Download 7 . RP . A . 2 - Poudre School District

Curriculum Guide 2014-2015
Curriculum Guide Key
Abbreviation
CCSS
CCSSM
PARCC
SMP
Meaning
Common Core State Standards
Common Core State Standards Mathematics
Partnership for Assessment of Readiness for College and Careers
Standards for Mathematical Practice
Indicated Mathematical Modeling CCSS and Modeling SMP
(p. 57 CCSSM)
Connected Mathematics Project Textbook Series
Prentice Hall 2007 Algebra 1 Textbook
Prentice Hall 2007 Algebra 2 Textbook
Prentice Hall 2007 Geometry Textbook
College Preparatory Mathematics
Conceptual Understanding
Procedural Skill and Fluency
Application
★
CMP
PH A1
PH A2
PH G
CPM
C
P
A
Poudre School District
Common Core State Standards Mathematics Key
Understanding the Standards Naming Convention (6th, 7th, and 8th Grade)
Grade Level
Cluster
7 . RP . A . 2
Domain
Standard
Understanding the Standards Naming Convention (High School)
Grade Level
Standard
Domain
HS . N . CN . A . 2
Conceptual
Category
Cluster
**Underlined standards represent standards that will be
assessed at both the Algebra 1 and Algebra 2 levels.
Curriculum Guide 2014-2015
Conceptual Category/
Domain Abbreviation
NS
RP
EE
G
SP
NS
RP
EE
G
SP
NS
EE
F
G
SP
N
RN
Q
CN
VM
A
SSE
APR
CED
REI
F
IF
BF
LE
TF
G
CO
SRT
C
GPE
GMD
MG
S
ID
IC
CP
MD
Domain Meaning
Poudre School District
6th Grade
The Number System
Ratios and Proportional Relationships
Expressions and Equations
Geometry
Statistics and Probability
7th Grade
The Number System
Ratios and Proportional Relationships
Expressions and Equations
Geometry
Statistics and Probability
8th Grade
The Number System
Expressions and Equations
Functions
Geometry
Statistics and Probability
High School
Number and Quantity
The Real Number System
Quantities
The Complex Number System
Vector Quantities and Matrices
Algebra
Seeing Structure in Expressions
Arithmetic with Polynomials and Rational Expressions
Creating Equations
Reasoning with Equations and Inequalities
Functions
Interpreting Functions
Building Functions
Linear, Quadratic, and Exponential Models
Trigonometric Functions
Geometry
Congruence
Similarity, Right Triangles, and Trigonometry
Circles
Expressing Geometric Properties with Equations
Geometric Measurement and Dimension
Modeling with Geometry
Statistics and Probability
Interpreting Categorical and Quantitative Data
Making Inferences and Justifying Conclusions
Conditional Probability and the Rules of Probability
Using Probability to Make Decisions
Curriculum Guide 2014-2015
Textbook Resource Key
Abbreviation
CMP
Meaning
Connected Mathematics Project
PH A1
PH A2
PH G
Statistics Through
Application
Navigator
Ramp Up to Algebra
Prentice Hall 2007 Algebra 1
Prentice Hall 2007 Algebra 2
Prentice Hall 2007 Geometry
Common Core
Pearson
NCTM
CPM
Poudre School District
Reasoning and Sense Making in HS Math
College Preparatory Mathematics
Where can I find this?
1st ed: Printed Edition (District
Middle School Textbooks)
2nd ed: online
District High School Textbook
District High School Textbook
District High School Textbook
District Textbook
District Textbook
Textbook used at PHS, FCHS,
Lincoln MS
Copy at FRHS
ISBN# 978-0-87353-631-8
Available on Capella
Connected Mathematics Project Textbook Resources
Red
Bits and Pieces I
Bits and Pieces II
Covering and Surrounding
Data About Us
How Likely Is It?
Prime Time
Ruins of Montarek
Shapes and Designs
Common Core Additional
Investigations (6)
Blue
Accentuate the Negative
Comparing and Scaling
Data Around Us
Filling and Wrapping
Moving Straight Ahead
Stretching and Shrinking
Variables and Patterns
What Do You Expect?
