👨👩👧 How to Teach Multiplication Tables: Complete Guide for Families
Guide for patient families
Because learning times tables doesn't have to be torture
Times tables are one of children's first major academic challenges. With the right approach, they can go from being a source of frustration to a skill they master with confidence. This guide will give you proven methods to make the process more effective and, above all, more fun.
🧠Before Memorizing: Develop Number Sense
What is number sense? It's the ability to approximate, decompose, and recompose numbers, not just recite results. Before times tables, make sure the child understands:
📦 Multiply = Groups of
4 × 5 means "4 groups of 5 objects"
Use LEGO, cookies, or marbles to form groups and count.
➕ Multiply = Repeated addition
4 × 5 = 5 + 5 + 5 + 5 = 20
When the child understands this, times tables will make sense.
🔢 Distributive Property
7 × 8 = 7 × (5+3) = 35 + 21 = 56
Decomposing numbers allows building new tables from known ones.
🔄 Commutative Property
3 × 7 = 7 × 3 = 21
Order doesn't change the result! This almost halves what needs to be memorized.
💡 Tip: Spend 1-2 weeks working on the concept with physical objects BEFORE starting to memorize. This time investment pays off later.
🧱Use Manipulatives and Arrays (CPA Approach)
The National Research Council (2001) concluded that manipulatives help when teachers support students in building links between the object, the symbol and the mathematical idea. The CPA (Concrete → Pictorial → Abstract) approach:
1. Concrete
Cuisenaire rods, blocks, LEGO. Form a 4×7 array and count it.
2. Pictorial
Draw the array on graph paper. Divide into sections (4×5 + 4×2).
3. Abstract
Write: 4×7 = 4×(5+2) = 20+8 = 28
📋Fundamental Principles
Little and often
10 minutes daily is more effective than 1 hour weekly
Make it fun
Games, songs, and family challenges
Celebrate progress
Each mastered table is an achievement worth recognition
🎯Recommended Learning Order
Logical order: First those with clear patterns (1, 2, 5, 10), then those built on others (4=2×2, 6=3×2, 8=2×2×2)
✨Property-Based Strategies for Each Table
1 Times Table
Strategy: Identity element: N × 1 = N
Example: 1 × 7 = 7, 1 × 123 = 123
📝 Why it works: 1 is the identity element of multiplication.
2 Times Table
Strategy: Double the number (add to itself)
Example: 2 × 7 = 7 + 7 = 14
📝 Why it works: 2×N = N+N. Connects multiplication with addition.
5 Times Table
Strategy: Half of ×10, or 0/5 pattern
Example: 5 × 6 = 30 (even→0), 5 × 7 = 35 (odd→5)
📝 Why it works: 5 = 10÷2, so N×5 = (N×10)÷2
9 Times Table
Strategy: ×10 minus the number, or finger method
Example: 9 × 7 = 70 - 7 = 63
📝 Why it works: 9×N = 10×N - N (distributive property)
10 Times Table
Strategy: Add a zero (shift decimal position)
Example: 10 × 7 = 70
📝 Why it works: Decimal system: multiplying by 10 shifts each digit one position.
11 Times Table
Strategy: ×10 plus the number
Example: 11 × 7 = 70 + 7 = 77
📝 Why it works: 11×N = 10×N + N (distributive property)
4 Times Table
Strategy: Double twice (×2×2)
Example: 4 × 6 = (6×2)×2 = 12×2 = 24
📝 Why it works: 4 = 2×2, so N×4 = (N×2)×2 (associative)
6 Times Table
Strategy: ×3 doubled, or ×5 + the number
Example: 6 × 7 = 5×7 + 7 = 35 + 7 = 42
📝 Why it works: 6 = 5+1, so N×6 = N×5 + N (distributive)
8 Times Table
Strategy: Double three times (×2×2×2)
Example: 8 × 5 = 5×2×2×2 = 10×2×2 = 40
📝 Why it works: 8 = 2³, so N×8 = ((N×2)×2)×2
7 Times Table
Strategy: ×5 + ×2, or flexible decomposition
Example: 7 × 8 = 5×8 + 2×8 = 40 + 16 = 56
📝 Why it works: 7 = 5+2, so N×7 = N×5 + N×2
3 Times Table
Strategy: Add three times, or ×2 + the number
Example: 3 × 8 = 2×8 + 8 = 16 + 8 = 24
📝 Why it works: 3 = 2+1, so N×3 = N×2 + N
12 Times Table
Strategy: ×10 + ×2, or ×6 doubled
Example: 12 × 7 = 10×7 + 2×7 = 70 + 14 = 84
📝 Why it works: 12 = 10+2, so N×12 = N×10 + N×2
🎓5 Teaching Methods
Musical Method (with scientific evidence)
6-8 years
A meta-analysis of 55 studies (Akın, 2023), with about 78,000 participants from kindergarten to university, found a positive effect of music on mathematics achievement, largest when music is integrated into the math lesson itself: in that case, about 73% of students scored above the average of the no-music group.
