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Mark D. Martin
Instruction Outline 7th Grade Math Using State Standards
Text, Prentice Hall Mathematics, Course 2 (2004)
Introduction- Stella Maris Academy follows California State Standards and the diocesan standards. The California Standards are more specific, although consistent with the
diocesan standards. The focus in this document is hence on the California Standards. Mr. Martin in general follows the topics as they are presented in the text for consistency and
to ensure students have sufficient background knowledge to understand new topics. Where necessary, Mr. Martin deviates from that order, and frequently supplements materials, to
ensure students are learning what is required in the State Standards. Tests are almost always hand designed by Mr. Martin to accurately assess students understanding of the
concepts in the State Standards. The outline here, of course, is just that – a brief outline. In the notes column I have tried to highlight some of the key concepts or areas of
difficulty. The timeline is approximate. Teaching is a day-by-day process constantly evaluating how the students are doing.
Instruction is clear and straight-forward. I introduce practical examples and applications as much as practical. I also try to introduce a sense of humor. Students are shown how to
do small chunks of concepts consistent with their background knowledge. Alternately, and preferably, they are given situations or problems to help them discover a concept new to
them consistent with their background knowledge. They are then given sufficient practice so that concept becomes part of their long-term memory. Part of that practice is
homework. I try to make homework short enough to not be unduly burdensome while giving sufficient practice. Homework is posted on my class Web site.
Seventh grade math is tough. Concepts build upon those in all prior grades. Concepts come at a much higher pace than in prior years. More abstract concepts are being introduced.
It is also probably the year in math that is most useful in real life. Most people indeed use fractions, decimals, percents, proportions, volume, area, probability, etc. in our daily
lives even though we have forgotten how to, and don’t need to, factor polynomials, write geometric proofs, or do calculus. (Those things are vitally important to advancing math,
science, engineering, technology and society in general. Most of us do not use them in our daily lives, however.)
Because the concepts are tough, and because middle school students brains are changing as fast as their physical development, and are as varied as their physical development,
there is a wide range of abilities in seventh grade math. In one sense it would be great if I could teach each student one on one at exactly their own pace. When you think about it,
however, this is probably not desirable. In the classroom setting, students are given the opportunity to see how others think and in doing so learn new problem solving skills. In a
classroom students can also explain concepts to other students. A concept is not really mastered if you cannot explain it to someone else. The way to become the best learner is
often to learn to be a good teacher. This benefits both the “teaching” student and the other student. Of course, in dealing with other students, students also learn valuable social
skills – obviously important not only in their future professional life, but also in their life as a Christian. All students are expected to learn the concepts set forth here. Some will
learn them with a high degree of mastery and will also be able to explore some of the nuisances of the concepts. Those students will be able to proceed to the Algebra class next
year. Other students will have knowledge of the concepts but will have further opportunity in 8th grade math to master the concepts before going on to Algebra in high school.
In the following chart the California State Standards sections are referred to by the following abbreviations: NS= Number Sense, A = Algebra and Functions, MG = Measurement
and Geometry, S = Statistics, Data Analysis and Probability, MR = Mathematical Reasoning. Brief descriptions of the standards are given, but refer to the actual standard for a
complete description. The 7th Grade Math Standards are at: http://www.cde.ca.gov/be/st/ss/mthgrade7.asp. The Mathematical Reasoning Standards are meet throughout all topics
and therefore are not separately set forth below.
Topics
Qtr
1
Decimals and Integers (Chapter 1)
 Rounding and Estimation
 Add, subtract, multiply and divide decimals
 Metric Measurement and conversion (King
Henry died Monday drinking chocolate milk.)
