The order to teach multiplication facts
Teach the tables in four groups, easiest first. Math Builders introduces new multiplication and division facts in this same order by default. What you teach and what the app offers as new facts follow the same sequence.
- Step 1: 2s, 5s and 10s, with the 1s
42 new facts. Add the 0 rule, which is one rule and has no count. Students already double, count by 5 and add a zero. Every later table borrows from these.
- Step 2: 3s and 4s
15 new facts. The 4s are double the 2s. The 3s are the 2s plus one more group.
- Step 3: 6s, 7s, 8s and 9s
18 new facts. The hardest group. It holds the 10 facts among the 6s to 9s, such as 7 × 8, and the 8 facts that pair one of them with 11 or 12, such as 7 × 12. After steps 1 and 2, nothing else is left but these and step 4.
- Step 4: 11s and 12s
3 new facts. Only 11 × 11, 11 × 12 and 12 × 12 are new. If your standard stops at 10 × 10, stop after step 3.
Each count is of unique facts, so 3 × 7 and 7 × 3 are one fact. The counts are for the 1 to 12 grid, which has 78 unique facts: 42 + 15 + 18 + 3. The 0 facts are one rule, so they are not in the counts.
A fact belongs to its easier table
Order facts by their easier factor, not their larger one. 7 × 10 is a 10s fact, and 4 × 7 is a 4s fact. By the time the class reaches the 7s, it already knows 7 × 1, 7 × 2, 7 × 3, 7 × 4, 7 × 5 and 7 × 10. Only 7 × 6, 7 × 7, 7 × 8, 7 × 9, 7 × 11 and 7 × 12 are new. Say this to students. The hard table is smaller than it looks.
Teach the division facts of a table right after its multiplication facts. 56 ÷ 7 is a 7s fact. See multiplication and division fact families.
The 0s and 1s are rules, not drills
Teach them in one short lesson: any number times 1 is that number, and any number times 0 is 0. The lessons on the identity property and the zero property show why. Then keep them in the mix. Put a few 0 and 1 facts in every warm-up and every weekly check, so the two rules stay in daily use.
Start each table with meaning, before any strategy or trick. Equal groups and arrays show what 4 × 7 asks. See multiplication arrays. In the United States, the Common Core standard for Grade 3 (3.OA.C.7) asks students to know from memory all products of two one-digit numbers by the end of the year. See the standard for Grade 3 operations and algebraic thinking.
From strategy to recall: when a derived fact becomes a known fact
A student who works out 6 × 8 as 5 × 8 + 8 = 48 is not recalling it. The answer is derived. That is the right place to start. It is the wrong place to stay, because a derived answer takes several steps and the next problem needs the same thinking space. Your job is to move each fact from derived to known.
One strategy for each group
- 2s, 5s, 10s
Double it. Count by 5, or take half of the 10s answer. Add a zero.
- 3s and 4s
3 × 7 is 2 × 7 plus one more 7. 4 × 7 is double 2 × 7: 14, then 28.
- 6s
Anchor at 5. 6 × 8 is 5 × 8 + 8 = 40 + 8 = 48.
- 9s
One group fewer than 10. 9 × 7 is 70 − 7 = 63.
- 7 × 8
Say the run 5, 6, 7, 8: 56 = 7 × 8. Many students need a trick for this one fact.
- 11s and 12s
11 × 4 is 44: the digit repeats up to 11 × 9. 12 × 7 is 10 × 7 + 2 × 7 = 70 + 14.
The 6s, 9s and 12s rest on the distributive property: break a fact into two easier facts and add. Teach it once, and it carries every table.
The 3-second check
Ask for the fact and count three seconds in your head. If the student answers correctly in that time with no counting, no fingers and no spoken steps, the fact is known. If the answer is right but slower, or comes with the steps, it is still derived. Check on two different days before you move a fact to known. A fact that is right once may be luck.
The 3-second line is the one Math Builders uses. It is a working rule for the classroom, not a research finding. Use it as a sort, not a grade.
Known facts go into short mixed review. Derived facts go back to the strategy. Keep the strategy for the day a known fact slips. It is the way back.
A 5-minute daily routine
Run this at the same time every day. Each student needs one thing to write an answer on: a mini whiteboard, a sheet of paper or answer cards.
- 0:00 to 1:00. Warm up
Ask 8 to 10 facts the class already knows, mixed. Include a 0 or 1 fact. Students write the answer and hold it up.
- 1:00 to 2:30. Teach the new set
Pick 3 to 5 facts from the current group. Say the strategy for each once. Students answer, then answer again in a different order.
