Systems Word Problems Scaffolded

Word problems are challenging for many students. Writing a system of equations to model a word problem has unique challenges. This post provides details about a scaffolded handout with color coding can unpack the process for generating the appropriate system of equations.

Unpacking the Word Problem

A mistake I have witnessed over the years is students mistakenly using given values for both equations. In the problem below, students are far more likely to generate the equation for the yellow part: 2x + 3y = 24. The challenge is that the blue part has only 1 number so students will often write 2x + 3y = 10, using the dollar quantities a second time.

By highlighting the two parts of the word problem with given values, the students can match parts of the word problem with respective equations. The scaffolding separates the parts, and the color allows for matching.

Solving

The rest of the problem is prior knowledge with the students using one of the methods for solving. The scaffolding continues to lower the task demand by reducing the need to remember all the steps. This allows them to focus more bandwidth on the new steps.

Access to Handout

Here is a link to the handout.

Intro to Systems of Equations: Camry vs Mustang Depreciation

The scatterplot above is an approach I use to introduce systems of equations. Here is the process I use. (Note: I have found that students like math associated with buying a car – relevant, real life application for them.)

  • In my class, students would have seen a scatterplot with mileage and price for a single car. I explain that we will now compare two cars.
  • To review, in a do now or initiation at the start of class I would have one group generate a scatterplot for the Toyota Camry data and the other groups, Mustang (Excel sheet for all of this note: this data is old). Then they would share with each other
  • We would revisit the relationship shown and revisit the idea of depreciation.
  • I show a Camry and Mustang and ask two questions: Which car do you think costs more brand new? Which do you think depreciates faster and why?
  • Then I show them the scatterplot above and ask which car has higher dots at the far left? Explain what this means (Mustangs start off with a higher price). Then I ask about the dots at the far right.
  • The students are then asked to estimate when the cars have approximately the same value.
  • Then I present scatterplot below, with lines of best fit (trend lines) and they are asked the same question. We estimate the specific mileage and price and write as an ordered pair.
  • Finally, I explain that this is known as a system of equations and the ordered pair is the THE solution. The entire unit will focus on finding an ordered pair as a solution.

Cat Chasing Mouse as System of Equations

 

 

 

 

 

This is a screen shot from explorelearning’s Gizmos. This site has various simulations related to science and math. This one shows multiple reprsentations for a system of equations. The site has 5 minute test trials which can be used to present a topic in class. I used the one for photosynthesis for a 7th grader with asperger’s who was collecting data for his science fair project.gizmo simulation of cat and mouse

 

Scaffolding Solving Systems by Graphing

intro to solving systems by graphing

The photo shows a snippet of a handout I use as a discovery activity for solving systems by graphing. It shows the use of color coding as well. I start the lesson with a do now handout  that reviews graphing, checking a solution for a system and previews a word problem modeled by a system.