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.

Algebra starts by writing a worded rule as an expression using a variable, then substituting known values in to evaluate it, and finally solving an equation to find the unknown value that makes it true. Model the method clearly, thinking aloud:

• Start with translating simple worded phrases into expressions, one operation at a time ('5 more than n' before '5 more than double n').
• Teach substitution as replacing the variable with a number, then following the order of operations to evaluate.
• Introduce solving as 'undo the operations in reverse order', always doing the same thing to both sides.
• Insist every solution is checked by substituting it back into the original equation.
• Use real formulas (perimeter, cost, distance) so substitution and solving feel purposeful, not abstract.

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

• Solve 5n - 8 = 27
• Add 8 to both sides: 5n = 35
• Divide both sides by 5: n = 7
• Check: 5(7) - 8 = 35 - 8 = 27, correct

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:

• Reading '3 less than a number' as 3 - n instead of n - 3.
• Undoing operations in the same order they were applied, instead of reversing the order.
• Changing only one side of the equation instead of keeping both sides balanced.
• Skipping the order of operations when substituting (adding before multiplying).

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.