Last updated 2026-10-11. Written by the TernQuest team. This guide is for parents of 3rd graders (and older kids who never quite got there) who want a specific order for learning the times tables and a routine short enough to actually happen.
What order should kids learn the multiplication facts in?
Direct answer: Learn them in order of how easy they are to derive, not in order from 1 to 12. Start with 2s, 5s and 10s (they are skip counting), then 1s and 0s, then the squares, then the 9s with a trick, and finish with the small set of leftovers. Using the turn-around rule (3 × 7 is the same as 7 × 3) means most facts get learned once, not twice.
Under the California Common Core standards, knowing all products of two one-digit numbers from memory is a 3rd grade year-end expectation, and it is the row that most other 3rd and 4th grade math depends on. Your school's pacing may differ. Where facts sit among the other year-end skills is in the 3rd grade math skills checklist.
Quotable version: "Learn the times tables by ease, not by number: 2s, 5s, 10s, then squares, then 9s, then the six leftovers."
| Stage | Facts | Why here | How they are learned |
|---|---|---|---|
| 1 | 2s, 5s, 10s | Skip counting a 2nd grader already knows | Count by 2, 5, 10; connect to "groups of" |
| 2 | 1s, 0s | Rules, not memory | 1 × anything is itself; 0 × anything is 0 |
| 3 | Squares (3×3 to 9×9) | Kids find them memorable; they anchor the grid | Say them as a chant; draw them as squares |
| 4 | 9s | A reliable trick | Digits add to 9; tens digit is one less |
| 5 | 4s | Double the 2s | 4 × 6 is double 2 × 6 |
| 6 | 3s, 6s | 3s from skip counting; 6s are double the 3s | Counting by 3; double |
| 7 | Leftovers: 6×7, 6×8, 7×8, 3×7, 3×8, 4×7 | The ones with no easy pattern | Small set, learned by repetition and rhymes |
Why 2s, 5s and 10s first?
Direct answer: Because a child who can count "5, 10, 15, 20" already knows the 5s table; they just have not been told that "4 × 5" means "count by 5 four times." Starting here gives a fast win and teaches what multiplication means before asking for any memory work.
Connect the count to the fact
Lay out four groups of five coins. Count them by 5s while touching each group: "5, 10, 15, 20." Then write 4 × 5 = 20 and say "four fives are twenty." Do the same with 2s (pairs of socks) and 10s (fingers on hands). If your child cannot yet skip count by 5s reliably, the routine in skip counting activities comes first.
What is the turn-around rule and why does it matter?
Direct answer: The turn-around rule (the commutative property) says 3 × 7 and 7 × 3 give the same answer, so each pair only has to be learned once. A full grid from 1 to 10 has 100 facts; remove the turn-around twins and the 1s and 0s, and the set a child actually has to memorize is a small fraction of that.
Show it, do not just say it. Draw a 3-by-7 array of dots, count 21, then turn the paper sideways. It is now a 7-by-3 array with the same 21 dots. Kids who see this stop treating 7 × 3 as a new fact and start treating it as "the one I already know, flipped."
How does the 9s trick work?
Direct answer: For any 9s fact from 9 × 1 to 9 × 10, the tens digit is one less than the number you are multiplying by, and the two digits of the answer add up to 9. So 9 × 6: tens digit is 5, and 5 + 4 = 9, so the answer is 54. Kids who prefer their hands can hold up ten fingers and fold down the sixth finger: five fingers on the left, four on the right, 54.
| Fact | One less | Digits add to 9 | Answer |
|---|---|---|---|
| 9 × 3 | 2 | 2 + 7 | 27 |
| 9 × 6 | 5 | 5 + 4 | 54 |
| 9 × 8 | 7 | 7 + 2 | 72 |
The trick is a bridge, not a destination. After a couple of weeks of using it, a child typically finds that 9 × 7 = 63 simply arrives without the trick. That is the goal for every fact: strategy first, then recall.
