Math-Related Credit Crosswalk
Career Technical Education Classes
in Macomb County
District: Chippewa Valley Schools
Program Name: Small Engines
CIP Code Number: 47.0606
Career Pathway: EMIT
Instructor Name: Rex Phelps
Strand STANDARDS CTE APPLICATION and PRACTICE
REASONING ABOUT NUMBERS, SYSTEMS AND QUANTITATIVE LITERACY
L1.1 Number Systems and Number Sense
L1.1.1 Know the different properties that hold in Two Stroke engine measurements.
different number systems and recognize Shop math worksheet
that the applicable properties change in the Grade sheets
transition from the positive integers to all
integers, to the rational numbers, and to the
L1.1.2 Explain why the multiplicative inverse of a Two Stroke piston/cylinder measurements
number has the same sign as the number,
while the additive inverse has the opposite
L1.1.3 Explain how the properties of associativity, Two Stroke worksheet.
commutativity, and distributivity, as well as Oversize service limits
identity and inverse elements, are used in Shop math worksheet
arithmetic and algebraic calculations.
L1.1.4 Describe the reasons for the different Shop math worksheet
effects of multiplication by, or
exponentiation of, a positive number by a
number less than 0, a number between 0
and 1, and a number greater than 1.
L1.1.6 Explain the importance of the irrational Cylinder bore area
numbers √2 and √3 in basic right triangle Engine displacement calculations
trigonometry, the importance of ╥ because
of its role in circle relationships, and the role
of e in applications such as continuously
L1.2 Representations and Relationships
L1.2.1 Use mathematical symbols (e.g., interval Cylinder bore area calculations
notation, set notation, summation notation) Shop math worksheet
to represent quantitative relationships and
L1.2.2 Interpret representations that reflect Service manual reading
absolute value relationships (e.g.,│x-a│< b, Service limit ranges
or a± b) in such contexts as error tolerance.
L1.2.4 Organize and summarize a data set in a Horsepower vs. rpm charts
table, plot, chart, or spreadsheet; find Shop math worksheet
patterns in a display of data; understand Tool crib organization
and critique data displays in the media.
L1.3 Counting and Probabilistic Reasoning
L1.3.1 Describe, explain, and apply various Piston/cylinder wear predictions
counting techniques (e.g., finding the
number of different 4-letter passwords;
permutations; and combinations); relate
combinations to Pascal’s triangle; know
when to use each technique.
L1.3.2 Define and interpret commonly used Career search / motivational survey
expressions of probability (e.g., chances of
an event, likelihood, odds).
L1.3.3 Recognize and explain common probability Career search / job trends
misconceptions such as “hot streaks” and
Multiply and Divide Fractions
N.MR.06.01 Understand division of fractions as the Grade sheets
inverse of multiplication.
N.FL.06.02 Given an applied situation involving dividing Shop math worksheet
fractions, write a mathematical statement to
represent the situation.
N.MR.06.03 Solve for the unknown. Shop math worksheet
Two stroke worksheet
N.FL.06.04 Multiply and divide any two fractions, Shop math worksheet
including mixed numbers, fluently.
Represent Rational Numbers as Fractions or Decimals
N.ME.06.05 Order rational numbers and place them on Shop math worksheet
the number line. Measuring instruments
N.ME.06.06 Represent rational numbers as fractions or Shop math worksheet
terminating decimals when possible and Measuring instruments
translate between these representations.
N.ME.06.07 Understand that a fraction or a negative Shop math worksheet
fraction is a quotient of two integers. Measuring instruments
Add and Subtract Integers and Rational Numbers
N.ME.06.08 Understand integer subtraction as the Two stroke worksheet
inverse of integer addition. Understand
integer division as the inverse of integer
N.FL.06.09 Add and multiply integers between -10 and Two stroke power curve charts
10; subtract and divide integers using the
related facts. Use the number line and chip
models for addition and subtraction.
N.FL.06.10 Add, subtract, multiply and divide positive Grade sheets
rational numbers fluently. Two stroke worksheet.
Find Equivalent Ratios
N.ME.06.11 Find equivalent ratios by scaling up or Electrical anolog multi-meter
Solve Decimal, Percentage and Rational Number Problems
N.FL.06.12 Calculate part of a number given the Grade sheets
percentage and the number. Gas/oil mixtures or two-stroke engines
N.MR.06.13 Solve contextual problems involving Customer work orders parts/labor
percentages such as sales taxes and tips.
