Before approaching the study of volume, learners have had experience with solids in their environment using the Pink Tower, the Brown Stairs, and the Geometric Solids. Another concept that aids learners in understanding the concept of volume are the study of matter, which takes space, and the study of area where they learn about units of measurement. With all this knowledge combined, learners ages nine and up can grasp the concept of measuring space within a solid, starting with the simplest parallelepiped (rectangular prism) to spherical and conical solids. In the last lower elementary year (age 8-9), learners are invited to build solids using unit cubes. They are sensorially familiarized with adding neutral cubes to increase volume.
Materials
Optional: Geometric Solids with Bases & Planes, Brown Stair
The Study of Volume Task Cards set invites your learners to reapply the knowledge acquired through formal presentations. The set is designed to follow the Montessori curriculum timeline; each section aims to progressively reactivate the prior knowledge necessary to carry on the next task. This post will walk you through the seven sections and share the expected progression.
Section 1 – Constructing and Calculating
Section one is the entry point to measuring space using unit cubes. Learners use the Volume Box with 250 Cubes to build various prisms and sensorially calculate each prism they have built. The formula is provided on the back of each card to reinforce this concept: Volume = length x width x height.
Section 2 – Calculating Pink Tower and other Prisms
This section challenges learners to explore the Pink Tower and reconstruct its parts using the Volume Box with 250 Cubes. Using critical thinking, learners will realize that only some prisms can be constructed with the Volume Box with 250 Cubes. Learners will continue estimating the volume of objects around them using word problems. This broadens their understanding that anything that contains space can be measured using volume’s formulae.
Section 3 – Comparing using the Five Yellow Prisms
In section 3, learners work with the Five Yellow Prisms, which equates the Volume Box with 250 Cubes in terms of volume. Learners begin to calculate the volume of one yellow prism, then two, three, four, and five yellow prisms. They calculate and find that one yellow prism is 50 cubic units and observe that each additional yellow prism is an additional 50 cubic units. They can mentally predict that five prisms will be 250 cubic units, equivalent to the 250 cubes from the Volume Box with 250 Cubes. Comparing materials helps learners develop critical thinking and make connections between mathematical concepts.
Section 4 – Calculating Brown Stair Prisms
Section 4 provides additional work with measuring rectangular prisms, which formula is the area of the base times the height – V = Ab x h. Again, in this section, learners will encounter prisms that they cannot measure using the Volume Box with 250 Cubes because some are not measurable with 2 cm cube units.
Section 5 – Calculating Cylinders
Section 5 is straightforward. The six Task Cards require learners to calculate the volume of various cylinders and provide the radius and the height. Some cards contain visuals, so learners don’t need concrete materials from around the classroom. The formula and detailed answers are provided on the back of each card.
Section 6 – Calculating Spheres
Section 6 is similar to section 5. Learners calculate the volume of other solids, such as a sphere. Many examples are provided with ample guidance on the back of each card, such as the formula for calculating a sphere and the value of pi (π).
Section 7 – Calculating Cones
Section 7 deals with calculating the volume of a cone. Once your learners have calculated the volume of a sphere in the previous section, they will be prepared to calculate the volume of a cone which requires a similar process: π x the square of the radius x the height divided by 3.
The Study of Volume Task Cards are easy to follow and will ensure that your learners have plenty of practice with calculating volume of common solids. Task Cards are supplemental materials that aim to provide independent practice with instant feedback. We hope you enjoy working with our professionally-developed materials!
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