Algebra begins as a way of saying what stays the same while something grows. This unit starts with patterns you can build and count, then gives them a language: a letter for a number that can change, a rule that jumps to any term, and a way to simplify what you write. It finishes by running machines backwards and balancing equations, so an unknown number can be found and checked.
Every idea is something you can move: add a frame to a row and count the canes, change the number in every bag, sort terms into kinds, run a machine in both directions, take the same amount from both sides of a balance. No calculator is needed anywhere in this unit.
The lessons, in order
- Lesson 1 · Growing patterns A pattern as a diagram, a table, words and a rule; the core of a repeating pattern; linear patterns and patterns that are not linear. Add one square at a time and count the canes, then compare six patterns by the gaps between neighbours. No calculator
- Lesson 2 · Letters and expressions A letter as a number that can vary, 7h as 7 times h, translating between words and expressions, and substituting a value. Change the number in each bag and watch the total, then run the same two steps in both orders. No calculator
- Lesson 3 · Term-to-term and position rules Term-to-term rules and position rules for linear patterns, finding any term, and deciding whether a number is in a sequence. Change the first term and the step to see both rules, then test whether a number is a term of the sequence. No calculator
- Lesson 4 · Collecting like terms Like terms, collecting them to simplify an expression with one or two letters and numbers, and checking by substitution. Sort the terms into kinds and combine each kind, then test the short form against the original with numbers. No calculator
- Lesson 5 · Function machines One- and two-step function machines, the rule as an expression, the inverse of each step and running a machine backwards. Run a two-step machine and swap its steps, then run it backwards from the output to find the input. No calculator
- Lesson 6 · Solving simple equations One-step and two-step equations of the form x + b = c, ax = c and ax + b = c, balancing both sides, and checking by substitution. Solve ax + b = c with bars that stay balanced, then test guesses until both sides match. 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.