Students critique and improve their work on the Self Check.
No new concepts are introduced in this lesson. To solve the problems in the Self Check, students use fraction division and operations with decimals.
Goals and Learning Objectives
- Use knowledge of fraction division and decimal operations to solve problems.
Students should look at the results of their Self Check from Lesson 11 and respond to the questions in the Critique.
SWD: Some students with disabilities may struggle to complete all the tasks in the time allotted. Consider the following supports for students:
- Reduce the number of tasks that some students need to complete during the lesson; however, make sure that students demonstrate understanding of necessary skills.
- Partner SWDs and typically-developing peers to provide support; or, assign partners different jobs to reduce the number of tasks each student is expected to complete.
- On the rubric, highlight the specific areas or skills that students should focus on.
Review your work on the Self Check problem and think about these questions.
- How can you check whether your answer to each part of the problem is reasonable?
- What methods do you know for dividing with fractions? How can you use these methods to divide with mixed numbers?
- When you multiply or divide by a decimal, how can you figure out where to put the decimal point in the answer?
Discuss the Math Mission. Students will apply their knowledge of fraction and decimal operations to solve a real-world problem.
Apply your knowledge of fraction and decimal operations to solve a real-world problem.
Revise Your Work
Organize students into pairs to revise their work. Encourage students to incorporate ideas from their partner into their work. If several students in the class are struggling with the same issue, you could write a relevant question on the board. You might also ask a student who has performed well on a particular part of the task to help a struggling student.
While students work, note different approaches to the task:
- How do they organize their work?
- Do they notice if they have chosen a strategy that does not seem to be productive? If so, what do they do?
ELL: When forming partnerships, consider the task at hand. Since the work is less language dependent and more computational, this task may be used as an opportunity to pair students based on math comprehension instead of language mastery.
Try not to make suggestions that move students toward a particular approach to this task. Instead, ask questions that help students to clarify their thinking. If students find it difficult to get started, these questions might be useful:
- For which questions were you asked for feedback?
- How could you and your partner work together to address one of those feedback questions?
In problem 1, student multiplies by instead of dividing by .
- Think about a simpler problem with whole numbers: What if Jan had 6 yards of fabric and used 2 yards for each elephant? What operation would you use to solve the problem? Finding a fraction times a number is the same as finding that fraction of the number. Is this what you want to do?
In problem 2, student tries to divide without changing to an improper fraction.
- What method can you use to divide a whole number by a fraction?
- Can you use that method for this problem?
- How can you write a mixed number as a fraction?
Student has difficulty starting problem 4.
- What do you know?
- What are you trying to find?
- List all the materials Jan spends money on.
- How can you find the cost of these materials for each elephant?
Student’s work is hard to follow.
- How can you organize your work so someone else can understand what you did?
- How can you label your work so it is clear what the numbers and calculations represent?
Student gets an unreasonable answer.
- Go back and read the problem. Is your answer reasonable?
- How can you use estimation to check your answer?
Mathematical Practice 1: Make sense of problems and persevere in solving them.
Students must make sense of each problem. They must plan and carry out a solution strategy. After they solve a problem, they must verify that their solution makes sense. Students also have the opportunity to work with another student and try to understand his or her approach to the problems.
- Jan has enough gray fabric for elephants.
- Jan has more than enough beans to stuff 14 elephants. She actually has enough for elephants.
- Jan bought $22.25 ÷ $0.89 per pair = 25 pairs of eyes. She has more than enough eyes for the 14 elephants she has sewn and stuffed.
- One elephant costs to make. If Jan sells all of her elephants, then she will make .
Revise Your Work
Work with your partner. Revise your work on the Self Check based on the questions from the Opening and feedback from your partner.
Jan makes and sells beanbag animals. Her most popular animal is her beanbag elephant.
- For each elephant, she uses yard of gray fabric, pounds of dried beans, and a pair of plastic eyes.
- Fabric costs per yard, beans cost per pound, and plastic eyes cost per pair.
- She sells each elephant for .
Show all of your work.
- Jan has yards of gray fabric. How many elephants can she make?
- Jan has 28 pounds of dried beans. Does she have enough beans to stuff all of the elephants that she made with the fabric?
- Jan spends $22.25 on plastic eyes. How many pairs did she buy? Is this enough for all of the elephants she stuffed?
- After subtracting the cost of the materials that she used to make the elephants, how much money will Jan earn if she sells all of the elephants?
If you get confused about what operation to use, think about a simpler version of the problem in which all the numbers are whole numbers.
Prepare a Presentation
Preparing for Ways of Thinking
Look for examples of the following to be presented during Ways of Thinking:
- Different ways of organizing work
- Incorrect and correct solutions for each problem
- Different approaches for solving problem 4. For example, students may find the total cost of the materials for 14 elephants and subtract it from the total income from 14 elephants. Or, they may find the amount Jan makes for each elephant and then multiply by 14.
Mathematical Practice 6: Attend to precision.
Students are asked to present their work in a clear, precise way. They should try to use correct mathematical language and symbols and to carefully label their work so it is easy to follow.
- Answers will vary.
Prepare a Presentation
Explain how you revised your Self Check problem. What did you do differently today compared to yesterday?
Write a word problem with decimals that requires using two different operations to solve.
What types of real-world situations involve decimals?
What types of real-world problems would require two operations to solve?
Organize a whole-class discussion to consider issues arising from student revisions. You may not have time to address all these issues, so focus class discussion on the issues most important for your students.
Have students share their work and talk about how they approached the problem.
Have students who had strategies that didn’t work share so they can talk about how and when they realized their strategy didn’t work and what they did about it.
Have students share the questions from the teacher or from the lesson that they addressed and how they addressed those questions.
Have students ask questions and make observations as they view each other’s work.
Ways of Thinking: Make Connections
Take notes on your classmates' approaches and solutions to the problem.
As your classmates present, ask questions such as:
- What information is known?
- What information are you trying to find?
- Can you explain how you organized your work?
- What strategy did you use to solve the problem?
How did using that strategy to help you?
- How did you decide what operation to use in that part of the problem?
- How does your model represent the problem situation?
Reflect On Your Work
Have students write a brief reflection before the end of the class. Review the reflections to find out their understanding of fraction division.
Write a reflection about the ideas discussed in class today. Use the sentence starter below if you find it to be helpful.
Something I learned about fraction division that really helps me solve problems is …