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* *Reflection: Grappling with Complexity
Translating Expressions - Section 2: Investigation

*translating_expressions_video_narrative_investigation.MOV*

*Grappling with Complexity: Translating Expressions*

# Translating Expressions

Lesson 3 of 15

## Objective: SWBAT translate an algebraic expression into an English sentence.

## Big Idea: Successful mathematics students can use the vocabulary of mathematics to explain their ideas.

*40 minutes*

#### Opening

*10 min*

This opening activity should be completed by students with their partners. While students are working make note of which students are having difficulty with the first set of questions under #1. Students who are struggling in this portion of the lesson may have difficulty in the investigation portion.

**What to watch out for: **Questions "1b" and "1c" are typically the most difficult for students because they often will not see that the entire quantity (4+n) is being multiplied or divided by 5 respectively. During both this lesson and the following lesson, students will solidify that understanding. In order to help students achieve this objective, you can prompt them to explore expressions using numerical values. For example, working with the expression "Add a number to 4 and then multiply by 5", a student can pick a number like 2, add it to 4 to get 6, and then multiply by 5 to get 30. Then, they can use a calculator to evaluate 4+2 * 5 into a calculator and discuss why the result is 14 and not 30.

In question #2 students will have to work with their partner to critique the mathematical equations that are given to them. This error analysis will help students to meet mathematical practice 3. When the students are finished with the warmup, I like to get a sense of how the class did on question #2. I use a non-verbal cue activity by having students hold up a thumbs up if the equation is true and a thumbs down if the equation is false for each of the three equations in #2. This does not show me the specific misunderstandings, but it is helpful to have a general sense about where the class stands.

I will plan to collect this opening activity once students have completed it. I will use it as a pre-assessment. The items in question #1 will be investigated more deeply in today's lesson. The items in question #2 will appear in the next days lesson. Having a good idea which students are struggling with these concepts ahead of time enables me to prepare for the next day's discussion more effectively.

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#### Investigation

*25 min*

This is the first part of a two day lesson on looking at expressions from multiple perspectives including algebraic, written language, tables, and area models. Students are given the cut-out cards for both the algebraic representations and the written version from Translating_Expressions. I will explain to students that their task is to match each expression with the verbal description of that expression. However, I will also warn students that not all cards have a match. If a card does not have a match, then they need to make either an algebraic expression to match the words or write the words to match an algebraic expression.

**Teacher's Note:** Students will need to make word cards to match E10 and E12. They will also need to make expression cards to match W3 and W10.

This task requires students to discuss their thinking and reason abstractly (MP2) about the information contained on each card and how to represent that information in written form. Once students have found their matches they should put a paper clip on them and return them so that they can be used in the next lesson.

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#### Closure

*5 min*

Each student takes out a half piece of paper for this Ticket out the Door. I ask students to look at the matches that they made with their partner and individually choose one that they feel would be the most difficult match for another student to make. Once they write down the expression and the verbal description, ask them to write 2-3 sentences explaining why this was the most difficult expression in their opinion. Remind students to cite specific examples from the expression and verbal description when writing their explanation.

#### Resources

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- LESSON 1: Understanding Expressions
- LESSON 2: More with Expressions
- LESSON 3: Translating Expressions
- LESSON 4: Connecting Expressions to Area
- LESSON 5: Equivalent Expressions: Distributive Property
- LESSON 6: Investigating Properties using expressions
- LESSON 7: True & False Equations (Day 1 of 2)
- LESSON 8: True & False Equations (Day 2 of 2)
- LESSON 9: Solution Sets to Equations/Inequalities
- LESSON 10: Solving Equations
- LESSON 11: Solving and Justifying Equations
- LESSON 12: CAUTION: Equation Solving Ahead
- LESSON 13: Solving Linear Inequalities: Addition and Subtraction
- LESSON 14: Solving Linear Inequalities: Multiplication and Division
- LESSON 15: Compound Inequalities