3rd grade is the first time students are exposed to formal multiplication!
When we memorize without having context or a concrete experience to ground the learning, the information is stored in our short-term memory and easily vanishes from our body of knowledge because there is nothing to anchor it in place.
Good memorization skills or not, students NEED concrete experiences if we want them to develop a conceptual understanding of multiplication. Join me on a short CRA journey as we take a look at just one of the many activities you can do to support Standard 3.OA.A.. We will build students' conceptual understanding by anchoring the learning in a Concrete activity, moving that activity through the Representational phase, and then smoothly ending with the Abstract understandings we expect students to know at the end of the process.
Phase I: CONCRETE
The Concrete phase of learning requires us to get our hands on tangible items that we can touch and sort and move and then move again when needed. For this Standard, there is no one specific item that will do that best, so look around and see what you have on hand that can be grouped and sorted and touched – and, yes, simple counters work just fine.
Let's begin with an exploratory task:
- Give each student 24 counters (I like to start with 24 because it is not an overwhelming number of objects for students to manage and there are so many grouping options that allow for even groups – 1, 2, 3, 4, 6, 8, 12, 24)
- Ask students to pretend that the 24 counters represent children playing.
- The children decide to break off into groups. If every group has an equal number of children, how many groups are there?
- So at this point, your job is to walk around and closely observe how students are approaching this tasks. Limit your interactions and allow them to work through their thoughts.
- Once students students are satisfied with the groupings they created with their counters, refocus them to the task by asking, "Does every group that you created on your desk have the same number of counters? Count to be sure. Adjust if you need to." Give time as needed.
- Next ask students to share how they decided to group the counters into equal amounts.
- Listen carefully. Allow the student time to explain. Record the student's thoughts by drawing representational models of the groupings their described.
- Repeat the process multiple times seeking ideas that are different than the ones presented already.
Phase II: REPRESENTATIONAL
- Give each student a piece of blank paper that they can use to represent that ideas of their classmates.
- Ask students to fold the paper in half and then in half again. When they open the paper, they will have 4 sections clearly marked by the fold lines.
- Have students walk around the room to find 4 different ways that their classmates created equal groups with 24 counters – emphasize the importance of equal groups. Have them draw a representation of the model in each of the four sections of their paper.
Phase III: ABSTRACT
- When students have finished drawing their representations of the concrete models, ask them to return to their desks.
- Ask students to share one of the ways they drew on their paper.
- Draw that model on chart paper or reference the earlier drawing you created during the Concrete Phase of the lesson.
- Ask students how many groups are in that model. Write the number they say below the drawing (6).
- Ask students how many items are in each group. Write that number to the right of the group number (4)
- Discuss the multiplication symbol. Add it between the numbers saying "6 groups of 4 means 6 times 4" – while saying these words you are writing in mathematical notation 6 x 4
- It may be obvious to you, but not them, so ask, "Boys and girls, if I have 6 groups of 4, how many total counters do I have?" (24) Then ask, "How do you know?" (yes, go back and count here to verify as needed)
- Repeat this process for each equation shared (1x24, 24x1, 2x12, 12x2, 3x8, 8x3, 6x4, 4x6 – point out how 6x4 and 4x6 use the same numbers but the model looks different. Be sure to help students see that the product, either way, is exactly the same!)
Won't these be great on your bulletin board
as a collection of Anchor Charts?
