Level 5: Equations and linear relations

Algebra · level 5 of 8 · rough age 12-13 (a guide for parents; anyone can start anywhere)

In level 4 you solved equations with the letter on one side. In this level the equations grow up: brackets, the letter on both sides, fractions, and whole formulas to rearrange. Then algebra meets the real world. You describe a situation that changes at a steady rate with a table, a graph and an equation, solve inequalities with the full set of rules (including the famous sign flip), and turn stories into equations whose answers you check for sense.

Lesson	You will be able to
The distributive law	Expand \(3(x + 4)\) and \(-2(x - 5)\), explain why with an area picture, and take out a common factor
Equations with brackets and x on both sides	Solve \(5x - 3 = 2x + 9\), equations with brackets and equations with fractions, and spot equations with no solution or every solution
Rearranging formulas	Make any letter the subject: \(r\) in \(C = 2\pi r\), \(C\) in \(F = \tfrac{9}{5}C + 32\), \(t\) in \(v = u + at\)
Linear relations	Describe one situation with a table, a graph and an equation, and tell direct variation from partial variation
Solving inequalities	Solve two-step and compound inequalities like \(-3 < 2x + 1 \le 7\), explain the sign flip, and show the answer on a line
Modelling with equations	Turn a story into an equation, solve it, and check that the answer makes sense

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