Download Math - Cherokee County Schools

Seventh Grade Mathematics
Instr
Seq
COS #
Course of Study Objective
Suggested Lesson Resources/Activities
Lesson Plan
(description,
number, etc.)
Date
Implemented
Ratios and Proportional Relationships
Analyze proportional relationships and use them to solve real-world and
mathematical problems. (7-RP)
2
2
7.1
7.2
Compute unit rates associated with ratios of fractions,
including ratios of lengths, areas, and other quantities
measured in like or different units. [7-RP1]
Example: If a person walks ½ mile in each ¼ hour, compute the
unit rate as the complex fraction 1/2/1/4 miles per hour,
equivalently 2 miles per hour.
Recognize and represent proportional relationships between
quantities. [7-RP2]
Intro/Writing ratios – 67182 (I), MA6812 (Q)
Unit Rates – M7049 (I), M7050 (Q)
Relationships M7051 (I), M7052 (P), M7053 (Q),
M7053 (R), M7055 (P), M7056 (Q)
Word Prob 67183 (I), MA6814 (Q)
2
7.2a.
Decide whether two quantities are in a proportional
relationship,
e.g., by testing for equivalent ratios in a table or graphing on a
coordinate plane and observing whether the graph is a straight
line through the origin. [7-RP2a]
Tables M7057 (I), M7058 (Q)
Constant Ratios M7059 (I), M7060 (Q)
2
7.2b.
Identify the constant of proportionality (unit rate) in tables,
graphs, equations, diagrams, and verbal descriptions of
proportional relationships. [7-RP2b]
Scale M7073 (I), M7074 (P), M7075 (Q), M7076 (R),
M7077 (P), M7078 (Q)
Linear Graphs M7245 (I), M7246 (P), M7247 (Q),
M7248 (R), M7249 (P), M7250 (Q)
2
7.2c.
Represent proportional relationships by equations. [7-RP2c]
Example: If total cost t is proportional to the number n of items
purchased at a constant price p, the relationship between the
2010 Alabama Course of Study Mathematics
Ratio, Rates, Proportions 8076 (part I), 8118 (part
2), MA8ZZ35 (Q)
1
Seventh Grade Mathematics
total cost and the number of items can be expressed as t = pn.
2
7.2d.
Explain what a point (x, y) on the graph of a proportional
relationship means in terms of the situation, with special
attention to the points (0, 0) and (1, r) where r is the unit rate.
[7-RP2d]
Compass does not discuss points (0,0) or (1,r) in
regard to proportional relationships
Linear Graphs M7245 (I), M7246 (P), M7247 (Q),
M7248 (R), M7249 (P), M7250 (Q)
Basic Percent (is/of)
MA6871 (I), MA6872 (Q)
8073, 8115, MA8ZZ32 (Q)
2
7.3
Use proportional relationships to solve multistep ratio and
percent problems. [7-RP3]
Examples: Sample problems may involve simple interest, tax,
markups and markdowns, gratuities and commissions, fees,
percent increase and decrease, and percent error.
Increase/Decrease (incl. Sales tax) M7061 (I),
M7062 (P), M7063 (Q), M7064 (R), M7065 (P),
M7066 (Q)
76258 (part 1), 76259 (part 2), MA7ZZ06 (Q)
8074 (part 1), 8116 (part 2),
MA8ZZ33 Q)
8075 (part1), 8117 (part 2),
MA8ZZ34 (Q)
The Number System
Apply and extend previous understandings of operations with fractions to add,
subtract, multiply, and divide rational numbers.
