Mathematics Lesson Study Plan

Math Journeys – Dr. Martin Luther King Jr. Elementary - June 27, 2013

5th Grade – Unit within a unit problem

Lesson Facilitator:Anna FriemelMilli Butler

Lesson Study Team: Sarah Isgrig, Natalie Holliman, Bronson Melton, Amber Ochoa, Sherra Wallace, Larrissa Williams, Glennis Allen, Katie Phippin, Zsuzsanna Diamond, Jason Crader

Lesson Objective:

The goal of this lesson is for students to problem solve andrepresent the problem using various models:

  • Pictures
  • Equations

Long Term Goals:

  • Students will be able to express themselves verbally and in writing.
  • Students will develop resilience and perseverance to better face difficult tasks.
  • Students will have confidence in themselves and their abilities.

Mathematical Practice Standards focus:

  • Standard 1: Make sense of the problem and persevere
  • Standard 3: Construct viable arguments and critique the reasoning of others
  • Standard 6:Attend to precision
  • Standard 7: Look for and make use of structure

Common Core focus:

Apply and extend previous understanding of multiplication and division to multiply and divide fractions.

  • 5.NF.7a Interpret division of a unit fraction by a non-zero whole number, and compute such quotients.
  • 5.NF.7c Solve real world problems involving division on unit fractions by non zero whole numbers and division of whole numbers by unit fractions, e.g. , by using visual fraction models and equations to represent the problem.

SLEs focus:

  • NO.1.5.1 Use models and visual representations to develop concepts of the following: Fractions – parts of unit wholes.

Materials needed:

  • Partner work mat, SmartBoard, Power Point, iPad to display student work. Two pans of brownies, wax paper, cardboard

Lesson Process:

Teacher’s statements, directions, and questions / Expected Student Responses / Notes
Pre-opening(Quick discussion of group norms & how to use the workmat, which will have already been discussed before the beginning of the lesson.)
Opening for Problem 1(1-2 minutes)
Math Journeys story: Did you know that at the end of Journeys on Parent’s Day, we have a party and serve cake to all of our guests?
Problem #1 (9 minutes)
“I have a problem for you to work on today. Last year, we only had ½ of one cake left over at the end of the day. Mrs. Butler and Mrs. Knott got to take the leftover cake home.
How much of the leftover cake did Mrs. Knott get if they shared it equally?”
Show students half of a cake. Have materials ready to go. Make sure students have an understanding of the problem.
“Think about how to solve this on your own for two minutes. Here is a piece of paper with the problem for you to display your thinking”
How much of the leftover cake did Mrs. Knott get if they shared it equally?
At the end of two minutes, the partners should share their work and discuss how they solved the problem. After they come to an agreement, they should put their work on the workmat. Students will only have four minutes to do this.
Close Problem #1 (5 minutes)
The teacher will mini-close at this point looking for a partnership that worked the problem correctly and can explain their work to the other students. The teacher will take a picture of their work with the iPad and display it for all to see and then the students will explain their thinking. / “I divided the cake by ½ because there are two teachers.”
“If there was a complete cake, I would cut it into fourths. I know there were two people so 2/4 equals ½ .
Opening for Problem 2 (3 minutes)
“For our second problem today, we’ve created a story for you to do involving real brownies.”
“Last night, my mom baked a pan of brownies for my sister and me. After she went to bed, they smelled so good I could not stop thinking about them. So, I sneaked into the kitchen after everyone went to sleep, and ate ¼ of the pan of brownies.”
Show students the ¾ pan of brownies.
“I felt wonderful while I was eating the brownies, but when I went back to bed I didn’t feel so good about my choice. So, I sneaked back into the kitchen and moved the brownies into another pan that fit them perfectly.”
The teacher will place the brownies into another pan
“The next day Dad (who had no idea what pan my mom used) cut the “new” pan of brownies (hee-hee) in half so we could share them equally.”
“How much of the original pan of brownies did my sister get to eat?”
Place the problem on the board (the teacher reads the problem again to reinforce student understanding):
Problem #2(15 minutes)
We had ¾ of a pan of brownies left over. My sister and I split the leftover pan of brownies in half. How much of the pan of brownies did Jennifer get?
Students will partner talk and then several students will explain the problem in their own words to the whole group.
“Who can say in your own words what is happening?”
“I want you to show me both a model and an equation that applies to this model.”
Give students oneminute to think on their own. After time is up, the partners should share their thinking. Students will have nine minutes to work together to solve the problem on their workmat. / “I’ve crossed out the fourth and I split it into half.”
3/6 = 1/2
“I split the cake into fourths. I crossed out the one-fourth. Now looking at my ¾, I know ½ of a fourth is an eighth.”
Close Problem #2 (12 minutes)
Several students’ work will be selected and they will share their answers.
The teacher will look for misconceptions during work time.
Possible misconceptions:
½ of ½
  • Each teacher got half of a cake
½ of ¾
  • ½ of ¾ is equal to 6/8
  • ½ of ¾ is equal to 3/6
  • ½ of ¾ is equal to ½
  • ½ ÷ ¾ vs. ½ x ¾
  • ½ ÷ ¾ vs. ¾ ÷ ½
  • ¾ ÷ 2 vs. ¾ ÷ ½
  • ¾ ÷ ½ vs. ¾ x ½
  • ¾ x ¾ is equal to 3/16
Sample questions to ask:
  • What are we counting?
  • What is the whole?
  • Remember to use talk moves
Neriage~ Understanding the mathematics in the problem (10 minutes)

At this time the teacher will place a mathematical model of fictional Charlie’s work on the board for students to analyze. The teacher will ask the student to discuss what each of the representations means to them. Then allow the students to share and the teacher will ask the following question:
“So when we say 3/6 in this model, what is our whole?” (Expected student response: ¾ pan of brownies)
“So when we say 3/8 in this model, what is our whole?” (Expected student response: 1 whole pan of brownies)
“When Charlie said 3/6, what is the whole?” (Expected student response: The whole is 3/6 of ¾ pan of brownies)
“When Charlie said 3/8, what is the whole?” (Expected student response: The whole is 3/8 of 1 pan of brownies)
“So is it correct to say it is 3/6 of a whole pan of brownies?” No, because it is only correct if you say 3/6 of ¾ pan of brownies.
“So, what do we know about wholes when discussing fractional parts?” Wholes can change
You have done some excellent thinking today. This is a very difficult concept. You have done some great work! We have one final task for you to complete in your journal.
Journal Prompt:(5 Minutes)
We found out how much brownie Mrs. Friemel’s sister received. Now we’d like to know how much brownie Mrs. Friemel has in all. So here’s your question: How much of the pan of brownies did Mrs. Friemel actually get? Prove your thinking with a model or an equation.

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