Reflection: Rigor Equivalent Expressions - Section 3: Exploration

 

At first many of my students focused on superficial characteristics of the cards rather than on equivalence. For example some of my students put all the number lines in a group, all the addition in a group, and all the subtraction in a group. When I see this I know they are not attending to the meaning of equivalence. I don't know if this is because they aren't understanding the concept or because they have been accustomed to lower expectations that don't require thinking. If they have put all the number lines in one group I ask:

  • "what is the value of each one?"
  • "Are they all equal in value?"

When they say no, I tell them "if they are not equivalent they don't belong in the same category". That is usually enough to clarify the task.

Similarly, they may group all subtraction together or all addition.  Some may put together expressions like -3 + 5 and -3 - 5. In addition to the above questions I may also relate these to the context of hot and cold cubes and ask if adding positives is the same as adding negatives (or hot and cold cubes).

The key to asking questions like this is that you don't ONLY ask when they are wrong about something otherwise you give them hint just by asking. In other words you have to question their work when it's right as well. For example "you're telling me that subtracting positives is the same as adding negatives, is that true?"

  Getting beyond superficial characteristics
  Rigor: Getting beyond superficial characteristics
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Equivalent Expressions

Unit 4: Operations with Integers
Lesson 15 of 24

Objective: SWBAT explain why a single number line can represent both an addition and a subtraction problem.

Big Idea: Students will see that adding the opposite is equivalent to subtracting.

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Subject(s):
Math, Number Sense and Operations, Operations and Expressions, subtracting integers, Sorting Activity, Partner, collaborati, questioning, cognitive demand, rigor, complexities
  54 minutes
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