Common Core Additional
Investigations (7)
Green
Clever Counting
Frogs, Fleas, and Painted Cubes
Growing, Growing, Growing
Kaleidoscopes, Hubcaps, and
Mirrors
Looking for Pythagoras
Samples and Populations
Say It with Symbols
Thinking with Mathematical
Models
Common Core Additional
Investigations (8)
Pearson SuccessNet Registration Codes
PH A1: PHMA07NTENA1TB
PH A2: PHMA07NTENA2TB
PH G: PHMA07NTENGMTB
nd
CMP (2 edition only): PHMABN06NTENCMT
Access the online textbook through http://www.pearsonsuccessnet.com.
Curriculum Guide 2014-2015
Web-Referenced Resource Key
Name
Alabama Learning Exchange
Better Explained
CCSS Math
Cut-the-Knot
Dan Meyer
Financial Fitness for Life
GeoGebra Wiki
Howard County
Illustrative Mathematics
Inside Mathematics
InterActMath
Interactive Maths
Interactivate
Interactives
Irvine Mathematics Project
IXL
Khan Academy
Learn Zillion
Learnist
MARS Shell Center
Math Forum
Math Is Fun
Math Warehouse
Mathalicious
Math’s Mate Skill Builder
Math Snacks
Mesa Community College
Michigan Virtual University
National Library of Virtual
Manipulatives
NCSSM
NCTM Illuminations
Oregon State University
PBS
Shmoop
SMART Exchange
Stat Trek
Tools for the Common Core Standards
YouTube
Yummy Math
Poudre School District
URL
http://alex.state.al.us
http://betterexplained.com
http://ccssmath.org
http://www.cut-the-knot.org
http://blog.mrmeyer.com
http://fffl.ncee.net
http://www.geogebra.org/en/wiki
http://secondarymathcommoncore.wikispaces.hcpss.org
http://www.illustrativemathematics.org
http://www.insidemathematics.org
http://www.interactmath.com
http://www.interactive-maths.com
http://www.shodor.org
http://www.learner.org/interactives
http://sites.uci.edu/irvinemathproject/
http://www.ixl.com/math
http://www.khanacademy.org
http://www.learnsillion.com
http://learni.st
http://map.mathshell.org/materials/index.php
http://mathforum.org/problems_puzzles_landing.html
http://www.mathisfun.com
http://mathwarehouse.com
http://www.mathalicious.com
http://www.mathsmate.com
http://mathsnacks.com
http://mesacc.edu
http://www.mivu.org
http://nlvm.usu.edu
http://www.ncssm.edu
http://illuminations.nctm.org
http://www.oregonstate.edu
http://www.pbs.org
http://www.shmoop.com
http://exchange.smarttech.com/#tab=0
http://stattrek.com
http://www.commoncoretools.me
http://www.youtube.com
http://www.yummymath.com
Curriculum Guide 2014-2015
Standards for Mathematical Practice
Poudre School District
1. Make Sense of problems and persevere in solving them.
Mathematically proficient students start by explaining to themselves the meaning of a problem
and looking for entry points to its solution. They analyze givens, constraints, relationships, and
goals. They make conjectures about the form and meaning of the solution and plan a solution
pathway rather than simply jumping into a solution attempt. They consider analogous
problems, and try special cases and simpler forms of the original problem in order to gain
insight into its solution. They monitor and evaluate their progress and change course if
necessary. Older students might, depending on the context of the problem, transform algebraic
expressions or change the viewing window on their graphing calculator to get the information
they need. Mathematically proficient students can explain correspondences between equations,
verbal descriptions, tables, and graphs or draw diagrams of important features and
relationships, graph data, and search for regularity or trends. Younger students might rely on
using concrete objects or pictures to help conceptualize and solve a problem. Mathematically
proficient students check their answers to problems using a different method, and they
continually ask themselves, “Does this make sense?” They can understand the approaches of
others to solve complex problems and identify correspondences between different approaches.
2. Reason abstractly and quantitatively.
Mathematically proficient students make sense of quantities and their relationships in problem
situations. They bring two complementary abilities to bear on problems involving quantitative
relationships: the ability to decontextualize – to abstract a given situation and represent it
symbolically and manipulate the representing symbols as if they have a life of their own,
without necessarily attending to their referents – and the ability to contextualize, to pause as
needed during the manipulation process in order to probe into the referents for the symbols
involved. Quantitative reasoning entails habits of creating a coherent representation of the
problem at hand, considering the units involved, attending to the meaning of quantities, not just
how to compute them, knowing and flexibly using different properties of operations and
objects.
