Peterson Family Ski Trips

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Objective

SWBAT solve multi-digit multiplication problems within a problem solving context.

Big Idea

Students will determine how much it will cost for the Peterson family to visit two different ski resorts by visiting the webpage of each resort.

Opening

20 minutes

Today's Number Talk

For a detailed description of the Number Talk procedure, please refer to the Number Talk Explanation. For this Number Talk, I am encouraging students to represent their thinking using an array model. For each task today, students shared their strategies with "someone new across the room." It was great to see students inspiring others to try new methods and it was equally as great to see students examining each other work for possible mistakes!

 

Task 1: 42 x 3

For the first task, some students decomposed the 42: 42 x 3 = (40+2) x 3. Others decomposed both multiplicands: 42 x 3 = (40+2) x (2+1). I always ask students to try multiple methods. 

 

Task 2: 42 x 53

During the next task, I asked: How many more 42s are there than the last task? Students responded, "50... because 50 + 3 = 53." I encouraged students to compute the answer using mental math by asking: What is 50 x 40? (2000) And what's 50 x 2? (100) What will the product of 42 x 53 be then? Students added 2000 + 100 and then added the product of 42 x 3 to get 2,226. I responded: Well, let's see if you're right! Represent your thinking using an array! Here, a student proved that 42 x 53 really does equal 2226! Others took a more complicated path: 42 x 53, Complicated.

 

Task 3: 84 x 53

Then, students solved 84 x 53. I loved watching this student, 84 x 53 = (42 x 2) x 53, push herself to use multiple strategies: array, standard algorithm, and partial products! 

 

Throughout every number talk, I continually model student thinking on the board to inspire other students. This also requires students to use math words to explain their thinking instead of relying on a model to represent the math. As students solved each task, I wrote the answers on the board to encourage students to use prior tasks to solve the more complex tasks.

 

Teacher Demonstration

20 minutes

Presentation 

We have a class set of student laptops in our classroom this year. Each student also has a Google email address. Often, I'll create a Google Document and share it with students. They will then copy the presentation, making it their own. For this lesson, I created and shared the following presentation: Peterson Family Ski Trips. My goal was to provide students with a real-world scenario (Math Practice 6: Model with Mathematics) in which 2-digit x 2-digit multiplication is necessary. 

Introductory Video

To begin today's lesson, I asked students to get laptops and mice. While students got ready, I played the following video to encourage student engagement and personal connections with today's lesson. Immediately, students were intrigued and involved in conversations about skiing! 

 

Goal & Modeling

Once students were ready, I introduced today's Goal on the first page of the shared document: I can solve multistep word problems involving multiplication. I asked student to highlight the word "multistep" and we discussed its meaning: having more than one step or operation, such as adding and then multiplying.

The Peterson Family

Next, I showed students a picture of the Peterson Family. I made sure the Peterson family was quite large (20 members) in order to provide students with 2-digit x 2-digit multiplication practice. Also, I purposefully included 6 older children and 12 younger children. By including children of multiple ages, students will need to pay close attention to the ski tickets offered to different age groups when problem solving later on. 

Then, I explained: Today, the Peterson family needs your help! As you can see, the Peterson family is quite large... One of my students who comes from a large family giggled and shared, "Finally, a family larger than mine!" I always love when students begin to make personal connections with the stories in math!

Bridger Bowl Ski Resort

I continued: For Problem #1, the Peterson family needs help calculating the cost for their family to go skiing at Bridger Bowl Ski Resort for one day. (This resort is one of the two major ski resorts in the Bozeman area.) For Problem #2, the family needs help calculating the cost to go skiing at Bridger Bowl for three days in a row. I showed students how to access the ticket prices at the Bridger Bowl website by clicking on the included link. 

Big Sky Ski Resort

I scrolled through the shared document and explained: Later on, for Problem #3, you will also be calculating the cost for the Peterson family to go skiing at Big Ski Ski Resort (the other major ski resort in the Bozeman area)

320 Guest Ranch

Finally, for students who finish early, I've also included a challenge problem, Problem #4, that involves the Peterson family going to dinner at the 320 Guest Ranch

Teaching Perseverance 

Besides outlining the assignment and sharing minimal information about the ski resorts today, I chose to exclude teacher modeling. I wanted to provide students with the opportunity to engage in Math Practice 1: Make sense of problems and persevere in solving them. In particular, I wanted students to analyze the problems on their own, attend to details, calculate solutions, and determine if their answers made sense. 

Student Practice

60 minutes

Choosing Partners

Picking math partners is always easy as I already have students placed in desk groups based upon behavior, abilities, and communication skills. Before students began working, I asked them to discuss how they would like to support each other today. I gave them many examples: Do you want to take turns talking out loud? Do you want to solve quietly and then check with each other? Or do you want to turn and talk anytime you get stuck? Students always love being able to develop a "game plan" with their partners! 

Monitoring Student Understanding

Once students began working on Problem #1, I conferenced with every group. My goal was to support students by providing them with the opportunity to explain their thinking and by asking guiding questions. I also wanted to encourage students to construct viable arguments by using evidence to support their thinking (Math Practice 3). 

  1. Can you explain your thinking?
  2. What steps are you going to take to solve this problem?
  3. What are you trying to figure out?
  4. What can you do to make sure your calculations are correct?
  5. Is this the answer? How do you know?
  6. How can you make your work more precise?

Problem #1

As students began working on problem #1, many overlooked the ski ticket age requirements. For example, any child 13 and older has to purchase an adult ticket. I couldn't wait for a student to discover this: Attending to Ticket Details!. I then asked her to share her discovery with the rest of the class: Number of Adult Tickets.

I also encouraged students to use their white boards to calculate costs: Calculating Problem #1

During this conference, Supporting a Student with Problem #1, I try to call the student's attention to the number of children in the family. I also took this opportunity to reteach the standard algorithm.

Problem #2

When conferencing with this student, she explains a problem that she discovered and I support her as she finds a solution: Supporting a Student with Problem #2. Once this student gets past this confusion she becomes successful on her own: Problem #2 Success.

Problem #3

For the third problem, students had to adjust the number of tickets needed based upon family member's ages: Student Explaining Problem #3.

Problem #4

Here, I ask guiding questions to support a student with the last problem: Supporting a Student with Problem #4.

 

Completed Work

Most students were able to complete the first three problems within this time frame:

A couple students were also able to get to problem #4.