How Math Formulas Work
Stop memorizing steps and start seeing the underlying logic of numbers. Discover how arithmetic patterns, fractions, and algebraic equations connect so you can solve problems on your own with confidence.
Like Duolingo, but for How Math Formulas Work. Tomo turns the whole topic into a game you play five minutes a day, until it actually sticks.
A short one: 11 levels across 2 sections, about 22 minutes end to end, roughly 4 days at five minutes a day. It moves through Making Numbers Work for You and The Logic of Equations. It starts from scratch.
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Key ideas in How Math Formulas Work
- A number like 23 splits naturally by place value into 20 and 3
- Multiplying by a tens value like 20 is just multiplying by 2 and appending a zero
- Multiplying the parts separately and adding the results gives the exact same product as multiplying all at once
- Friendly multiples of 10, 5, and 2 are easy to compute mentally and serve as nearby reference anchors
- Multiplying by 9 is identical to taking 10 groups and removing 1 group
- Multiplying by 6 is 5 groups plus 1 more group
- Transferring an amount from one number to another keeps the total sum unchanged
- Stealing a small amount to turn a number ending in 8 or 9 into a multiple of 10 eliminates messy mental regrouping
- Halving one factor and doubling the other leaves the total product exactly the same
- Numbers ending in 5 or 25 quickly become round multiples of 10 or 100 when doubled
- Even factors can be halved repeatedly until an awkward problem becomes trivial
- A fraction a/b represents sharing 'a' items equally among 'b' recipients (a ÷ b)
- The numerator is the quantity being divided and the denominator is the number of equal shares
- A fraction can describe an exact quantity even when smaller than a whole number
- Multiplying both numerator and denominator by the same number slices existing parts into smaller, equal sub-parts
- Because each part becomes proportionately smaller, the total quantity remains unchanged
You've tried the other tabs
Thirty open tabs. Four facts you actually kept.
You watched. You nodded. By Sunday it was gone.
One answer, then back to scrolling.
Eight weeks. You meant to finish. You didn't.
Tomo gives How Math Formulas Work the Duolingo treatment: levels, streaks, and quick quizzes that test what you just learned. That game loop is what the tabs above never had, so it's the one you actually finish.
Here's what playing it feels like
A real question from this course. Take your best guess.
How can you quickly calculate 7 × 20 in your head?
Get it right to open this lesson and 10 more in the app.
Where How Math Formulas Work takes you
- 1
Making Numbers Work for You
- Decomposing Numbers for Mental Calculation
- Seeing Fractions as Ratios and Operations
- 2
The Logic of Equations
- Balancing and Isolating the Unknown
- Translating Real Situations into Formulas
2 sections · 4 units · 11 levels. Built to play, not to enroll.
Tomo is in ChatGPT
Tomo is also a ChatGPT plugin: the same playable courses, built and played inside your chat.
Add Tomo to ChatGPT- What to ask
- “Make me a Tomo course on black holes.” “Turn this chat into a Tomo course.”
- What you get
- Quick questions with instant feedback, hearts and stars, ready to play in about a minute.
- Where it goes
- No sign-up to start. Connect your Tomo account and your streak carries on in the app.
You pick the voice
How Math Formulas Work is taught in the Professor style: clear, structured, thorough. Want a different feel? In the app you can spin up the same topic in any of Tomo's teaching styles. Same facts, totally different vibe.
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