N.FL.06.14 For applied situations, estimate the answers Customer work order estimates
to calculations involving operations with Shop math worksheet
N.FL.06.15 Solve applied problems that use the four Four stoke valve adjustment using shims
operations with appropriate decimal
Understand Rational Numbers and Their Location on the Number Line
N.ME.06.17 Locate negative rational numbers (including Micrometer reading using various adaptors and
integers) on the number line. Know that standards
numbers and their negatives add to 0 and
are on opposite sides and at equal distance
from 0 on a number line.
N.ME.06.18 Understand that rational numbers are Shop math worksheet
quotients of integers (non zero
N.ME.06.19 Understand that 0 is an integer that is Micrometer reading using various adaptors and
neither negative nor positive. standards.
N.ME.06.20 Know that the absolute value of a number is Two stroke worksheet
the value of the number ignoring the sign; or Cylinder taper and out of round
is the distance of the number from 0.
Understand Derived Quantities
N.MR.07.02 Solve problems involving derived quantities Syllabus /grading procedure
such as density, velocity and weighted
Understand and Solve Problems Involving Rates, Ratios, and Proportions
N.FL.07.03 Calculate rates of change including speed. Horsepower vs. rpm
Engine design… bore vs. stroke, camshaft design
N.MR.07.04 Convert ratio quantities between different Torque wrench inch lbs./foot pounds
systems of units, such as feet per second to Metric/inch
miles per hour.
N.FL.07.05 Solve proportion problems using such Shop math worksheet
methods as unit rate, scaling, finding Service manual worksheets
equivalent fractions, and solving the
proportion equation a/b = c/d; know how to
see patterns about proportional situations in
Compute with Rational Numbers
N.FL.07.07 Solve problems involving operations with All worksheets
N.FL.07.08 Add, subtract, multiply and divide positive Most worksheets
and negative rational numbers fluently.
N.FL.07.09 Estimate results of computations with Customer work orders
Understand Real Number Concepts
N.ME.08.02 Understand meanings for zero and negative Measuring tools and instruments
N.ME.08.03 Understand that in decimal form, rational Grade sheets
numbers either terminate or eventually Shop math worksheet
repeat, and that calculators truncate or
round repeating decimals; locate rational
numbers on the number line; know fraction
forms of common repeating decimals.
N.ME.08.04 Understand that irrational numbers are Grade sheets
those that cannot be expressed as the Four stroke cylinder bore and engine displacement
quotient of two integers, and cannot be calculations
represented by terminating or repeating
decimals; approximate the position of
familiar irrational numbers.
N.MR.08.07 Understand percent increase and percent Customer purchase order worksheets
decrease in both sum and product form.
N.MR.08.08 Solve problems involving percent increases Customer purchase order worksheets
N.FL.08.09 Solve problems involving compounded
interest or multiple discounts.
N.MR.08.10 Calculate weighted averages such as Syllabus and grade sheets
course grades, consumer price indices and
N.FL.08.11 Solve problems involving ratio units, such Four stroke basic physics
as miles per hour, dollars per pound or Two stroke fuel/oil mixtures
persons per square mile.
L2 STANDARDS CTE APPLICATION and PRACTICE
CALCULATION, ALGORITHMS, AND ESTIMATION
L2.1 Calculation Using Real and Complex Numbers
L2.1.1 Explain the meaning and uses of weighted Syllabus and grade work sheets
averages (e.g., GNP, consumer price index,
grade point average).
L2.1.2 Calculate fluently with numerical Four stroke engine displacement calculations
expressions involving exponents. Use the
rules of exponents, and evaluate numerical
expressions involving rational and negative
exponents, and transition easily between
roots and exponents.
L2.1.6 Recognize when exact answers aren’t Compression and leakdown tests
always possible or practical. Use
appropriate algorithms to approximate
solutions to equations (e.g., to approximate
L2.2 Sequences and Iteration
L2.2.3 Use iterative processes in such examples Compression and leakdown estimates
as computing compound interest or
applying approximation procedures.
L3 STANDARDS CTE APPLICATION and PRACTICE
MEASUREMENT AND PRECISION
L3.1 Measurement Units, Calculations, and Scales
L3.1.1 Convert units of measurement within and Shop math worksheet
between systems; explain how arithmetic Service manual usage
operations on measurements affect units, Two stroke worksheet
and carry units through calculations
L3.2 Understanding Error
L3.2.1 Determine what degree of accuracy is Four stroke valve adjustment and shim calculations
reasonable for measurements in a given
situation; express accuracy through use of
significant digits, error tolerance, or percent
of error; describe how errors in
measurements are magnified by
computation; recognize accumulated error
in applied situations.
