MathematicsMathsMiddle schoolKey Stage 3
How to teach algebraic expressions
Writing algebraic expressions starts with deciding which number stays the same and which changes with the variable. This page shows how students practice it, with a free activity where each student writes a rule for their own savings and tests it in a spreadsheet.
Jemel Fanfan | Founding Member at Flint
"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 Bernabe, Middle School Math Teacher at Shanghai American SchoolWhy 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.
Writing algebraic expressions
An algebraic expression uses a letter, the variable, to stand for a number that can change. With $40 saved and $15 earned for each dog walk, the $40 stays the same and the $15 is multiplied by the number of walks, so the expression is 40 + 15w. Students check an expression by putting in a value for the variable, and the order of operations says to multiply before adding: 40 + 15 × 3 is 85, not 165. Terms with the same variable combine, so 15w + 5w is the same as 20w (Common Core 6.EE.A.2 to 6.EE.A.4).
In the Flint activity, each student writes an expression for money they earn and types it as a formula into a spreadsheet in their chat. When a row doesn't match their real money, Sparky, Flint's AI tutor, asks them to count that row by hand instead of telling them the rule is wrong. Each right answer brings a harder step: a second variable for spending, then a bonus to combine.
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.
Jordan
Sparky
Jordan
Walking dogsSparky
Jordan
40 + 15 = 55, then 55 x 3 = 165. So $165Sparky
Jordan
15 + 40wSparky
Jordan
I typed it in B2Sparky
Jordan
$70. But the spreadsheet says $95Sparky
Jordan
the 40 gets multiplied by w... but i only get 15 each walk. so it should be 40 + 15wSparky
Jordan
done!Sparky
Jordan
i added 40 and 15 first and then did times 3. the spreadsheet did 15 x 3 = 45 first and then added 40Sparky
Jordan
40 + 15w - 12mSparky
Jordan
15 x 6 = 90 and 12 x 2 = 24. 40 + 90 - 24 = 106. so $106Sparky
Jordan
40 + 15w + 5wSparky
Jordan
40 + 20wSparky
Jordan
because every walk i get 15 and 5 more, so thats 20 a walkFound his own mistake, then wrote and simplified a rule with two letters
Jordan is an example student, and Sparky's replies are shortened.
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.
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 Use activity to copy it into a free Flint account, and move it to a class. In the activity's Preview tab, 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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