Understanding Volume

Constructing Conceptual Understanding
Constructing Conceptual Understanding

This past week second and third grade students at my school are learning about measurement. The students are making progress. The classes have become more fluent with understanding perimeter and area, and are now starting to explore the concept of volume. Throughout the process students have used various manipulatives, such as prisms and nets to deepen mathematical understanding.   Even with all the activities  some students that are still struggling with the concept of volume. In about three weeks or so students will be assessed on this particular topic. Providing extra sessions for students to develop a conceptual understanding of volume is important. I wanted to find or create a math task that gave students intentional time to review geometry and measurement terms, while at the same time allow opportunities for students to create different products. After reviewing different options I decided on having students use the project detailed below.

Students were given a full sheet of colored centimeter graph paper.  They were then asked to read through the directions.

Directions: Create a net for a rectangular prism using the graph paper provided. The rectangular prism you build should have a volume of 20 cm3. Cut out your net and build a rectangular prism using glue or tape. Write the dimensions of the prism you built in the charts below.

Looking back, it seems like there were more than enough questions about what was expected.   Students always seem to have questions when there are multiple solutions/products.  After I answered their questions I took about 10 minutes to model the activity with the students.  This was important as it cleared up expectations for the activity.  I then passed out the assignment.

Click for sheet
Click for sheet

Students then used the centimeter grid paper to create a rectangular prism net.  They then filled out the top portion of the sheet.

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Some students had to use multiple attempts to create a net with a volume of 20 cubic centimeters. This was great opportunity for students to show perseverance and find a solution that worked.  I went around the classroom and asked students questions to help them think of a solution.  The students then cut out the nets and constructed their prisms.  The students then presented their rectangular prisms to the class.

 

 

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How do you construct meaning in geometry?


Geometry Explorations

Compass
Geometry Explorations               #mtbos post two

My fourth grade class is now studying geometry.  Geometry at the elementary level allows opportunities for students to get out of their seats and learn while using their compass and protractor.  Last week my students dusted off their protractor and compass in preparation for the geometry unit.  Throughout the years I’ve added different geometry explorations to this unit.  Some of the activities in this post have been modified from the curriculum and others I’ve created or borrowed from some amazing teachers.  I’m going to highlight four specific geometry explorations that I find valuable.


1.

Students are given different types of polygons and asked to find interior angle measurements.   I tend to group the students and have them work collaboratively to find a solution.  Students can use any method to find a solution.  I find that some groups use a protractor, while others find the measurement of the triangle and use it to find the interior angles of other regular polygons. Near the end of the session the class creates an anchor chart that shows similarities/differences between the polygon shapes and their sum of measures.

Polygons

Polygon Angles

2.

I pass out a notecard/piece of paper to each student.  Students are asked to make an arc on each corner of the sheet.  The arcs don’t have to be the same size.  The arcs are cut out and put together to form a circle.  Essentially, students use a rectangle and turn the rectangle into a circle and both have the same interior angle measurements. Students are then asked what conclusions can be made by completing this activity.

Circle

3.

I generally use this activity before teaching about adjacent and vertical angles.  Students are asked to draw and label two intersecting lines.  This should be review, but most students haven’t been using angles in math class for about eight months.  Once the angles have been created, students measure each angle.  Students are then asked what they notice about the measures of the angles?  Do they notice any similarities?  This is a great opportunity to fill out an anchor chart indicating what angles are close in measurement.

IMG_2352

4.

After all the above activities take place I give students a quick formative assessment.  It looks like this:

Finding Angle Z

Students are asked to find and explain the reasoning for the measurement of angle Z.

Overall, these exploration activities allow opportunities for students to engage in math in unique ways.  Math manipulative and explorations often open doors that ignite interest in many students.