Rolling with Fractions

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Objective

SWBAT convert between fractions and decimals by creating their own fractions with dice.

Big Idea

Students use dice to create their own fraction conversion problems.

Do Now

10 minutes

Students enter silently and find today's Do Now on their desk. It instructs students to have their pencils ready for a sprint. This assessment will include 10 questions to be completed in 3 minute.

Fluency is an important aspect to the new Common Core curriculum and it is important to practice with assignments like Sprints. I think that they help my students to improve flexibility and efficiency with number operations. This does not mean that I expect all students to be able to perform tasks like this in the prescribed amount of time. I make sure to let students know this before reviewing the answers.  I say:

While the speed with which these problems are completed should increase over time, "fast" doesn't necessarily make you "better". Accuracy is more important than speed.

Five of the questions will be adding and subtracting fractions with like and unlike denominators (i.e. ¼ + 1/5). The other five questions will be integer operations with larger or smaller numbers (i.e. -59+16). Students will be instructed to turn their paper over if they finish within 3 minutes. If I see this, I will stamp the student’s paper. This will help me make note of students finishing within the given amount of time.

At the end of 3 minutes, students will be asked to take out a pen to score their own work. The power point attached includes slides with timers set for the animations. If students are not ready within this amount of time, the lesson will continue. Only students who have completed all directions in a timely manner and get at least 8 questions correct will be eligible for a prize: the option to help me put up a bulletin board displaying their work and an achievement star.

Class Notes - Intro to Lesson

10 minutes

Students will be asked to take out a blank sheet of paper and set it up using Cornell Notes style. A picture will be provided using Day 21 - PPT - Fractions and Decimals for students to use as a guide. Students copy the information for fraction/decimal conversions completing example problems for each topic listed below.

The notes cover the topics:

  • When Converting Fractions to Decimals...
  • Rounding…
  • When Converting Decimals to Fractions…
  • Fractions Greater than 1

Of most importance in these notes is reviewing the process for converting fractions to decimals, a question that comes up in several of our unit and mock assessments.

 

Task

20 minutes

Students will work in pairs to create their own fraction/decimal conversion questions with dice. Each pair will receive dice-in-dice, a die that has another one inside. Using the dice, students will first create five fractions that are less than 1 (p/q < 1) and two that are greater than 1 (p/q > 1). Next, they will then use the outside dice only to create 5 decimal problems and convert them to fractions. 

Before letting students start these tasks, I give clear and concise directions:

Part 1 - Fractions to Decimals 

Create 7 fractions and convert each to a decimal. Follow these steps.

  1. Roll the die. Notice that two numbers land on top, the one on the outside die and the one on the inside die.
  2. Use one number for the numerator and the other for the denominator
    Note: the first 5 fractions should be less than 1 and the other 2 fractions should be greater than one. Think - how does this affect the number you choose to place in the numerator/denominator?
  3. Convert the fractions to decimals.

Part 2 - Decimals to Fractions

Create 3 decimal numbers and convert each to a fraction. Follow these steps.

  1. Each problem has blanks that need to be filled in. Roll the die and use the outside surface. 
  2. Choose where each number will be written on the blanks.
  3. Convert the decimals to fractions.

During the last 5 minutes of this section I will be walking around to determine what were the most challenging questions in the worksheet. I will also be looking for students who showed clear and comprehensive work to solve these targeted questions correctly. These students will be asked to display their answers on the board before the end of this section. 

 

 

Closing

10 minutes

Having determined what were the most challenging problems from the task and after having students put up their correct work and answers I will ask all students to put their pencils down and take 1.5 minutes to review the answers to some of the questions on the board. Everyone must identify the first, second, third, etc. steps taken to solve and check the computations included on the board. Giving students clear expectations on what it means to "review" answers is important. This way, there is no way to opt out with the excuse "I don't get it" or "I don's know what I'm supposed to do..."

After giving these initial 1.5 minutes, I ask students talk with one another, asking questions if there are steps they do not understand, or sharing out the solutions. For example,

Turn to your neighbor. Ask, "do you get that solution?"

If the answer is "no" explain the steps you DO understand. If the answer is "yes" ask, "what did they do first? next? do you agree with the solution?"

If you notice an error, ask, "isn't that a mistake?" and explain why you think it's an error.

Switch roles for the next question to review.

If there are question neither of you knows the answer to, write it down to ask in the last five minutes.

Students engaging in this discussion are using MP1 and MP2 to make sense of this process.

After having about 5 minutes to review, I will stop all students and ask if there are any such question neither partner could answer. My goal is to get another student to answer this question, with my answer and explanation being the last resort.

Before dismissing them, students receive the Homework.