MR. POLSKY
Help

Linear Relations

Patterns, equations and graphs—with your classroom resources in one clear place.

Know what achievement looks likeCBE Proficiency & Achievement Indicators
Read the achievement indicators here

Patterns and Relations · Model and solve problems using linear equations (PR2, N7)

Level 1

  • Solve simple equations by applying preservation of equality using concrete or pictorial representations.
  • Distinguish between an expression and an equation.
  • Evaluate an expression, given the value of the variable.

Level 2

  • Solve a variety of equations including integral values by applying preservation of equality using concrete or pictorial representations.
  • Verify the solution to an equation using substitution.
  • Write the equation for a simple problem, solve the equation and verify the solution.

Level 3

  • Use a symbolic approach to solve a variety of equations including integral values by applying preservation of equality and inverse operations.
  • Apply the distributive property to solve an equation.
  • Write the equation for a variety of problems, solve the equation and verify the solution.

Level 4

  • Apply preservation of equality, inverse operations and fluency with number to efficiently solve equations of all forms.
  • Write the equation for a complex problem, solve the equation and verify the solution.

Transcribed from the linked CBE indicator document. Practice summaries on this website are not proficiency marks.

Class Notes

Your unit, at a glance

Linear Relations lessons

Build an algebra foundation or go straight to graphs and equations. Each lesson brings together explanations, your notes, a working model, examples and practice.

01Patterns, variables & expressionsDefine a variable, distinguish an expression from an equation, and check a rule against a table.02Algebra tiles & equivalent expressionsRepresent signed terms, combine like terms, and explain why equivalent expressions have the same value.03Solving equations with balanceSolve equations of the form ax + b = c using inverse operations and verify the solution.04Equations with divisionSolve x ÷ a = b and x ÷ a + b = c, with a non-zero divisor, and verify the result.05The distributive propertyExpand expressions and use distribution to solve and check equations.06Tables, coordinates & graphsGenerate ordered pairs, plot them correctly and choose a meaningful graph for the context.07Rate of change & starting valueCalculate change in output per unit input and distinguish the rate from the starting value.08Writing a rule from evidenceIdentify m and b, define variables and verify a linear rule using known pairs.09Comparing plans & interpreting modelsCompare two linear cost models, locate a break-even point and state the limits of the comparison.

What are you curious about?

Search lessons, class notes and interesting questions.