Algebra lets you say something that stays true while a number changes. This unit starts with one idea in two directions: a number outside a bracket multiplies everything inside it, and taking out a common factor puts it back. Both come from an area you can cut in two.
Then it uses that to solve equations by keeping a balance, with brackets and with the unknown on both sides, and it finishes with inequalities, where the answer is not one number but a range, and where multiplying by a negative number turns the sign round. Each idea is something you can move: cut a rectangle, slide a common factor, remove the same piece from both bars, test a value against two answers.
No calculator is needed anywhere in this unit.
The lessons, in order
- Lesson 1 · Expanding brackets Expanding a single bracket with a positive or negative multiplier, simplifying after expanding, and testing whether two expressions are equivalent. Cut one rectangle into two and watch both areas agree, then see how far a tempting slip is off. No calculator
- Lesson 2 · Factorizing Factorizing a linear expression by taking out the highest common number factor, including a 1 left in the bracket, and checking by expanding. Split two terms into equal groups, then slide the number taken out to see which choice finishes the job. No calculator
- Lesson 3 · Solving equations by balancing Solving one-step to multi-step linear equations with brackets and negative coefficients, two routes for a bracket, and checking by substitution. Solve a bracket equation by dividing first, then by expanding first, and see both reach the same x. No calculator
- Lesson 4 · The unknown on both sides Solving linear equations with the unknown on both sides, including a bracket and a negative solution, and checking by substitution. Compare two plans at any number of gigabytes, then balance the same equation by removing x from both bars. No calculator
- Lesson 5 · Inequalities on a number line The four inequality symbols, graphing a solution on a number line, and solving one-step and two-step inequalities with a positive multiplier. Choose a symbol and a boundary to see its ray, then watch the same whole numbers stay true through each solving step. No calculator
- Lesson 6 · Multiplying or dividing by a negative Why the sign reverses when multiplying or dividing by a negative, solving linear inequalities with a negative coefficient, and checking with a test value. Apply an operation to two numbers and see when their order reverses, then test a solution against the reversed and unreversed answers. No calculator
Every lesson has a teacher page with the answers, the misconceptions each wrong answer reveals, discussion questions, differentiation and support for students learning in English, and extra questions in three tiers.