# MARS: Interpreting equations

The ‘Interpreting equations’ resource is a concept development lesson from the ‘Mathematics Assessment Resource Service’ (MARS). The resource is intended to help students connect algebraic equations to real-life situations. It also helps to uncover and address misconceptions concerning the meaning of variables in an equation.

The resource contains a formative assessment for students to complete sometime before the lesson. This is carefully structured to highlight any difficulties students are having with the topic. Detailed guidance is provided in the teacher notes regarding common issues that students have with these topics, together with suggested questions and prompts.

The lesson begins with the equation y = 4x and asks: ‘Which is greater, x or y? Why?’

Two possible responses are shown, and the intention is that these are discussed with the class. At this point, students may be concerned about the possibility of x and y being negative, when words like ‘greater’ can be ambiguous. If this is raised, then it can be made clear that in today’s lesson all of the variables will take positive values.

The next task is to let e be the number of eggs in a box, b be the number of boxes, and given that there are six eggs in a box, find an equation to link e and b.

The boy’s response is quite a common reaction to the task, with the reasoning being ‘a box equals six eggs’. The guidance notes suggest asking students for two numbers for e and b that would make sense e.g. e = 18 and b = 3 The next step is to ask students which equation do these numbers fit? Clearly here there will be 6 x 3 = 18 eggs, which matches the girl’s equation but not the boy’s.

A final whole group task is to consider a situation where e and b have been redefined. Here we let e be the cost of an egg, and let b be the cost of a box of eggs.

Students sometimes think this is the same question as previously, so a prompt to look and see ‘what is the same here, and what is different’ can be helpful. Once again, it can be helpful for students to write down values for e and b that make sense, and then to test these in the two equations.

The next task is for students to work on a collaborative activity, where worded situation cards must be matched with equations. An additional challenge is introduced through there being some blank cards where students must make up either an equation or a situation to match with cards that don’t pair up.

The final element of the resource is a formative assessment to use with students sometime after the lesson, in order to assess the progress made with the topics. To download the resource click the link below:

The Mathematics Assessment Resource Service (MARS) is a collaboration between the University of California at Berkeley and the Shell Centre team at the University of Nottingham, with support from the Bill and Melinda Gates Foundation. The team is known around the world for its innovative work in maths education. Previous projects that members of the team have worked on include the DfE Standards Units and the Bowland Maths resources.

# Mathematics Assessment Resource Service (MARS) collection

*Article written by Simon Jowett*