Addition by Decomposition
Learn how to make multi-digit addition fast and visual by breaking numbers into friendly place-value pieces. Perfect for Ontario Grade 4 math learners building flexible mental strategies.
Like Duolingo, but for Addition by Decomposition. Tomo turns the whole topic into a game you play five minutes a day, until it actually sticks.
A short one: 9 levels across 2 sections, about 18 minutes end to end, roughly 4 days at five minutes a day. It moves through Breaking Apart by Place Value and Flexible Splitting and Mental Strategies. It starts from scratch.
Free forever · No credit card · iPhone & Android
Key ideas in Addition by Decomposition
- A digit's actual value depends on its place, so 4 in the hundreds place means 400
- Decomposing splits a number into an expanded sum of hundreds, tens, and ones
- Adding the largest place values (the hundreds) immediately gives the ballpark size of the total
- Adding 300 + 500 tells you right away that the sum will be at least 800
- Adding matching chunks groups hundreds with hundreds, tens with tens, and ones with ones
- Adding chunks like 200 + 500 uses the single-digit fact 2 + 5 = 7 with two zeros attached
- Adding tens chunks like 60 + 10 uses 6 + 1 = 7 with one zero attached
- Decomposition finishes by adding the sub-totals together (500 + 60 + 14)
- When the ones chunk exceeds nine (6 + 8 = 14), recombining simply merges the new ten into the running total without tiny regrouping marks
- 7 tens plus 8 tens equals 15 tens, which is written directly as 150
- Partial sums records the full value of 150 rather than writing 5 and carrying a tiny 1
- The rollover into hundreds happens naturally by writing the complete number
- Each decomposed pair produces a whole number that keeps its own trailing zeros
- Tens partial sums like 110 must stack with ones under ones, tens under tens, and hundreds under hundreds
- Dropping a zero or misaligning columns mixes hundreds with tens during the final addition
- Four-digit decomposition starts by isolating thousands (2,000 + 1,000) just like three-digit starts with hundreds
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 Addition by Decomposition 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.
When you decompose 458 into its place-value parts, what does it look like?
Get it right to open this lesson and 8 more in the app.
Where Addition by Decomposition takes you
- 1
Breaking Apart by Place Value
- Splitting Numbers into Place-Value Chunks
- Handling Rollovers with Partial Sums
- 2
Flexible Splitting and Mental Strategies
- Keeping One Whole and Jumping the Rest
- Using Friendly Numbers and Compensation
2 sections · 4 units · 9 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
Addition by Decomposition is taught in the Bestie style: your friend who just gets it. 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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Start Addition by Decomposition today.
Download Tomo, search Addition by Decomposition, and play your first lesson in under a minute.