L3.2.2 Describe and explain round-off error, Four stroke valve adjustment and shim calculations
rounding, and truncating. Grade sheets
L3.2.3 Know the meaning of and interpret Valve adjustment, flywheel / ignition coil clearances
statistical significance, margin of error, and
L4.1 Mathematical Reasoning
L4.1.1 Distinguish between inductive and Troubleshooting engine problems
deductive reasoning, identifying and Group work for cooperative units
providing examples of each.
L4.1.2 Differentiate between statistical arguments Troubleshooting engine problems
(statements verified empirically using
examples or data) and logical arguments
based on the rules of logic.
L4.1.3 Define and explain the roles of axioms Troubleshooting engine problems
(postulates), definitions, theorems,
counterexamples, and proofs in the logical
structure of mathematics. Identify and give
examples of each.
L4.2 Language and Laws of Logic
L4.2.1 Know and use the terms of basic logic (e.g., Syllabus and safety units
proposition, negation, truth and falsity,
implication, if and only if, contrapositive, and
L4.3.3 Explain the difference between a necessary Syllabus/teacher lesson
and a sufficient condition within the
statement of a theorem. Determine the
correct conclusions based on interpreting a
theorem in which necessary or sufficient
conditions in the theorem or hypotheses are
Convert within Measurement Systems
M.UN.06.01 Convert between basic units of Torque wrenches
measurement within a single measurement
A1 STANDARDS CTE APPLICATION and PRACTICE
EXPRESSIONS, EQUATIONS, AND INEQUALITIES
A1.1 Construction, Interpretation, and Manipulation of Expressions (linear,
quadratic, polynomial, rational, power, exponential, logarithmic, and
A1.1.1 Give a verbal description of an expression Shop math worksheet
that is presented in symbolic form, write an
algebraic expression from a verbal
description, and evaluate expressions given
values of the variables.
A1.1.2 Know the definitions and properties of Engine displacement calculations
exponents and roots and apply them in
A1.1.3 Factor algebraic expressions using, for Shop math worksheet
example, greatest common factor, grouping,
and the special product identities (e.g.,
differences of squares and cubes).
A1.2 Solutions of Equations and Inequalities (linear, exponential, logarithmic,
quadratic, power, polynomial, and rational)
A1.2.1 Write and solve equations and inequalities Shop math worksheet
with one or two variables to represent
mathematical or applied situations.
A1.2.9 Know common formulas (e.g., slope, Shop math worksheet
distance between two points, quadratic Power curves for horsepower vs. rpm
formula, compound interest, distance = rate
· time), and apply appropriately in
A2.4 Lines and Linear Functions
A2.4.2 Graph lines (including those of the form x = Power curve charts
h and y = k) given appropriate information.
A2.4.3 Relate the coefficients in a linear function to Power curve charts, usable horsepower
the slope and x- and y-intercepts of its
Calculate Rates - Algebra
A.PA.06.01 Solve applied problems involving rates, Power curve charts
Use Variables, Write Expressions and Equations, and Combine Like Terms
A.FO.06.06 Represent information given in words using Troubleshooting unit
algebraic expressions and equations.
Represent Linear Functions Using Tables, Equations, and Graphs
A.RP.06.08 Understand that relationships between Power curve charts
quantities can be suggested by graphs and
A.PA.06.09 Solve problems involving linear functions Power curve charts
whose input values are integers; write the
equation; graph the resulting ordered pairs
A.RP.06.10 Represent simple relationships between Power curve charts
quantities using verbal descriptions,
formulas or equations, tables and graphs.
Understand and Apply Directly Proportional Relationships and Relate to
Linear Relationships - Algebra
A.AP.07.01 Recognize when information given in a Power curve charts
table, graph or formula suggests a directly
proportional or linear relationship.
A.PA.07.04 For directly proportional or linear situations, Calculating oil / fuel ratios
solve applied problems using graphs and Compression ratios
Understand and Solve Problems about Inversely Proportional Relationships
A.PA.07.09 Recognize inversely proportional Oil / fuel / air ratios
relationships in contextual situations; know
that quantities are inversely proportional if
their product is constant.
