Multiplication tables for 2, 5 and 10 are the first set of multiplication tables students learn in 2nd Grade because they follow easy-to-remember patterns and are therefore more “friendly” than other multiplication tables. In this blog post, we’ll talk about some of the more important concepts to focus on, extending what we’ve learned in the introduction lesson.

# Interpret Product of Whole Numbers

Before we formally introduce Multiplication tables for 2, 5 and 10, first make sure we know what multiplication means, i.e. we should be able to interpret 4 x 2 as meaning “four groups of two”.

Then to introduce each of the multiplication tables for 2, 5 and 10, we can start with skip counting, i.e. 2,4,6,… 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:

The dot paper representation is particularly useful in introducing the distributive property of multiplication. For example, in the second example above, 7×2 can be arranged into “landmark” numbers we learned in ten frames, i.e. 5 and 10.

Many 2^{nd} grade students may already know the answer to 7×2, and may not understand why we need to break up the numbers using the distributive property, but it is important that we set the stage to prepare for bigger numbers later on.

# Interpret Whole-Number Quotients of Whole Numbers

Here, we revisit the two related concepts of division, e.g. 12 ÷ 4 can mean the number of objects in each group when 12 objects are partitioned into 4 equal groups. It can also mean the number of groups when 12 objects are partitioned into groups of 4.

# Related Facts and Family Facts

Related facts and family facts are great tools for solving multiplication and division problems. For example, if 6 x 2 = 12, a related fact is 12 ÷2 = 6. 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,

- 2 x 4 = 8
- 4 x 2 = 8
- 8 ÷ 2 = 4
- 8 ÷ 4 = 2

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

# Introduce Bar Models

It is a good time now to introduce bar modeling. For example,

This lets students get comfortable with seeing multiplication and division problems in bar models, which will come in handy when we solve word problems.

# Determine Unknown Whole Number

This can be tricky for some students if they are not fluent with their multiplication and division family facts (see above). For example,

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

- 2 x ? = 8
- 15 = ? x 3
- 5 x 5 = ?

One way we can practice is to write the family of 4 basic facts given any one of the basic fact (e.g. given 2 x 4 = 8, find the rest of the family facts – 4 x 2 = 8, 8 ÷ 2 = 4, and 8 ÷ 4 = 2).

# Properties of Operation

These are the

- cumulative property (e.g. 2×5 = 5×2),

- associative property (e.g. 2x5x10 = (2×5) x10), and
- distributive property (e.g. 7×5 = (5×5) + (2×5)).

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

2 x 6 = 12

Then, hiding one of the factors,

2 x ? = 12

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

? = 12 ÷ 2

# Related Resources

## Video explanation and lesson plan (member’s resource)

## 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.
- BC 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 (2A) Chapter 5 – Multiplication and Division (pages 107 to 126)
- Primary Mathematics workbook (Common Core Edition) (2A) Chapter 4 – Multiplication and Division (pages 112 to 134)

## Supplementary Worksheets

- G2S1W12-MW Multiplication Tables of 2
- G2S1W13-MW Multiplication Tables of 5
- G2S1W14-MW Multiplication Tables of 10

## Related Resources

For more related resources, please refer to our Multiplication and Division page.