Students were given unifix cubes to show how they could be counted quickly.

Part 2

The first lesson I tried using the You, You all, We approach involved teaching the concept of equal groups for multiplication.  I presented this problem to the students:

What is the best or fastest way to count 12 cubes?

I gave each student 12 unifix cubes and a blank sheet of paper of which they folded into fourths.  We read the question together.  I made sure everyone understood what was being asked and what the cubes and the paper were for.  With the unifix cubes they had to use to figure out a way to count the cubes quickly.  The paper was to record either by drawing or writing what they did with the cubes.  They had to figure out as many ways as possible.  I also told them they were on a deserted island and so they could not talk to anyone, including me.  They just had to get to work and figure it out.  

I then started to walk around as they were trying to figure it out.  Immediately I saw some children putting the cubes into groups to count by 2s or 3s or 4s, etc.  Once I saw that a child had recorded what they had done, I quietly asked the child to go up to the white board with the paper and copy what they had done.  I kept walking and selected another child. I did this 4 times.  Once the 4 students had copied their work onto the white board, I asked each one to come up and explain what he or she had done.  I purposely chose students who had counted by different numbers.  It was exciting to see the students explain what they had done!  I feel this part of the lesson was so important because in many instances in the Go Math book, students MUST explain how they got the answer….and the replies I have been getting have been hilarious:

“I read the question and just did it.”

“I sat for awhile and figured it out.”

“I guessed.”

However, when these students came up, they confidently explained how they grouped the cubes by 3s (or 2s or 4s, etc.) and then skip counted by that number to 12.  The underlined words offer insight into the student’s thinking:  I need to make equal groups of the same number so I can count by that number to quickly get to 12!  The lesson did not end here.  The next step (You All) was to have the students work with their table partner and combine their cubes to make 24 total.  They worked together to find ways to quickly count the 24 cubes.  This time they were even more confident and quickly figured out how to count them by 2s, 3s, 4s, 6s, 8s, even 12s!  Again, I strategically chose students to come up record their work on the board and then explain to the class.   Their explanations again were spot on with the use of groups, skip counting and that the groups had to be equal.  

Then it was my turn (the We part) in which I help them label their paper (which were now called notes) with terms such as:  4 groups of 3 equals 12 or 3 equal groups of 4 equals 12.  We did that for all the ones that were recorded by the students on the board.  Then I excitedly announced to the students:  You just discovered MULTIPLICATION!  You should have seen the looks on their faces.  Yes, I said:  multiplication is the quick counting or adding of equal groups.  From there, I then assigned the workbook pages from the Go Math book.  They worked for about 15-20 minutes and I only had about 2-3 students ask for help.  They completely understood the concept of counting equal groups and were able to apply it to the word problems and problem solving workbook problems.  Thank goodness for unifix cubes!

Part 3 coming soon:  repeated addition with the You, You All, We approach.
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