1
1
7.4
7.4a
Apply and extend previous understandings of addition and
subtraction to add and subtract rational numbers; represent
addition and subtraction on a horizontal or vertical number
line diagram. [7-NS1]
Describe situations in which opposite quantities combine to
make 0. [7-NS1a]
Example: A hydrogen atom has 0 charge because its two
2010 Alabama Course of Study Mathematics
Student Activity # M7500 (for whole class
instruction, use math toolkit and choose operations
in the drop-down box in top-left corner)
Add/subtract on Number Line
M7085 (I), M7086 (P), M7087 (Q), M7088 (R),
M7089 (P), M7090 (Q)
Additive and Multiplicative Inverse – M7079 (I),
M7080 (P), M7081 (Q), M7082 (R), M7083 (P),
M7084 (Q)
2
Seventh Grade Mathematics
constituents are oppositely charged.
Additive and Multiplicative Inverse – M7079 (I),
M7080 (P), M7081 (Q), M7082 (R), M7083 (P),
M7084 (Q)
Add/Subtract Integers
67203 (I) MA6534 (Q)
1
7.4b
Understand p + q as the number located a distance |q| from p,
in the positive or negative direction depending on whether q is
positive or negative.
Show that a number and its opposite have a sum of 0 (are
additive inverses).
Interpret sums of rational numbers by describing real-world
contexts. [7-NS1b]
76238 (part 1), 79239 (part 2) MA7ZZ24 (Q)
Fractions – like denominators
MA64121 (I), MA64122 (Q)
Fractions – unlike denominators
MA64131 (I), MA64132 (Q)
76250 (I), MA7ZZ32 (Q)
Mixed Numbers
76251 (I), MA7ZZ33 (Q)
1
7.4c
Understand subtraction of rational numbers as adding the
additive inverse, p – q = p + (–q).
Show that the distance between two rational numbers on the
number line is the absolute value of their difference, and apply
this principle in real-world contexts. [7-NS1c]
Subtraction as “add the opposite” 67203 (I),
MA6534 (Q)
Add/Subtract Integers
76238 (part 1), 79239 (part 2) MA7ZZ24 (Q)
1
7.4d
Apply properties of operations as strategies to add and subtract
rational numbers. [7-NS1d]
1
7.5
Apply and extend previous understandings of multiplication
2010 Alabama Course of Study Mathematics
Properties of Real Numbers
M7105 (I), M7106 (Q)
3
Seventh Grade Mathematics
and division and of fractions to multiply and divide rational
numbers. [7-NS2]
Distributive and Inverse Property
MA6241 (I), MA6242 (Q)
1
7.5a
Understand that multiplication is extended from fractions to
rational numbers by requiring that operations continue to
satisfy the properties of operations, particularly the distributive
property, leading to products such as (–1)(–1) = 1 and the rules
for multiplying signed numbers. Interpret products of rational
numbers by describing real-world contexts. [7-NS2a]
Basic Mult/Div Rule with Integers (no fractions,
decimals)
MA6541 (I), MA654 (Q)
Mult/Div with integers, fractions, decimals
M7091 (I), M7092 (P), M7093 (Q), M7094 (R),
M7095 (P), M7096 (Q)
Dividing Whole Numbers
76230 (I), MA7ZZ21 (Q)
Understand that integers can be divided, provided that the
divisor is not zero, and every quotient of integers (with nonzero
divisor) is a rational number.
1
7.5b
 p   p 
p

.
If p and q are integers, then    
 q 
q
q
Interpret quotients of rational numbers by describing real-world
contexts. [7-NS2b]
Divide Decimal Numbers
76246 (part 1) 76247 (part 2), MA7ZZ30 (Q)
Divide Whole # by Fractions
76253 (part 1), 76254 (part 2), MA7ZZ35 (Q)
Divide Fractions
76255 (I), MA7ZZ36 (Q)
Divide Mixed Numbers
8067 (part 1), 8110 (part 2), MA8ZZ28 (Q)
1
1
7.5c
Apply properties of operations as strategies to multiply and
divide rational numbers. [7-NS2c]
7.5d
Convert a rational number to a decimal using long division;
know that the decimal form of a rational number terminates in
0s or eventually repeats. [7-NS2d]
2010 Alabama Course of Study Mathematics
Basic Intro
67187 (worksheet available)
4
Seventh Grade Mathematics
Fractions, Decimals, Percents
M7027 (I), M7028 (P), M7029 (Q), M7030 (R),
M7031 (P), M7032 (Q)
1
7.6
Solve real-world and mathematical problems involving the four
operations with rational numbers. (Computations with rational
numbers extend the rules for manipulating fractions to
complex fractions.) [7-NS3]
Order of Operations
M7015 (I), M7016 (P), M7017 (Q), M7018 (R),
M7019 {P), M7020 (Q)
Other topics covered in activities listed above.
