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# Introduction to solving equations

Lesson 1 of 16

## Objective: SWBAT introduce solving equations in one variable

*75 minutes*

#### Warm-up

*10 min*

Each day, students complete a warm-up that usually consists of spiraling the previous day's material, in addition to older material. Warm-up problems also sometimes extend lessons that students have encountered before to more unfamiliar contexts.

In this lesson's warm-up, students are immediately pushed to apply an equation to a real-world context, and then to solve it. I purposely ask them to identify the equation BEFORE solving it to ensure that kids make the link between these two tasks, which are too often separated. I also push kids to ask how they would do it mentally, which then further solidifies the understanding of why we use inverse operations in general.

Early in the year, as this lesson is, I want to push the importance of understanding not only the right answer, but why each wrong answer is wrong. I love the second part of this task, which pushes kids to explain why each is wrong. Students come up with good descriptions of why certain answer choices are wrong that demonstrate and develop strong conceptual understanding.

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#### Homework

*15 min*

The homework includes questions related to this lesson, as well as spiraled review. I also provide answers to the problems on page 2.

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*Responding to Edward Schmalz*

Edward - thanks so much for your kind words. I really appreciate it. I hope the lessons continue to be helpful.

It's my belief that a HUGE part of our job is to get kids to love math, love school, love the process of doing mathematics. And so I invest a lot of time and thought to how best to increase their engagement. Or as Jim Collins, author of Good to Great, puts it, "How do we get people to WANT to do what must be done?"

Thanks again, and hope all is well.

Best,

Jeff

| 2 years ago | Reply

This is great! I am very happy to have found this, I am a first year teacher struggling to make Math interesting and still hitting standards and I must say your lessons are well written, easy to understand and awesome!

| 2 years ago | Reply*Responding to Errol Van Stralen*

Errol - thanks so much for this thoughtful feedback! It is really helpful. I love the ideas you write about.

Hope you are well. I am glad this stuff has been somewhat helpful.

Jeff

| 2 years ago | Reply

Great intro to solving equations. The Enigma video really can kick off the "reverse PEMDAS" thinking.

I solve a simple problem (like starting with 2(7) - 4 = 10) to review the Order of Operations. Then I re-write the problem with x for the 7: 2(*x*) - 4 = 10.

I found that NOT doing the arithmetic on the 10 while isolating the *x* allows the students to see where the numbers 'go" when they are removed from the variable: x = (10+4)/2. *Then* use the regular order of Ops to simplify.

Also, I found The Return to Innocence video on Vimeo, where there is an mp4 download link for the video file. http://vimeo.com/23890777" href="http://vimeo.com/23890777" target="_blank" >http://vimeo.com/23890777">http://vimeo.com/23890777 .

| 2 years ago | Reply

Do you post your ppts? I'm interested in the progression of ideas. Lesson plan or set of directions for the lesson somewhere?

Thanks!

Lisa

| 2 years ago | Reply*expand comments*

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- UNIT 1: FLUENCIES AND THE LANGUAGE OF ALGEBRA
- UNIT 2: SOLVING LINEAR EQUATIONS
- UNIT 3: INTRODUCTION TO FUNCTIONS
- UNIT 4: INTERPRETING AND COMPARING LINEAR FUNCTIONS
- UNIT 5: SYSTEMS OF LINEAR EQUATIONS
- UNIT 6: EXPONENTS AND SCIENTIFIC NOTATION
- UNIT 7: PARALLEL LINES, TRANSVERSALS, AND TRIANGLES
- UNIT 8: CONGRUENCE AND SIMILARITY THROUGH TRANSFORMATIONS
- UNIT 9: PATTERNS OF ASSOCIATION IN BIVARIATE DATA
- UNIT 10: SLOPE REVISITED
- UNIT 11: VOLUME OF CYLINDERS, CONES, AND SPHERES
- UNIT 12: POLYNOMIALS AND FACTORING
- UNIT 13: QUADRATIC FUNCTIONS

- LESSON 1: Introduction to solving equations
- LESSON 2: Solving Equations- Distributive Property
- LESSON 3: Collect like terms first
- LESSON 4: Fractional coefficients
- LESSON 5: Variables on both sides (Day 1 of 2)
- LESSON 6: Variables on both sides (Day 2 of 2)
- LESSON 7: Assessment #2
- LESSON 8: Understand one, infinite, or no solutions (Part 1 of 2)
- LESSON 9: Understand one, infinite, or no solutions (Part 2 of 2)
- LESSON 10: Apply algebra to solve problems (Part 1 of 2)
- LESSON 11: Apply algebra to solve problems (Part 2 of 2)
- LESSON 12: Assessment #3
- LESSON 13: Equations with mixed numbers and fractions
- LESSON 14: Solve for a given variable (Part 1 of 2)
- LESSON 15: Solve for a given variable (Part 2 of 2)
- LESSON 16: Assessment #4