Mathematics Skills for Automotive and Machine Tool Technology
The list of imbedded math skills for Automotive and Machine Tool Technology was developed through a
partnership of technical instructors from Nashua Community College in New Hampshire and staff from the
New England Board of Higher Education. The Resource Map was developed aligning math content skills
and Khan Academy Videos and Practice Sets. In addition to Khan Academy there are other mapped
resources. These are highlighted in maroon.
Math Skill
Content Area
Use a ruler, protractor, and
compass to draw polygons and
circles.
Geometry
Convert from one system of
measurement to another.
Measurement
Solve linear equations using
tables, graphs, models, and
algebraic methods.
Automotive Machine
Khan Videos
Technology Tool
Technology
Khan Problem Sets
X
Compass
Construction
Using a Protractor
X
Conversion Within
Unit Conversion
Metric System
Customary vs. Metric
Untis
Patterns,
relations, algebra
X
Solving Equations
Algebraically
Solving Equations
Graphically
Equations from
Tables
Use linear equations to model
Patterns,
and analyze problems involving relations, algebra
proportional relationships.
X
Linear Equation Word Linear Equation Word
Problems
Problems
X
Representing a
Number as a Decimal,
Percent, and Fraction
Converting Fractions
to Decimals
Converting Decimals
to Fractions 1
Converting Decimals
to Percents
Converting Fractions
to Decimals
Select, create, and interpret an Data Analysis,
appropriate graphical
Probability and
representation (e.g., scatterplot, Statistics
table, stem-and-leaf plots, boxand-whisker plots, circle graph,
line graph, and line plot) for a
set of data and use appropriate
statistics (e.g., mean, median,
range, and mode) to
communicate information about
the data. Use these notions to
compare different sets of data.
X
Reading Bar Graphs
Histograms
Reading Line Graphs
Reading Circle
Graphs
Reading Pictographs
Reading Tables 1
Reading Tables 2
Reading Bar Charts 1
Reading Bar Charts 2
Reading Stem and
Leaf Plots
Reading Pictographs 1
Reading Pictographs 2
Demonstrate the ability to
visualize solid objects and
recognize their projections and
cross sections.
X
Visualizing Solid
Shapes
Compare, order, estimate, and
translate among integers,
fractions and mixed numbers
(i.e., rational numbers),
decimals, and percents.
Numbers
Geometry
X
X
Compass Construction
Solving Equations
Algebraically
Solving Equations
Graphically
Equations from Tables
Recognize and solve problems Geometry
involving angles formed by
transversals of coplanar lines.
Identify and determine the
measure of central and inscribed
angles and their associated
minor and major arcs.
Recognize and solve problems
associated with radii, chords,
and arcs within or on the same
circle.
X
Angles Formed by
Transversals
Inscribed and Central
Angles
Parts of a Circle
Angles Formed by
Transversals
Inscribed and Central
Angles
Circles and Arcs
Calculate perimeter,
Measurement
circumference, and area of
common geometric figures such
as parallelograms, trapezoids,
circles, and triangles.
X
Perimeter and Area
Basics
Area of Quadrilaterals
and Polygons
Radius, Diameter and
Circumference
Area of a Circle
Area 1
Area of Squares and
Rectangles
Area of Triangles 1
Perimeter 1
Perimeter of Squares
and Rectangles
Radius, Diameter and
Circumference
Area of a Circle
Given the formula, find the
Measurement
lateral area, surface area, and
volume of prisms, pyramids,
spheres, cylinders, and cones,
e.g., find the volume of a sphere
with a specified surface area.
X
Solid Geometry
Volume
Volume and Surface
Area
Volume of a Sphere
Solid Geometry
Area, Volume and
Surface Area
Describe the effects of
approximate error in
measurement and rounding on
measurements and on
computed values from
measurements.
X
Calculating Percent
Error
Estimating and
Rounding
Rounding Numbers
Estimation with
Decimals
X
Algebraic Word
Problem
Mixture Problems
Systems and Rate
Problems
Problem Solving
Word Problems
Systems of Equations
Word Problems
Find linear equations that
represent lines either
perpendicular or parallel to a
given line and through a point,
e.g., by using the "point-slope"
form of the equation.