Expressions and Equations
Use properties of operations to generate equivalent expressions.
Evaluate Expressions
M7103 (I), M7104 (Q)
4
7.7
Apply properties of operations as strategies to add, subtract,
factor, and expand linear expressions with rational
coefficients. [7-EE1]
Simplify by Adding Like Terms
67205
Simplify with Like Terms and Distributive Property
M7115 (I), M7116 (P), M7117 (Q), M7118 ®, M7119
(P), M7120 (Q)
Factoring Polynomials by GCF and by Grouping
A11011 (I), A11012 (Q)
1
7.8
Understand that rewriting an expression in different forms in a
problem context can shed light on the problem, and how the
quantities in it are related. [7-EE2]
Example: a + 0.05a = 1.05a means that ―increase by 5%‖ is the
same as ―multiply by 1.05.‖
Intro to Variables and Translating Verbal to
Numerical
M7107 (I), M7108 (P), M7109 (Q), M7110 (R),
M7111 (P), M7112 (Q)
Solve real-life and mathematical problems using numerical and algebraic
expressions and equations.
3
7.9
Solve multistep real-life and mathematical problems posed
with positive and negative rational numbers in any form
2010 Alabama Course of Study Mathematics
5
Seventh Grade Mathematics
(whole numbers, fractions, and decimals), using tools
strategically. Apply properties of operations to calculate with
numbers in any form, convert between forms as appropriate,
and assess the reasonableness of answers using mental
computation and estimation strategies. [7-EE3]
Examples: If a woman making $25 an hour gets a 10% raise, she
will make an additional of her salary an hour, or $2.50, for a new
salary of $27.50.
If you want to place a towel bar 9 inches long in the center of a
door that is 27 inches wide, you will need to place the bar about
9 inches from each edge; this estimate can be used as a check
on the exact computation. 1 10 34 12
Basic Multi-step Problems
M7213 (I), M7214 (P), M7215 (Q), M7216 (R),
M7217 (P), M7218 (Q)
Multi-step Problems with Tables, Fractions, %
M8063 (I), M8064 (P), M8065 (Q), M8066 (R),
M8067 (P), M8068 (Q)
Multi-step Problems with Ratios, Rates,
Proportions
M8069 (I), M8070 (P), M8071 (Q), M8072 (R),
M8073 (P), M8074 (Q)
Advanced Multi-step Problems
M8075 (I), M8076 (P), M8077 (Q), M8078 (R),
M8079 (P), M8080 (Q)
Assessing Reasonableness/Justifying Solutions
MA61031 (I), M61032 (Q)
4
4
7.10
7.10a
Use variables to represent quantities in a real-world or
mathematical problem, and construct simple equations and
inequalities to solve problems by reasoning about the
quantities. [7-EE4]
Solve word problems leading to equations of the form px + q = r
and p(x + q) = r, where p, q, and r are specific rational numbers.
Solve equations of these forms fluently. Compare an algebraic
solution to an arithmetic solution, identifying the sequence of
the operations used in each approach. [7-EE4a]
Example: The perimeter of a rectangle is 54 cm. Its length is 6
cm. What is its width?
