The standards outlined here are guidelines for, and examples of, CAD Craft's reinforcement of Common Core Standards for Measurement & Data and is not exhaustive of the topics students will intuit from designing their own toy.

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Standards Key:

CCSS Measurement & Data Domain

CCSS Standard definition link (goes to specific page on http://www.corestandards.org/Math/Content/MD/)

CCSS Measurement & Data Standard definition

• CAD Craft goals and application to standard
  

Examples and clarification

Colorado Academic Standard

CAS definition
21st Century Skills

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Grades 1 & 2

Measure lengths indirectly and by iterating length units.

Content Area: Mathematics
Grade Level Expectations: First Grade
Standard: 4. Shape, Dimension, and Geometric Relationships

Prepared Graduates: Understand quantity through estimation, precision, order of magnitude, and comparison...

Concepts and skills students master:
2. Measurement is used to compare and order objects and events

CCSS.MATH.CONTENT.1.MD.A.2

Express the length of an object as a whole number of length units...

• Before a student begins designing or planning their toy, they will use estimation to draft a rough outline of their toy's height & width
  
• Students will use rulers, tape measures, estimation, and computer software measurement tools to construct toys that will fit onto sheets of letter-sized paper using whole inches as their standard of measurement

21st Century Skill & Readiness Competencies
Nature Of:
With only a few words, mathematicians use measurable attributes to describe countless objects.

Measure and estimate lengths in standard units.

Content Area: Mathematics
Grade Level Expectations: Second Grade
Standard: 4. Shape, Dimension, and Geometric Relationships

CCSS.MATH.CONTENT.2.MD.A.1

Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes.

• Students will utilize measuring tools to create precisely dimensioned toys
  

e.g. a car that is 6 inches long, 4 inches tall, and 3 inches wide

• Students will use measuring tools and references within a 2D graphics program to create a toy design that adheres to the dimensions they defined in a plan
  

CCSS.MATH.CONTENT.2.MD.A.3

Estimate lengths using units of inches, feet, centimeters, and meters.

• Students will express their toy dimensions using standard units of measurement (either inches or centimeters)
  
• Students will create a toy design that can fit on sheets of 8.5" x 11" (US Letter) paper or printable fabric sheets, and will use this measurement to create a "bounding box" in a computer graphics program
  

Click to see larger image

CCSS.MATH.CONTENT.2.MD.A.4

Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit.

Understand quantity through estimation, precision, order of magnitude, and comparison...

• Students will utilize estimation and proportions to design and construct a toy
  

e.g. A student would estimate and determine length of toy components such as doll arms or car wheels by utilizing their main design as reference (doll body or car body, in these examples)

• After estimating students will define these components with actual units (e.g. the arms for a 7 in. doll are 3 in. long)
  

Relate addition and subtraction to length.

Nature Of:
Mathematicians use measurable attributes to describe countless objects with only a few words.

• Students will utilize arithmetic to determine the amount of material they need (either paper or fabric)
  
• Students will use arithmetic to define component parts of their toy
  

e.g. My toy car is 7 inches long.  The hood is 2 inches long.  The cab is 3 inches long, and the trunk is 2 inches long.

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Grade 3

Solve problems involving measurement and estimation.

Content Area: Mathematics
Grade Level Expectations: Third Grade
Standard: 4. Shape, Dimension, and Geometric Relationships

• Students will utilize estimation and proportions to design and construct a toy
  

e.g. A student would estimate and determine length of toy components such as doll arms or car wheels by utilizing their main design as reference (doll body or car body, in these examples)

• After estimating, students will define these components with actual units (e.g. the arms for a 6 in. doll are 2.5 in. long)
  

Inquiry Questions:
What kinds of questions can be answered by measuring?
What are the ways to describe the size of an object or shape?

Represent and interpret data.

CCSS.MATH.CONTENT.3.MD.B.4

Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch...

• Students will utilize rulers and computer software measurement tools to create toy designs that are precisely dimensioned
  
• Students may create toys that are the same size as, or are scaled to work with, their existing toys.  In which case, they will precisely measure their reference toy before creating an original toy design.

e.g. A student might make a car that is the same size as cars in their mini car collection
e.g. A student might make furniture for Barbie, baby dolls, or other popular commercial toys

Geometric measurement: understand concepts of area and relate area to multiplication and to addition.

CCSS.MATH.CONTENT.3.MD.C.5

Recognize area as an attribute of plane figures and understand concepts of area measurement.

CCSS.MATH.CONTENT.3.MD.C.7

Relate area to the operations of multiplication and addition.

• Students will estimate approximate areas of their toys to determine how to fit their flat designs onto sheets of paper.

e.g. A student might estimate the surface area of a doll body by drawing a box around it and using the box as a reference guide.  This same process could be used for flattened paper boxes or other complex designs

CAS Grade 4
Inquiry Questions:
How do you decide when close is close enough?

Click to see larger image

Geometric measurement: recognize perimeter.

CCSS.MATH.CONTENT.3.MD.D.8

Solve real world and mathematical problems involving perimeters of polygons...

• Students might use perimeter to determine the dimensions of embellishments for their project
  

e.g. Use perimeter of dollhouse around sides and across front to make decorative trim or use perimeter to make fencing
e.g. Use perimeter of toy car to cut paper strips for "decals" around bottom edge of car

Concepts and skills students master:
2. Linear and area measurement are fundamentally different and require different units of measure

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Grade 4

Solve problems involving measurement and conversion of measurements.

