Activities
The activities in this unit flow from one to the next but will be separated into 5 general steps. I estimate that, with the final art project, it will take three to four weeks to complete the unit. These steps are meant to scaffold hands-on use of measurement and the understanding of units, shapes, and forms in math and art. We will look at the size of art pieces and how they compare to each other and how they compare to our typical sized work in class. Most students are familiar with and like sports, therefore we will briefly discuss the size of a basketball court, an Olympic pool, and a football field’s markings. I feel it is a way to get students to better relate what they are learning to the real world.
“All areas of human experience are measured and counted, but few as visibly as sports. Sports are ruled and regulated by numbers. Playing fields and courts are laid out, scores are counted, records are broken- all of which demand a basic level of numeracy.”15
Andrew Elliot states in his book, Is That a Big Number?, “The glamorous sister of memory is imagination.”14 He impresses on the reader that imagination not only lets us create, but also enables us to “see the future”, visualize possibilities, work out issues, and plan a complex process that we can later follow. This is something that I will share with my students at the beginning of our unit when showing them the final product that they will be working toward so they will perhaps be a little more open to the process and mindset of the unit.
Rulers and Measuring
Basics of Standard Measuring Instruments
After showing students an example of the final pieces, they will make, we will start off with a review of the use of rulers. This will be basic so that students who don’t have a solid understanding will gain a little competence here, but not taking so long as to bore those who already have a solid grasp of measuring. The time it takes to finish this will depend on the individual class, of course. I will show my students a giant version of a ruler. We will discuss the importance of starting at 0 and using the lines to determine whole numbers. We will briefly discuss halves and quarters, though we won’t dwell on them since we aren’t going to be using them in this unit. The activity will help students understand how to properly use a ruler, yardstick, and measuring tape through cooperative learning and reciprocal teaching strategies. Students will get in 5-6 groups of mixed understanding of measurement and each group will be given a ruler, a yardstick, and a measuring tape. Items will be presented for students to measure in their groups using the three tools (straw, dowel rod, pipe cleaner/chenille stem, etc.). The answers will then be given for students to check their answers against. Student volunteers will come show the class how they found the correct answer, so that groups that did not get it can understand how the answer was found. As a group they will then compare the three items in a three circle Venn diagram. Given a short period of time to write answers, we will then discuss the answers as a class. Some important points for students to understand are when to use each tool, how to use each tool, and difference between standard and metric measurements.
Using Our Measurement Tools
For this part of the activity we will look at two art pieces: Kehinde Wiley’s “Louis the XIV of France”15 and “The Mona Lisa”16 by Leonardo Da Vinci. After discussing the pieces, we will use our large roles of paper to measure and cut out the sizes of paper that match the two pieces to compare to the size of paper that we typically use for our own art pieces in class (12”×18”). The importance of the unit attached to a task will be emphasized in measurement. We will stick with standard measurements and students will be advised to “choose your units wisely to allow yourself to work with numbers that are modest in size, balanced by your ability to visualize the unit you’re working with”.17 It will be observed that “The Mona Lisa” should be measured in inches, while “Louis the XIV” should be measured in feet.
We will then work in small groups to measure an artwork in a frame with a ruler and a yardstick for perimeter, the school’s pool deck with a measuring tape for area, and the classroom sinks with a ruler to determine volume, and finally measuring out a walking track on the school field using a walking tape measurer to find the volume of cement needed for a track and determine the amount of cement that would be needed for a 3 foot wide, 4 inch thick track around the entire field. After doing these measurements we will discuss the varying sizes of the sports arenas that we know and love, for swimming, basketball, football, and soccer.
Finally, we will look at the use of the body for measurement to relate to the visualization of size, such as a fathom that “originally came from a word meaning ‘outstretched arms’, it becomes easier to remember that a fathom is 6 feet (equally, 2 yards, the yard being more or less as long as nose to tip of outstretched arm).”18 Students will work with their partners to measure their own wing span to compare it to the 6 foot estimate. Being as most of the students are not full grown, and everyone’s arms are different lengths, they will see the variance, but understand the point of the exercise. We can also look at the fingers for inches, between elbow and wrist (or fingertips) for feet, etc.
