I taught this lesson before, about a week ago. Afterwards, I realized that while the students were drawing appropriate models, they still were unable to express their understanding of multiplication. I decided to re-teach the lesson, this time adding reflection time for students to consider their own work, and the work of their peers.
This will be a two day lesson, as I will give the students one session to explore their multiplication problem and create a display. The second day I will have them working together to critique their peer's thinking and offer comments and suggestions.
As you prepare for this lesson, remind yourself that this is one of those lessons when you don’t want to talk too much. The reason for this is to listen in and allow the students to struggle with the concept of equal groups in multiplication. It also allows students time to grapple with each other’s strategies and thinking. Remember, when the students do the talking, they are the ones learning.
To introduce this lesson, I rolled two dice and write the results on the board as factors. I ask students to turn and tell their partners the product. After some wait time, I put the product on the board, asking this question:
Mathematicians, what does this number sentence tell us? What does it really mean?
At this point, I am looking for more understanding of multiplication as units, of units (groups). Most, if not all, of the students should be able to explain it means there the number sentence tells us a specific number of equal sized groups.
After they explain, with prompting as necessary, I will ask someone to create a story to fit the number sentence. I then write that on the board. Next, I ask if there is another way to show the story…maybe an array, a picture, fact triangles, etc.
Following the group practice, I give the students a poster paper and tell them to come up and roll the dice. This will create their title: “The story of ___x____=___”. They are instructed to write at least one word problem (MP2) and then model the math two to three other ways (MP1).
As they work, I will enter into conversations with them to prompt them to push further and also in order to gain an understanding of their misconceptions, if any. This is a perfect time to do some one-on-one, or small group lessons with students. Working along side of them on their work is much more valuable, I think, than seeing if they have the correct answer in a workbook.
This is a video of one of my students, who has a learning difference, explaining his drawing. It is amazing what happens over time when students have time with their own thinking, and have an opportunity to grow their thinking by talking with each other (MP3).
These boys have a great poster, including their story. However, there's a problem with the array. Check out my reflection about that...
Because today is the first part of a two day lesson, at the end of this lesson, I wrap up in a different way. If you choose to teach this lesson and the next, this is a good stopping point.
Boys and girls, as I looked around at your work and listened in to your discussions, I am impressed with your work with equal groups and your ability to be good teaching partners.
Tomorrow we are going to have a chance to look at each other's work and make comments using some "thinking sentences" I will teach you. Right now, take the next 10 minutes to finish up and make sure you are ready to share your piece with your classmates tomorrow. You and your partner may want to look at each thing you did carefully and make sure it represents your story.