Teaching Multiplication – Grade 3

Reflecting on the PCK model and the TPCK model, I think that our individual curriculum documents do a great job at breaking down the content (subject) knowledge. For instance, our Math curriculum has a list of outcomes at each level, descriptions of what each outcome means,  suggested assessments, manipulatives that can support the outcomes, success criteria, etc. The second part, pedagogical knowledge, is not so black and white. As Shulman (1987) suggests, it doesn’t matter how much the teacher understands the outcomes they need to be able to foster understanding of them in such a way that is accessible to all learners.

Teaching Multiplication

Many students come into my class with their time’s tables memorized (or somewhat memorized). When teaching multiplication, though, I do not want them just to be able to regurgitate their multiplication facts, but instead, understand that multiplication is counting equal groups (repeated addition) and learn strategies to multiply larger numbers using mental Math. When students grasp this concept, it helps them when applying it in their real life. The following break down is done over several weeks.

Prior-Knowledge

I always start a multiplication unit after an addition unit, and before even uttering the words ‘times tables’ or ‘multiplication’ I activate prior knowledge by looking at skip counting. We practice counting up by different numbers and then look at how many times we counted.

E.g. 7, 14, 21, 28. How many times did we count by 7? So, 4 groups of 7 equal 28.

Looking at Concrete Materials

Next, we will look at how we can represent this counting using manipulative and pictures. Students first use different types of manips to create equal groups and then practice various counting strategies on their own. I formatively assess how students are counting. The ones who are still counting by 1’s, I know need more time and support with these activities. After they have mastered using manips they can start to draw simple representations of equal groups and show how they count them.

After, we move onto word problems where students solve problems using the strategies above. When addressing these problems students are expected to answer by drawing a representation of the numbers in the form of a picture, and write a concluding statement, i.e., 7 equal groups of 4 is 28.

Looking at the Abstract

Once they have mastered this, we add an extra element by  representing problems with a number sentence i.e. 7 + 7 + 7 +7 = 28 and 7 x 4 = 28.

Practice and Reinforcement

When students reach this point where they can look at multiplication abstractly is when I would introduce quick warm-ups where students are practicing their recall.

The last skills I teach students are different ways to solve multiplication problems by applying different written and mental strategies other than using the traditional algorithm. For instance, we look at partitioning numbers first by looking at small numbers and 2 by 1 multiplication and then move to larger numbers and 2 by 2 multiplication.

Example: 12 x 4

10 x 4 = 40

2 x 4 = 8

40 + 8 = 48

This type of teaching, allows we to do ongoing assessments and easily differentiate for students who ate struggling as well as those who are excelling. Furthermore, by introdcuing a wide range of strategies allows students to find one they can identify with.