In this lesson, students will learn how to write and solve two-step equations for word problems. Students will review how to write two-step expressions. Then, they will expand on that expression to help them write and solve an equation. Students have a practice sheet for the first day. You can expect this lesson with additional practice to take two `45`-minute class periods.
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Modeling a situation through equations is a challenge for most students in middle school. Students at this age prefer to work with the concrete than the abstract. This lesson builds on the stage of student development and uses this to push towards a conceptual understanding. It also provides students with a way of thinking about writing equations.
We start off with a problem that is rooted in the concrete - no variables, no expressions or equations; just numbers. For most students, this is accessible.
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Most students would have answered these questions with a number. Let students explain how they found the total amount of money spent. Ask students what they did each time to help them find the new amount. Encourage students to write an expression for each question to represent the total, such as `3(15) + 20`. From there, pose an additional question: “How much money did she spend if each sweater cost `x` dollars?”
Some students will be baffled with this question - How can we find how much she spent if we don’t know the cost of one sweater. Some students in the class would be able to explain using the expressions we wrote for the warm-up that we are following the same pattern, except now we are putting a variable instead of a number. Discuss what the variable means and why it is useful to write an expression like this. Help them think of this as a rule - that the moment we know the value of the variable, we can find the value of the expression.
Once students have an expression to help represent the scenario, give them the total amount of money that was actually spent. Remind students that they already have an expression to represent the total amount she spent if needed.
Typically, before this you would have reviewed solving equations with positive coefficients and constants. Always encourage students to write an answer sentence using their answer from the equation. Checking answers when students have written the equation themselves is tricky - if you have written a wrong equation, checking your answer by substituting will not tell you that. Writing an answer sentence is like a common sense check to see if it sounds right.
This next example is similar to the previous example, where students can find the hypothetical amount of money spent if the cost of each shirt was known to help them write an expression for the total amount spent. You may want to confirm that your students understand a store credit makes her cost go down.
With the scaffolding, students should be able to write and solve the equation to find the value of `x`. It can also help to reiterate the importance of understanding what the variable means in context, so encourage students to explain what their answer means.
Give students a copy of the Student Practice sheet to continue practicing writing two-step equations. This should be the final activity for the first day.
Review students’ work from the Student Practice sheet to help refresh students’ memories on the processes they used to help them write and solve an equation. Make sure students understand how they can write an equation for the challenge problem.
Once students have recalled the processes they previously used, allow students time to work on the online practice.
After you’ve completed the examples with the whole class, it’s time for some independent practice! ByteLearn gives you access to tons of practice problems for writing and solving two-step equations for word problems. Check out the online practice and assign to your students for classwork and/or homework!
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