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Massachusetts Math Standards

Math Learning Standards (Grades 7-8)
Below is a fairly long list of math standards (from the Math Curriculum Framework, May 2001) that are applicable to the design tasks in DITC. Many of the standards are followed by a bulleted list enumerating the sections of DITC that could help you meet those standards. While the design tasks are not specifically geared towards math, many of the tasks provide concrete and memorable examples of applying mathematical concepts that middle school students are required to learn.

8.N.1 Compare, order, estimate, and translate among integers, fractions and mixed numbers (i.e., rational numbers), decimals, and percents.
8.N.3 Use ratios and proportions in the solution of problems, in particular, problems involving unit rates, scale factors, and rate of change.
8.M.4 Use ratio and proportion (including scale factors) in the solution of problems, including problems involving similar plane figures and indirect measurement.
8.N.10 Estimate and compute with fractions (including simplification of fractions), integers, decimals, and percents (including those greater than 100 and less than 1).
As students record trials of their investigations they must utilize many
estimation and computation skills:

  • interpreting and comparing numbers as decimals, fractions, ratio and percents,
  • converting input units into proper output units,
  • and using a reasonable amount of precision and accuracy when conducting their tests.
8.P.1 Extend, represent, analyze, and generalize a variety of patterns with tables, graphs, words, and, when possible, symbolic expressions. Include arithmetic and geometric progressions, e.g., compounding.
  • Students may create charts and tables based on the data sets collected and identify the relationships between different properties that are revealed to guide them in making design decisions.
8.P.5 Identify the slope of a line as a measure of its steepness and as a constant rate of change from its table of values, equation, or graph. Apply the concept of slope to the solution of problems.
8.P.8 Explain and analyze both quantitatively and qualitatively, using pictures, graphs, charts, or equations how a change in one variable results in a change in another variable in functional relationships, e.g., C = pd, A = pr2 (A as a function of r), Arectangle = lw (Arectangle as a function of l and w).
8.P.6 Identify the roles of variables within an equation, e.g., y = mx + b, expressing y as a function of x with parameters m and b.
  • Students can use formulas that describe natural phenomena (i.e. formulas that calculate the rate of descent of a parachute), predict the effect of changing a variable, and observe the results after the change.
8.G.8 Recognize and draw two-dimensional representations of three-dimensional objects, e.g., nets, projections, and perspective drawings.
8.M.1 Select, convert (within the same system of measurement), and use appropriate units of measurement or scale.
  • Creating sketches and scale drawings is important to every designer and is a hallmark of many activities found in DITC.
8.M.2 Given the formulas, convert from one system of measurement to another. Use technology as appropriate.
8.M.3 Demonstrate an understanding of the concepts and apply formulas and procedures for determining measures, including those of area and perimeter/circumference of parallelograms, trapezoids, and circles. Given the formulas, determine the surface area and volume of rectangular prisms, cylinders, and spheres. Use technology as appropriate.
8.M.5 Use models, graphs, and formulas to solve simple problems involving rates, e.g., velocity and density.
8.D.3 Find, describe, and interpret appropriate measures of central tendency (mean, median, and mode) and spread (range) that represent a set of data. Use these notions to compare different sets of data.
  • As students iterate through, and record their trials, they compile extensive data sets that can be used to make calculations on

8.G.8 Recognize and draw two-dimensional representations of three-dimensional objects, e.g., nets, projections, and perspective drawings.

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