5.MD.C.5 Find Volume by Packing Cubes

5.MD.C.5a  Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base.

5.MD.C.5c  Recognize volume as additive. Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the non-overlapping parts, applying this technique to solve real world problems.









To begin this lesson, I gave each child a solid wooden block and showed them how to trace around it to form a rectangular prism net.

I showed them how to place the block at the top center of their graph paper and roll the block down the paper as they traced each of the four faces around the prism.

Next, they line the wooden block up again on one of the faces and tip the block on its end to trace one face on the left and another on the right of the four faces they have just finished tracing.

Make sure when they cut out the net that they do not cut on any of the fold lines.

The net should cut out as one piece. Then the children fold on each of the pencil lines.










If the students correctly followed all of the directions, it should form a prism that matches the solid wooden block.










Well done, Alejandra.  :)

Before determining the volume, the children find the surface area. Here Cristal has written the square units and will then add them up to get a total of 112 square units for the entire net.









Angel and Ediverto are also having fun doing the activity with my class. Way to go, men!










After taping some of the edges of the prism, the students are ready to pack the net or package with cubes.










You may need to include a discussion about why we carefully pack the centimeter cubes inside in an orderly manner.

How does this help us add or multiply later?








Alejandra is trying to figure out how many cubes fit into her package without just counting each centimeter cube.

Is there a way to use mathematics to help us find this easily?






Patricio carefully emptied his package to determine how many centimeter cubes were in each layer and how many layers he had.










Fatima built only the bottom layer of cubes and then multiplied this times the number of layers in her package (multiplying by the height).










Leslie figured out the volume using numbers. She saw that there were 8 layers of 16 cubes for a total of 128 cubes.

I told the children that these were called cubic units.






Great photo, Esmeralda!!

Solving Problems with More Difficult Volumes

I teach a course at UCLA called Classroom Practices in Elementary School Mathematics (Math 71SL). During one of the sessions, an engineering student decided to create a net that was more interesting than just a rectangular prism. When I showed his net to my 4th grade students, they were inspired to try different variations of their own.

Such a great end-of-the-year activity...especially when our minds are focused more on summer vacation!!

4.MD.C.6 Measure Angles Using a Protractor

4.MD.C.6 Measure angles in whole number degrees using a protractor.












Using Microsoft Word, I inserted images into a Word document to create various shapes.

The children had a lot of fun using protractors, sharing answers, and trying to determine the angle measurements.

I like to use these circular protractors, because it is easy for the children to understand that there are 360 degrees in a circle and each little edge mark around the outside edge of the protractor is one degree.








I was also pleased with how successful many of the students were with measuring.

Rigoberto knew that every quadrilateral has 360 degrees. He also knew that all triangles have 180 degrees, so he used this information to divide the arrow polygon into two non-overlapping shapes--a rectangle and a triangle.








Next, Rigoberto proved that the angle measurement inside the arrow shape was 540 degrees. He demonstrated this by adding 360 degrees + 180 degrees.

Very sharp thinking, Rigo!!

After sharing answers with each of the polygons, I told the students to turn their papers over and trace two circles around their protractors.

I told them to put 4 points anywhere on the circle, connect the dots to form a quadrilateral, and measure each of the inside angles.

I was impressed with how well the children were able to measure! Even though Jorge did not know that all quadrilaterals have inside angles that total up to 360 degrees, he still came very close with 359 degrees in his measurements.  Well done, Jorge!!

 After sharing answers at their tables, several came up to the overhead to show the class their solutions.



Ediverto was VERY proud of his 55 degree measurement on his quadrilateral and showed it to the class.

Terrific measuring everyone.  :)