Sign In | Starter Of The Day | Tablesmaster | Fun Maths | Maths Map | Topics | More

- "Show that" with number
- "Show that" with algebra
- "Show that" with shape
- "Show that" with angles
- "Show that" with data
- "Show that" with congruent triangles

For higher-attaining pupils:

- "Show that" with vectors
- Formal proof with congruent triangles

This page should remember your ticks from one visit to the next for a period of time. It does this by using Local Storage so the information is saved only on the computer you are working on right now.

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.

- Mix and Math Determine the nature of adding, subtracting and multiplying numbers with specific properties.
- Identity, Equation or Formula? Arrange the given statements in groups to show whether they are identities, equations or formulae.
- Prison Cell Problem A number patterns investigation involving prisoners and prison guards.
- Linear Programming A selection of linear programming questions with an interactive graph plotting tool.
- Recurring Decimals Change recurring decimals into their corresponding fractions and vica versa.
- Proof of Circle Theorems Arrange the stages of the proofs for the standard circle theorems in the correct order.
- Satisfaction This is quite a challenging number grouping puzzle requiring a knowledge of prime, square and triangular numbers.
- Comparing Graphs Would you recognise a misleading graph if you saw one? Try this comparative judgement exercise to rate statistical graphs.
- Delightfully Divisible Arrange the digits one to nine to make a number which is divisible in the way described.

Here are some exam-style questions on this topic:

- "
*State whether each of the following statements is true or false. Give reasons for your answers.*" ... more - "
*One is added to the product of two consecutive positive even numbers. Show that the result is a square number.*" ... more - "
*(a) Give a reason why 0 is an even number.*" ... more - "
*Betsy thinks that \((3x)^2\) is always greater than or equal to \(3x\).*" ... more - "
*Given that \(n\) can be any integer such that \(n \gt 1\), prove that \(n^2 + 3n\) is even.*" ... more - "
*Use algebra to prove that \(0.3\dot1\dot8 \times 0.\dot8\) is equal to \( \frac{28}{99} \).*" ... more - "
*The diagram shows a quadrilateral ABCD in which angle DAB equals angle CDA and AB = CD.*" ... more - "
*m and n are positive whole numbers with m > n*" ... more - "
*(a) Prove that the recurring decimal \(0.\dot2 \dot1\) has the value \(\frac{7}{33}\)*" ... more - "
*Express as a single fraction and simplify your answer.*" ... more - "
*(a) Prove that the product of two consecutive whole numbers is always even.*" ... more - "
*The number \(T\) can be expressed as \(T = 4k + 3\) where \(k\) is a positive integer.*" ... more - "
*Consider the sum of the squares of any two consecutive odd integers.*" ... more - "
*Prove that the integers \(a\) and \(b\) cannot both be odd if \(a^2+b^2\) is exactly divisible by 4.*" ... more

Here is an Advanced Starter on this statement:

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

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

How did the clock break if the numbers on each of the pieces added up to the same total?

A number placing puzzle which, when solved, raises the notion of proof.

To find out whether a number is happy or not, square each of its digits, add the answers and repeat. If you end up with 1 the number is happy! How many other happy numbers can you find?

Use the flowchart to generate a sequence of numbers. Which number will reach 1 the fastest?

How can you put the dice into the tins so that there is an odd number of dice in each tin?

If two squares overlap, what shapes can the overlapping region make?

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.