The standards outlined here are guidelines for, and examples of, CAD Craft's reinforcement of Common Core Standards for Mathematical Practice and is not exhaustive of the topics students will intuit from designing their own toy.
CCSS Standard definition link (goes to specific page on http://www.corestandards.org/Math/Practice/)
CCSS Mathematical Practice Standard
CCSS definitions (cluster)
- CAD Craft goals & application to standard
CO Academic Standard 21st Century Skills, Inquiry Questions, Nature of Mathematics
Standards for Mathematical Practice (Grades 1-5)
1. Make sense of problems and persevere in solving them.
- Students will develop a toy from concept to final product.
- Students will identify their goal:
e.g. “I want to make a race car for my action figure.”
- Students will create a toy design plan explaining their methodology, toy dimensions, and timeline for creating the toy.
- Students will use available materials, tools, software, resources, and mathematical concepts to make project drafts and a final toy.
- After successfully making a toy, students will complete a challenge project to teach others how to make their unique toy.
2. Reason abstractly and quantitatively.
- To meet their project goal, students will:
- Sketch designs and articulate their project goal
- Assess pros/cons of each design by asking questions:
- Decide on the best design using resources available
- Decide on the size of their project, based on their goal
- Decide what tools and materials are needed
- Decide how much material is needed
- Document their design plan and include measurements and materials list
3. Construct viable arguments and critique the reasoning of others.
"Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades."
- Students will articulate a plan for their design.
I will make a car for my action figure. It will have two sides and a base. I will use a tissue box for the base. I will draw my design on the computer to fit the tissue box. The car will be 8 inches long and 4 inches tall. I will print my design. I will need 2 sheets of paper for this design.
- Students will elaborate on their design:
How did they come up with the design?
Why is it a certain size?
How would they make their toy better in the future? Would those changes make it easier or harder for someone to make?
- Students will ask for peer feedback on their project, identify areas of design where they need help, and problem solve collaboratively
"They reason inductively about data, making plausible arguments that take into account the context from which the data arose."
- Students will explore concrete and abstract thinking challenges.
- Why wouldn’t you make a human-sized bed to fit a Barbie doll?
- Concrete Thinking: Can you make a 3-foot tall teddy bear out of one letter-sized sheet of paper? How many more sheets of paper would you need to make a 3-foot bear?
- Abstract Thinking: How could you make a 3-foot tall teddy bear with one letter-sized (8.5" x 11") piece of paper? (See Goals for explanation)
- Students will question why toys are small. Do toys need to be small?
4. Model with mathematics.
- Students will use estimation and proportions in deciding scale for their toys.
e.g. Older students might make toys that follow standard toy scales such as 1:6, 1:12, or HO. In this case, they might solve problems like: What does 1/12th scale mean? How big would I make a 1:12 scale airplane if a real airplane is about 150-ft long? [150/12 = 12.5] What are my final units of measurement and why?
CAS Grade 4 21st Century Skills Inquiry Questions:
How do you decide when close is close enough?
How can you describe the size of geometric figures?
- Students will use arithmetic to calculate parts and materials.
e.g. How many pieces of fabric do I need to make a doll with moveable arms? [front; back; 2 arms, front & back; 2 legs, front and back [1+1+(2 x 2)+(2 x 2) = 10]
e.g. How many 1-inch or 3-inch Barbie doll accessories could I make to fit on one piece of 8.5" x 11" paper?—Students might solve this problem arithmetically and then implement the solution practically by orienting and organizing individual objects on a page layout in a graphic design program.
- Students will utilize basic geometry to construct designs. (See Geometry Standards)
e.g. What type of 3D forms can I combine to make my toy model?
e.g. How do I modify a box to be a car?
e.g. How can I change the shape of a box to make different objects?
e.g. Older students would learn basic principles of 3D design software and drafting techniques as they make a toy prototype
5. Use appropriate tools strategically.
- Students will use rulers, tape measures, and proportional estimation to construct toys.
- Students will understand how to construct their toys using basic computer graphics software or 3D modeling software.
- Students will understand the limitations of the dimensions of their material.
e.g. How could I print something at a larger scale?
e.g. How small could I really make something and still be able to use it?
e.g. How can I make my toy with the least amount of waste?
6. Attend to precision.
- Students will make designs according to their goals and keep within the size limits they set for their project.
- Students will use measuring tools to meet their goals.
- Students will make their designs to scale by using computer software to create designs with accurate dimensions.
- Students will learn to use visual references and settings in computer software to produce images that will print to set sizes.
- Students will make a toy design plan for others to follow, focusing on the clarity of their methods
7. Look for and make use of structure.
- Students will identify basic forms used in toy construction.
e.g. What are the basic components of a doll house? (walls, windows, doors, floors, roof, etc.)
e.g. How do I make a 3D object that can be flattened onto a piece of paper, cut out, and folded back into a 3D object?
e.g. How can I make a basic template for my toy that can be adapted to make different variations (dolls of varying height, cars of different body styles, etc.)
- Students will recognize relationships between sizes of people and everyday objects.
e.g. Older children might make toys that conform to standard scales using precise measurements and proportionality
8. Look for and express regularity in repeated reasoning.
Make sound predictions and generalizations based on patterns and relationships that arise from numbers, shapes, symbols, and data
- Students will identify shortcuts and methods for creating scaled toys.
- Students might recognize patterns and shortcuts for creating series or sets of toys.
e.g. A student may adapt patterns and create multiple variations of their toy (for example, making a car longer or shorter by adjusting one dimension of their car pattern)
e.g. A student might compare and contrast commercial toy designs (e.g. Barbie dolls vs. Monster High) and use their findings to inform their design process
- Students will understand relationships of shapes and approximation in making designs
- Older students will begin to generalize ideas about shapes, forms, and approximation
e.g. Basic shapes can be combined to make new shapes for a toy design.
e.g. Objects are made from 3D forms that can be simple or complex.
e.g. Objects can be reduced to basic forms (A cup is a hollow cylinder. A toy tree can be made from a cone.)
e.g. Extending thinking—Polygons and polyhedrons can be used to make paper toys that are more complex. Students will observe that they can make paper models of curved objects by visualizing them as faceted objects (see the unfolded teapot example, below). Students will observe that by adding more faces to their basic forms (or more folds in their model) they can create toys that appear rounder or smoother.
CAS Grade 5 21st Century Skills & Readiness Competencies
Mathematicians use creativity, invention, and ingenuity to understand and create patterns.
The search for patterns can produce rewarding shortcuts and mathematical insights.
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