The large effect appears when music and math are worked on together in the same activity, not with background music (Akın, 2023).
Games Method
7-10 years
Turning practice into a game makes children want to repeat it, which is exactly what times tables need to become automatic.
In MatesRetos, Challenge Mode lets children practice times tables as a game and see their own progress.
Spaced Repetition
8-12 years
Reviewing at increasingly longer intervals, instead of all at once, improves long-term recall: the spacing effect is one of the most robust findings in learning research (Cepeda et al., 2006).
Mixing tables during review (7×8, 6×4, 9×3...) forces real recall instead of following the sequence.
Manipulative Method
6-7 years
Using physical objects helps understand the concept of multiplication as 'groups of'.
Always start with objects the child likes.
Daily Routine
All ages
Consistency is key. 10 minutes daily is more effective than sporadic long sessions.
Regularity creates habit. In Lally et al. (2010), a new habit took a median of 66 days to become automatic, with large differences between people.
📅Sample Weekly Plan
| Day | Tables | Time | Activity |
|---|---|---|---|
| Monday | 2 and 5 | 10 min | Introduction with objects and arrays |
| Tuesday | 2 and 5 | 10 min | Memory game |
| Wednesday | 2 and 5 | 10 min | Songs and rhythm |
| Thursday | 2, 5 and 10 | 10 min | Practice on MatesRetos |
| Friday | Mixed review | 10 min | Family challenge (everyone plays) |
| Saturday | 2, 5 and 10 | 10 min | Board games |
| Sunday | Rest | - | Day off! |
This is a typical week once the 2 and 5 tables are being worked on. Move on to the next pair (3 and 4, then 6 and 8, then 7 and 9) only when these come out confidently: one or two weeks per pair is normal.
⚠️Common Mistakes to Avoid
1-hour sessions on weekends
10 minutes every day
Memory consolidates better with distributed practice
Learning all tables at once
One or two tables per week
Avoids confusion and allows consolidation before advancing
Only reciting the table in order
Combining objects, drawings (arrays), words and numbers
Seeing the same idea in several ways helps everyone. Matching teaching to a supposed visual or auditory 'learning style' has no scientific support
Getting angry when they make mistakes
Celebrating effort, not just results
Anxiety blocks learning
🚨Learning Diversity: Recognize and Support
Not all children learn at the same pace. The Cleveland Clinic notes that people with dyscalculia (about 3-7% of the population) have difficulty memorizing tables and doing mental calculations. The earlier the intervention, the better.
⚠️ Warning signs:
Persistent difficulty recognizing small quantities without counting
Constant confusion between similar numbers (6 and 9, 12 and 21)
Extreme anxiety or blocking with any mathematical task
No improvement after 3+ months of regular, varied practice
Difficulty understanding the concept of 'groups of' with objects
Keeps forgetting, for months, tables that seemed mastered
💡 Important: Having difficulties does NOT mean the child is "bad at math". With specialized intervention and individualized programs, everyone can progress. Early diagnosis allows adapting methods.
📚 References and Recommended Reading
- • Boaler, J. (2015). Fluency Without Fear: Research Evidence on the Best Ways to Learn Math Facts. Youcubed, Stanford University.
- • Akın, A. (2023; print 2025). Let me make mathematics and music together: A meta-analysis of the causal role of music interventions on mathematics achievement. Educational Studies, 51(4), 386–404. DOI: 10.1080/03055698.2023.2216826
- • National Research Council (2001). Adding It Up: Helping Children Learn Mathematics. National Academies Press.
- • Cleveland Clinic. Dyscalculia: Symptoms, Causes, and Treatment.
- • Willingham, D. T. (2009). Why Don't Students Like School? Jossey-Bass.
- • Cepeda, N. J., Pashler, H., Vul, E., Wixted, J. T., & Rohrer, D. (2006). Distributed practice in verbal recall tasks: A review and quantitative synthesis. Psychological Bulletin, 132(3), 354–380.
- • Pashler, H., McDaniel, M., Rohrer, D., & Bjork, R. (2008). Learning styles: Concepts and evidence. Psychological Science in the Public Interest, 9(3), 105–119.
- • Lally, P. et al. (2010). How are habits formed. European Journal of Social Psychology, 40(6), 998–1009.
Note: The goal is to develop numerical flexibility and number sense, not just speed. Strategies are based on mathematical properties and are transferable to new situations.
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