Volume - Building and Measuring

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Students will be able to build and measure volume by counting unit cubes.

Big Idea

Volume - Build it , Measure it!


I open the lesson today with 5 Minute Math. I write 3-5 math questions on the board and students copy and answer the questions in their math journals.  I don't grade them but use it as another opportunity for students to answer the questions "Why?" "How do you know?" and "Can you Explain?" I use 5MM as an informal assessment, and the final unit test as my formal assessment - all go into a student portfolio of work I save for report cards and conferences.  I found a great pattern that has this down to the 5 minutes - of giving answers.  Students need all different amounts of times to complete math problems.  As I rewrite the question on a large piece of paper hung on a hanger - I problem solved not having enough white board space - throw the Koosh to one student, they give their answer and the how and why and then they throw it to another student.  They need to be done talking and have tossed the Koosh by the time I have written their response on the paper.  Each question has three or four students answer.  The last minute I lead a discussion on the best solutions, the most creative thinking and any Ah Ha moments. 

This lesson is based on the Measurement and Data standard 5.MD.3 or recognizing volume as an attribute of solid figures and understand concepts of volume measurement.  It uses visuals to link the abstract formula of  Volume = L x W x H to the spatial representation, and takes the thinking one step further by introducing another volume formula of V = b x h. 

The preparations for this lesson are easy.  Sort centimeter cubes into separate containers for each group, and have copies of foldable 3D shapes.   I use shape foldables from my teacher resources but you can Google 3D shape foldables and find tons to print out and use.  Keep in mind, the fifth grade common core standards focus on rectangular prisms. 

Exploring Volume with Base Ten Blocks

20 minutes

At the close of 5 Minute Math, I ask, "Where do you find volume?"  "Talk to your table. I am going to draw sticks and ask what your partner said."  This keeps the students focused on volume "target talk" because they have to listen to their table mates and share out someone else's thinking.

As students talk, I walk around putting the bins with the centimeter cubes and the 3D foldable shapes on the floor next to their desks.  I have found if I put them on the tables they get distracted.  

I am hearing great volume target talk! 

"Volume is in anything you can put something else into."

"The desk tops have volume because you can measure how think it is."   

"A picture of a swimming pool on the SmartBoard does not have volume, because the picture is flat."  I had to stop and ask what this student meant, because a pool holds water so it has volume.  He put his hand up, lifting the picture on his palm.  "See there is nothing to the picture."  I ask, "But if you were standing at the edge of the pool in real life does it have volume?"  "Yes of course it does!" 

Okay, brains are activated and ready to go into the lesson - both theirs and mine (the pool example). 

Today you are going to find the volume of rectangular shaped prisms by putting centimeter cubes into the foldables - but first you have to build the prisms.  And how do you label volume?  Many say out "cubic units."  I hear a student say - "Like the cubes we will be using." Take every opportunity you can to reinforce volume is measured in cubic units. 

Cut the shapes out leaving the flaps so you can tape them leaving a side open, fill it with cubes, keeping track of how many you used.  Check with the volume formula we used yesterday. 

Any questions? 

Hint:  If cutting out shapes with flaps is new for your class, you may want to show them one that is already cut out and color the flaps so they can see what you are talking about.  The student who I am working with in the video needed help putting hers together. 

Extending Thinking

10 minutes

As I walked around the room checking for understanding - students creating the volume models, counting the cubes and applying the formula - I noticed quite a few students who needed to take it a step further.  I asked them to see if they can find a way to use the area formula in combination with the volume formula to create a simpler one. 

Kids started to gather together on the carpet and brainstorm.  They build shapes with cubes, created drawings of rectangular prisms and written down the formulas for volume, area and perimeter.  It only took ten minutes for Jon Paul, Hayden and Joseph to see the area of one side of the shape times the number of "layers" would also equal the total volume. 

I then wrote on the board for them the second formula of Volume = base x height where base is the area of one side.  I sent them out to visit the students at the tables to share their new information.  We will be checking back in on this with the entire class at another time and I will pull and work with my 5th graders to ensure they understand it. 

While I am working with 5th graders, and any 4th who would like to learn the new formula I will have the rest of the class working in their math workbooks on volume.  As they finish this I have another handout I use called Finding Mystery Solids.  

Reflection Wrap-Up

5 minutes

Reflection is a big component in developing critical thinking.  It requires student to think about what they have learned and should include  students think about their own thinking - metacognition.

I do my best to integrate reflection questions throughout the lessons.  Reflection at the beginning of a lesson activates prior knowledge and gives students the hook to hang new information on.  Reflection in the middle of a lesson allows new information to start to move into long term memory. 

What did you learn about the volume formula and measuring the volume of shapes?

What were some of your thoughts as you were counting the cubes? 

Did your table work together well or were there some challenges.  Give examples.

Please write your answers in your math journals. 

Yes!  Every student wrote about volume as length times width times height in one way or another.  Another word used was layers.  Students who were introduced to the new formula used it in their notes as something new they had learned.  I am still going to check back in with the 5th graders to insure they remember the formula and what it looks like. 

We are ready to move on to using different units of measure and real life examples!  Also recognizing volume as additive.