3. Construct viable arguments and critique the reasoning of others.
Mathematically proficient students understand and use stated assumptions, definitions, and
previously established results in constructing arguments. They make conjectures and build a
logical progression of statements to explore the truth of their conjectures. They are able to
analyze situations by breaking them into cases, and can recognize and use counterexamples.
They justify their conclusions, communicate them to others, and respond to the arguments of
others. They reason inductively about data, making plausible arguments that take into account
the context from which the data arose. Mathematically proficient students are also able to
compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning
from that which is flawed, and – if there is a flaw in an argument – explain what it is. Elementary
students can construct arguments using concrete referents such as objects, drawings, diagrams,
and actions. Such arguments can make sense and be correct, even though they are not
generalized or made formal until later grades. Later, students learn to determine domains to
Curriculum Guide 2014-2015
Poudre School District
which an argument applies. Students at all grades can listen or read the arguments of others,
decide whether they make sense, and ask useful questions to clarify or improve the arguments.
4. Model with Mathematics
Mathematically proficient students can apply the mathematics they know to solve problems
arising in everyday life, society, and the workplace. In early grades, this might be as simple as
writing an addition equation to describe a situation. In middle grades, a student might apply
proportional reasoning to plan a school event or analyze a problem in the community. By high
school, a student might use geometry to solve a design problem or use a function to describe
how one quantity of interest depends on another. Mathematically proficient students who can
apply what they know are comfortable making assumptions and approximations to simplify a
complicated situation, realizing that these may need revision later. They are able to identify
important quantities in a practical situation and map their relationships using such tools as
diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those
relationships mathematically to draw conclusions. They routinely interpret their mathematical
results in the context of the situation and reflect on whether the results make sense, possibly
improving the model if it has not served its purpose.
5. Use appropriate tools strategically.
Mathematically proficient students consider the available tools when solving a mathematical
problem. These tools might include pencil and paper, concrete models, a ruler, a protractor, a
calculator, a spreadsheet, a computer algebra system, a statistical package, or dynamic
geometry software. Proficient students are sufficiently familiar with tools appropriate for their
grade or course to make sound decisions about when each of these tools might be helpful,
recognizing both the insight to be gained and their limitations. For example, mathematically
proficient high school students analyze graphs of functions and solutions generated using a
graphing calculator. They detect possible error by strategically using estimation and other
mathematical knowledge. When making mathematical models, they know that technology can
enable them to visualize the results of varying assumptions, explore consequences, and
compare predictions with data. Mathematically proficient students at various grade levels are
able to identify relevant external mathematical resources, such as digital content located on a
website, and use them to pose or solve problems. They are able to use technological tools to
explore and deepen their understanding of concepts.
6. Attend to precision.
Mathematically proficient students try to communicate precisely to others. They try to use clear
definitions in discussion with others and in their own reasoning. They state the meaning of the
symbols they choose, including using the equal sign consistently and appropriately. They are
careful about specifying units of measure, and labeling axes to clarify the correspondence with
quantities in a problem. They calculate accurately and efficiently, express numerical answers
with a degree of precision appropriate for the problem context. In the elementary grades,
students give carefully formulated explanations to each other. By the time they reach high
Curriculum Guide 2014-2015
Poudre School District
school they have learned to examine claims and make explicit use of definitions.
7. Look for a make use of structure.
Mathematically proficient students look closely to discern a pattern or structure. Young
students, for example, might notice that three and seven more is the same amount as seven and
three more, or they may sort a collection of shapes according to how many sides the shapes
have. Later, students will see 7 × 8 equals the well-remembered 7 × 5 + 7 × 3, in preparation
for learning about the distributive property. In the expression 𝑥𝑥 2 + 9𝑥𝑥 + 14, older students can
see the 14 as 2 × 7 and the 9 as 2 + 7. They recognize the significance of an existing line in a
geometric figure and can use the strategy of drawing an auxiliary line for solving problems.
They also can step back for an overview and shift perspective. They can see complicated things,
such as some algebraic expressions, as single objects or as being composed of several objects.