2010 Alabama Course of Study Mathematics
Intro to Variables and Translating Verbal to
Numerical
M7107 (I), M7108 (P), M7109 (Q), M7110 (R),
M7111 (P), M7112 (Q)
Writing Equations from Word Problems
M8101 (I), M8102 (Q)
Basic Multi-step Problems
M7213 (I), M7214 (P), M7215 (Q), M7216 (R),
M7217 (P), M7218 (Q)
Multi-step Problems with Tables, Fractions, %
M8063 (I), M8064 (P), M8065 (Q), M8066 (R),
M8067 (P), M8068 (Q)
6
Seventh Grade Mathematics
Multi-step Problems with Ratios, Rates,
Proportions
M8069 (I), M8070 (P), M8071 (Q), M8072 (R),
M8073 (P), M8074 (Q)
Advanced Multi-step Problems
M8075 (I), M8076 (P), M8077 (Q), M8078 (R),
M8079 (P), M8080 (Q)
Exploring Graphs of Linear Inequalities
M7504
4
7.10b
Solve word problems leading to inequalities of the form px + q >
r or px + q < r, where p, q, and r are specific rational numbers.
Graph the solution set of the inequality, and interpret it in the
context of the problem. [7-EE4b]
Example: As a salesperson, you are paid $50 per week plus $3
per sale. This week you want your pay to be at least $100. Write
an inequality for the number of sales you need to make, and
describe the solutions.
Solving Inequalities of One Variable
M8111 (I), M8112 (P), M8113 (Q), M8114 (R),
M8115 (P), M8116 (Q)
Graphing Inequalities incl. Word Problems
M8195 (I), M8196 (P), M8197 (Q), M8198 (R),
M9199 (Q)
Geometry
Draw, construct, and describe geometrical figures and describe the
relationships between them.
Solve Problems with Scales on Maps
67242 (I), MA6844 (Q)
2
7.11
11. Solve problems involving scale drawings of geometric
figures, including computing actual lengths and areas from a
scale drawing and reproducing a scale drawing at a different
scale. [7-G1]
2010 Alabama Course of Study Mathematics
Scale with Geometry
67241 (I), MA6842 (Q)
Scale with maps, geometry, etc.
M7073 (I), M7074 (P), M7075 (Q), M7076 (R),
M7077 (P), M7078 (Q)
7
Seventh Grade Mathematics
Drawing/Measuring Angles with Protractor
GE132
Theorems for Angle Measures in Triangles
AL120
3
7.12
Draw (freehand, with ruler and protractor, and with
technology) geometric shapes with given conditions. Focus on
constructing triangles from three measures of angles or sides,
noticing when the conditions determine a unique triangle,
more than one triangle, or no triangle. [7-G2]
67253 (I), MA6926 (Q)
Classifying Triangles
AL123
Determine Angle Measures of Specific
Triangles (Isosceles, Right, etc)
M7127 (I), M7128 (P)), M7129 (Q), M7130 (R),
M7131 (P), M7132 (Q)
3
7.13
Describe the two-dimensional figures that result from slicing
three-dimensional figures, as in plane sections of right
rectangular prisms and right rectangular pyramids. [7-G3]
67236 (student worksheet available)
67238 (student worksheet available)
Solve real-world and mathematical problems involving angle measure, area,
surface area, and volume.
