##
* *Reflection: Problem-based Approaches
Making Tables For Multiplication - Section 3: Try It On Your Own

During this part of the lesson, I moved from group to group to listen in on their discussions and look at their plan to map out the different outcomes. Each group came up with a different strategy to determine the different outcomes. Some students relied on the cubes by building each color for the dogs connected to a collar.

Another group just recorded the collar colors and the dog colors and filled in their table. This group of students included both a student receiving special education services and one of the higher students in my class. I discovered through some questioning that the special education student suggested this plan.

One group listed all collar colors individually by dog color. They took the brown dog and listed all the collar colors on the brown dog. Next, the took the black dog and listed all the collar colors in a different order from the first dog. This random list continued with the yellow and white dog.

One group put the dog cubes in a horizontal row and the collar cubes in a column beneath the dog cubes. The students recorded this information, and then just moved the column to the next color for each dog and recorded their findings.

Each group came up with the correct number of possible outcomes of 28. There was much discussion between students on what type of strategy to use to solve the problem. Some of the students just wanted to find the right answer, and I had to reinforce it was not about the right answer. I explained this problem was about being able to explain their strategy for solving a problem and explaining the different possibilities.

*Team Plans*

*Problem-based Approaches: Team Plans*

# Making Tables For Multiplication

Lesson 4 of 6

## Objective: SWBAT create a table to find different outcomes when combining options.

#### Warm-Up

*10 min*

This activity must allow time for exploration and sharing of ideas among students. Without the sharing it will lose most of its learning impact. You may want to plan this lesson as a two day lesson if you have short math periods or defined periods.

I open this lesson with idea of choices at an ice cream store. I say, *Let's imagine we get to go to the ice cream store, and we get to choose one type of ice cream and one type of topping. Today, there are three ice cream flavors, and four toppings. Does anyone know how we can figure out how many different types of sundaes we could make at the store today?*

I choose this scenario because it is a very familiar activity to most students, and one that hooks them into the problem solving strategy of the lesson.

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#### Guided

*10 min*

Using the example of the ice cream store, I ask the students to think about a possible way to keep track of all the different types of sundaes, and write down their plan or strategy in their math journal. This notebook is kept in their desk, and they can write a picture, diagram, or words, to record their thinking. I have the students share their plan with a partner at their table group. During this time, I circulate through the room to asses their understanding and plans.

I call the students back to the carpet area to share out some possible ideas. Because the Common Core Math Practice of constructing arguments and critiquing the work of others, I have many several students share their plan with the group. This allows the students to see if they think the same way as another student, or to present their own unique idea and see if makes sense.

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#### Try It On Your Own

*15 min*

I give the students the scenario of how my dog loves to wear a dog collar, and she cries if we take it off of her. So we always have to have an extra one available, especially if it gets dirty and muddy. Plus we don't want her to be without an ID tag. I explain that she has many collars because she is so spoiled, and my children like to buy new ones for her.

I then present the situation of what happens at an animal shelter, when they are trying to find the best collar for different dogs to help them look their best for families that come in to adopt a dog.

I ask the students to determine how many different outcomes would be possible if there are four dogs and seven different collars. Each dog could only wear one collar at a time, and there is only one collar in each color.

I provide the student teams with linking cubes in yellow, white, black and brown to represent the dogs. The collars are represented with linking cubes in orange, red, green, blue, light blue, light green, and a dark red color.

Each team of four students develops a plan and creates a table to present to the class to explain how many different dog and collar combinations can be created. At this point, the teams work together and create a chart. I provide a piece of white construction paper and they use crayons to record their tables.

This math lesson can be extended or modified into division by giving the total number of collar and dog color combinations and having the students come up with different explanations. Additionally, I think it is worthwhile to offer students the opportunity to explore and consider other math examples connected to an animal shelter. There are many other stories to consider at an animal shelter with area of kennels, division of food, and volume of water.

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#### Team Sharing / Wrap Up

*20 min*

The wrap up of this lesson is longer than most closings of lessons, because the groups are presenting their ideas to the class. I have each student team tape their diagram to the classroom whiteboard, and each team explains their strategy to the group.

During the presentations, I say to the teams, *"Please explain the strategy your team used to find the different possibilities and your table." *Students listening are encouraged to ask questions of the team presenting especially if they need clarification of their strategy. Students also ask questions about the table. If there are not any questions from the students, I will ask, *"How does your table show each dog and each collar? What was your strategy for keeping track of each combination?* These presentations also address the Listening/Speaking standards of the Common Core Standards, and I also use these presentations and team discussions as an observational assessment for this standard.

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