Mastering Multiplication: Tips and Tricks for Learning Maths Tables Quickly

The transition from addition and subtraction to multiplication and division can be challenging for students. Educators may sometimes rush through lessons or introduce complex concepts prematurely, leading to discouragement and hindering learning. Fortunately, effective strategies exist to overcome these hurdles and make learning multiplication an engaging and successful experience.

A Six-Step Guide to Teaching Multiplication

1. Connect Multiplication to Addition

Avoid starting with rote memorization, which can intimidate students. Instead, build upon their existing knowledge of addition. Multiplication is simply repeated addition. Use relatable examples to illustrate this connection.

For example:

2 x 2 is the same as 2 + 2
3 x 4 is the same as 4 + 4 + 4

Writing out examples helps students visualize the concept.

2. Begin with Multiples of Zero and One

Multiplying by zero: The zero property

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Adding zero to a number doesn't change its identity: n + 0 = n. Similarly, any number multiplied by zero is zero: n x 0 = 0. Encourage students to find examples of the zero property in their surroundings. For instance, a classroom with 25 chairs and no monkeys on them means there are zero monkeys in the classroom.
Multiplying by one: The identity property
The identity property states that the product of a number and one is the number itself: n x 1 = n. Highlight that multiplying by one results in the same value. Ask students to identify instances of the identity property in the classroom, such as one group of eight desks equaling eight desks, or a single row on a calendar showing seven days equaling seven days.

3. Covering the Multiplication Table: Starting with the "Easy" Numbers

At this point, students should understand multiplication as repeated addition and grasp the zero and identity properties. Now, introduce the multiplication table.

Display a 12 x 12 or 10 x 10 multiplication chart.
Teach students how to use the chart to find products by matching numbers on the vertical and horizontal axes.
Discuss patterns within the chart, such as multiples of ten ending in zero and multiples of five ending in zero or five.
Identify the "easy" facts (ones, tens, twos, fives, elevens) and eliminate them from the chart.

4. Leveraging the Commutative Property

Like addition, multiplication is commutative: the order of factors doesn't affect the product. Multiplying 8 x 2 yields the same answer as multiplying 2 x 8.

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Communicate this property effectively to encourage students. Show them that each answer repeats, effectively halving the number of facts they need to memorize. Learning 3 x 6 is the same as learning 6 x 3. If students know the fact families of 0-3, they also know four numbers each of 4-10.

Use visual models to further reinforce the commutative property. Ask students if different arrangements of blocks are the same, just different versions of each other, and if the total number of units remains the same.

Encourage students to create their own models to illustrate that a x b results in the same product as b x a.

5. Breaking Down Memorization into Manageable Steps

Students are now ready to memorize the multiplication table. Emphasize the importance of understanding the meaning behind multiplication facts and their real-world applications.

Consider these rules:

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Practice Regularly: Encourage students to practice verbally or in writing.
Introduce Facts Gradually: Introduce new multiplication facts incrementally, progressing from multiplying by 2, 3, 4, and so on.
Strategic Order: Memorize facts in a strategic order: 0-3, then 4-7, and finally 8-10 (and optionally 11 and 12).
Visual Aids: Keep visual materials and math manipulatives readily available.

6. Introducing the Associative and Distributive Properties

These more advanced concepts can significantly improve students' mental math skills.

The Associative Property
The way you group factors doesn't change the product: (a x b) x c = a x (b x c) or (1 x 2) x 3 = 1 x (2 x 3). Relate this to column addition, where addends are grouped to find the sum. Students can group factors in the most convenient way to find the answer. This rule can be explained as an extension of the commutative property.
The Distributive Property
The distributive property is symbolized as a(b + c)=(ab)+(ac). This property spreads out the value of 'a' equally to 'b' and 'c'. For example, 6 x 8 can be thought of as (6 x 5) + (6 x 3), or 30 + 18. Use materials like cups and beans or grid paper to explain the property to visual or tactile learners.

Fun Ways to Teach Multiplication

Play Classroom Math Games

Classroom math games can alleviate the fear associated with multiplication.

