# Solving and Setting Up Equations

Scheme of work: GCSE Foundation: Year 10: Term 4: Solving and Setting Up Equations

#### 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

## Solving and Setting Up Equations Resources

### Mr Mathematics Blog

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Planes of Symmetry in 3D Shapes for Key Stage 3/GCSE students.

Use isometric paper for hands-on learning and enhanced understanding.

#### GCSE Trigonometry Skills & SOH CAH TOA Techniques

Master GCSE Math: Get key SOH-CAH-TOA tips, solve triangles accurately, and tackle area tasks. Ideal for students targeting grades 4-5.

#### Regions in the Complex Plane

Explore Regions in the Complex Plane with A-Level Further Maths: inequalities, Argand diagrams, and geometric interpretations.