Adding & Subtracting Fractions with Unlike Denominators (Centers)

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Objective

SWBAT add and subtract fractions with unlike denominators.

Big Idea

During choice time, students have an opportunity to select the activities that will help to develop their mathematical fluency.

Introduction

5 minutes

This lesson is designed to help students increase fluency in the skills we have been learning throughout our unit on adding and subtracting fractions.  The next topic is about adding and subtracting mixed numbers.  Since this is the last instructional day before the assessment, I provide students with choices of problem activities to practice these skills. 

I start with a quick introduction to the lesson by sharing the agenda for the day.

  • Must Do
  • Choice Time
  • Conferences

 

I explain that throughout the class, students will all complete a must do, then they may make choices about how to spend the rest of the time.  Throughout the class, I pull students to conference with me about their recent work with fractions.

Launch

10 minutes

To introduce the choices, I have students come up and play a demonstration round of each game.  I also provide the students with a hand out that includes the rules and expectations of each game.

The choice time activities are:

Problem Solving: Showcase What You Know

  1. Make a diagram and write an equation to match the story
  2. Solve it
  3. Include a picture to show what is happening in the problem.

First to 12 Wholes

The focus of this game is for students to practice using benchmark fractions to estimate.

  • Player A flips 4 fraction cards.  
  • Player B estimates the size of each fraction using benchmark fractions.  (Explaining his/her thinking out loud to the other player). 
  • Player B then estimates the sum of the benchmark fractions and records it.
  • Player B flips 4 fraction cards and the cycle continues. 
  • The first player to get to 12 is the winner.

 

Possible extensions include incorporating subtraction of benchmark fractions, or try estimating the sum of more than 2 fractions.

Fraction War

The focus of this choice to to have students compare fractions.

Draw a giant fraction bar on a sheet of note book paper (like the model on the board)

Divide a set of fraction cards in half.

Flip 2 number cards to create a fraction.  The first card flipped is the numerator, the second is the denominator

Determine which player has the largest fraction (use number sense or create common denominators). Each player must explain their way of knowing which was the largest.

If two players have equivalent fractions, play "war".

It is important to model the rules of the game to make sure students are clear of the expectations. With in the structure of each choice, I allow room for students make some of their own agreements with in their choice activities like how to deal with wild cards.  

Define Expectations:

Because there will be a combination of group work, independent work, conferences, and partners working on various activities, it is important to make an agreement of expectations for the lesson. 

I ask students to share the expectations they have for themselves and their classmates during the lesson.  As each student shares, the others promise to meet these expectations. 

Conferences

5 minutes

Throughout the independent practice, I meet with students one-to-one to discuss their recent work with problem solving. 

Students previously solved addition and subtraction word problems that involved fractions with unlike denominators. 

When I conference with students I ask three major questions:

  1. How are you feeling about your work with fractions?
  2. Do you have any questions for me?
  3. Will you read the story problem that you solved that you are most proud of, and then explain how you solved it.  If there were any parts that you got stuck, can you talk about them?

 

While students explain their thought process, I listen for and provide prompts to assess three criteria.

• Vocabulary Use

• Ability to explain that when making equivalent fractions the numerator and denominator are both multiplied by the same number because n/n is 1 whole. Multiplying by 1 whole doesn't change the value of a fraction.

• A bar diagram is a part-part-whole model, but the "whole" refers to the entire amount of whatever the problem is about, not a whole number.  It is appropriate to have a fraction in the "whole" position of a bar diagram.

Independent Practice

20 minutes

First, students work on the "must do". This independent activity is used to assess a skill learned in a previous topic. 

Must do:

1) .67 x .35

2) 32 divided by 1.5

3) 3.2 divided by 15

4) .32 divided by .15

I choose the same digits in the dividend and divisor so students have to focus on the place value and decimal manipulation, and reasonableness of their answers.  

Then students move to their choices, while I meet with one student at a time for conferences.

Group Share

5 minutes

It may seem unconventional to have a group share at the end of a lesson when so many students were working on different things.  However, I find that students are more articulate when they have to explain a unique experience rather than describe an event that was shared by everyone. 

The group share prompts for this lesson are:

  • What choice did you make today?
  • What did you learn while you were working?

I record all recap statements that students share.  Moving forward, these statements will be revisited to improve student thinking, address misconceptions, and solidify understandings.