Today is rung 5 of 5 on this topic
Systems of equations in real problems
Can do: Sets up and solves systems from word problems, choosing an efficient method.
Why it matters
Setting up the system is the actual skill; solving it is mechanical. Word-to-equation translation is where marks are lost.
What it looks like when it's wobbly
Can solve a given system but cannot construct one from a described situation.
⏱️ Two-minute check
"Tickets: adults $12, children $8. 200 tickets sold, $2,000 taken. How many of each?"
Solid looks like: The system set up correctly, then solved: 100 each.
The full activity for this topic · 25 minutes
Define Your Variables First
- 1Always start by writing what each variable stands for, in words, with units.
- 2Write one equation per constraint in the problem — usually a count and a total.
- 3Choose the method: substitution when a variable is already isolated, elimination otherwise.
- 4Check both equations with the answer, not just one.
- 5Sanity check against the story: can you sell −20 tickets?
If it's too hard
Two-equation problems with the variables defined for them.
If it's too easy
Mixture and rate problems, and systems of inequalities with a feasible region.
Say this
"Write down what x actually is, in words, with units. Half the errors die right there."