3 of 11

Notes for teachers

This lesson takes place in the classroom setting for one or more hours.
Students MUST work in groups. Ideal group size is 3-4 students.
The emphasis is on students dialoguing and debating and coming to agreement about how to build the surface areas and volumes correctly.
All students in the group should be able to explain to their teacher how they know their model has a specific volume or surface area before moving on to the next question on the worksheet. (If one student cannot do so, the other students in the group must keep working with that student until they are able to explain it.)
Homogenes groups work best for this activity so group highs with highs, mediums with mediums, lows with lows as much as possible for this activity.
The Magna-Tiles do not measure to exactly 3in by 3in squares, but I tell students that we can use 3in as the measurement for this activity.

List of Materials

Magna-Tiles (4-6 boxes for a class of 30)

Rulers (ideally one per student)

Worksheet -Exploring Volumes with Fractional Edge Lengths Using Magna-Tiles

4 of 11

AZ 6th Grade Math Standards

6.G.A.2

Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Understand and use the formula V = B · h, where in this case, B is the area of the base (B = l x w) to find volumes of right rectangular prisms with fractional edge lengths in mathematical problems and problems in real-world context.

AZ 6th Grade ELA Standards

6.SL.4

Present claims and findings, sequencing ideas logically and using pertinent descriptions, facts, and details to accentuate main ideas or themes; use appropriate eye contact, adequate volume, and clear pronunciation.

5 of 11

Objective(s):

Today we will build models of rectangular prisms with fractional edge lengths.

Today we will determine how to pack these rectangular prisms with cubes to find their volumes.

6 of 11

Agenda (lesson time)

8 min -Mini-Lesson (Review the concepts of volume and how to calculate it.)

50 min- Group work- build and discuss and complete worksheet questions

7 of 11

How do you find volume? V= L x W x H

8 of 11

How would the volume be impacted if the sides were not whole units?

Does the volume

formula still work?

9 of 11

Hands-on Activity Instructions

In groups of 3-4 build shapes with the desired volumes.
Groups should work together to build shapes with the desired dimensions.
The whole group needs to agree that the shapes has been built correctly.
If a group member does not agree, discuss why they think that. Show each other evidence of why you agree or disagree with the models you have built.
For this activity, it is best to group students by ability levels (so high with high, medium with medium, low with low)
Students will probably only have enough Magna-Tiles to build one model at a time, so let them know that they need to build their models as a group- not individually.
Students might only be able to build an outline for their figure due to the limited number of Magna-Tiles. To build the outline, students must at least show the length, width, and height of the figure.

Actual student worksheet

Students need to at least build an outline of the shape as shown above showing the length, width, and height of the shape.

10 of 11

Assessment

The goal of this activity is exploration volume and how fractional sides impact the overall volume.. This lesson also focuses on communication with peers; therefore, I like to do an informal assessment for this activity where one group member has to explain their answer to each question before the group can go on to the next question. (If students are waiting for the teacher to come to their group they can move on until I’ve had a chance to check in with them.) The teacher chooses which group member will explain the answer to the question. I often pick a group member who I am not sure totally understands the concept. If the group member explains the answer incorrectly, their group has to keep working with them to get them to understand it and the teacher will come back around to their group when that group member thinks he/she can accurately explain the concept. (I look for accuracy in the numbers, but give reminders about correct terminology. A student will say things like this side has an area of 9, so you’ll need to remind them that it is 9 square inches, etc.) If group members do not agree, encourage them to explain their understanding using the model they have created. I also assess the students ability to recreate the 3-dimensional shape as a 2-dimensional drawing. Students should compare drawings with their fellow students and make sure that they agree on what the drawing should look like.

11 of 11

Differentiation

This activity assumes a basic understanding of volume of rectangular prisms. Students should be familiar with the terms, “faces, sides, edges, and base.” and should know the formulas for calculating volume of rectangular prisms. If students are rusty on this, I recommend doing a mini-lesson reteach before having students do this activity as they will need to be familiar with all of that information to be successful at this activity. (This concept desires an 5 minute mini-lesson before doing this activity. Review slide is slide 7.)

Remediation

Extension/Enrichment

The worksheet is set up so that each question gets increasingly more difficult and requires different levels of critical thinking. Questions 1-5 can be built using the Magna-Tiles and will give students a strong understanding of the concept. The dimensions on questions 6 and 7 CANNOT be built with the Magna-Tiles, so students have to take what they have observed in the earlier questions and build generalizations. Questions 6 and 7 lead to a greater level of abstract understanding of the concept.

It is okay if groups don’t make it through the entire worksheet. The richness of this activity comes from students being able to build the models and debate their ideas with their peers and come to a greater understanding of volume with fractional edges. The other beneficial aspect of this lesson is that it forces students to verbalize their understanding and explain it to peers who do not agree or understand while having a tangible model to help them clarify their thinking.

1 of 11

2 of 11