Repeated addition as it relates to multiplication. |

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__Part 3__

__Part 3__

I continued

the next day with a lesson on repeated addition. I posed this question to the students:

*Making
groups of three, what addition sentence could you write for 12 cubes?*

This part of

the lesson is the **YOU** part in which each student has to find the solution on

his/her own. Of course as the teacher,

if I did see a student not even attempting I tried to go over and encourage

him/her and have the student think of some possible approaches but I never did

any of the problem solving for the child.

__ The learning is in the struggle! __ Each student received a bag of cubes and a

blank sheet of paper which they divided into fourths to record their

solutions. We reread the question and I

made sure they understood what was being asked.

Then I let them start while I walked the room looking for students who

had recorded their solutions. When I saw

the first student who had drawn and recorded 3 + 3 + 3 + 3 = 12, I had that

student go up and record that on the white board.

The student

explained to the class what they did and then I proceeded to give the next

instruction.

*What other
ways can you add equal groups to get 12?
*

Find some

more ways I instructed them. Again, I

went around and noticed how the students were quickly grouping by 4s, 6s, and

2s. I had some come up and record their

solutions. Those same students explained

to the class their addition sentences.

Students come to the board to record their solutions. |

Now came the

YOU ALL part. The students now worked

with a table partner to combine their 12 cubes to make 24. The students now had to work together to see

how many addition sentences they could come up with for 24 cubes. Students were very motivated to get the first

solution because they really wanted to share the solution on the board. But at the same time I was amazed at the rich

discussions that were going on about how to proceed, which groups would they

use, and of course the skip counting.

They easily constructed repeated addition sentences for the different

ways to make 24. I had partners come up

and record their solutions and explain how they did it.

Next, is the

WE part. In this part, I take over more

and now show the students how this relates to multiplication. I asked: in this addition sentence (3 + 3 + 3 + 3 = 12), how many “times” did we write

3? Of course they responded 4

times. So I asked: does that mean 4 “times” 3 is 12? I was practically blinded by all the light

bulbs going off over all the students heads!

They could now see the connection of “times” to repeated addition. From there, I modeled how to turn another

repeated addition sentence into a multiplication sentence. At this point I also introduced the

vocabulary of factors and products. They

then had more practice by turning all the repeated addition sentences that they

had recorded on their papers into multiplication sentences. Once that was done, it was time to open the

Go Math book and do the independent work in the book (which matched perfectly

what we had just learned).

amazed at how easier and more productive this “reverse gradual release of

responsibility” model is working for my students. They are more engaged, eager to try and find

solutions, better at explaining their work and are far less frustrated than the

beginning of the year when I relied solely on what Go Math provided.

That is the

end of the series on implementing the Japanese style of teaching math. By the way, if you care to Google it, it is

called Bansho in Japanese.

Hi TBAAD! You have been nominated for the Liebster award! You can see your nomination here: http://www.studentsavvyontpt.blogspot.com

Wow, that's really exciting! Thank you!