This is an activity where there are 4 systems story problems that each group will solve, but each group will get their "needed" level of support. For each story, there are the following supports.
• Identify the x & y variables and what they represent
• Write the two equations from the story
• Replace the "mx+b" into the standard form equation (without distributing)
• The standard form equation with the substitution AND distributed, but like terms not yet combined.
• Listed an answer as an ordered pair.
See the last page for an "answer key" to see a complete set of answers.
From there, you may determine what supports each group might need. These are meant to be "cards" where I can give each group JUST enough cards to help them successfully solve the problems.
High Groups--get the defined variables (but mixed up, so they have to sort it out). They would have 4 x= cards and 4 y= cards, with the variables clearly defined. This will just help them write useful equations given the story and to make sure their variables match what is expected. If, at any time, they get stuck, you can provide them the equations, the substituion, or the solutions as a self-check.
Middle Groups--get the defined variables (as above) and the 8 equations. Again, the 8 equations are all separated, so the students will still need to interpret the stories to "match" the stories to the correct equations. From there, they should be able to substitute and solve. If, at any time, they get stuck, you can provide them the substituion, or the solutions as a self-check.
Low groups--the ones that will need step-by-step guidance, or one-on-one support. These groups can get ALL of the information, if needed. One strategy is to HIGHLIGHT the mx+b in the original equations (what will be substituted) and highlight WHERE it is substituted into the standard form equations. Students in this group will still need to sort and solve, but have more steps along the way to get them there and help them see the process clearly. Many students can match everything except the answers with very little understanding, but the one on one support will push them to make sense of why everything “goes together.”
Every group will have the "extra cards" available, if needed, to support them with more details, or want to provide a support for them in self-checking.
Key words: Systems of equations, substitution, differentiated, story problems, real world, context, card sort, group work, MathCoachNat
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