Count Bys to Multiply

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Objective

Students will be able to identify patterns in repetitive addition of 5 to begin learning to multiply by 5.

Big Idea

Students are able to skip count by 5's easily at this level. That ability will be used to launch into an understanding of multiplication using patterns and drawings.

5, 10, 15, 20...

30 minutes

It is important in this lesson to begin with what the students already know.  They have been counting by 5's since kindergarten probably, so this beginning will launch them into using that knowledge to gain insight into a new skill; multiplication.

The goal is to have students know that when they are skip counting by 5, they are not counting one 5, they are counting one "group" of 5. It is critical to spend some time on this with the students. Have them draw sets of five x's and then begin the counting.  Or line up blocks in groups of 5's. I will add what my class did on white boards in the resources. 

Students, I would like you to circle sets of 5 on your board.  Now, next to each set write the total number.  Yes, it does count by 5's!  Your labels should go from 5 to 50.  So, what are we counting here?  Where do the numbers 5, 10, 15, 20, 25, 30... come from?  We call these numbers multiples of 5 because they are the totals we arrive at when we count by 5. 

Discuss this as long as you need to. In the past, I have thought of counting by 5's is basic knowledge, but every year it is a conversation that lasts a few minutes.  Many students don't the growing count as cumulative totals (e.g., 5, 10, 15 I've counted by 5s three times, 3 groups of 5 is 15 altogether).

Yes, those numbers are the total we have in our groups.  Do you notice any patterns in the labels?

Listen for students to see that the digits in the ones place alternate 0, 5, 0, 5.  Begin now to have the students list the equations, both addition and multiplication for each skip count.  This activity gives you the perfect time to introduce multiplication as repetitive addition, which is counting by, or skip counting!  The kids get super excited when they realize they have been multiplying for years! Now we just give it a new name for the total (product).

During this lesson, I also begin to address the vocabulary words: product, factors, and equation, and equal groups. I use them often, within a concrete frame of reference, so that students begin to acquire, and retain, meaning.

The full time in math for this lesson is devoted to discussing patterns and observations.  I do not give out practice sheets on this day, as the conversation and observations by the students are what I am after.  Don't worry, this is math! As a matter of fact, I believe this sort of time spent is crucial to the development of mathematical communication and reasoning skills, and the math community that supports it. 

Multiplication Chart

15 minutes

Following our lengthy, yet important, conversation about repetitive addition, multiplication, patterns in count bys, and vocabulary, I put up a multiplication chart with the equations, products, and different multiplication symbols.  I then ask the students to spend 2-3 minutes using the turn and talk strategy to discuss patterns they see and wonderings they have.

Allow time for sharing these observations and then lead the children through a guided observation. My role is ask questions, when needed, rather than to "tell" students what or how to find and describe patterns.

Boys and girls please find the column that has five at the top and look down the column and notice patterns.  Do you see a pattern in the one's place or tens place?  What do those patterns tell us?  Is there another place on this chart that looks similar?  How is it different? When we look at the 5 row, the equations look a bit different.  Can you think of why that might be?

Here you may want to draw some of the arrays for the equations in the column and the equations in the rows.  This will help the students visualize that the equations, though having the same product, describe different numbers of equal amounts.  

For example:  

2x3=6  (2 equal groups of 3)

      xxx

      xxx

3x2=6  (3 equal groups of 2)

      xx

      xx

      xx

Closing

5 minutes

Mathematicians, you have worked hard today to make sense of count bys, multiplication, factors, and products being a total of count bys.  I was impressed with the patterns you noticed today.  Tomorrow we are going to put your observations to work to see if we can figure out some rules for multiplication. 

Does anyone have any wonderings still?  What was the most interesting thing you learned today?  Turn and talk to your partner about that please.