Calculator Constants: If calculators have a constant function, use them to discover multiples of a number, linking multiplication and addition. Pick a factor (e.g., seven), enter it, hit the + button, and then press the = button. The calculator should show seven again. Continue pressing the = button to see incremental multiples (7, 14, 21, 28, etc.). Have students record the multiples and look for patterns.
Times Table Buzz: This game reinforces knowledge of the multiplication table. Pick a multiplication table (e.g., multiples of five). Have students stand in order. The first student counts "one," the next "two," and so on. When the sequence reaches a multiple of five, the student shouts "buzz!" Students who forget to say "buzz" or say it at the wrong time are out. The counting continues until ten times five (or at the teacher's discretion), then starts again. The last three students standing win.

Use Fun Math Books in Class

Many math books offer a variety of activities, such as multiplication facts and word problems.

How NOT to Teach Times Tables

Avoid rote practice as the primary method. Practice and drill are helpful, but they should come at the end of the learning process, not the beginning.

The Importance of Multiplication Facts

The multiplication facts (times tables) include all multiplication problems from 1 × 1 = 1 up to 10 × 10 = 100. Mastery of these facts is crucial for tackling division, fractions, and problems with larger numbers. Without it, students struggle and have less working memory for understanding new concepts.

When Should Children Learn Multiplication Facts?

Aim for third grade. This prepares them for third- and fourth-grade math topics like multi-digit multiplication, equivalent fractions, and division. However, learning multiplication facts will benefit children of any age.

Prerequisites for Memorizing Multiplication Facts

Before memorizing multiplication facts, children should learn addition and subtraction facts. They should also understand the meaning of multiplication (e.g., 3 × 8 means "3 groups of 8"). It also helps if they can mentally add one-digit numbers to two-digit numbers.

Desired Speed for Recalling Multiplication Facts

Aim for no more than 3 seconds per fact, faster if possible. Adjust expectations to the individual child. Keep practice relaxed and positive. Timed tests and drills are unnecessary unless the child enjoys them.

A Step-by-Step Plan for Teaching Multiplication Facts

Break it up: Don't overwhelm the child with all 100 facts at once. Focus on one times table at a time.
Make the facts concrete with a multiplication array: Ensure the child understands what the multiplication problems mean. Use a dot array to visualize "groups of."
Teach your child to use easier facts as stepping stones to the harder facts: Use known facts as stepping stones to learn harder facts.
Practice each times table on its own until it’s mastered: Focus on a specific times table for several days, using recitation, games, and worksheets.
Practice a mix of multiplication facts: Mix mastered facts with new facts for cumulative review.

Additional Tips and Tricks

Memory is key! Memorizing the multiplication table allows for quick recall of facts.
Every multiplication fact has a twin, which may be easier to remember.
Use finger tricks for the nine times tables.
Utilize catchy music to aid memorization.
Play card games that make learning times tables fun.
Create multiplication flowers for a creative activity.
Test knowledge during everyday activities.
Offer rewards to heighten enthusiasm and encourage persistence.

Charlotte Mason's Approach to Learning Multiplication Tables

Charlotte Mason emphasized a "best way possible" that allows children to discover patterns and investigate how numbers behave.

Begin with Multiplication as Repeated Addition

Use concrete objects like coins to reinforce multiplication as repeated addition through simple problems.

Introduce the Times "x" Symbol

Explain that the symbol means "multiplied by" and that 2 × 5 means five twos. Have the child write and work sums using the multiplication sign, then read the entire multiplication sentence.

Construct a Multiplication Table Using Concrete Objects

Use concrete objects to create a simple multiplication table and solidify understanding.

Written Table

Help the child construct a written multiplication table, formatting it as vertical equations in a row.

Say the Table Through and Write It

Have the child look at the table, visualize it, and say it through several times. Erase numbers and ask the child to fill them in. Have the child write the table in a math notebook.

Practice with Table Work Until Learned

Give the child a variety of questions, allowing them to refer to their written table until it is memorized.

When to Advance

Advance to the next table when the child no longer needs to use their written tables. Progress should be measured against the child's own abilities, not against others.

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