 Absolute value
 Inverse operations
 Add, subtract, multiply and divide integers
 Properties of Addition and Multiplication
 Distributive property
 Order of operations
 Mean, median and mode
Equations and Inequalities (Chapter 2)
 Evaluating and writing algebraic expressions
 Solving equations by adding or subtracting
 Solving equations by multiplying or dividing
 Solving two step equations
 Write equations
California State
Standards
NS1.2 decimal and integer
operations
NS2.5 absolute value
A1.3 associative and
commutative properties of
+ and x, identity
properties of + and x,
distributive property,
inverse operations
MG 1.1measurement
conversions
Notes
A1.1 writing equations
A1.3 properties
A1.4 algebraic
terminology
A4.1 two step equations
and inequalities
A4.2 multi step problems
Basic rules:
 Get variable by itself
 Whatever you do to one side of the equation do to the other side
Same rules apply to inequalities except when multiplying or dividing by a negative
number, you must reverse the inequality symbol.
-Rounding and estimation are review from prior years. Place value is also
reviewed.
-Decimal operations - also largely review, but frequently forgotten by students.
We review the rules with plenty of practice.
-Integer operations have previously been introduced, but are stressed in 7th grade.
Students are expected to memorize the following rules:
-Addition
* Same sign- add absolute values, give result sign of that the numbers have
* Different signs – subtract absolute values, give result sign of the number with
the greater absolute value.
-Subtraction – add the opposite
-Multiplication (two numbers)
*same sign, product is positive
*different signs, product neg
-Division – same rules as multiplication
-Order of Operations – PEMDAS
 Graph and write inequalities
 Solving inequalities by adding or subtracting
 Solving inequalities by multiplying or dividing
Exponents, Factors and Fractions (Chapter 3)
 Exponents
 Scientific notation
 Divisibility rules
 Prime factorization
 Finding Greatest Common Factor (GCF)
 Finding Least Common Multiple (LCM)
 Simplifying fractions by dividing by the GCF
 Equivalent fractions
 Comparing and ordering fractions by finding
the Least Common Denominator (LCD) (i.e.
the LCM of the denominators)
 Mixed numbers and improper fractions
 Writing fractions as decimals and writing
decimals as fractions
 Defining rational numbers
 Comparing and ordering rational numbers
Qtr
2
Operations With Fractions (Chapter 4)
 Estimating with fractions and mixed numbers
 Adding and subtracting fractions
 Adding and subtracting mixed numbers
 Multiplying fractions and mixed numbers
 Dividing fractions and mixed numbers
 Solving equations with fractions
NS1.1 Scientific Notation
NS1.3 decimal fraction
conversions
NS1.4 and 1.5 rational and
irrational numbers
NS2.1 Exponents (in part.
Operations with common
base done in 8th grade
math or algebra)
A2.1 and 2.2 exponents
(in part – exponent
operations reserved until
8th grade math or algebra)
NS2.2 Add subtract
fraction with uncommon
denominators
NS2.3 in part – primarily
reserved until 8th grade
math or algebra.
MS1.1 measurement
A big challenge is getting students to understand the difference between a factor
and a multiple. For example factors of 6 are 1, 2, 3, 6. Multiples of 6 include 12,
18, 24 . . .
Likewise, a challenge is the difference in calculating the GCF and LCM. In both
you can start by factoring each number using factor trees. To calculate the GCF,
you find all the common factors; then multiply the common factors together. To
calculate the LCM, you circle each factor where it occurs the greatest number of
times, and then multiple all those factors together.
Students also need to understand where we use GCF and LCM. For example, GCF
is used to simplify fractions, and LCM is used to find a common denominator
(LCD) in order to add or subtract fractions or to order fractions. Students learn that
the GCF is always less than or equal to the smallest number and the LCM is always
greater than or equal to the larger number.
Students learn how to convert fractions to decimals and vice versa. They are also
required to learn common fraction decimal equivalents by memory for halves,
thirds, fourths, fifth, sixths, eighths, ninths and tenths. This is a real life skill for
quick conversions in business or for standardized tests in the future.
Building on what was learned in chapter 4, we use the LCM to add and subtract
fractions. We learn that whole numbers and fractions in mixed numbers can be
added separately. Unlike in prior years, however, students now combine their
knowledge of integer operations and can calculate a problem with a result that has a
negative sign. Students are reminded that mixed numbers must be converted to
improper fractions to multiply or divide. To multiply, just multiply across. Cross
cancel if you can. To divide, you multiply by the reciprocal of the second number.

