Massachusetts Math Standards
Math Learning Standards (Grades
78)
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 twodimensional representations
of threedimensional 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 twodimensional representations
of threedimensional objects, e.g., nets, projections,
and perspective drawings.