Radius, Diameter, Circumference
67160 (I), MA69122 (Q)
3
7.14
Know the formulas for the area and circumference of a circle,
and use them to solve problems; give an informal derivation of
the relationship between the circumference and area of a
circle. [7-G4]
Radius, Diameter, Area
67224 (I), MA69132 (Q)
Circumference and Area
M7143 (I), M7144 (Q)
76273, MA7ZZ44 (Q)
8087 (part 1), 8129 (part 2), MA8ZZ17 (Q)
2010 Alabama Course of Study Mathematics
8
Seventh Grade Mathematics
Angles from Parallel Lines and Transversals
67218 (I), MA69210 (Q)
76267 (I), MA7ZZ41 (Q), student worksheet
3
7.15
Use facts about supplementary, complementary, vertical, and
adjacent angles in a multistep problem to write and solve
simple equations for an unknown angle in a figure. [7-G5]
Interior and Exterior Angles in Triangles
M7125 (I), M7126 (Q)
Suppl/ Compl/Corr/Vert/Adj Angles
M7151 (I), M7152 (P), M7153 (Q), M7154 (R),
M7155 (P), M7156 (Q)
Apply to Real World Problems
M7157 (I), M7158 (Q)
Area
67208 (I), MA6282, worksheet
Surface Area
67225 (I), MA69152 (Q), worksheet
4
7.16
Solve real-world and mathematical problems involving area,
volume, and surface area of two- and three-dimensional
objects composed of triangles, quadrilaterals, polygons, cubes,
and right prisms. [7-G6]
M7179 (I), M7180 (P), M7181 (Q), M7182 (R),
M7183 (P), M7184 (Q)
76274 (part 1), 76275 (part 2), lesson quiz
Volume
67226 (I), MA69162 (Q), worksheet
M8145 (I), M8146 (P), M8147 (Q), M8148 (R),
M8149 (P), M8150 (Q)
Statistics and Probability
Use random sampling to draw inferences about a population.
2010 Alabama Course of Study Mathematics
9
Seventh Grade Mathematics
Intro
67228 (I), MA6692, worksheet
3
7.17
Understand that statistics can be used to gain information
about a population by examining a sample of the population;
generalizations about a population from a sample are valid
only if the sample is representative of that population.
Understand that random sampling tends to produce
representative samples and support valid inferences. [7-SP1]
Differentiate Sampling Techniques
M8233 (I), M8234 (Q)
M8235 (I), M8236 (Q)
Sample Bias
M8237 (I), M8238 (P), M8239 (Q), M8240 (R),
M8241 (P), M8242 (Q)
Mean, Median, Mode, Range, Outliers
67229 (I), MA6682 (Q), worksheet
3
7.18
Use data from a random sample to draw inferences about a
population with an unknown characteristic of interest.
Generate multiple samples (or simulated samples) of the same
size to gauge the variation in estimates or predictions. [7-SP2]
Example: Estimate the mean word length in a book by randomly
sampling words from the book; predict the winner of a school
election based on randomly sampled survey data. Gauge how
far off the estimate or prediction might be.
Data Analysis (what if the data changes…)
MA6683 (I), MA6684 (Q), worksheet
Mean, Median, Mode from Charts, Graphs, etc
M7271 (I), M7272 (P), M7273 (Q), M7274 (R),
M7275 (P), M7276 (Q)
Apply Mean, Median, Mode
M7277 (I), M7278 (Q)
Interpreting Statistical Graphs
M7279 (I), M7280 (Q)
Draw informal comparative inferences about two populations.
3
7.19
Informally assess the degree of visual overlap of two numerical
data distributions with similar variabilities, measuring the
difference between the centers by expressing it as a multiple
of a measure of variability. [7-SP3]
Example: The mean height of players on the basketball team is
2010 Alabama Course of Study Mathematics
10
Seventh Grade Mathematics
10 cm greater than the mean height of players on the soccer
team, about twice the variability (mean absolute deviation) on
either team; on a dot plot, the separation between the two
distributions of heights is noticeable.
3
7.20
Use measures of center and measures of variability for
numerical data from random samples to draw informal
comparative inferences about two populations. [7-SP4]
Example: Decide whether the words in a chapter of a seventhgrade science book are generally longer than the words in a
chapter of a fourth-grade science book.
Investigate chance processes and develop, use, and evaluate probability
models.
4
4
7.21
7.22
Understand that the probability of a chance event is a number
between 0 and 1 that expresses the likelihood of the event
occurring. [7-SP5]
Larger numbers indicate greater likelihood. A probability near 0
indicates an unlikely event, a probability around ½ indicates an
event that is neither unlikely nor likely, and a probability near 1
indicates a likely event.