Changing customary units
Ratios, Rates and Proportions (Chapter 5)
 Ratios (comparing two quantities by division)
o Writing ratios
o Writing ratios as decimals
o Writing equal ratios
o Writing ratios in simplest form
 Unit rates
 Dimensional analysis
 Proportions (two equal ratios)
 Cross products and solving proportions
 Proportional analysis
 Similar figures (same shape, not necessarily
the same size)
 Maps and scaled drawings
Percents (Chapter 6)
 Understanding what a percent is
 Decimals, fractions and percents
 Percents greater than 100% or less than 1%
 Finding part, base or whole using percent
proportion method and using “equation”
method
 Finding sales tax, tips and commissions
 Finding percent of change
 Writing equations involving percent
conversions
A4.2 multi step problems
involving rate
MG1.1 Measurement
conversions
MG1.2 scaled drawings
MG1.3 unit rates,
dimensional analysis
NS1.6 percent increase or
decrease (i.e. percent of
change)
NS1.7 discounts,
markups, commissions,
profit
All of this is also used to solve equations involving fractions. Students also
eliminate fractions in equations by multiplying both sides of the equation by the
LCM.
Having learned about fractions and rational numbers, students now look at fractions
as ratios. Students learn that two equal ratios are a proportion. They can then solve
proportions using cross products. (E.g. find x in ¾=5/x.) They can also use cross
products to determine if two ratios indeed form a proportion. Proportions have
many practical uses such as in maps and drawings. With the help of shadows or
photos, we find heights of telephone poles and trees without climbing them!
Again building on prior chapters and prior grades, students convert between
decimals, fractions and percents. In doing so they begin to understand why percents
are such a useful comparison device in everyday life. Students learn to deal with
percents greater than 100% (i.e. greater than 1) and percents less than 1% (i.e. less
than .01).
With careful attention and practice students will no longer be threatened by dreaded
problems on standardized exams or elsewhere like: (1) Find 25% of 50, (2) 12.5 is
what percent of 50? or (3) 25% of what number is 12.5. We do this by using both
Part rate
the percent proportion:
and the equation or what I call the “translation

Base 100
method.” In the equation or translation method we translate from “English” to
“Algebra” knowing some useful vocabulary. Find, what, etc. represents the

variable. “Of” means multiplication. “Is” means equals. “Percent” or “%” means
the rate expressed as a decimal. For example, in #1 above, x=.25(50). (#2)
12.5=x(50) (#3) .25x=12.5. Now, just solve for x.
Qtr
3
Geometry (Chapter 7)
 Points, lines, rays, segments
 Measuring and classifying angles (acute, right,
obtuse, straight) – complementary and
supplementary pairs of angles
 Constructions – perpendicular bisector, angle
bisector, congruent angles using straight edge
and compass
 Triangles (by sides – equilateral, scalene,
isosceles; by angle – acute, right, obtuse) –
sum of angles = 180
 Quadrilaterals and other polygons
o Classification
o Sum of angles
 Congruent figures
 Circles
o Parts – chord, central angle, radius,
diameter, arcs, semicircle
 Circle graphs
MG3.1 identifications,
constructions, etc.
MG3.4 Congruent figures
MG3.6 elements of 3D
objects, plane
intersections, skew lines,
etc.
Geometry and Measurement (Chapter 8)
 Estimation length and area
NS2.4 roots
MG2.1to 2.4 area,
Percent of change is another useful topic for middle show students. For example,
the iPhone, purse, video game, etc. was $300. Now it is $240. What is the percent
of increase or decrease. Take the difference divided by the original amount.
Geometry is divided into two chapters. In this chapter students must master a lot of
vocabulary. They get a break from the vocabulary section by being able to do
constructions using only a straightedge and compass and also get a glimpse of what
ancient civilizations had learned about geometry. They will build upon their
knowledge in the next chapter.
