More with Expressions

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Objective

SWBAT reason about the quantitative value of an expression based on the individual parts of that expression.

Big Idea

Relate the size of the components of an expression in order to meaningfully understand the overall value of the expression.

Opening

10 minutes

This Opener Activity requires students to create meaning around the variables in an expression based on their context.  Students will need to make sense of the expression in terms of what the individual variables represent.  It is an important message to convey to your students that they may not understand the meaning of the whole expression after one read through and will need to persevere in trying to understand what the expression represents (MP1). I encourage my students to read each expression and each description of the variables several times. By being deliberate, they are able to construct a better understanding of what the expression represents as a whole.  

Launch

5 minutes

During the Opening Activity students were asked to make meaning about an expression based on the meaning of the individual variables in that expression.  The slides on Pages 2 and 3 of More with Expressions Launch get students thinking about the overall quantity represented by an expression based on the variables in that expression.

I developed Slide 2 because my students often look at an equation and don't give a thought to the structure  and meaning of the variables that make up that equation. So, I want to push them to engage more in MP7. This slide will get students thinking about how the components of an equation combine, rather than focusing completely on the whole.

I plan to have students do a Think-Pair-Share about the two questions on this slide.  Once students have had an opportunity to process the questions, I will guide the share out in order to make sure that the discussion focuses on how the structure of the equation creates meaning.

When we turn our attention to Slide 3, I will start by having students try to answer this individually.  After a few minutes I will use a non-verbal cue to review the answers. I will ask students to hold their hand on their desk and point a thumbs up to the right or left to indicate their choice of the larger expression.  Depending on the results of this quick survey, I may have students turn-and-talk to discuss the problem further.  If most students chose the correct expression, I will have one student share their thinking. If more students are interested in sharing, I will let them respond to or build on what they heard from the first student.  

Independent Practice

20 minutes

This Independent Practice gives students more opportunity to see how the structure of an expression can effect its overall quantity based on the individual variables it contains.  I will ask my students to work on this worksheet with a partner for 10 minutes.  Then, I will assign numbers to split the pairings (#1 and #2).  In each partnership, #1 will stay in their seats and all of the #2's will find another #1 to work with (this is my version of Stay and Stray). 

When students get into their new partnerships, I want them to take turns sharing their answers. I will circulate encouraging students to offer an explanation in support of an answer  and to listen to their partner's ideas and suggestions (MP3).  I will also encourage Student #2 in each group to try to take one interesting explanation back to share with their original partner. 

 

Teaching Note: If necessary, I am prepared to explain to students that this activity is not about telling the other person which expression their group chose.  They should be explaining WHY they chose the expression, citing specific reasons to back up their choices.  Their partner can either:

  1. Agree and say what they liked about the explanation they heard
  2. Agree and offer a different explanation
  3. Disagree and explain why and offer their thinking as to why the other expression should have been chosen.

Closure

5 minutes

Today's closing allows for some creativity: More with Expressions Close. When I distribute the task, I will explain to students that their answer for the second portion of the question will depend on the story that they write.

In students' writing, I will be able to discern if they understand the meaning of the expression. I share some final observations in the following video:

More with Expressions Closure