Filling and Measuring

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Objective

SWBAT: • Define volume. • Use a fractional unit cube to find the volume of rectangular prisms and cubes. • Use a formula to find the volume of rectangular prisms and cubes including fractional edges.

Big Idea

What’s the volume of the sugar in this container? How would you solve this problem? Students apply their knowledge of volume to answer more complex problems.

Do Now

7 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 review their strategies for filling a rectangular prism.  Some students may multiply the length by the width by the height to determine how many cubes it will take.  Other students may figure out the number of cubes in one layer and multiply that by the height of the box.  I also want students to review how to multiply with fractions.  A common mistake is for students to multiply the whole numbers together and then add on the fraction.  Some students may create improper fractions to multiply. Other students may use the box method and multiply 6 by 4 and ¾ by 4 and then add the products together. 

I ask students what strategies they are thinking about to answer the questions.  I call on students share what they think and why.  Students are engaging in MP3: Construct viable arguments and critique the reasoning of others.

Problem

3 minutes

I read over the question.  Students participate in a Think Write Pair Share.  I chose not to include the measurements so that students will focus on the process of solving this problem.  Some students may share that you can figure out the height of the sugar and multiply it by the length and width to find the volume of the sugar.  Other students may share that you can find the total volume of the container and then subtract the volume of the empty space.  Students are engaging in MP2: Reason abstractly and quantitatively.

Fractional Unit Cubes

7 minutes

We fill in the notes together.  I read over the problem.  I give students a few minutes to write down their own strategy.  I walk around and monitor student progress.  Some students may find the volume of the smaller cube and then multiply it by 27 to find the volume of the larger cube.  Other students may use the unit cube to find the dimensions of the larger cube and then multiply.  Other students may find the volume of one layer and then multiply that volume by 3.  Students are engaging in MP6: Attend to precision.

I call on 2-3 students who used different strategies to come up and show and explain their work.  I tell students that they are responsible for copying at least one strategy that is different than how they solved the problem. 

Practice

18 minutes

Notes:

  • Before this lesson, I use the ticket to gos from the previous lesson to Create Homogeneous Groups.
  • I give each group a Group Work Rubric.
  • I Post a Key for these problems around the room.

We go over directions and expectations.  I inform students that they should start with Practice B.  If they struggle with the first question, they should go back and start with Practice B. My goal is that students complete Practice B.   As students work I walk around to monitor student progress and behavior.  Students are engaging in MP6: Attend to precision.

 If students are struggling, I may ask them one or more of the following questions:

  • What do you know? What are you trying to figure out?
  • Make an estimate for your answer. 
  • What strategies do you have for finding volume?
  • Does your answer make sense?

When students complete their work, they raise their hands.  I quickly scan their work.  If they are on track, I send them to check with the key.  If there are problems, I tell students what they need to revise.  If students successfully complete a practice set they can move onto the next set.  If they complete Practice C they can move onto the challenge problems. 

Closure and Ticket to Go

15 minutes

For the Closure, I have students turn to the sugar problem that now has measurements.  Students participate in a Think Write Pair Share.  If students get stuck, I encourage them to flip back to their notes on this problem from the beginning of the lesson.  I call on students to share their answer and explain their thinking.  Students are engaging in MP1: Make sense of problems and persevere in solving them, MP2: Reason abstractly and quantitatively, and MP3: Construct viable arguments and critique the reasoning of others.

I pass out the Ticket to Go and the Homework.