👨👩👧 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 matter! This cuts in half 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 concluded that manipulatives "provide valuable support when teachers help build links between the object, symbol, and 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 competitions
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 (Akin, 2023) with 78,000 students found that 73% of those who integrated music and mathematics showed significant improvements in arithmetic.
Integrated music-math learning reduces anxiety and promotes strong transfer (Akin, 2023).
Games Method
7-10 years
Turning learning into play activates the brain's reward system, making them want to practice more.
In MatesRetos, Challenge Mode turns times tables into an exciting competition.
Spaced Repetition
8-12 years
Scientifically proven technique: reviewing just before forgetting strengthens long-term memory.
Flashcard apps like Anki automate this process.
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. According to Lally et al. (2010), it takes about 10 weeks on average to consolidate a habit.
📅Sample Weekly Plan
| Day | Tables | Time | Activity |
|---|---|---|---|
| Monday | 2 and 5 | 10 min | Introduction with objects |
| Tuesday | 2 and 5 | 10 min | Memory game |
| Wednesday | 3 and 4 | 10 min | Songs and rhythm |
| Thursday | 3 and 4 | 10 min | Practice on MatesRetos |
| Friday | Review | 15 min | Family competition |
| Saturday | 6 and 7 | 10 min | Board games |
| Sunday | Rest | - | Day off! |
⚠️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 repeating out loud
Combining methods (visual, auditory, kinesthetic)
Each child learns differently; use multiple channels
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 (5-7% 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
Forgets tables that seemed mastered just days ago
💡 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). Let me make mathematics and music together: A meta-analysis of the causal role of music interventions on mathematics achievement. Educational Studies, 49(3), 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.
- • Dehaene, S. (2011). The Number Sense. Oxford University Press.
- • 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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