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MathematicsMathsHigh schoolKey Stages 4 and 5

How to help every student write inequalities from choices they'd make

Each student picks something they'd pay for every month. Sparky turns it into two plans and a spreadsheet, and the student writes the inequality that says which plan is cheaper.

Jemel Fanfan

Jemel Fanfan | Founding Member at Flint

Title card reading 'How to help every student write inequalities from choices they'd make', next to three students' cards from a linear inequalities activity built around a gym, music lessons and a game pass.

"I saw engagement in a high school math classroom like never before. My students look at this AI platform as a safe place to ask a personalized question that they did not necessarily feel like asking out loud or have the time to ask me personally."

Thomas YatesThomas Yates, High School Math Teacher at Graded - The American School of São Paulo

Why this matters

A student who can solve 15 + 5v = 40 can still write the inequality pointing the wrong way, or count the tie as a win. Few students will ask out loud whether 5 belongs in the answer. On a worksheet the mistake looks like a right answer, and the teacher has to wait for quiz day to find out.

Marcus picks a gym plan and writes the inequality that proves it

Every student in the class gets the same activity: compare two monthly plans, then write and solve the inequality that says when one is cheaper. The plans, the numbers and every question after the first come from the student's own chat. Marcus is a made-up 9th grader, and this chat is an example we wrote for this page from two test runs of the activity.

Sparky uses what Marcus would pay forSparky answers what Marcus just wrote
M

Marcus

Interest: Club soccer, training at a gymStarting point: Solves two-step equations, treats < like =

Sparky

Today you'll pick between two monthly plans and write the math that proves which one is cheaper. First, what's something you'd pay for every month, like a gym, a game pass or music lessons?

Marcus

A gym. I play club soccer and I want to train more in the off season.

Sparky

Gym training for soccer it is. Plan A is $40 a month with unlimited visits. Plan B is $15 a month plus $5 a visit. Change any number in the Visits column and both costs update. Which plan is cheaper when you go only a few times, and which is cheaper when you go a lot?
A spreadsheet Sparky made in the chat with three columns: Visits from 0 to 7, Plan A Cost at 40 in every row, and Plan B Cost rising by 5 from 15. The Plan B cell for 5 visits is selected and shows 40, the same as Plan A.
SpreadsheetGym Plan Comparison

Marcus

Plan B is cheaper if I go less. Like at 4 visits it's 35 bucks. At 6 visits Plan A is cheaper.

Understanding check

Exactly right. Can you write an inequality that shows when Plan B is cheaper than Plan A? Use v for the number of visits.

Marcus

15 + 5v > 40 so v < 5

Sparky

Check the sign in your first line. Your inequality says Plan B costs more than Plan A. Which plan did you want to show is cheaper?

Marcus

oh Plan B. so 15 + 5v < 40. from the table I think it's v ≤ 5

Sparky

15 + 5v < 40 is right. Now solve it. And look at the row for 5 visits in the spreadsheet. Are the two plans different there?

Marcus

5v < 25 so v < 5. at 5 visits they're both 40 so plan B isn't cheaper there. so it's v < 5 not ≤

Understanding check

That's right: Plan B is cheaper for fewer than 5 visits, and at 5 they tie. Here's a harder one. Your budget for the gym is at most $50 a month. Write an inequality for Plan B that shows how many visits you can afford.

Marcus

15 + 5v ≤ 50. 5v ≤ 35 so v ≤ 7. I can go 7 times a month

Sparky

Correct. With $50 a month, you can go to the gym up to 7 times on Plan B.

Fixed the sign himself, then solved the $50 budget with ≤

What Flint did for Marcus

  • Sparky built both plans around the gym Marcus said he'd pay for, so the numbers meant something to him.
  • Sparky made a spreadsheet whose formulas recalculate, so Marcus could check any number of visits himself.
  • When Marcus wrote the inequality the wrong way, Sparky asked which plan it said was cheaper instead of fixing it.
  • When Marcus guessed v ≤ 5 from the table, Sparky sent him back to the 5-visit row, where both plans cost $40.
  • Once he got it right, Sparky gave him a harder question with a budget and ≤.

A teacher can't build 30 sets of plans and watch 30 inequalities as they're written. Sparky does it in every student's chat.

See which students still treat < like =

Each student's chat shows up on the activity page as they work. Activity analytics sums up what the class did well and which mistake to practice next.

Flint's activity page for an activity called Which Plan Is Cheaper? Write the Inequality. Needs attention shows a live alert that one student wrote that they don't get which way the sign goes and stopped answering. Activity analytics lists what the class does well, an area of improvement where 7 students included the tie in their answer, and a follow-up with a button to create a follow-up activity. The Sessions table shows two submitted students and one still in progress.

Example activity page

After an Algebra 1 class finishes the plans activity

The school and students are made up for this page. In this example, most of the class found where the cheaper plan switches, and the mistake to practice is counting the tie as cheaper.

Set up the activity for free

The plans activity is in Flint's public library, with Sparky's role, guidelines, greeting and greeting suggestions already written. Open it, select Try this activity to copy it into a free Flint account, and move it to a class. Every student gets their own chat with Sparky, and the activity page fills in as they work.

In the activity settings, select Try session myself to test the activity as a student before you assign it. Add a rubric and Sparky grades each chat for you.

For another Algebra 1 activity, see how to give every student a personal tutor. For more math activities, see Flint for math.

Start the activity for free

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