Reflection: Problem-based Approaches Introduction to systems of equations - Section 2: Investigation

 

The students did a really nice job finding the various combinations of coins in questions #1-5.  This year, I let students share out after question number 1 how they came up with their equations.  I had various students in the class explain to the rest of the class how to construct the equations to represent that particular situation.  

We also got into an interesting discussion when one student suggested using the equation 5x+y=11 rather than 0.05x+0.01y=.11.  I asked the students if they could show if these two equations were really the same.  After discussing it with their partners for a short amount of time, many students were able to see that one equation was a multiple of the other.  

Students did well with moving into the more abstract scenarios in questions 6 and 7.  They were able to use a similar line of reasoning to determine the correct combination of bills to give them the values.  As predicted, most students struggled with question #8.  Quite a few students were able to determine the missing values using trial and error but it did take some time.  The fact that the cost of a bag of chips was a decimal value (0.75) also slowed students down.  I noticed once again how uncomfortable many students are with decimals and how to reason about their quantities in calculations.

  Investigation-Reflection
  Problem-based Approaches: Investigation-Reflection
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Introduction to systems of equations

Unit 3: Systems of Equations
Lesson 1 of 13

Objective: Students will be able to set up a system of equations that can model a real world situation. Students will understand how the constraints of a system of linear equations leads to one simultaneous solution.

Big Idea: This lesson gives students a hands on approach to learning about systems of equations with something that they can all relate to...money! By placing constraints on the value of coins and the number of coins students see that there is only one way to meet

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Subject(s):
Math, Algebra, systems of equations, Constraint, 9th grade
  30 minutes
intro to systems image
 
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