## Mathematics Support Materials

### Mathematics snapshot: Summative assessment

Mathematics/ Number and Algebra/Linear and non-linear relationships and Patterns and algebra

Content Description Relevant aspects of the Achievement Standards

Solve problems involving linear equations, including those derived from formulas (ACMNA235)

Solve linear simultaneous equations, using algebraic and graphical techniques including using digital technology (ACMNA237)

Substitute values into formulas to determine an unknown (ACMNA234)

Students solve problems involving linear equations and inequalities. They find unknown values after substitution into formulas.

They solve pairs of…simultaneous equations.

Written test

### Purpose of the assessment

To gather summative evidence for reporting.

### Stage in the teaching sequence

End of a lesson sequence.

The following is an extract of a written test. Questions range in complexity from the application of basic skills through to solution of more complex non-routine problems.

Q1.

The rule below shows how to determine the cooking time (T), expressed in minutes given the mass (m) expressed in kilograms, for different cuts of meat.

Complete the table

T= 30m + 20

m (kg) 1 2 3 4 0.4 1.5
T (min)

Explain the meaning of the:

‘30’ in front of the variable above.

‘20’ which is in the rule.

Q2.

A plumber has a callout fee of \$98 and charges at a rate of \$80 per hour.

(a) Write an equation that a plumber can use to calculate how much he should charge clients.

(b) The total cost of a job was \$418. Use the equation from (a) to determine the numbers of hours the client was charged for.

Q3.

Kane and Luke each took money to spend at the Royal Show. Kane, who has a part-time job, took \$35 more than Luke. Between them, they spent all of their money which was \$257.

Let x represent the amount of money Kane spent and y the amount of money Luke spent.

(a) Write down two equations which represent the above information.

(b)Solve your equations in (a) to determine the amount of money Kane spent and the amount of money Luke spent at the Royal Show.

### Assessment process

Students were given a set time to provide written answers. The teacher marked the completed test and provided detailed feedback to students about the errors, recommendations for areas that required further work and setting goals for future work.

### Using the information

The results were recorded for grading and reporting.

It was evident from the results that only a few students could set up the simultaneous equations from the word problem and consequently she was not able to determine whether some students could actually perform the skill of solving simultaneous equations. She planned for further instruction and practice with solving simultaneous equations as well as translating word problems.