Adding and Subtracting Fractions Day 1

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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

If Ashley ate ½ pizza, Tatyana ate 1/3 of a pizza, and Tiffany ate 5/8 of a pizza, how much pizza did they eat altogether? What’s the smallest number of pizzas they ordered? How much was left? Students work to develop strategies for adding and subtracti

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 and subtracting fractions.  This is the only example in the lesson that has fractions with common denominators.  I use the do now to see that students can add fractions with the same denominator.  If they can’t I will add some additional practice in before we move on with the lesson.  Some students may draw pictures and combine them. Other students may use the algorithm to add and subtract the fractions. 

Students participate in a Think Pair Share.  I call on students to share out their thinking. I put a couple student’s work under the document camera to show how they approached the problem.  I want students to see that they smallest number of pizzas that they could have bought was 2.  To find out how much pizza is left, we need to subtract 2 – 1 2/4 (of 1 ½).  I want students to see that they should be able to find that answer in their head, or by looking at a picture.  It would be more complicated and time consuming to use an algorithm.

Pizza Problem Example

10 minutes

Notes:

  • I use the data from the Fractions Pretest to Create Homogeneous GroupsStudents will work in partners.
  • I have a class set of Marilyn Burns’ Fraction Kit, where each student has his/her own set of paper fraction manipulatives.  Students can choose to use these to help them, but they are not required to use them.

I have students move to their partners.  I have a volunteer read the problem and part a.  Before students write anything, I ask them to think of an estimate for the amount of pizza Jessika and N’Yshma ate.  If students can develop strong estimation skills, it will help them check their answers to see if they are reasonable.  If students struggle with this I ask, “Do you think they ate more than 1 pizza or less than 1 pizza?”  I have students share out their estimates.  Some students may comment that they know 3/8 is less than ½ (because 4/8 is equivalent to ½) so their estimate is less than one pizza.

I give students time to solve part a on their own.  I remind students that they need to show their work.  Some students will draw and combine pictures.  Some students may know that ½ is 4/8, so they will add 4/8 and 3/8.  Some students may use an algorithm, but may not understand it.  For example, a student may turn the fractions into fractions out of 16, since 16 is a common denominator.  Technically, this approach will work, but it takes far longer and it tells me they are not able to see the connection between ½ and 4/8.  If I see this, I quickly draw a picture of ½ and 3/8.  I ask the student how many eighths make up a half.  If they struggle, I ask them to split up the circle with ½ into eighths. 

After a couple minutes, I have students share out their answers.  Again I have a couple students who used different strategies show and explain their work.  I ask the class whether they agree or not.  Students are engaging in MP3: Construct viable arguments and critique the reasoning of others.

We go through part b and c together.  I emphasize that it can sometimes be much quicker to use your fraction number sense for subtracting.  If we are solving 1 – 7/8, we know that there are 8/8 in a whole, so there must be 1/8 of the pizza left.

Pizza Problems

25 minutes

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.  This way I can quickly check student work and identify any glaring problems.  Students are engaging in MP4: Model with mathematics

If students are struggling I have them explain their models and their estimates.  Do you think they ate more or less than 1 pizza?  Why?  How can we add halves, fourths, and eighths?  How do you know?  How can you find how much pizza is leftover?  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.

If students successfully complete their work I give them a choice:

  • Create a poster for one of the problems, showing and explaining their work.
  • 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

15 minutes

 For Closure I ask students, “What is your strategy for adding and subtracting fractions?”  I have them share out their answers.  Then I write the question on the board and I ask, “How would you add a/3 + b/4?” Students participate in a Think Pair Share.  They are engaging in MP7: Look for and make use of structure.  I want students to tell me that they can change both the halves and the fifths into twelfths.  Then they can add them.

My last question is, “How would you subtract 1 – d/12?”  I want students to apply what they have worked on to answer the question.  I want them to think, I know there are 12/12 in a whole.  Then they can easily compare the two fractions, even though they don’t know the value of d.

I pass out the Ticket to Go.  Then I pass out the HW Adding and Subtracting Fractions Day 1.