For example, they can see 5 − 3(𝑥𝑥 − 𝑦𝑦)2 as 5 minus a positive number times a square and use
that to realize that its value cannot be more than 5 for any real numbers 𝑥𝑥 and 𝑦𝑦.
8. Look for an express regularity in repeated reasoning.
Mathematically proficient students notice if calculations are repeated, and look both for general
methods and for shortcuts. Upper elementary students might notice when dividing 25 by 11
that they are repeating the same calculations over and over again, and conclude they have a
repeating decimal. By paying attention to the calculation of slope as they repeatedly check
whether points are on the line through (1, 2) with slope 3, middle school students might
abstract the equation (𝑦𝑦 − 2)/(𝑥𝑥 − 1) = 3. Noticing the regularity in the way terms cancel when
expanding (𝑥𝑥 − 1)(𝑥𝑥 + 1), (𝑥𝑥 − 1)(𝑥𝑥 2 + 𝑥𝑥 + 1), and (𝑥𝑥 − 1)(𝑥𝑥 3 + 𝑥𝑥 2 + 𝑥𝑥 + 1) might lead them
to the general formula for the sum of a geometric series. As they work to solve a problem,
mathematically proficient students maintain oversight of the process, while attending to the
details. They continually evaluate the reasonableness of their intermediate results.
Curriculum Guide 2014-2015
Poudre School District
PARCC Calculator
Policy
Approved
7/23/12
Grades 3 – 5 Calculator Policy
• PARCC mathematics assessments for Grades 3 – 5 will not allow for
calculator usage. (AAF will consider an accommodation policy)
Grades 6 – 8 Calculator Policy
• PARCC mathematics assessments for Grades 6-7 will allow for an online four
function calculator with square root.
• PARCC mathematics assessments for Grade 8 will allow for an online
scientific calculator.
• PARCC mathematics assessments are to be divided into calculator and noncalculator sessions, provided that the other sessions of the assessment are
locked.
• The same calculator with maximum functionality is to be used for all items
on calculator sessions.
High School Calculator Policy
• PARCC mathematics assessments for High School will allow for an online
calculator with functionalities similar to that of a TI-84 graphing calculator.
• PARCC mathematics assessments are to be divided into calculator and noncalculator sessions, provided that the other sessions of the assessment are
locked.
• The same calculator with maximum functionality is to be used for all items
on calculator sessions.
Curriculum Guide 2014-2015
Poudre School District
Assessment Reference Sheet
Grade 5
1 mile = 5.280 feet
1 mile = 1,760 yards
1 pound = 16 ounces
1 cup = 8 fluid ounces
1 ton = 2,000 pounds
1 pint = 2 cups
1 quart = 2 pints
1 gallon = 4 quarts
1 liter = 1000 cubic centimeters
Right Rectangular Prism
𝑉𝑉 = 𝐵𝐵ℎ or 𝑉𝑉 = 𝑙𝑙𝑙𝑙ℎ
Grade 6
1 inch = 2.54 centimeters
1 meter = 39.37 inches
1 mile = 5,280 feet
1 mile = 1,760 yards
1 mile = 1.609 kilometers
Triangle
1 kilometer = 0.62 mile
1 pound = 16 ounces
1 pound = 0.454 kilograms
1 kilogram = 2.2 pounds
