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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.

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 - "
*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

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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