrams to find the surprising result that probabilities of different situations are the same. more**What Question?**

Write down all the possible questions that could have been asked if this was the Venn diagram provided in a mathematics exam. more

Click on a topic below for suggested lesson Starters, resources and activities from Transum.

- Combinations "A combination is a way of selecting several things out of a larger group, where (unlike permutations) order does not matter. In smaller cases it is possible to count the number of combinations. For example given three fruit, say an apple, orange and pear, there are three combinations of two that can be drawn from this set: an apple and a pear; an apple and an orange; or a pear and an orange." - Wikipedia In Primary school pupils should practise sorting and grouping items noting similarities and differences. They should develop strategies for finding all the ways a small number of items can be arranged so that missing or duplicates can be found quickly. By the end of Secondary school pupils will have learnt the formulas for combinations and permutations and apply them when solving probability problems.
- Probability Probability is a measure of the weight of evidence, and is arrived at through reasoning and inference. In simple terms it is a measure or estimation of likelihood of the occurrence of an event. The word probability comes from the Latin word probabilitas which is a measure of the authority of a witness in a legal case. Some of the earlier mathematical studies of probability were motivated by the desire to be more profitable when gambling. Today however the practical uses of probability theory go far beyond gambling and are used in many aspects of modern life. We believe that even adults can, in many cases, have a poor intuition regarding the effects of probability. These activities are designed to help pupils calculate but also get a 'feel' for the principles of probability.
- Shape (3D) A particular skill is required to be able to excel in this area of Mathematics. Spatial awareness is important for solving multi-step problems that arise in areas such as architecture, engineering, science, art, games, and everyday life. Children have varying abilities visualizing three dimensional relationships but these abilities can be developed through practical activities and working through mathematical problems. Breaking down three dimensional situations into smaller two dimensional parts in an important strategy for problem solving. See also the "Shape" Starters.
- Statistics Statistics is the study of the collection, organisation, analysis, interpretation and presentation of data. It deals with all aspects of data, including the planning of data collection in terms of the design of surveys and experiments. It also includes describing mathematical relationships between variables and presenting these to an audience in a way that best conveys meaning. See also the topics called Data Handling, Probability and Averages.

Here are some suggestions for whole-class, projectable resources which can be used at the beginnings of each lesson in this block.

In how many different ways might Tran decide to wear his hats in one week?

How many different ways can you make a given total with Thai coins?

In how many different ways can the first X and O by placed on the grid?

Some of the Starters above are to reinforce concepts learnt, others are to introduce new ideas while others are on unrelated topics designed for retrieval practice or and opportunity to develop problem-solving skills.