Fun with Polyominoes
I will work with students on the board (as a class) and on grid paper (individually or in pairs) to show the build-up of polyominoes from 1 to 5 using the grid method shown in the Polyominoes section in the unit, and discuss. Students will calculate the area and perimeter of given shapes (polyominoes) by decomposing the shapes and will apply this experience to understand that a simple rectangle is an array of unit squares. Working in pairs students will then create hexomino (6 square units) nets based on square inches using a ruler and paper, noting the perimeter and area of each shape, which will be presented on the board as a class (these will be used in the next activity). Students will be challenged with an exit ticket to create three 8-unit polyominoes, and to answer the question: “What is the area and perimeter of each shape you created?” As an extra challenge, students can create an octomino with a perimeter as large as possible, and one with a perimeter as small as possible. There will be many of the large perimeter shapes, but only a couple of the small perimeter shapes. This will be an informal assessment to insure understanding of the activity. The reason for this activity is to practice measurement and to better understand our next step, nets, which are polyominoes.
2-D Net to 3-D Cube
In pairs, students will pick out the hexomino nets (from the last activity) that can be folded and put together to make a cube. Some students will be able to visually figure this out, others may have to cut out individual nets and fold them to check the legitimacy of the cube. After a given period, students will share out their discoveries and we will discuss why some work, and some don’t.
Each of the two partners will choose a net that will fold into a cube properly and recreate it on cardstock based on 3 by 3-inch squares, with area of 9 inches2 (and 12-inch perimeter) and a final cube volume of 27 inches3. They will need to add tabs along one side of the edges that touch (I will demo this before students start). Before folding up the net and putting gluing it together, students will be required to add texture and color to each square. They will have 6 different sides featuring textures and color wheel properties- primary, secondary, tertiary, cool, warm, analogous, monochromatic, tints, tones, or shades. This could be used as an opportunity to review or teach the properties of the color wheel in an art class, if it hasn’t already been done, or in a math class the students could just be given the opportunity to color and design the cube as they wish. When finished coloring, students will fold and glue the net into cube form.
For an exit ticket, students will find the surface area of their individual cube. “We can calculate the surface area of a prism by adding together the area of the base(s) and the lateral faces.”19 With a cube, it is easiest to find the area of one square and multiply it by 6, however, it will be up to the students comprehension of what we have learned so far to determine if they understand this or not.
Discovering Tetradic Cuboids
Each pair of partners from the previous activity will join with one other pair so that they have 4 cubes between the four students (for groups of three a spare cube can be given to finish the tetrad needed or a group may need 5 students, but will still only use 4 cubes). Students will then create all variations of tetradic cuboids they can. For a tetradic cuboid each of the four cubes must have a planar surface that matches up to at least one other cube planar surface as shown in the Tetradic Cuboids section of the unit discussion. With each tetradic cuboid discovered, students will draw it on paper to the best of their ability (they will need these drawings for the final project). Some students may be interested in the Soma Cube Puzzle. It is a puzzle cube that is created by fitting together all the possible combinations of three- or four-unit cuboids (soma cubes), joined at their faces, such that at least one inside corner is formed.
Tetradic Cuboids in Clay
Finally, as the culminating art project, students will pick their favorite tetradic cuboid and use their tetradic cuboid drawings (and possibly cardboard tetradic cuboids) to create a tetradic cuboid net. They will each create templates for the individual faces of their chosen form (as shown in the Tetradic Cuboids section of the unit above). These templates will be used on clay slabs to cut out the shapes that will then be joined to replicate the paper tetradic cuboids. They can then add texture and design to their pieces before firing and glazing. It could be interesting to see if pieces made by students (along with a - unit cuboid made in advance by me) could form a Soma Cube and if students could then find the area and volume of the cube.
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