Grade 7: 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 function rule like y = mx + c connects an input (x) to an output (y). This unit covers evaluating a rule at a given x, finding the rule from a table of values, and reading a real-world rate directly from a graph or description. Model the method clearly, thinking aloud:

• Start with evaluating a given rule (substitute x, follow the order of operations) before working backward to find a rule.
• To find a rule from a table, show how y changes for each step in x (the gradient m), then read off y when x = 0 (the constant c).
• Connect function tables to real contexts (a tank filling, a taxi fare) so the gradient has a real meaning (a rate).
• Practise reading a rate directly from a worded description: total change divided by total time (or other input).
• Plot a few (x, y) pairs from a table on the Cartesian plane to connect the numeric table to its graph.

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

• A rule is y = 4x - 3. Find y when x = 5
• y = 4(5) - 3 = 20 - 3 = 17

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 x incorrectly into the rule, e.g. forgetting the order of operations (multiply before subtract).
• Finding the gradient by looking at y-values alone, without checking that x increases by exactly 1 each row.
• Confusing the gradient (rate of change) with the constant (starting value, where x = 0).
• Reading a rate from a graph using two points that are not both clearly on the line.

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.