## Problems for Direct Instruction and Active Note-taking - Section 4: Direct Instruction and Active Note-taking - Creating and Solving Equations

*Problems for Direct Instruction and Active Note-taking*

*Problems for Direct Instruction and Active Note-taking*

# Introduction to Linear Equations and Inequalities in One Variable

Lesson 1 of 10

## Objective: SWBAT... 1. Define key vocabulary terms for the unit. 2. Solve equations and inequalities in one variable.

Earlier in the year we reviewed the Mathematical Practices (MPs). I framed MPs to my students as tools that expert mathematicians and thinkers use all the time. For today's Entry Ticket I ask students to create a visual representation of one of the Mathematical Practices. Students can work in pairs if they would like and I provide colored pencils, construction paper, and other art supplies for the activity. The reason for this activity is that I want to provide opportunities for students to use their visual and artistic intelligence capabilities to present their current thinking about an important learning objective of this Algebra class visible.

Since this is the first lesson in a unit, I also want to remind students of the MPs and provide some momentum for developing them as we make sense of the forthcoming strand of topics. For sure, I want students to get the message that the MPs are not just a another list of skills or ideas posted on the classroom wall. They are a set of tools that are relevant and useful for every unit in this course, and, important habits of mind throughout their lives!

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Next, I have students work independently on the **Vocabulary: Solving Equations and Inequalities in One Variable** introduced during this unit. I explicitly teach students the difference between **brick words **and **mortar words.**

I believe students need to be taught what types of conversation and language are valued in school AND how to engage in those skills.

During this section, students work on iPad Minis using a math dictionary to look up the definitions for the terms. As an alternative, students could use an online math dictionary. I recommend Wolfram Alpha as it provides excellent knowledge, is accurate and also provides good visual examples for many terms.

**Instructional Note**: With some classes, I might choose to provide students with the definitions of the words (see: Vocabulary: Solving Equations and Inequalities in One Variable (with definitions) to allow students to focus more on generating multiple representations of meaning for each word to develop a deeper understanding of the vocabulary terms. I have included two versions of the vocabulary for teachers - one with definitions and one without.

Today, as the students wrap up, I have students file the work in a vocabulary section of their notebook and remind them vocabulary is part of the **Notebook Check**. We will be using the vocabulary later in the unit for a writing exercise on creating their own functions.

**Technology Note**: The use of iPad Miinis is supported by a technology grant for Modeling with Mathematics and Universal Design for Learning in the Math Classroom.

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To gauge student understanding entering the unit, I give students a short Pre-test: Solving and Graphing Inequalities. I find that giving a pre-test allows me to better compare student understanding pre/post instruction. I prefer doing this analysis at the unit level. I find it gives a broader picture of learning and retention than a short quiz or entry/exit ticket. It is also more focused than an end of year summative assessment.

Students may get frustrated during the pre-test. I encourage students to persevere and do the best they can. This Pre-Test is a good opportunity to practice test-taking strategies for multiple choice items (looking to see if they can figure out any answer that is wrong and reduce possible answer choices from 4 to 3 for example). I plan to make recommendations like this to my students to encourage them to make full use of the opportunities the Pre-test affords.

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During the next section of class we work on creating equations from word problems, and, how to solve the problems. The Problems are relatively straightforward since this is the introductory lesson to the unit.

The way I structure this section is I have students take out their notebooks and take **2 Column Notes **on the problems we solve together as a class. Students can write the steps/work on the left column of their notes and then jot down explanations and strategies in the right column to create a nice reference on how to create equations from word problems and also how to solve equations in one variable.

I like to put the first couple of problems from the worksheet (resource in this section) on the projector and hold off on giving the worksheets to students until the end of class. The reason for this is I want students focused on taking comprehensive note on a few problems rather than rush ahead and simply get the answers to a wider number of problems.

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#### Exit Ticket and Homework

*10 min*

For the remaining 10 minutes of class I pass out the worksheet on Creating and Solving Equations from Word Problems. I remind students that we already completed the first few problems as a class (see previous section) and they can use their notes to complete the first few problems (another incentive for students to take good notes - if they followed along the first few problems of the homework should be a piece of cake!).

The homework is to complete the worksheet - I like to remind students that I am not only looking for them to get answers, but to document the thinking process and strategies they are using to solve the problems. I give half credit for the correct answers and half credit for showing the work to symbolize the importance of showing their thinking!

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- UNIT 1: Thinking Like a Mathematician: Modeling with Functions
- UNIT 2: Its Not Always a Straight Answer: Linear Equations and Inequalities in 1 Variable
- UNIT 3: Everything is Relative: Linear Functions
- UNIT 4: Making Informed Decisions with Systems of Equations
- UNIT 5: Exponential Functions
- UNIT 6: Operations on Polynomials
- UNIT 7: Interpret and Build Quadratic Functions and Equations
- UNIT 8: Our City Statistics: Who We Are and Where We are Going

- LESSON 1: Introduction to Linear Equations and Inequalities in One Variable
- LESSON 2: Solving and Proving Equations with One Unknown
- LESSON 3: Solving and Proving Multi-Step Equations with One Variable
- LESSON 4: Solving and Proving Linear Inequalities in One Variable
- LESSON 5: Manipulating Rational and Irrational Numbers
- LESSON 6: Solving and Proving Compound Inequalities
- LESSON 7: I Absolute(ly) Don't Care About Direction: Solving and Proving Absolute Value Equations and Inequalities
- LESSON 8: Estimation, Measurement and Significant Figures
- LESSON 9: Writing in Math Classroom, Part 1: Functions and Linear Functions
- LESSON 10: Unit Assessment: Linear Equations in 1 Variable