Solving and Setting Up Equations

Students learn how to solve an equation using the balance method and trial and improvement.  As learning progress they are taught how to form equations from known geometrical facts and real life problems.

This topic takes place in Term 4 of Year 10 and follows on from algebraic manipulation.


Solving and Setting Up Equations Lessons
4 Part Lesson
Solving Quadratics by Factorising
4 Part Lesson
Equations with Function Machines
4 Part Lesson
Equations with Fractions
4 Part Lesson
Equations with the Unknown on Both Sides
4 Part Lesson
Solving Equations

Additional Resources
Extended Learning
Function Machines
Extended Learning
Two-Step Equations
Extended Learning
Equations with Unknown on Both Sides
Problem Solving
Linear Equations
Revision
Function Machines
Revision
Solving Equations
Revision
Solving Equations with Fractions
Revision
Equations with the Unknown on Both Sides
Prerequisite Knowledge
  • use simple formulae
  • generate and describe linear number sequences
  • express missing number problems algebraically
  • find pairs of numbers that satisfy an equation with two unknowns
  • use and interpret algebraic notation
  • simplify and manipulate algebraic expressions by:
    • collecting like terms
    • multiplying a single term over a bracket
Success Criteria
  • Solve linear equations in one unknown algebraically (including those with the unknown on both sides of the equation)
  • Solve two simultaneous equations in two variables algebraically;
  • Find approximate solutions to simultaneous equations in two variables using a graph;
  • Translate simple situations or procedures into algebraic expressions or formulae; derive an equation (or two simultaneous equations), solve the equation(s) and interpret the solution.
Key Concepts
  • To solve an equation is to find the only value (or values) of the unknown that make the mathematical sentence correct.
  • For every unknown an equation is needed.
  • Students need to have a secure understanding of adding and subtracting with negatives when eliminating an unknown.
  • Coefficients need to be equal in magnitude to eliminate an unknown.
Common Misconceptions
  • Students can forget to apply the same operation to both sides of the equation therefore leaving it unbalanced.
  • Students often struggle knowing when to add or subtract the equations to eliminate the unknown. Review addition with negatives to address this.
  • Equations need to be aligned so that unknowns can be easily added or subtracted. If equations are not aligned students may add or subtract with non like variables.
  • Students often try to eliminate variables with their coefficients being equal

Mr Mathematics Blog

Volume of Similar Shapes

In this lesson, we learn about the length and volume scale factor of 3D shapes and the relationship between them.

Solving Simultaneous Equations by Substitution

How to solve simultaneous equations using the substitution method.

Using Box Plots to Interpret Sets of Data

How to compare datasets using box and whisker diagrams.