Volume as Additive

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Students will be able to find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the non-overlapping parts.

Big Idea

Practice volume formula with a riddle!


Students need to practice paper and pencil formulas as well as use hands on manipulatives.  We have been building rectangular prisms and counting the cubic units to find the volume in previous lessons.  We discovered the formula L x W x H = volume and with this handout students can practice the more abstract paper pencil use of the formula.  With this handout you can assess if your students see that their are two rectangular prisms that need to be added together to get the total volume.    Students need to be able to look for and make use of structure and look for and express regularity in repeated reasoning and in this activity they had to add the two prisms together to get the answer. 

This is a wonderful simple lesson that assesses whether or not my students could use the formula to find volume.  It was an insight for me to see who could figure it out and who needed guiding through adding the two prism shapes together to get the total volume.     

Students Solving Volume

20 minutes

After we have reviewed the formula for rectangular prisms, I tell the student they are going to be working with a handout that will answer a riddle.  We review the formula for volume and students group together to work through this worksheet. There are a variety of worksheets available for free online through a search of standard 5.MD.5c.

This worksheet also combined finding total volume of rectangular prisms that were stacked on top of each other.  This gave me another insight into individual students level of complexity of thinking.

This allows time for me to work with any students who need extra support and I gather them onto the carpet and we work through the problems one by one - I have a small whiteboard I use to do this.  I start with the first problem modeling how to work through it, answering any questions they have.  Then I model the next problem and again answering any questions.  After modeling two problems I ask for a student to walk us through the next one.  If no one volunteers I ask what is the first step, what is the next step and so forth.  We get through half the problems when it is time to go over the answers - focusing on quality of practice and not quantity of the problems.

I also love using activities where the answer spells out an answer to a riddle - students can self check to see if they have complete the problems accurately.  While helping the small group of students on the floor I was able to draw out the strategy of working backwards and estimation to finding the correct answer.

You will have to reinforce the purpose of the worksheet is to give students practice with the math, not to guess the answers because they have figured out the answer to the riddle.

I am not worried about the group of students who do not finish the worksheet.  They will have another practice and review as we go over the answers.

Mistakes Happen -  Video 1

Student Explanation on How to Find Volume of Two Rectangular Prisms - Video 2

Student Helping Classmate - Video 3

In the videos, you will see fourth and fifth grade students explaining their answers and mistakes.  At the very end of the video you can hear AJ say "Because I didn't have any sideways paper."  What he found out was he made a mistake because he had not turned his paper sideways and use the lines to keep his work organized - you can see his organization on the the sticky-note and exactly where he made the mistake.  After I had taped him I sent him back to his seat with the comment.  "There is a mistake in your organization but not in your math."  He immediately went back to rework his math, lining it up in correct columns.

As you look into my classroom you may notice something different.  I teach students in a multiage 4th and 5th grade, but I hope the difference you see is not who is 4th and who is 5th.  I hope you see students working together and taking responsibility for their own learning.   It is not always a 5th grader helping a 4th grader and every time it happens this is building self-esteem, leadership skills and the best way to learn is to teach.  It also reflects a real world working environment - people of all ages working to solve a problem.  My goal is to have students take responsibility for their own learning and always be ready to help someone else.  




Reflection Wrap-Up

5 minutes

Students need to reflect on learning to increase retention and comprehension.  This quick lesson is practice of volume formulas, so I keep the reflection short, but still make sure the students have an opportunity to reflect.

Today, I ask my students to talk at their tables about one thing they learned today or something they taught another classmate.

I hear comments covering both volume formulas: V = l x w x h and V = b x h where b is the area of the base. I can also hold them accountable by collecting their papers to put into their portfolios as evidence of practicing the volume formula.  

One of the students I work with on the carpet says, "We found a pattern and kept repeating it!  Length times width times height." (MP7)

Another talks about using estimation by rounding the numbers and multiplying them to decide on one out of two possible answers.  Then they work through the math to verify this strategy. (MP2) 

I collect their papers to place in their portfolios as evidence of practicing the volume formula.  I am looking to see if students complete the problems and which volume formula they use.