International Baccalaureate Mathematics

Syllabus Content 1.6

Simple deductive proof, numerical and algebraic; how to lay out a left-hand side to right-hand side (LHS to RHS) proof. The symbols and notation for equality and identity

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.

Identity, Equation or Formula? Arrange the given statements in groups to show whether they are identities, equations or formulae.

Satisfaction This is quite a challenging number grouping puzzle requiring a knowledge of prime, square and triangular numbers.

Here are some exam-style questions on this statement:

"Use algebra to prove that $0.3\dot1\dot8 \times 0.\dot8$ is equal to $ \frac{28}{99} $." ... more

"m and n are positive whole numbers with m > n" ... 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 two consecutive positive even numbers, $2n$ and $2n + 2$." ... more

See all these questions

Here is an Advanced Starter on this statement:

Two Equals One
What is wrong with the algebraic reasoning that shows that 2 = 1 ? more

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

Proof A mathematical proof is a sequence of statements that follow on logically from each other that shows that something is always true. Presenting many cases in which the statement holds is not enough for a proof, which must demonstrate that the statement is true in all possible cases.

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This video on Deduction is from Revision Village and is aimed at students taking the IB AA Maths Standard level course

Official Guidance, clarification and syllabus links:

Example: Show that $ \frac{1}{4} + \frac{1}{12} = \frac{1}{3} $. Show that the algebraic generalisation of this is $ \frac{1}{m+1} + \frac{1}{m^2+m} \equiv \frac{1}{m} $

LHS to RHS proofs require students to begin with the left-hand side expression and transform this using known algebraic steps into the expression on the right-hand side (or vice versa).

Example: Show that $ (x-3)^2+5 \equiv x^2-6x+14 $.

Students will be expected to show how they can check a result including a check of their own results.

Example, Show that the algebraic generalisation of the following is true.

$$ \frac{1}{m+1} + \frac{1}{m^2+m} \equiv \frac{1}{m} $$

Let's start by finding a common denominator for the left-hand side of the equation:

$$ \frac{1}{m+1} + \frac{1}{m(m+1)} $$ $$ \frac{m + 1}{m(m+1)} $$

Now, let's simplify the expression:

$$ \frac{1}{m} $$

It is now evident that the original equation:

$$ \frac{1}{m+1} + \frac{1}{m^2+m} \equiv \frac{1}{m} $$

Is generally true, as the left-hand side simplifies to $ \frac{1}{m} $.

Thus, the algebraic generalisation provided does hold true for all values of $ m $.

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International Baccalaureate Mathematics

Number and Algebra

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