Multiplication tables of 2, 5 and 10 and 3 and 4, are introduced at the 2nd grade level. In third grade, we add the multiplication tables of 6, 7, 8 and 9 to our multiplication tool-belt. There is a reason for this spiral approach to span two grades. Multiplication tables for 6,7,8 and 9 are usually much more challenging than that for 2,3,4,5, we should ensure that students have mastered the multiplication tables for 2,3,4 and 5 before moving on on 6,7,8 and 9. Otherwise, it is going to get really confusing.
The approach we use for each of these numbers is similar to what we used for the easier numbers in 2nd grade.
Interpret Product of Whole Numbers
We start with skip counting, i.e. 6, 12,18… then, move on to using dot paper to represent the total as dots in arrays of rows and columns. Finally, we’ll use the distributive property of multiplication to break up the product into easier “landmark” numbers. For example:
As numbers become more complex, we develop fluency for square numbers (usually through card games, and fun activities) to add more “anchor” or “landmarks” numbers to the students’ tool-box. For example, if the student knows 5×5=25, then she can derive 6×5 from 5×5 by using the distributive property (although she doesn’t know the term yet), i.e. 6×5 = 5×5 + 1×5.
Practice using the distributive property to derive multiplication from square numbers using dot paper as visualization aids, e.g.
Division – Difference in Context
As with the smaller numbers, we want students to appreciate the difference in the two context that is represented through a division operation.
In the first example below, we’re looking for the number of elephants in each group if all the 42 elephants are divided into 6 equal groups.
In the second case, we’re looking for the number of groups if we want to group the elephants into groups of 6.
Related Facts and Family Facts
Just as with the easier numbers, we would practice writing related and family facts such as
6 x 8 = 48, 8 x 6 = 48, 48 ÷ 8 = 6, 48 ÷ 6 = 8
We’d also learn how to use the related multiplication facts when dividing.
Properties of Operation
Properties of Operations for Multiplication and Division
- Distributive – 7×6 = (5×6) + (2×6)
- Associative – 3 x 8 x 10 = (3×8) x 10 = 3 x (8×10)
- Commutative – 4 x 8 = 8 x 4
Division as an Unknown-Factor Problem
Please refer to previous blog posts for the detailed steps.
Solving Word Problems
After students understand the multiplication tables, we can introduce simple word problems and solve them using bar models, e.g.
Video explanation and lesson plan (member’s resource)
Common Core Standards
- 3OA.A1 Interpret products of whole numbers.
- 3OA.A2 Interpret whole-number quotients of whole numbers.
- 3OA.A3 Use multiplication and division to solve word problems.
- 3OA.A4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers.
- 3OA.B5 Apply properties of operations as strategies to multiply and divide.
- 3OA.B6 Understand division as an unknown-factor problem.
- 3OA.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 (3A) Chapter 6 – Multiplication Tables of 6, 7, 8, and 9 (pages 93 to 119)
- Primary Mathematics workbook (Common Core Edition) (3A) Chapter 4 – Multiplication Tables of 6, 7, 8, and 9 (pages 125 to 175)
For more related resources, please refer to our Multiplication and Division page.