Adding and Subtracting Fractions Day 2

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Objective

SWBAT: • Make an estimate for a fraction addition or subtraction problem. • Develop strategies for adding and subtracting fractions.

Big Idea

How would you add 2 ½ and 2/3? How would you find the difference between 2 ½ and 2/3? Students continue to develop strategies for adding and subtracting fractions.

Do Now

10 minutes

See my Do Now in my Strategy folder that explains my beginning of class routines.

Often, I create do nows that have problems that connect to the task that students will be working on that day.  Today I want students to work on adding mixed numbers.  Some students may draw a picture and figure out how to combine them.  Other students may add the wholes and then add the fractions using common denominators. 

Students participate in a Think Pair Share.  I call on students to share out their thinking. I put a couple students’ work under the document camera to show how they approached the problem.  I want students to recognize that they are applying the same strategies that they have worked on with proper fractions, except now the fractions are larger.

Recipe Problems

20 minutes

Section 2:  Recipe Problems: (20 minutes) 

Notes:

  • I use the data from the ticket to go from Adding and Subtracting Fractions Day 1 to Create Homogeneous GroupsStudents will work in partners.
  • Each student will need a Recipe Cards handout

I have students move to their partners.  I ask students when they have used spices.  We work through problems 1 and 2 together.  For each part of the problem, I ask students to identify which operation they need to use and why.  Then I ask them to think of an estimate and then find the answer.  I encourage students to draw pictures to help them.

For part 1b, I have students draw a picture and we shade 2 5/8.  To compare, we take away 5/8 and we can clearly see that there are 2 ounces leftover.  For part 1c, again I have students draw a picture of 1 1/8.  Now we are taking away 5/8.  I ask students how we could do this? Some students may take (cross out) 5/8 form the 1, leaving 3/8 and 1/8 leftover.  Other students may cross out the 1/8 and then realize that they need to take way (cross out) 4/8 or ½ from the whole, leaving 4/8 or ½ of an ounce leftover.  Other students may try to use an algorithm involving trading 1 whole for 8/8 and go from there.  If a student does this, I still require them to draw a picture and use it to show what they are doing.  I do not want students to apply an algorithm that they do not fully understand.  In my experience when I try to teach this algorithm many students get confused and make careless mistakes without applying all that they already know about fractions.

We go through problem 2 in a similar manner.  Problem 2c involves subtracting 2/5 from 1 1/10.  I have students draw a picture of 1 1/10 and then ask students to brainstorm what we could do.  Student ideas will be similar to problem 1b and 1c.  The difference comes with how we interpret what is leftover.  If a student takes 2/5 away from the whole, he/she is left with 3/5 and 1/10.  The student must then use their knowledge of adding fractions to figure out what is left. 

I have students work with their partner on problem 3.  I walk around and monitor student work.  Common mistakes include using the incorrect operation and making mistakes in creating common denominators.  If I see this happen, I ask students to read and explain the question to me.  Then I have them create or show me their model. 

If students successfully complete the problems, they can move on the “Looking for Patterns” problems.

Looking for Patterns

20 minutes

Notes:

  • This will not be enough time for students to work through all of the problem sets.
  • Students will start working on these problems and they have more time to work on them in the next lesson.

I have students come back together as a class.  I explain to them that they are going to apply what they’ve been working on for the past two lessons and look for patterns.  They can choose to draw pictures or not, but it is important that they show all of their work.

As students work, I walk around and monitor student progress and behavior.  I make sure that partners check in with me when they have completed a page.  I ask them to share what they noticed from the problems in the different groups. This way I can quickly check student work and identify any glaring problems.  Students are engaging in MP4: Model with mathematics and MP8: Look for and express regularity in repeated reasoning

If students are struggling I have them explain their models and their estimates. How could you draw a picture to represent that?  If students struggle with equivalence, they need to use the fraction kit to model their thinking.  This way they can make comparisons between fractions and create their own equivalent fractions.

I do not anticipate many partner pairs finishing this work.  But if students successfully complete their work I give them a choice:

  • Create a poster for one of the groups of problems.  They will show their work and explain what they problems have in common.
  • Work as a teacher’s assistant with a partner pair who needs help
  • Play “The Smaller Answer Wins” with their partner
    • This game requires dice.  I start off with students replacing the 5 on the die with an 8.  This makes it easier to create common denominators and compare answers.
    • If students need an extra challenge, I have them use the 5 on the die, instead of replacing it.

Closure and Ticket to Go

10 minutes

For Closure I ask students, “ How would you add 3 4/5 and 1 ¾?  I call on students to share out their answers.  I want students to realize that they can just add the whole numbers and then figure out how to add the fifths and fourths by creating common denominators.

Then I ask, “How would you subtract 4 3/5 and 1 1/3?”  I call on students to share their ideas.  I want students to make connections between their strategies.

I pass out the Ticket to Go.  Then I pass out the HW Adding and Subtracting Fractions Day 2.