## Reflection: Grappling with Complexity The Ellipse (Day 3 of 3) - Section 2: General form of an Ellipse

On the Solving equations test my students struggled with question 2.  There were 2 main issues students had on this question. The first was working with the fraction and either finding a common denominator or multiplying both sides by the common denominator.

The other issue was multiplying binomials.  As we work on writing the standard form equation into general form on the example I am able to work again with the students over these  issues.  On page 2 of the resource you can see that I went to the side of the board to multiply the out the binomials.  Many students are still struggling with using shortcuts to multiply a the squared binomials. I let the students explain how to multiply and write the steps out.

Once the students have the binomial multiplied the next issue is distributing the constant. Again I write out each step so that the students see how to do the process.

Many times I have a student say I have another way to do the problem.  I have the students explain the method.  These students commonly share that (a+b)(a+b) has a middle term of 2ab.  We look at our work to show the class how that works.

Grappling with Complexity: Dealing with Algebra Misconceptions

# The Ellipse (Day 3 of 3)

Unit 5: Conics
Lesson 7 of 13

## Big Idea: How can I determine the equation is an ellipse by looking at the equation.

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Standards:
Subject(s):
Math, ellipse, conic sections, Conics
50 minutes

### Katharine Sparks

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