Working Backwards with Formulas - How do I undo a formula?

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Students will be able to determine unknown dimensions when given the area or circumference of a known figure.

Big Idea

It’s more fun to go in reverse, just ask Mater! This lesson requires students to manipulate formulas to solve for unknown values.


10 minutes

Opener:  As students enter the room, they will immediately begin working on the opener.  See my Instructional Strategy - Process for openers clip for more information on how I run openers! This portion of the lesson is a good way to incorporate mathematical practice 3, critiquing the reasoning of others.

Learning Target:  After completion of the opener, I will address the day’s learning targets to the students.  In today’s lesson, the intended target is, “I can determine unknown dimensions when given the area or circumference of a known figure.”   


30 minutes

Working Backwards with Formulas Notes:  I will begin the lesson by passing out the notes sheet, and drawing their attention to the first example problem.  The first example is a basic formula, and should pull from their prior knowledge of working with formulas in 6th grade.  I will ask that students discuss the question with their table groups, and raise their hand to share out only when they can share an equation – not just an answer.  During their discussion, I will walk around the room to hear the various conversations taking place.  I will take a volunteer to come to the board to work out the first example, and then I will ask that they discuss the next example, following the same procedures they used in the first example.  I again will monitor progress by listening in on table conversations, and will ask for another volunteer to work out the second example.  

Table Practice:  Following the second example, I will ask that tables work together to complete the remaining five example exercises – using their knowledge from the first two examples to guide them.  I will set the timer for 8 minutes, and then I will call on tables to work and verbally explain the problems at the board.  Students will need to pay close attention to precision, MP 6, when working backwards with formulas, as the incorrect inverse operation could lead them astray!


20 minutes

Instructional Strategy - How do table challenges work?As a way to assess student progress with the concepts learned this week, I will conduct a table challenge using the Smart Clickers. I will not be offering any assistance during this time, giving students an opportunity to grapple with the mathematics, MP 1. At the conclusion of the activity I will reward the top scoring group(s). Students will be regrouped for tomorrow’s lesson based on results and teacher observation during the clicker activity. After the clickers, I will summarize the lesson by posing the question, “How can I find unknown side lengths when given the area or circumference of a figure?” We will discuss as a group.