# Multiplication Tables of 3 and 4

Having learned the multiplication facts for the “friendly” numbers of 2, 5 and 10 in the previous blog post, we’re now ready to tackle multiplication tables of 3 and 4, usually in the latter half of second grade.

Under a spiral approach, students move on to learn other topics after learning multiplication tables for 2,5, and 10, before coming back to learn about multiplication for numbers 3 and 4.

Most of the instruction is identical to the last lesson for numbers 2,5 and 10, i.e.

• Skip counting to dot paper to the distributive property using landmark numbers
• Writing family facts and Divide using related multiplication facts
• Properties of Operations for Multiplication and Division
• Division as an Unknown-Factor Problem

# Interpret Product of Whole Numbers

First make sure we remember what multiplication mean, i.e. we should be able to interpret 4 x 3 as meaning “four groups of three”.

Similar to introducing multiplication tables for 2,5 and 10, we start with skip counting, i.e. 3,6,9,… and then move on to using dot paper (dots in rows and columns to represent the total).

Finally, we’ll introduce the distributive property for multiplication – express the final product as a sum or difference of two “easier” multiplication operations. For example: # Revisit the Two Meanings of Division Equations

With the number 3 and 4, we can more effectively illustrate the two meanings of a division equation. For example, In the first interpretation, we’re finding the number of groups if 12 is divided into groups of three. In the second, we’re finding the numbers of objects in each group if 12 objects are divided into 4 equal groups.

# Related Facts and Family Facts

Related facts and family facts are great tools for solving multiplication and division problems. For example, if 4 x 3 = 12, a related fact is 12 ÷ 4 = 3. Let students practice coming up with their own related facts to get fluent.

Then have the students group related facts into family facts, for example,

• 3 x 4 = 12
• 4 x 3 = 12
• 12 ÷ 3 = 4
• 12 ÷ 4 = 3

Students can use heuristics such as ‘act it out’ or ‘draw a diagram’ for multiplication and division, and share their ideas with the class.

# Solving Word Problems Using Bar Modeling

It is also more meaning to see problems with numbers 3 and 4 represented in bar models, e.g. Don’t worry about assigning practice problems for bar models at this time, we’ll focus an entire lesson on Bar Models for multiplication and division in the next lesson.

# Determine Unknown Whole Number

Here we want to determine an unknown number in a multiplication or division equation relating three whole numbers. For example,

Determine the unknown number that makes the equation true in each of the following:

• 4 x ? = 12
• 4 = ? ÷ 3
• 4 x 3 = ?

One way we can practice is to write the family of 4 basic facts given any one of the basic fact (e.g. given 3 x 4 = 12, find the rest of the family facts – 4 x 3 = 2, 12 ÷ 3 = 4, and 12 ÷ 4 = 3).

# Properties of Operation

These are the

• cumulative property (e.g. 4×8 = 8×4), • associative property (e.g. 3x4x10 = (3×4) x10), and
• distributive property (e.g. 9×3 = (5×3) + (4×3)).

At this point, we do not want to emphasize the jargons, but we want the students to understand each of these property and practice using them to help with recognizing different ways to solve problems.

# Division as an Unknown-Factor Problem

Division can be interpreted as the missing number in an unknown factor problem. For example, we can start with

4 x 3 = 12

Then, hiding one of the factors,

4 x ? = 12

Then, see that the missing (unknown) number is just

12 ÷ 4 = ?

# Related Resources

## Common Core Standards

• A1 Interpret products of whole numbers.
• A2 Interpret whole-number quotients of whole numbers.
• A3 Use multiplication and division to solve word problems.
• A4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers.
• B5 Apply properties of operations as strategies to multiply and divide..
• B6 Understand division as an unknown-factor problem.
• C7 Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division or properties of operations.

## Suggested Workbook Series

• Math in Focus workbook (2B) Chapter 15 – Multiplication Tables for 3 and 4 (pages 133 to 154)
• Primary Mathematics workbook (Common Core Edition) (2A) Chapter 5 – Multiplication and Division for 3 (pages 159 to 175)
• Primary Mathematics workbook (Common Core Edition) (2B) Chapter 7 – Multiplication and Division for 4 (pages 28 to 41)

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