What are the "leftover" facts and how do you learn them?
Direct answer: Once 2s, 5s, 10s, 1s, 0s, squares, 9s and 4s are learned and turn-arounds are counted, a small cluster remains: 3 × 6, 3 × 7, 3 × 8, 4 × 6, 4 × 7, 6 × 7, 6 × 8 and 7 × 8. These have no clean pattern and are the facts most adults still pause on. Attack them last, a couple at a time, with a strategy each.
A strategy for each
- 3 × 7, 3 × 8: double the number, then add one more group. 3 × 7 is 14 + 7 = 21.
- 4 × 6, 4 × 7: double the 2s fact twice. 4 × 7 is 14 doubled, 28.
- 6 × 7, 6 × 8: the 5s fact plus one more group. 6 × 8 is 40 + 8 = 48.
- 7 × 8: the one everyone remembers as a rhyme, "5, 6, 7, 8" (56 = 7 × 8). It works.
The pattern across the list: use a fact you know to get to the one you do not. That is what fluency actually is, and it is why memorizing from a blank table of 100 facts takes so long. The distinction between fluency and speed is drawn out in math fact fluency: what it is and what it isn't.
What does a 3-minute daily routine look like?
Direct answer: Pick one stage from the table, make cards for just those facts (both turn-arounds), and spend 3 minutes a day on them: say the fact, say the answer, say the strategy if it did not come right away. Move a card to the "known" pile when it comes fast three days running. 3 minutes × 5 days is 15 minutes a week, and one stage usually takes a week or two at that pace.
The routine, step by step
- Sort. Three piles: known, learning, not started. Start with everything in "not started" and move one stage into "learning."
- Three minutes. Go through the learning pile. Right and fast: set it aside. Right but slow: say the strategy out loud, put it back. Wrong: show the array or the strategy, put it back.
- Promote. Any card that was fast three days in a row goes to "known." When the learning pile is empty, pull in the next stage.
- Review. Once a week, run the "known" pile so nothing decays.
What to avoid
- Whole-table drills. Practicing 100 facts at once means the known ones crowd out the ones that need work.
- Timers at home. Speed under a clock is a different skill from recall, and for some children the clock is what makes the answer disappear. If your child tenses up around math, look at the signs in math anxiety in kids before adding pressure.
- Skipping the strategy. A child who says "I don't know" should hear "use the fact you know," not the answer.
How do multiplication facts connect to division?
Direct answer: Every multiplication fact carries its division facts with it: if 6 × 7 = 42, then 42 ÷ 7 = 6 and 42 ÷ 6 = 7. Once the multiplication side is solid, teach division as "what times 7 gives 42?" rather than as a new set of facts to memorize.
Write the four facts of each family together on one card (6 × 7, 7 × 6, 42 ÷ 6, 42 ÷ 7) once the multiplication fact is in the known pile. This is the bridge to the division work in how to teach division to 3rd graders.
Where does a game fit, and where does it not?
Direct answer: A game is the right tool for the repetition phase, once a stage's strategies are understood: it gives the daily reps without a grown-up holding cards, and a child will often do more rounds than they would with paper. A game is the wrong tool for the first explanation of what 4 × 5 means; that belongs to coins on the table.
TernQuest's 3rd grade multiplication games are grouped by the same stages as this guide (2s, 5s and 10s first) and Pip, the tutor, gives a strategy hint rather than the answer when a child stalls; it is not the right tool if your child is not yet comfortable counting by 5s and 10s, and that is where the skip counting work above comes first. Whatever you use, keep the sessions short and the timer off.
Related reading
- 3rd grade math skills checklist — where facts sit in the year.
- Math fact fluency: what it is and how to build it — why "fast" is not the goal.
- How to teach division to 3rd graders — the natural next step.
Next step
Make the first stage's cards tonight, or let TernQuest handle the reps; it is free to start for one child. Three minutes a day, one stage at a time, and the table fills in.