Expressions in Geometry

 Today’s standard: CCSS.MATH.CONTENT.7.EE.B.4  Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.

 Our new topic builds on our previous unit: we are still working with geometric shapes so we will be able to use our knowledge of properties and formulas.  However, the main difference is that instead of working with only numbers, today we will also have variables. Therefore, our answers may be algebraic expressions instead of simply numbers.  Several of our upcoming lessons also focus on writing expressions and equations so today is an important introduction to them.

Objective  Students will be able to write algebraic expressions for finding perimeter and area of rectangles and explain how each term relates to the shape by extending their prior knowledge of solving these problems with only constants with 75% accuracy on Nearpod in the whole group lesson.  Think-pair-share:  What are you expected to be able to do by the end of the lesson?  How will you prove that you understand this?

Objective  What are you expected to be able to do by the end of the lesson?  How will you prove that you understand this?

 This is an example of a problem you are expected to be able to solve by the end of the lesson.  You do not actually need to solve the problem, but how comfortable with the problem do you currently feel? (1 is not confident at all and 10 is extremely confident.)

Follow-up questions for previous problem set  How do we know the values of the missing sides?  What is the definition of perimeter?  Why do we add together all the terms?  How is the third example, with a variable, related to the first two?

 In order to write algebraic expressions for the perimeter and area of rectangles, perform the same calculations you would do if everything was a number.  Be careful to follow the rules of only combining like terms with adding and subtracting.  A very common mistake is to try to combine unlike terms, such as thinking that 2 + 3x = 5x

Follow-up questions for previous problem set  What is the coefficient of the term n?  Why does area require multiplication?  What is the reason that the area of a triangle formula has a ½ in it?

 Remember, our objective is to get 75% of questions correct on Nearpod. How well do you think you are doing?

Direct Station  As we saw, there are usually several different ways to write expressions that are all correct.  At the direct station we will use the distributive property to help determine if two expressions are equal or not.  We will do practice problems on Educreations and everyone will keep track of their own points to see if they are getting 75% correct.

Independent Station  We could not have figured out all these expressions if we did not know the perimeter and area of rectangle formulas.  Therefore, we will review other formulas (Volume/Surface Area/Circles).  You will take a mini-quiz to help determine which topic to focus on. You will then go over the review materials posted for that topic and then take another short quiz to see if you have improved.