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MathematicsMathsMiddle schoolKey Stage 3

An expressions lesson where each student writes the rule for their own money

Every student writes a rule for their own savings and tests it in a spreadsheet. When the rule is wrong, Sparky asks a question that sends the student back to their own numbers.

Title card reading 'An expressions lesson where each student writes the rule for their own money', next to three cards: a student's rule 15 + 40w that gives $95 for 2 walks instead of $70, the spreadsheet Sparky filled down from that rule, and the fixed rule 40 + 15w.

"Students can just explore a passion topic of their choice and can go as deep into the knowledge as they can comprehend. This gives me a chance to see how they think, what motivates them to learn, and makes me know more about each of my students."

Oliver BernabeOliver Bernabe, Middle School Math Teacher at Shanghai American School

Why this matters

A middle schooler who saves $40 and earns $15 a walk can write 15 + 40w, try 1 walk, get $55, and decide the rule works. The same student can add before multiplying and get $165 for 3 walks instead of $85. Both mistakes look like right answers on a worksheet, and the teacher has to wait for quiz day to find out.

Jordan writes a rule for his dog-walking money

Jordan is a middle schooler who walks dogs. He knows a letter can stand for a number, but he hasn't written a rule from his own life before. Every student in the class gets the same task: write a rule for money they earn, test it in a spreadsheet, then add spending and a bonus. The situation, the numbers and the questions below are Jordan's own chat.

Sparky uses Jordan's interestSparky's next move depends on Jordan's last answer
J

Jordan

Interest: Walks dogsStarting point: Knows a letter can stand for a number

Sparky

Today you'll write a math rule for your own money and test it in a spreadsheet. How do you earn or save money?

Jordan

Walking dogs

Sparky

Let's say you have $40 saved, and you earn $15 for each dog walk. How much money will you have after 3 walks?

Jordan

40 + 15 = 55, then 55 x 3 = 165. So $165

Sparky

Got it, $165. Now write an expression for your savings after any number of walks, using a letter for the number of walks.

Jordan

15 + 40w

Sparky

Let's test it. I made you a spreadsheet. Click cell B2 and type your expression as a formula: start with =, and use A2 in place of w.

Jordan

I typed it in B2

Sparky

The formula is filled down. Look at 2 walks: it shows $95. Count your real money for 2 walks: $40 + $15 + $15 = ?
A spreadsheet in the chat named Dog Walking Savings. Column A, Walks, holds 1 to 10. Column B, My rule, shows 55, 95, 135, 175 and so on up to 415. Cell B3 is selected, and the formula bar shows =15+40*A3.
SpreadsheetDog Walking Savings, filled down from =15+40*A2

Jordan

$70. But the spreadsheet says $95

Sparky

$70 is right, so something's off in the rule. In your rule 15 + 40w, which number changes with each walk?

Jordan

the 40 gets multiplied by w... but i only get 15 each walk. so it should be 40 + 15w

Sparky

That's it. The $40 is your savings and stays the same. The $15 changes with each walk. Type =40+15*A2 in B2.

Jordan

done!

Sparky

Now 2 walks shows $70. Look at 3 walks: the spreadsheet says $85, but earlier you said $165. Why do you think the spreadsheet got a different answer?
The same spreadsheet after the fix. Column B, My rule, shows 55, 70, 85, 100 and so on up to 190. Cell B4 is selected, and the formula bar shows =40+15*A4.
SpreadsheetDog Walking Savings, filled down from =40+15*A2

Jordan

i added 40 and 15 first and then did times 3. the spreadsheet did 15 x 3 = 45 first and then added 40

Sparky

Exactly. That's the order of operations: multiplication happens before addition, so 40 + 15 × 3 is 40 + 45 = 85. Next challenge: you buy movie tickets at $12 each. Write an expression for your savings after w walks and m movie tickets.

Jordan

40 + 15w - 12m

Sparky

Now work it out for 6 walks and 2 movie tickets.

Jordan

15 x 6 = 90 and 12 x 2 = 24. 40 + 90 - 24 = 106. so $106

Sparky

That's right, $106. A new client pays a $5 bonus on top of every walk. Write a new expression that includes the bonus.

Jordan

40 + 15w + 5w

Sparky

Can you write a shorter expression that means the same thing?

Jordan

40 + 20w

Sparky

Yes. Why does 15w + 5w = 20w?

Jordan

because every walk i get 15 and 5 more, so thats 20 a walk

Found his own mistake, then wrote and simplified a rule with two letters

Jordan and his chat are examples. Sparky's replies are shortened from a test run of the library activity in which a test student typed Jordan's answers and formulas, and both spreadsheets are from that run.

What Flint did for Jordan

  • Sparky set every problem in dog walking because Jordan said that's how he earns money.
  • Sparky made a spreadsheet in Jordan's chat, read the formula he typed in B2, and filled it down the column.
  • Sparky used its calculator to work out Jordan's real savings for 1, 2 and 3 walks. When 2 walks didn't match, it asked him to count his money instead of telling him the rule was wrong.
  • Sparky kept Jordan's $165 answer and brought it back once the spreadsheet showed $85.
  • Each right answer got a harder question: a second letter for movie tickets, then a bonus to combine.

A teacher can't read 30 spreadsheets and pick the next question for each student during one class. Sparky does it in every student's chat.

See who mixed up the starting amount and the amount per walk

Each student's chat shows the rule they wrote and how they fixed it. The activity page sums up the whole class and flags any student who is stuck right now.

Flint's activity page for an activity called Write the Rule for Your Own Money. Needs attention shows a live alert that one student has typed three formulas that all multiply her starting amount by the letter. Activity analytics lists what the class does well, an area of improvement where 9 students first multiplied the starting amount by the letter, 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 a middle school math class finishes the money rule activity

The school and students are made up for this page. In this example, most of the class fixed their rule after checking a second row, and the next thing to practice is the order of operations without a spreadsheet.

Set up the activity for free

The money rule activity is in Flint's public library, with Sparky's role, guidelines and greeting already written. Open it, select Try this activity to copy it into a free Flint account, and move it to a class. In the activity settings, select Try session myself to test it as a student before you assign it.

For more math activities, see Flint for math.

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