Content Area: Mathematics
Grade Level Expectations: Fourth Grade
Standard: 4. Shape, Dimension, and Geometric Relationships

Concepts and skills students master:
1. Appropriate measurement tools, units, and systems are used to measure different attributes of objects

• Students will understand how to scale their designs, and check their dimensions using pull-down menus in graphics software

Click to see larger image

• Students will understand will be able to define the unit "pixels"

• Students will convert units within the computer software, and recognize the relationship between standard units of measurement and pixels
  

A pixel is the smallest part of a digital image.  Pixels are small squares.  You can see them when an image is enlarged so much it looks "blocky."  Painting programs, like Photoshop, use pixels.  Drawing programs, like Inkscape, do not.  You can easily enlarge or reduce images you create in Inkscape without them looking "pixelated."  Drawings created in programs like Inkscape are considered "infinitely scalable", meaning you can enlarge or reduce them to any size, forever.  You have to be careful in painting programs when enlarging images, or else they will start to look pixelated.  We can also use pixels in a drawing program to define how big our image is.  Pixels "tell" the computer how big the image is on-screen.  It is usually easier to convert pixels to standard units like cm. or in. for us to understand how big our image will print.

Scaling an image in a drawing program (Inkscape)

Scaling an image to see pixels

Represent & Interpret Data

Concepts and skills students master:
2. Geometric figures in the plane and in space are described and analyzed by their attributes

CCSS.MATH.CONTENT.4.MD.A.3

Apply the area and perimeter formulas for rectangles in real world and mathematical problems.

• Students will calculate approximate areas of their toys using "bounding boxes" to determine how to fit their flat designs onto sheets of paper.
  

e.g. A student might estimate the area of a doll body by drawing a box around it and using the box as a reference guide.  Then, they would calculate the area of their bounding box and the area of their paper to determine how much material they have and how much they need to print their designs.  This same process could be used for flattened paper boxes or other complex designs.

Click to see larger image

Geometric measurement: understand concepts of angle and measure angles.

CCSS.MATH.CONTENT.4.MD.C.6

Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure.

• Students will utilize angle measurements to create their projects in 2D and 3D programs
  
• Students will understand how to create straight lines at a predefined angle measurement in drawing programs like Inkscape
  
• Students will understand the importance of angles in designing toys such as dollhouses, furniture, or cars

e.g. A chair back is usually 90°, as are the backs of most furniture.  A student will need to make sure their lines are perfectly straight when designing the sides and backs of toys like doll furniture.
e.g. It is important to make sure lines are precise so that when a paper toy is folded together, all the sides line up.

Relevance & Application:
The understanding and use of spatial relationships helps to predict the result of motions...
The application of spatial relationships of parallel and perpendicular lines aid in creation and building...

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Grade 5

Convert like measurement units within a given measurement system.

CCSS.MATH.CONTENT.5.MD.A.1

Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems.

• Students will understand how to scale their designs, and check their dimensions using pull-down menus in graphics software and 3D modeling software.
  
• Students will convert units within the computer software, and recognize the relationship between standard units of measurement and pixels
  

• Extending thinking—Students will understand and be able to define print resolution & dpi

dpi stands for "dots per inch."  Inkjet printers print a series of dots to make an image.  Usually, these dots are almost too small to see.  dpi is a measurement of how many dots the printer will print in a square inch.  The higher this number, the more closely spaced the dots are.  Closely spaced dots (a high dpi) makes a clearer and sharper image.  300 dpi is a good print resolution.  When making a final image export from a 2D graphics software, it is best to set the output resolution of our design to 300 dpi, to get a very good final image that can be printed.

Using pull-down menus to check image dimensions—These measurements (in standard units) correspond to the actual dimensions of the printed toy.

Exporting a toy design for printing at 300 dpi

Click each image to enlarge

This doll, shown in previous images, was printed at 300 dpi onto printable fabric then sewn and stuffed. As you can see, the printing turned out well!

Geometric measurement: understand concepts of volume.

Content Area: Mathematics
Grade Level Expectations: Fifth Grade
Standard: 4. Shape, Dimension, and Geometric Relationships

Concepts and skills students master:
1. Properties of multiplication and addition provide the foundation for volume an attribute of solids.

CCSS.MATH.CONTENT.5.MD.C.3

Recognize volume as an attribute of solid figures and understand concepts of volume measurement.

CCSS.MATH.CONTENT.5.MD.C.5

Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume.

CCSS.MATH.CONTENT.5.MD.C.5.B

Apply the formulas V = l × w × h and V = b × h for rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths in the context of solving real world and mathematical problems.

• Students will understand that their finished toys have measurements of height, width, and depth
  
• Students will recognize that they can estimate the volume of their toys by measuring them as if they fit into an invisible box (using rulers to take straight measurements from the tallest part of their toy, the widest part, and the deepest part)
  
• Students will understand why knowing the volume of their toy would be useful

e.g. to determine what size box they might need to package and ship the toy
e.g. to determine how much space it will take up in their room
e.g. to determine if it can it fit in a closet or toy box
Extending thinking—to determine how much material would be needed if the toy was printed in liquid plastic, instead (would be necessary for mass production in a toy factory, or if they were to use a 3D printer)

Nature Of:
Mathematicians create visual and physical representations of problems and ideas that reveal relationships and meaning.

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