Reflection: Discourse and Questioning Equivalent Line Segments - Section 2: Assignment Introduction: Equivalent Line Segments


The instruction at the top of this assignment says:

In each of the following diagrams, the length of line segment AB is equal to the length of line segment CD.  Your task is to find the length of the unknown line segment, labeled as x, in each diagram.

Every time a student a says they don't understand the assignment, I ask if they've read the instructions.  I help them notice the word "equal" in that first sentence, and I say, "What is equal to what?"  Then, we investigate the first problem.  "Where is line AB?" I ask.  They point to it.  "How about CD?" and, "How long is line segment CD?"  

It's clear that the length of CD is 25.  "So how about AB?" I ask.  They recognize that it is a combination of 18 and x, and I ask how we might express that.  The idea that it will be 18+x comes easily enough, and this is where kids suddenly recognize, "Oh!  X must be 7!" and want to move on from this problem.  Now, I have to slow them down a little: "Let's write this out, algebraically," I say.  

If we know that the lengths of these two segments are equal, and if we have algebraic expressions for each, then the equation follows from there, and it's easy enough for students to solve with confidence.  Once kids get that idea, they're rolling.  

  What Does and Equal Sign Mean, or, Did You Read the Instructions?
  Discourse and Questioning: What Does and Equal Sign Mean, or, Did You Read the Instructions?
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Equivalent Line Segments

Unit 6: Mini Unit: Patterns, Programs, and Math Without Words
Lesson 7 of 10

Objective: SWBAT construct linear equations in one or two variables, and translate between different representations of linear functions.

Big Idea: Students can see the limitations of the guess and check strategy as they use it to solve problems in one variable, and they can compare problems with one unknown to problems with two.

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