The Story of Multiplication Day 2

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Objective

Students will be able to evaluate peer-made multiplication problems with display and critique, offer comments, and suggestions to one another.

Big Idea

In the second day of a two day lesson students work on expressing multiplication in various ways, and also work to develop their math communication and critiquing skills.

Warm Up

15 minutes

Yesterday, students wrote their own multiplication story (word problem) and then modeled the math two to three other ways. Today, students poster tour their peer's work from yesterday. Prior to setting them off on a tour, I put up a poster of my own work, with a misconception and a well constructed word story with the factors misplaced. 

I then ask the students to view my work and discuss with their partner what they notice. Before they share out, I put up three sentence starters to guide thinking.  I then ask students to phrase their comments using these starters.  For today's lesson, the prompts are: 

  • I understand your equal groups because...
  • I disagree with_________because...
  • Maybe you could show your math by using this strategy....

Poster Tour

20 minutes

As the students rotate around the room in partnerships, they are instructed to respond to each other using talking moves and to the work using the sentence prompts.  This keeps the conversations focused on the math and not opinions.

In the previous lesson, the students were asked to multiply a 1 digit by 1 digit number obtained from rolling two dice. Their instructions were to write at least one word problem and then use other models.  I listened and watched for the following types:

  • groups of represented by arrays, drawings

  • repeated addition on a number line

Strategies can include use of what is known to determine what is unknown (e.g., I know that 2 x 2 is 4 so I know that 4 x 4 would be double the product because 4 is double the multiplicand/multiplier (not that we expect them to use this language).

At each poster, there is a chart with the sentence prompts and a pad of sticky notes. The students will use the note to write their comment and then will place them in the column with the appropriate sentence starter heading.

If you have not worked with talking moves yet, or sentence prompts, try using one at a time until your students are used to using them.  Both of these build life long communication and thinking skills, and are appropriate as mini-lessons.  

This activity is appropriate for all styles of learners, as you will see in this video.

 

These students work together to not only give feedback, but to make sense of "what doesn't make sense".

Poster Revision

10 minutes

Revision is one of the most powerful teaching tools we can use. Our work is no longer incorrect, it is thinking we can safely change to reflect a change in our understanding.

In order to practice revising their thinking, the students return to their work and read over the comments and suggestions left by the visiting mathematicians.  This is heavy work. It takes a safe working environment for students to get feedback from each other and value that input, rather than it coming from the teacher.  It is, as well, much more powerful.  As the children decipher the comments, they can begin to revise their work and add to it any strategies they saw from their own touring. 

This is an effective, and an important, math practice.  However, be prepared for the noise level to increase as the debates to begin. Remember, it may be noise, but when its accountable talk, huge growth is happening. 

The students here are beginning a conversation about how the suggested revision made them think of multiplication as it relates to division.  Listen to the natural and spontaneous dialogue regarding this issue with the whole class.  This is what we are looking for in a math community!

 

Wrap Up

15 minutes

After several minutes of debate and revision, I give the students time to share one thing from their poster with the whole group.  If you don’t have time for that, another model is to have two groups merge and share with each other.

While the share is happening, I listen in, model questioning such as, “Why did you choose to do it that way?" Or, “How did you know to make it 9 groups of 3 and not 3 groups of 9?”  As we progress, students will be asking each other these types of questions.

For home practice, I assign a number story by rolling the dice and ask the students to represent it with a word story and 2 other ways.