Here the memorization turns to formulas instead of definitions. We try to make
sense of the formulas, however, and some years even try to devise the formula for
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Qtr
4
Area of parallelograms and triangles
Area of trapezoids and irregular figures
Circumference and areas of circles
Square roots and irrational numbers
Pythagorean Theorem
Classifying three-dimensional figures
Surface area of prisms and cylinders
Volume of rectangular prisms and cylinders
Sequences, Patterns, Simple and Compound
Interest, Equations (Part of Chapter 9)
 Number Sequences (sec. 9-2)
 Patterns (sec. 9-3)
 Simple Interest (sec. 9-7)
 Compound Interest (sec. 9-7)
 Writing equations from words (sec. 9-8)
 Solving equations with multiple variables for a
particular variable (sec. 9-9)
Graphing and Functions (Part of Chapter 9 and
Chapter 10)
 The coordinate plane
o Definitions of x-axis, y-axis, origin,
ordered pair, x-coordinate, ycoordinate, quadrants
o Writing coordinates and graphing
points
o Horizontal and vertical lines
 Choosing scales and intervals (Sec. 9-1)
 Graphing linear equations by using a table
 Slope of a line
volume, surface area, etc.
MG3.3 Pythagorean
Theorem
MG3.5 2-D nets of 3-D
objects
the area of a circle by dividing a circle into small pie shapes and making it into a
parallelogram. Often concepts about the circumference of a circle fall around PiDay (3-14 get it!) and give rise to celebration. I try to use models so that the
students can visualize surface area and volume. For example, it is much easier to
find the surface area of a cylinder if you view it has a can with a rectangular label
and two lids.
NS 1.7 simple and
compound interest
A1.1writing equations
Chapter 9 is an introduction to several graphing concepts with several other
concepts thrown in. I separate out the other concepts and put the graphing material
with chapter 10 on graphing and functions.
A1.5 represent
quantitative relationships
graphically and interpret
graphs
A3.1 graph functions to
second and third powers
A3.2 reserved until 8th
grade
A3.3 graph linear
functions and determine
slope
A3.4 plotting
This is an important unit that students will use in the rest of their math studies
throughout 8th grade, high school and college. Students have previously had some
introduction to graphs in prior years. Graphing becomes much more formalized
now, however. Students go beyond just graphing points and learn how to graph
linear equations using tables and the slope intercept form of the line, y=mx + b
where m is the slope and b is the y intercept. They explore this and other forms of
linear equations in more depth in either 8th grade math or Algebra next year.
Students also look at non-linear relationships by graphing from a table. They will
delve into that topic in much greater detail either next year in Algebra or in Algebra
in high school. I try to have students be able to practically understand how the
graphing relates to the real world. For examples, some students will begin to
understand that slope is equal to a rate of change giving them an initial glimpse into
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Intercepts
Slope Intercept Form of line
Non-linear Relationships
Functions
Interpreting graphs
Translations, symmetry, reflections, rotations
(sometimes reserved until 8th grade)
Displaying and Analyzing Data (Chapter 11)
 Reporting frequency
 Spreadsheets and data display
 Stem and leaf plots
 Box-and-whisker plot
 Random samples and surveys
 Using data to persuade
 Exploring scatter plots
Probability (Chapter 12)
 Definition of outcome, even and probability
 Definition complement
 Definition odds
 Distinction between theoretical probability and
experimental probability
 Probability of independent and compound
events
 Permutations
 Combinations
A4.2 solve multi step
problems involving rate,
average speed, distance
time or a direct variation
MG3.2 plot figures,
translations, reflections
differential calculus. We supplement assignments with work in computer lab using
Excel and Apple Grapher.
S1.1 data display
S1.2 scatter plots
S1.3 box and whisker
plots – quartiles
This builds on introductory statistical analysis that students have been exposed to
earlier in the text like mean, median and mean. Often, we work on spread sheets
and data display in computer class. This, combined with the fact that it comes
towards the end of the year, means this is often one of our shorter chapters.
Not part of 7th grade standards. We cover only if we have sufficient time at the end
of the year.