Grade 10: Algebra

Warm up with a few quick algebra warm-ups on the board while the class settles, so every child starts thinking about the skill.

A quadratic expression has an x^2 term. Expanding two brackets into one quadratic, factorising a quadratic back into two brackets, and solving a quadratic equation by factorising are three connected skills, each the reverse of the last. Model the method clearly, thinking aloud:

• Teach expanding first: (x + a)(x + b) = x^2 + (a+b)x + ab, every term in one bracket times every term in the other.
• Show factorising as the reverse: for x^2 + Bx + C, find two numbers that ADD to B and MULTIPLY to C.
• Introduce solving only once factorising is secure: factorise, then set each bracket to zero separately (if AB = 0, then A = 0 or B = 0).
• Always check a factorisation by re-expanding it, and check a solution by substituting it back in.
• Keep to monic quadratics (coefficient of x^2 is 1) with whole-number roots until the pattern is fully secure.

Work this through step by step on the board, then have the class talk you through a second one.

• Factorise x^2 + 2x - 8
• Need two numbers that multiply to -8 and add to 2: 4 and -2
• So x^2 + 2x - 8 = (x + 4)(x - 2)
• Solve = 0: x + 4 = 0 gives x = -4; x - 2 = 0 gives x = 2

Do the first few questions of the practice worksheet together, one child explaining each step. Check for understanding before releasing the class to work alone.

Students complete the practice worksheet independently while you circulate and support.

Circulate and look for these, they are the usual sticking points:

• Mixing up which operation goes with which term: the two numbers ADD to the middle term, MULTIPLY to the constant.
• Reading (x + 3)(x + 4) = 0 as 'x = 3 and x = 4 at the same time' instead of 'x = -3 or x = -4'.
• Assuming every quadratic factorises into whole numbers, when many do not.
• Forgetting to check a factorisation by re-expanding it.

Pull the class back together. Ask one child to explain algebra in their own words, pose a single check question everyone answers on a mini whiteboard, and name what you will build on next lesson.

Use the independent worksheet as the evidence. A child who can complete it accurately and explain one answer has met the objective; anyone who cannot needs the easier level and a short reteach next session.