Reflection: Letters & Postcards, Day 2 of 2 - Section 3: Choose Your Own Adventure


When students are given a condition like “There may be at most three widgets for every grommet.”  they almost universally write the inequality incorrectly as 3w < g.  I've found that it's very difficult to help them see the error in this.  I suggest thinking about it without the equation; for instance, if you make 5 grommets, how many widgets can you make? Remember, you can have up to 3 widgets for every grommet. 

When the student answers, “15 widgets”, I then say, “Okay, that means that 5 grommets and 15 widgets should satisfy the condition.  But 3w < g is false if w = 15 and g = 5.  What’s wrong?” 

I also try asking them which is the smaller quantity, g or w.  It would make sense to multiply the smaller number by 3 to obtain an equality.  This is hard to understand because in this context we're really dealing with an inequality.

I'll have to think about this misconception some more, because at this point I'm not sure how else to explain it!

  The most persistent error
  The most persistent error
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Letters & Postcards, Day 2 of 2

Unit 1: Modeling with Algebra
Lesson 5 of 15

Objective: SWBAT write a system of linear inequalities and use the system to answer questions about balancing time and cost in a real world context. SWBAT explain their solutions to a modeling problem to their peers and respond to the explanations given by others.

Big Idea: Systems are useful mathematical models for situations with a several of constraints. Time is money!

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