1 ton = 2,000 pounds
Right Rectangular Prism
1 cup = 8 fluid ounces
1 pint = 2 cups
1 quart = 2 pints
1 gallon = 4 quarts
1 gallon = 3.785 liters
1 liter = 0.264 gallons
1 liter = 1000 cubic centimeters
1
𝑏𝑏ℎ
2
𝑉𝑉 = 𝐵𝐵ℎ or 𝑉𝑉 = 𝑙𝑙𝑙𝑙ℎ
𝐴𝐴 =
Curriculum Guide 2014-2015
Poudre School District
Grade 7
1 inch = 2.54 centimeters
1 meter = 39.37 inches
1 mile = 5,280 feet
1 mile = 1,760 yards
1 mile = 1.609 kilometers
1 kilometer = 0.62 mile
1 pound = 16 ounces
1 pound = 0.454 kilograms
1 kilogram = 2.2 pounds
1 ton = 2,000 pounds
1 cup = 8 fluid ounces
1 pint = 2 cups
1 quart = 2 pints
1 gallon = 4 quarts
1 gallon = 3.785 liters
1 liter = 0.264 gallons
1 liter = 1000 cubic centimeters
1
𝐴𝐴 = 𝑏𝑏ℎ
2
𝐴𝐴 = 𝑏𝑏ℎ
𝐴𝐴 = 𝜋𝜋𝑟𝑟 2
𝐶𝐶 = 𝜋𝜋𝜋𝜋 or 𝐶𝐶 = 2𝜋𝜋𝜋𝜋
𝑉𝑉 = 𝐵𝐵ℎ
Triangle
Parallelogram
Circle
Circle
General Prisms
Grade 8
1 inch = 2.54 centimeters
1 meter = 39.37 inches
1 mile = 5,280 feet
1 mile = 1,760 yards
1 mile = 1.609 kilometers
1 kilometer = 0.62 mile
1 pound = 16 ounces
1 pound = 0.454 kilograms
1 kilogram = 2.2 pounds
1 ton = 2,000 pounds
Triangle
Parallelogram
Circle
Circle
General Prisms
Cylinder
Sphere
Cone
Pythagorean Theorem
1 cup = 8 fluid ounces
1 pint = 2 cups
1 quart = 2 pints
1 gallon = 4 quarts
1 gallon = 3.785 liters
1 liter = 0.264 gallons
1 liter = 1000 cubic centimeters
1
𝐴𝐴 = 𝑏𝑏ℎ
2
𝐴𝐴 = 𝑏𝑏ℎ
𝐴𝐴 = 𝜋𝜋𝑟𝑟 2
𝐶𝐶 = 𝜋𝜋𝜋𝜋 or 𝐶𝐶 = 2𝜋𝜋𝜋𝜋
𝑉𝑉 = 𝐵𝐵ℎ
𝑉𝑉 = 𝜋𝜋𝑟𝑟 2 ℎ
4
𝑉𝑉 = 𝜋𝜋𝑟𝑟 3
3
1 2
𝑉𝑉 = 𝜋𝜋𝑟𝑟 ℎ
3
𝑎𝑎2 + 𝑏𝑏 2 = 𝑐𝑐 2
Curriculum Guide 2014-2015
Poudre School District
High School Assessment Reference Sheet
1 inch = 2.54 centimeters
1 meter = 39.37 inches
1 mile = 5,280 feet
1 mile = 1,760 yards
1 mile = 1.609 kilometers
1 kilometer = 0.62 mile
1 pound = 16 ounces
1 pound = 0.454 kilograms
1 kilogram = 2.2 pounds
1 ton = 2,000 pounds
1 cup = 8 fluid ounces
1 pint = 2 cups
1 quart = 2 pints
1 gallon = 4 quarts
1 gallon = 3.785 liters
1 liter = 0.264 gallons
1 liter = 1000 cubic centimeters
Triangle
1
𝐴𝐴 = 𝑏𝑏ℎ
2
Pythagorean
Theorem
Circle
𝐴𝐴 = 𝜋𝜋𝑟𝑟 2
Arithmetic
Sequence
𝑉𝑉 = 𝐵𝐵ℎ
Geometric Series
4
𝑉𝑉 = 𝜋𝜋𝑟𝑟 3
3
Degrees
Parallelogram
𝐴𝐴 = 𝑏𝑏ℎ
Circle
𝐶𝐶 = 𝜋𝜋𝜋𝜋 or 𝐶𝐶 = 2𝜋𝜋𝜋𝜋
Cylinder
𝑉𝑉 = 𝜋𝜋𝑟𝑟 2 ℎ
General Prisms
Sphere
Cone
Pyramid
1
𝑉𝑉 = 𝜋𝜋𝑟𝑟 2 ℎ
3
1
𝑉𝑉 = 𝐵𝐵ℎ
3
Quadratic
Formula
Geometric
Sequence
Radians
Exponential
Growth/Decay
𝑥𝑥 =
𝑎𝑎2 + 𝑏𝑏 2 = 𝑐𝑐 2
−𝑏𝑏 ± √𝑏𝑏 2 − 4𝑎𝑎𝑎𝑎
2𝑎𝑎
𝑎𝑎𝑛𝑛 = 𝑎𝑎1 + (𝑛𝑛 − 1)𝑑𝑑
𝑆𝑆𝑛𝑛 =
𝑎𝑎𝑛𝑛 = 𝑎𝑎1 𝑟𝑟 𝑛𝑛−1
𝑎𝑎1 −𝑎𝑎1 𝑟𝑟 𝑛𝑛
1−𝑟𝑟
1 𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 =
1 𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 =
where 𝑟𝑟 ≠ 1
180
𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑
𝜋𝜋
𝜋𝜋
𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟
180
𝐴𝐴 = 𝐴𝐴0 𝑒𝑒 𝑘𝑘(𝑡𝑡−𝑡𝑡0 ) + 𝐵𝐵0
Curriculum Guide 2014-2015
Geometry
Measurement
and Data
Number and
Operations in
Base Ten
Operations
and Algebraic
Thinking
Counting
and
Cardinality
Domain
Poudre School District
Kindergarten
•
•
•
Know number names and the count sequence.
