CyberMuse Teachers - Lesson Plans
Seeing Math in Art
Lesson Plan Activity:
Building Your Own Sculpture!: Grade 4-6
Students will calculate the volume and surface area of Jean-Marie Delavalle?s Black Volume and draw a sketch. To scale, they will then create a net and build a sample prism, making comparisons to the real sculpture.
Students will identify prisms and their measurable attributes, including formulae for surface area and volume.
Students will construct a net and build a prism to scale.
Students will determine the relationships between units and how the volume changes when calculated with different scales.
Cross Curriculum Links:
3 45 min lessons, including discussion and sketches
Look & Discuss
Present and discuss Jean-Marie Delavalle?s Black Volume. (Tabs will provide you with information on the theme, composition, interpretation and the artist.)
A downloadable Presentation that you can add to or manipulate will also help share these images in your classroom.
- Isometric dot paper
- (Black) Bristol board ? one per student
- Cellophane tape
- Measuring equipment (measuring tapes, rulers, metre sticks)
- Plain paper will allow students some planning space especially for conversion purposes
- Photocopy questions and chart, if desired.
- Photocopy isometric dot paper ? you may want to do this on the overhead or projector.
- Assemble and organize physical materials.
Students should have an opportunity to look at the work together. The dimensions of the work are 182.7 x 61 x 23 cm.
1) Create together a diagram using isometric dot paper (and parallel for all to see, on overhead or Smart Board) or with a 3-D sketch in order to label the three dimensions carefully. The diagram does not need to be to scale, but should indicate the various measurement differences.
2) What is the volume of the work? What are the units used to measure the volume?
3) What is the surface area of the piece? What are the units used to measure the surface area?
4) How would this work have been made? Is it solid inside? Is it just a shell? Hint: Take a look at the materials list and this should give you the answer.
5) What would the net have to look like in order to make this volume?
A net is a pattern that can be folded or bent to make the shell of a three-dimensional shape. Without a lot of paper, it would be hard to make a net as for a right prism as big as Black Volume! However, we can use a scale.
Together students will come up with an appropriate scale that would fit on Bristol board. A 6:1 ratio works well and fits on the board with some space remaining (you may want to round the measurements to 180 x 60 x 24, depending on the ability and experience of the students. 10:1 ratio makes the width quite small, although it is much easier to convert).
Draw a sketch of the net for Black Volume and write down the real measurements.
Use your appropriate scale to indicate the model measurements (scaled) on this sketch. Once you have checked that the measurements make sense and fit on the Bristol board, transfer your measurements to the board.
Design your net. Remember the famous Carpenter?s Rule: Measure twice, cut once! Once you have done this, build your very own sculpture!
How many of your sculpture?s would fit inside the real one?
a) There are definitely many ways to consider this problem. Look at the volume of your model and compare this to the real volume. Just looking at the volumes, how many do you think would fit inside the real one? How does this compare to your scale factor?
b) If you actually wanted to build enough models to fit inside, how many would you build to fit inside? Is this the same as the question above?
Take it Further
Students can use their scraps (cut offs) to make even smaller to scale Black Volumes!
The student calculates both the surface area and the volume incorrectly.
The student calculates only one of either the surface area or the volume correctly.
The student uses the formula for surface area and volume, correctly.
The student cannot construct a net on her/his own and does not have accurate scale anywhere.
The student constructs a net independently, and does not have accurate scale throughout.
The student constructs a net with an accurate scale in all areas.
The student is unable to compare the volume of the real sculpture with the volume of the model with any accuracy.
The student compares the volume of the real sculpture and relates to the volume of the model, with some errors.
The student compares the volume of the model and the model of the real sculpture accurately.