Geometry
Measurement
Solve everyday problems that
Patterns,
X
can be modeled using systems relations, algebra
of linear equations or
inequalities. Apply algebraic and
graphical methods to the
solution. Use technology when
appropriate. Include mixture,
rate, and work problems.
Write simple proofs of theorems Geometry
in geometric situations, such as
theorems about congruent and
similar figures, parallel or
perpendicular lines. Distinguish
between postulates and
theorems. Use inductive and
deductive reasoning, as well as
proof by contradiction. Given a
conditional statement, write its
inverse, converse, and
contrapositive.
Select an appropriate graphical
representation for a set of data
and use appropriate statistics
(e.g., quartile or percentile
distribution) to communicate
information about the data.
Data Analysis,
Probability and
Statistics
X
Choosing a Tool for
Data Representation
Describe a set of frequency
Data Analysis,
distribution data by spread
Probability and
(variance and standard
Statistics
deviation), skewness, symmetry,
number of modes, or other
characteristics. Use these
concepts in everyday
applications.
X
Measures of Central
Tendency
Sample Variance
Standard Deviation
Alternate Variance
Formulas
Measures of Central
Tendency
Variance
Standard Deviation
Reading Tables
Compare the results of
Data Analysis,
simulations (e.g., random
Probability and
number tables, random
Statistics
functions, and area models) with
predicted probabilities.
X
Simulation Showing
Sample Bias
Random Variables
Expected Value
Law of Large
Numbers
Expected Value
Apply properties of angles,
Geometry
parallel lines, arcs, radii, chords,
tangents, and secants to solve
problems.
X
Geometry Word
Problems
Parts of Circle
Problem Solving
X
Dimensional Analysis
Unit Conversion with
Dimensional Analysis
Describe the relationship
Measurement
between degree and radian
measures, and use radian
measure in the solution of
problems, in particular, problems
involving angular velocity and
acceleration.
Use dimensional analysis for
unit conversion and to confirm
that expressions and equations
make sense.
Measurement
Solve everyday problems that
Patterns,
can be modeled using
relations, algebra
polynomial, rational,
exponential, logarithmic,
trigonometric, and step
functions, absolute values, and
square roots. Apply appropriate
graphical, tabular, or symbolic
methods to the solution. Include
growth and decay; joint (e.g., I =
Prt, y = k(w1 + w2)) and
combined (F = G(m1m2)/d2)
variation, and periodic
processes.
X
No growth
and decay
Basic Linear Equation Linear Equation Word
Word Problems
Problems
Problem Solving
Word Problems
Trig Word Problems
Trig Word Problems 2
Word ProblemsGeneral
Find solutions to quadratic
Patterns,
equations (with real coefficients relations, algebra
and real or complex roots) and
apply to the solutions of
problems.
Solve a variety of equations and Patterns,
inequalities using algebraic,
relations, algebra
graphical, and numerical
methods, including the quadratic
formula; use technology where
appropriate. Include polynomial,
exponential, logarithmic, and
trigonometric functions;
expressions involving absolute
values; trigonometric relations;
and simple rational expressions.
Use matrices to solve systems Patterns,
of linear equations. Apply to the relations, algebra
solution of everyday problems.
X
Solving One-Step
Equations
Two-Step Equations
Multi-Step Equation
Example
Solving Equations
With the Distributive
Property
One-Step Inequalities
Multi-Step Inequalities
3
Solving a Quadratic
by Factoring
Solving a Quadratic
by Factoring 2
Using the Quadratic
Formula
Quadratic Formula
Application Problem
Solving Rational
Equations
Absolute Value
Equations
One-Step Equations
Linear Equations 2
Multi-Step Equations
With Distribution
One-Step Inequalities
Linear Inequalities
Solving Quadratics by
Factoring
Solving Quadratics by
Factoring 2
Quadratic Equation
Absolute Value
Equations