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Georgia Standards

IN MATH, the Georgia Performance Math Standards has created a number of Content Standards. Those related to DIATC design activities include: Numbers and Operations, Measurement, Geometry, Data Analysis & Probability, and Algebra.

Math Standards:

Numbers and Operations

  • The student will use four arithmetic operations with fractions and mixed numbers and solve problems with them (M6N1, 6th grade). The student will understand and compute positive and negative numbers, and rational numbers (M7N1, 7th grade).
    In the Parachute task, students can used fractions to figure out when they have followed the rule-of-thumb for having a vent hole of 1/10 of the canopy's total area. Any of the design tasks where a cost/benefit ratio can be calculated would be appropriate here.
  • Students will use algebraic symbols to find solutions to mathematical problems (M8N1, 8th grade).
    Students need to understand the use of algebraic symbols whene using Newton's Laws of Motion with the Vehicles In Motion task, when figuring out the mechanical advantage of Simple Machines they build. This understanding can help when students calculate the stresses on their Shopping Bags when loading them to failure.
  • Students will add, subtract, multiply, and divide monomials and polynomials (M8N3, 8th grade).
    Although special tools are needed, once acceleration of vehicles has been measured, the idealized distance traveled by the Vehicles In Motion can be calculated.
Measurement
  • The student will calculate volume of solid figures through measurement and experiments. Calculate volume and surface area of right prisms, cylinders and cones (M6M1, 6th grade).
    Students can calculate the volume of air in their chutes and the surface area of their canopies in Model Parachute task. Similar calculations can be done for the surface area and volume of the Shopping Bag and the Clay Boat that each designs.
  • The student will do measurements and calculate conversions (M6M2, 6th grade).
    In the Paper Bridge task, students can convert the weight of the paper they cut away from their bridge into the area of the bridge. In the Model Parachute and
Geometry
  • The student will understand line and point symmetry, scale drawings and shapes and sizes of plane figures (M6G1, 6th grade).
    Scale is an important concept when designers move from small- to full-sized versions of an item they are making. This is directly relevant to all projects with models in them, like Paper Bridge and Model Parachute, but in particular with the Cardboard Chair and Parade Float design challenges.
  • The student will understand solid figures solid figures including prisms, pyramids, cylinders and cones (M6G2, 6th grade). They will explore the manipulation of various geometric figures (cones, cylinders, pyramids, and prisms) and compare solid and plane figures Develop their understanding of the figures in space (M7G2, 7th grade).
    Students' study of solid geometry figures can be applied to different Shopping Bag designs, and to the making of a Clay Boat, where figuring out the surface area and volume of different shapes is important in creating a boat that can stay buoyant with the largest load.
  • Students will deepen their understanding and ability to construct plane figures. Construct bisector of an angel, perpendicular bisector of a line, circles, chords, etc. Reflection, rotation, symmetry, and translation (M7G1, 7th grade).
    The Cardboard Chair and Paper Bridge design challenges are good transfer tasks to test students capabilities in these issues of plane geometry.
  • Students will confirm properties of a figure using properties of parallel and perpendicular lines, triangles and parallelograms, and right triangles (including the Pythagorean Theorem) (M8G1, 8th grade).
    The above understanding is helpful in using the "distance-traveled method" to figure out the mechanical advantage of Simple Machines. Differentiating between triangles and parallelograms is important in discussing the strength of structures in the Cardboard Chair, Model Crane and Paper Bridge tasks.
Algebra
  • The student will understand ratios and how to use them (M6A1, 6th grade).
    In the Baking Soda challenge, students need to express the ideal ratio of baking soda to vinegar by weight to get the greatest amount of gas production, and least amount of by-products.
  • The student will understand relations between two quantities as well as how they vary. Direct proportion, proportional reasoning, inverse proportion are investigated through mathematical equations and graphing simple functions. Solve linear equations using whole numbers, decimals, and fractions (M6A2, 6th grade). The students will work with variables in formulas that represent relations and rules. Solve simple mathematical algebraic expressions. Utilize properties of numbers (commutative, associative, and distributive) to solve expressions (M7A1, 7th grade).
    Students need this understanding when working with the Design Rules-of-Thumb that they create for any of the design projects that involves them doing experiments with the impact of variables on the outcome performance of a product.
  • The will represent and analyze data. Build tables, graphs and show frequency distributions. Understand and show mean, central tendencies, mode, median, and range of data (M6A3, 6th grade).
    Students need to graph the performance of their products because it varies from test to test. This is true with almost all of the design tasks found in DITC and elsewhere.
  • Student must arrange and order data, use probability (theoretical and experimental), and predict the results of investigations (M6A4, 6th grade).
    After figuring out how much Mechanical Advantage they need to raise a heavy can of food in Simple Machines, students can make predictions on whether their devices will work or not.
  • Students must be able to solve problems involving linear equations and properties of equality (M7A2, 7th grade).
    Design tasks are a great context for solving problems involving linear equations -- the problems at the end of Model Parachute and the expressions of the design of the Electromagnet with the number of nails raised by the system are two instances of such problems.
  • Students will know how to use numbers in different representations and in a real world context (M8A1, 8th grade).
    When presenting their designs, as with a Pin-Up Session, Gallery Walk or Final Presentation, students need to display data in different ways to communicate best what they have learned to their audience.
  • Students will continue their development using linear functions and functional relations including: inverse and direct variations, proportionality, slope (rate of change).
    Any of the the challenges that have to do with motion (Model Parachute, Vehicles in Motion) can have students express changes in motion using graphics that display slop and relationships between predictor and outcome variables.
A Data Analysis and Probability
  • Students will develop their abilities utilizing funtions and linear relations. Representing a functional relation in a formula, table, graph, or by graphing coordinates on a plane (M7D1, 7th grade). Students analyze the nature of linear relationships through graphs. Understand and graphically represent direct and inverse proportions (M7D2, 7th grade).
    Supporting a Design Rule-of-Thumb with a graph that shows a direct or inverse relationship between a design variable and the product's performance (outcome) can be a powerful way to reinforce this learning objective.
  • Organize data in tables and solve problems involving central tendency, mode, median, and range. Make decisions based on the analyzed data. Represent the data in graphs and frequency distribution tables (M7D3, 7th grade).
    Data on product performance can come from actual measurements of how the product behaves, or it can be collected from users -- the latter can be especially important for tech ed students when they justify changing a design because they want the product to have a different aesthetic or ergonomic impact on the user.

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