Apply Basic Properties of Real Numbers in Algebraic Contexts
A.PA.07.11 Understand and use basic properties of real Grade worksheets
numbers: additive and multiplicative
identities, additive and multiplicative
inverses commutativity, associativity, and
the distributive property of multiplication
G1 STANDARDS CTE APPLICATION and PRACTICE
FIGURES AND THEIR PROPERTIES
G1.1 Lines and Angles; Basic Euclidean and Coordinate Geometry
G1.1.5 Given a line segment in terms of its Chain adjustment procedures on motorcycles. Both
endpoints in the coordinate plane, sides of the swing arm must come out equal lengths
determine its length and midpoint. and the chain must have proper slack.
G1.4 Quadrilaterals and Their Properties
G1.4.1 Solve multi-step problems and construct Riding mower, go- kart wheel alignment and steering
proofs involving angle measure, side length, adjustments.
diagonal length, perimeter, and area of
squares, rectangles, parallelograms, kites,
G1.6 Circles and Their Properties
G1.6.1 Solve multi-step problems involving Wheel lacing and different spoke patterns.
circumference and area of circles.
G1.6.3 Solve problems and justify arguments about Wheel lacing and different spoke patterns.
central angles, inscribed angles, and
triangles in circles.
G2 STANDARDS CTE APPLICATION and PRACTICE
RELATIONSHIPS BETWEEN FIGURES
G2.1 Relationships Between Area and Volume Formulas
G2.1.3 Know and use the relationship between the Combustion chamber shapes, compression ratios,
volumes of pyramids and prisms (of equal bore versus stroke dimensions.
base and height) and cones and cylinders
(of equal base and height).
G3 STANDARDS CTE APPLICATION and PRACTICES
TRANSFORMATIONS OF FIGURES IN THE PLANE
G3.1 Distance-preserving Transformations: Isometries
G3.1.1 Define reflection, rotation, translation, and Making gaskets for multiple engines.
glide reflection and find the image of a
figure under a given isometry.
G3.1.2 Given two figures that are images of each Gasket making
other under an isometry, find the isometry
and describe it completely.
G3.1.3 Find the image of a figure under the Gasket making
composition of two or more isometries and
determine whether the resulting figure is a
reflection, rotation, translation, or glide
reflection image of the original figure.
Understand and Apply Basic Properties – Geometry
G.GS.06.01 Understand and apply basic properties of Wheel alignments, gasket making, chain tension
lines, angles and triangles, including: adjustments, engine design of bore vs. stroke, etc
triangle inequality; relationships of vertical
angles, complementary angles,
supplementary angles; congruence of
corresponding & alternate interior angles
when parallel lines are cut by a transversal,
and that such congruencies imply parallel
lines; locate interior and exterior angles of
any triangle, and use the property that an
exterior angle of a triangle is equal to the
sum of the remote (opposite) interior
angles; know that the sum of the exterior
angles of a convex polygon is 360 degrees.
Solve Problems about Geometric Figures
G.SR.08.03 Understand the definition of a circle; know Four stroke engine design…..determining engine
and use the formulas for circumference and displacement by bore area X stroke X number of
area of a circle to solve problems. cylinders.
Understand Concepts of Volume and Surface Area, and Apply Formulas
G.SR.08.06 Know the volume formulas for generalized Calculations of engine displacement. Uses both
cylinders ((area of base) x height), metric and inch systems. Also used with combustion
generalized cones and pyramids (1/3 (area chamber shapes.
of base) x height), and spheres (4/3תּ
(radius) ) and apply them to solve problems.
S1 STANDARDS CTE APPLICATION and PRACTICE
UNIVARIATE DATA - EXAMINING DISTRIBUTIONS
S1.1 Producing and Interpreting Plots
S1.1.1 Construct and interpret dot plots, Examining power charts of engines using
histograms, relative frequency histograms, horsepower on the vertical and engine speed on the
bar graphs, basic control charts, and box horizontal lines. Charts are used to compare engine
plots with appropriate labels and scales; to engine, four-stroke to two-stroke, and
determine which kinds of plots are modifications to any particular engine.
appropriate for different types of data;
compare data sets and interpret differences
based on graphs and summary statistics.
S3 STANDARDS CTE APPLICATION and PRACTICE
SAMPLES, SURVEYS, AND EXPERIMENTS
S3.1 Data Collection and Analysis
S3.1.3 Distinguish between an observational study Used during engine troubleshooting unit and for lab
and an experimental study, and identify, in projects throughout open lab. Theories and
context, the conclusions that can be drawn observations are compared and added to test results
from each. using instrumentation.