Grade 6: Algebra

Warm up with a quick recall on the board. Build algebra from arithmetic: use a variable to stand for an unknown, write the situation as an expression or equation, then keep both sides balanced when solving and check by substituting the answer back in.

Early algebra uses a letter to stand for an unknown number, then finds its value. An equation like x + 5 = 12 is a balance: whatever you do to one side you must do to the other. Solving means undoing the operations around x using their inverses until x is alone. Model the method clearly, thinking aloud:

• Start with the balance idea using scales or a bar model, so an equation means both sides are equal, not 'work out the answer'.
• Begin with a missing number in a box (box + 5 = 12) before swapping the box for a letter.
• Teach inverse operations: addition undoes subtraction, multiplication undoes division. To solve x + 5 = 12, subtract 5 from both sides to get x = 7.
• Work steadily up to two steps: for 3x = 12 divide both sides by 3 to get x = 4, then combine with a plus or minus step.
• Always check by substituting the answer back into the original equation.

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 worksheet independently. Hand out the three difficulty levels below so every child works at the right stretch.

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

• Treating the equals sign as 'here comes the answer' rather than 'the two sides balance'.
• Changing one side of the equation without doing the same to the other.
• Using the same operation instead of its inverse (adding 5 again instead of subtracting it).
• Reading 3x as 3 followed by x rather than 3 multiplied by x.
• Treating the equals sign as 'work it out' rather than 'both sides are equal', dropping negative signs, and not applying an operation to every term.

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.