Approximate the probability of a chance event by collecting
data on the chance process that produces it and observing its
long-run relative frequency, and predict the approximate
relative frequency given the probability. [7-SP6]
Example: When rolling a number cube 600 times, predict that a
3 or 6 would be rolled roughly 200 times, but probably not
exactly 200 times.
AL071 (I) Lesson Quiz follows, worksheet
available
Overview incl. Compound Events
M7253 (I), M7254 (P), M7255 (Q), M7256 (R),
M7257 (P), M7258 (Q)
Experimental Results (Frequency Charts)
M7251 (I), M7252 (Q)
Independent Events
76286 (part 1), 76287 (part 2), lesson quiz
Dependent Events
76288 (part 1), 76289 (part 2), lesson quiz
4
7.23
Develop a probability model and use it to find probabilities of
2010 Alabama Course of Study Mathematics
11
Seventh Grade Mathematics
events. Compare probabilities from a model to observed
frequencies; if the agreement is not good, explain possible
sources of the discrepancy. [7-SP7]
4
7.23a
Develop a uniform probability model by assigning equal
probability to all outcomes, and use the model to determine
probabilities of events. [7-SP7a]
Example: If a student is selected at random from a class, find the
probability that Jane will be selected and the probability that a
girl will be selected.
4
7.23b
Develop a probability model (which may not be uniform) by
observing frequencies in data generated from a chance process.
[7-SP7b]
Example: Find the approximate probability that a spinning
penny will land heads up or that a tossed paper cup will land
open-end down. Do the outcomes for the spinning penny
appear to be equally likely based on the observed frequencies?
4
7.24
Find probabilities of compound events using organized lists,
tables, tree diagrams, and simulation. [7-SP8]
7.24a
Understand that, just as with simple events, the probability of a
compound event is the fraction of outcomes in the sample
space for which the compound event occurs. [7-SP8a]
7.24b
Represent sample spaces for compound events using methods
such as organized lists, tables, and tree diagrams. For an event
described in everyday language (e.g., ―rolling double sixes‖),
identify the outcomes in the sample space which compose the
4
4
2010 Alabama Course of Study Mathematics
Using Probability
MA61061 (I), MA61062 (Q)
Simulation Activities
M7507 (Choose type in drop down box – coin,
spinner, number cube, marbles)
Using Probability
MA61061 (I), MA61062 (Q)
Simulation Activities
M7507 (Choose type in drop down box – coin,
spinner, number cube, marbles)
Overview incl. Compound Events
M7253 (I), M7254 (P), M7255 (Q), M7256 (R),
M7257 (P), M7258 (Q)
8099 (part 1), 8173 (part 2), lesson quiz,
worksheet
12
Seventh Grade Mathematics
event. [7-SP8b]
4
7.24c
Design and use a simulation to generate frequencies for
compound events. [7-SP8c]
Example: Use random digits as a simulation tool to approximate
the answer to the question: If 40% of donors have type A blood,
what is the probability that it will take at least 4 donors to find
one with type A blood?
Simulation Activities (single events)
M7507 (Choose type in drop down box – coin,
spinner, number cube, marbles)
Ratios and Proportional Relationships [RP]
• Analyze proportional relationships and use them to solve real-world and mathematical problems.
The Number System [NS]
• Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.
Expressions and Equations [EE]
• Use properties of operations to generate equivalent expressions.
• Solve real-life and mathematical problems using numerical and algebraic expressions and equations.
Geometry [G]
• Draw, construct, and describe geometrical figures and describe the relationships between them.
• Solve real-life and mathematical problems involving angle measure, area, surface area,
and volume.
Statistics and Probability [SP]
• Use random sampling to draw inferences about a population.
• Draw informal comparative inferences about two populations.
• Investigate chance processes and develop, use, and evaluate probability models.
2010 Alabama Course of Study Mathematics
13