Looking for Patterns + Show What You Know

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Objective

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

Big Idea

How would you solve 3 ¼ - 1 5/6? What do students understand? What gaps do they have in their understanding? Students continue looking for patterns when they are adding and subtracting fractions and then they take a quiz.

Do Now

5 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 them to think about the strategies they have developed over the past couple days.  I explain that they will continue working on the “Looking for Patterns” problems and they will take a quiz.

Looking for Patterns

20 minutes

Notes:

  • This activity was started in the previous lesson, Adding and Subtracting Fractions Day 2.
  • I have students get out their work from the previous day and get with their partner from yesterday.
  • If students get to make posters, they will need paper and drawing materials.

 

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.

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 “Score the Difference”
    • 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.

Sharing Out Patterns

10 minutes

I ask students to share what they noticed about the problems Group 3 in part a.  Students will share that they both involved adding fractions that did not have common denominators.  Students may also share that they had to change both fractions before they added them.  I briefly display the answers.  I move on to part b.  I ask students how the strategies that they just shared apply to solving problems in group 3.

We move onto part c.  I ask students to share how these problems are similar or different.  I want students to recognize that all of the fractions in the second part of the problem are greater than the fractions in the first part of the problem.  I have a student come up to the document camera to show and explain their work.  I want students to see how they can apply the strategies they used in the last two parts to this part.  These problems are the kinds of problems that students typically struggle with.  In my experience, if students are trying to apply an algorithm that involves borrowing they are more likely to make mistakes.  This is why I emphasize the models that students can make and that they use what they know about fractions.

Quiz

25 minutes

I give students the Quiz.  Students engage with MP1: Make sense of problems and persevere in solving them.  If students do not finish in the allotted time, they set up a time (preferably that day) to come in and complete it.  I use this data to inform my instruction.   If students struggle with a concept, I will spiral it into do nows and homework assignments.  I may also add a few problems on that topic to the next quiz.