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Assessment Resource Centre (ARC)

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  1. Years 9-10
  2. Mathematics
  3. Activities
  4. Simultaneous Equations
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Simultaneous Equations


Grade Work Samples
End of Stage 5 (end of Year 10)
Grade B Frances(B8)   Jessie(B7)  

Description of activity

  1. Students will solve
    2. 3x + y = 17
    2x - y = 8
  2. How can students check their solution?
  3. How many different methods can students use to solve these simultaneous equations? Show these methods.

Context

Patterns and Algebra, Working Mathematically

This assessment activity could be presented to students at the end of a unit on Algebraic Techniques, where students have been solving simultaneous equations using non-algebraic and analytical methods.

Areas for Assessment

  • Working mathematically
    Knowledge, skills and understanding developed through inquiry, application of problem-solving strategies, communication, reasoning and reflection
  • Patterns and algebra
    Knowledge, skills and understanding in patterning, generalisation and algebraic reasoning

Outcomes

Algebraic Techniques (PAS5.2.2)
Solves linear and simple quadratic equations, solves linear inequalities and solves simultaneous equations using graphical and analytical methods

Applying Strategies (WMS5.2.2)
Selects and uses appropriate problem-solving strategies that include selecting and organising key information and identifying and working on related problems

Communicating (WMS5.2.3)
Uses appropriate mathematical language and algebraic, statistical and other notations and conventions in written, oral or graphical form

Reasoning (WMS5.2.4)
Uses mathematical arguments to reach and justify conclusions

Criteria for assessing learning

(These criteria would normally be communicated to students with the activity.)

Students will be assessed on their ability to:

  • solve simultaneous equations and check solutions
  • use a range of methods to solve simultaneous equations.

Possible prompts to assist student engagement

  • Could you use trial and error to find values for x and y that satisfy the equations?
  • How can you solve simultaneous equations?
  • Could you graph the two equations?

Suggested materials

Pen and paper, graph paper

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