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These are the Transum resources related to the statement: "Understand and use the structure of mathematical proof, proceeding from given assumptions through a series of logical steps to a conclusion; use methods of proof, including: proof by deduction, exhaustion and counter example.".

Here are some specific activities, investigations or visual aids we have picked out. 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.
- Area Maze Use your knowledge of rectangle areas to calculate the missing measurement of these composite diagrams.
- Numbasics A daily workout strengthening your ability to do the basic mathematical operations efficiently.
- Identity, Equation or Formula? Arrange the given statements in groups to show whether they are identities, equations or formulae.
- Vectors An online exercise on addition and subtraction of vectors, multiplication of vectors by a scalar, and diagrammatic representations of vectors.
- What Are They? An online exercise about sums, products, differences, ratios, square and prime numbers.
- Congruent Triangles Test your understanding of the criteria for congruence of triangles with this self-marking quiz.
- Angles Mixed Find the unknown angles by using the basic angle theorems.
- 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.
- Simultaneous Solutions Arrange the given pairs of simultaneous equations in groups to show whether they have no solution, one solution or infinite solutions.

Here are some exam-style questions on this statement:

- "
*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 - "
*(a) Show that \((2n + 1)^2 + (2n + 3)^2 = 8n^2 +16n + 10\) , where \(n \in \mathbb{Z} \)*" ... more

Here is an Advanced Starter on this statement:

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

Transum,

Saturday, August 17, 2019

"Here is a Starter for a lesson on proof:

Write down as many reasons you can think of that prove zero is an even number.

[Subscribers can find some of the ways that zero can be shown to be an even number here.]"

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