Unit 4, Lesson 8
Solving Any Linear Equation
Accelerated 7
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This Math Talk focuses on solving equations with negative numbers. It encourages students to think about valid moves and to rely on what they know about creating equivalent equations to mentally solve problems. The understanding elicited here will be helpful later in the lesson when students solve equations in this lesson.
In describing their strategies, students need to be precise in their word choice and use of language (MP6).
Tell students to close their books or devices (or to keep them closed). Reveal one problem at a time. For each problem:
Keep all previous problems and work displayed throughout the talk.
Solve each equation mentally.
To involve more students in the conversation, consider asking as the students share their ideas:
Some students may reason about the value of
MLR2: Collect and Display
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In this activity, students select a number and follow a series of instructions to change their number into a surprising result. Students then follow the same series of instructions for a variable to reveal how the result was not surprising at all, but a natural consequence of the instructions. This helps illustrate valid moves that can be done to an equation.
Monitor for students who combine like terms as they go as well as those who do not.
Begin the activity by telling students not to communicate with one another until instructed to do so. This includes talking or showing each other what is on their papers.
Tell students to select a number and write it on the first line. Then follow the instructions to write the correct number on the next line. Continue filling in the blanks until all have been filled.
After all students have had a chance to complete all of the instructions, tell students to compare the number on the last blank with one another.
Ask students, “What do you notice about the final answers?” (Everyone got 3, regardless of their starting number.)
Demonstrate how to begin the next part of the activity. Write "
To see why this works, tell students to write "
Select students who combine like terms as they follow the instructions, as well as those who do not. Ask them to share later.
Use Collect and Display to direct attention to words collected and displayed from an earlier activity. Ask students to suggest ways to update the display: “Are there any new words or phrases that you would like to add?” “Is there any language you would like to revise or remove?” Encourage students to use the display as a reference.
Invite selected students to share their equations involving
Tell students that all of these equations are equivalent because these are valid moves done correctly. Ask students what moves they have seen that create equivalent equations. Direct students’ attention to the reference created using Collect and Display. Invite students to borrow language from the display as needed, and update the reference to include additional phrases as they respond. Update the display to create a semi-permanent display of these valid moves to remain available in the classroom until the end of the unit.
Give students 2–3 minutes to think about all the equations they solved in today’s lesson and to describe to a partner things that they need to be careful about in the future.
Explain to students that some mathematicians describe their moves by writing them next to the new equivalent equation. This makes it easier to both identify wrong moves and to make moves visible to everyone. For example, this pair of equivalent expressions could be written either of these ways.
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