- 2:30 to 4:30. Retrieve a mix
Ask facts from today, yesterday and last week, mixed. No chart on the wall during this part. Slow answers go on your list for tomorrow.
- 4:30 to 5:00. Exit check
Each student writes the one fact they still count. You keep the notes. They tell you tomorrow's set.
If your class uses Math Builders, the app can be the retrieve step. The app gives each student 2 to 5 minutes a day, picks their facts and brings missed ones back on a schedule. The routine above works without it. See Math Builders for teachers.
A weekly check
Once a week, give a one-minute mixed check. The free multiplication timed test runs it online with no account and lists the missed and slow facts. Students can also take a printed version.
Sort every fact into one of three piles. Fast and right: known. Right but slow: derived, so keep the strategy. Wrong: teach it again. Carry only the slow and wrong facts into next week’s warm-up and retrieve steps. Record the result on a multiplication facts mastery tracker, so you can see which tables are done.
For quiet independent practice on one fact set at a time, use the color by code sheets. For how many facts per minute to expect in each grade, see multiplication fact fluency: facts per minute by grade.
Teaching multiplication facts to struggling students
A math fact fluency intervention is the same routine with a smaller set and more spacing. The goal is the same: known facts in under 3 seconds. The path is shorter and slower.
1. Find the missed facts
Give the one-minute check from the weekly step. Sort what you see. Wrong answers need teaching. Slow answers, or answers with finger counting, need strategy practice. Look for the table. Most students have a short list, often in the 6s, 7s and 8s, and not a hole in every table.
2. Work a small set at a time
Pick 3 to 5 facts from the list. Practice each fact with its turnaround and its division facts: 7 × 8, 8 × 7, 56 ÷ 7 and 56 ÷ 8. Practice them for 2 to 3 minutes a day. A fact missed today comes back today. A fact answered right comes back tomorrow, then in 3 days, then in a week. When all of the set comes back in under 3 seconds, add 2 new facts. See spaced repetition for math facts.
3. When a fact does not stick
- The student does not know what the fact means
Go back to equal groups and arrays. Build 7 × 8 as 7 rows of 8, then split it.
- The strategy is too long
Try another one. If the steps are slow, 7 × 8 can be 8 × 8 = 64, then take away one group of 8.
- The student mixes up two facts
Facts such as 6 × 7 and 6 × 8, or 7 × 8 and 6 × 9, get confused. Practice one alone until it is quick. Then mix them.
- Time pressure gets in the way
Drop the timer for this student. Practice for accuracy first, then speed.
For the stress side, see stress-free math practice. This guide is a classroom routine. It is not a diagnosis. If a student makes no progress after several weeks of daily practice, bring it to your school’s intervention team. Math Builders supplements an intervention program. It does not replace one.
What to use next
- Multiplication timed test
The weekly check. Free, no account.
- Mastery tracker PDF
Record which tables are known, slow or still to teach.
- Color by code sheets
Quiet independent practice on one fact set.
- Math fact fluency activities
Whole-class, small-group, center and partner activities for the same facts.
- Multiplication fact fluency
Facts-per-minute benchmarks by grade, and the untimed check.
- How to memorize multiplication tables
The same method written for a parent. Send it home.
Run the daily practice for your class
Math Builders gives each student 2 to 5 minutes a day on the facts they have not learned yet, in the teaching order above. It supplements your curriculum. Answer a few questions about your class to get a starting plan.
Frequently Asked Questions
Teach the 2s, 5s and 10s first, with the 1s and the 0 rule. Then teach the 3s and 4s, then the 6s through 9s, and the 11s and 12s last. Each group builds on the one before it, and a fact counts with its easier table, so 7 × 10 is a 10s fact.
Five minutes is enough for a whole class: a 1-minute warm-up, 1.5 minutes on the new group, 2 minutes of mixed recall and a 30-second exit check. Run it every day. Short and daily is easier to keep up than one long block.
When the student gives the right answer in under 3 seconds with no counting, no fingers and no spoken steps. Check it on two different days. Until then the fact is still derived, so keep teaching the strategy for it.
Find the missed and slow facts with a one-minute check. Work 3 to 5 of them at a time for 2 to 3 minutes a day, and add 2 new facts only when all of them come back in under 3 seconds. If a fact does not stick, change the strategy or separate it from the fact it is confused with. Do not add more of the same drill.
Teach them as two rules in one short lesson: any number times 1 is that number, and any number times 0 is 0. Then put a few of them in every warm-up and every weekly check. They are one rule you keep in daily use.
No. Math Builders is a fluency layer. It gives each student 2 to 5 minutes a day on the facts they have not learned yet. Your curriculum still teaches what multiplication means and how to use it.