Grade 9: 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.

Simultaneous equations are two equations sharing the same two variables, solved together to find the one pair of values that satisfies both. Linear inequalities are solved much like equations, with one extra rule when multiplying or dividing by a negative. Model the method clearly, thinking aloud:

• Start with simple simultaneous equations already set up for elimination, like x + y = 10 and x - y = 4, adding them to cancel y.
• Show that once one variable is found, substituting it back into either original equation finds the second.
• Extend to equations that need scaling first before a variable cancels, choosing whichever variable eliminates more simply.
• Introduce inequalities as 'solve like an equation', then add the one exception: flip the inequality sign when multiplying or dividing by a negative number.
• Have students verify simultaneous solutions by substituting into BOTH original equations, not just one.

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

• Solve x + y = 10 and x - y = 4
• Add the equations: 2x = 14, so x = 7
• Substitute into x + y = 10: 7 + y = 10, so y = 3

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:

• Substituting the found value into only one equation and assuming the answer is fully checked.
• Adding the equations when subtracting (or vice versa) would actually eliminate a variable.
• Forgetting to flip the inequality sign when multiplying or dividing both sides by a negative number.
• Treating an inequality's solution as a single value rather than a whole range of values.

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.