Count to tell the number of objects.
Compare numbers.
•
Understand addition, and understand
subtraction.
Grade 1
•
•
•
•
•
•
•
•
Work with numbers 11-19 to gain foundations
for place value.
•
•
Describe and compare measureable attributes.
Classify objects and count the number of objects
in each category.
•
•
•
Identify and describe shapes.
Analyze, compare, create, and compose shapes.
•
•
•
Grade 2
Represent and solve problems involving addition
and subtraction.
Understand and apply properties of operations
and the relationship between addition and
subtraction.
Add and subtract within 20.
Work with addition and subtraction equations.
Extend the counting sequence.
Understand place value.
Use place value understanding and properties of
operations to add and subtract.
•
•
•
Understand place value.
Use place value understanding and properties of
operations to add and subtract.
Measure lengths indirectly and by iterating
length units.
Tell and write time.
Represent and interpret data.
•
•
•
•
Measure and estimate lengths in standard units.
Relate addition and subtraction to length.
Work with time and money.
Represent and interpret data.
Reason with shapes with shapes and their
attributes.
•
Reason with shapes and their attributes.
•
•
Represent and solve problems involving addition
and subtraction.
Add and subtract within 20.
Work with equal groups of objects to gain
foundations for multiplication.
Curriculum Guide 2014-2015
Number and
Operations –
Fractions.
Number and
Operations in
Base Ten
Operations
and Algebraic
Thinking
Domain
Grade 3
•
•
•
•
•
•
Measurement and
Data
Grade 4
•
•
•
•
Grade 5
Represent and solve problems involving
•
multiplication and division.
Understand properties of multiplication and the
•
relationship between multiplication and division. •
Multiply and divide within 100.
Solve problems involving the four operations, and
identify and explain patterns in arithmetic.
Use place value understanding and properties of
•
operations to perform multi-digit arithmetic.
•
Use the four operations with whole numbers to
solve problems.
Gain familiarity with factors and multiples.
Generate and analyze patterns.
•
•
Write and interpret numerical expressions.
Analyze patterns and relationships.
Generalize place value understanding for multidigit whole numbers.
Use place value understanding and properties of
operations to perform multi-digit arithmetic.
•
•
Understand the place value system.
Perform operations with multi-digit whole
numbers and with decimals to hundredths.
•
Extend understanding of fraction equivalence
and ordering.
Build fractions from unit fractions by applying
and extending previous understandings of
operations on whole numbers.
Understand decimal notation for fractions, and
compare decimal fractions.
Solve problems involving measurement and
conversion of measurements from a larger unit
to a smaller unit.
Represent and interpret data.
Geometric measure: understand concepts of
angle and measure angles.
•
Use equivalent fractions as strategy to add and
subtract fractions.
Apply and extend previous understandings of
multiplication and division to multiply and divide
fractions.
Draw and identify lines and angles, and classify
shapes by properties of their lines and angles.
•
Develop understanding of fractions as numbers.
•
•
•
Geometry
Poudre School District
Solve problems involving measurement and
estimation of intervals of time, liquid volumes,
and masses of objects.
Represent and interpret data.
Geometric Measurement: understand concepts of
area and relate area to multiplication and
addition.
Geometric Measurement: recognize perimeter as
an attribute of plane figures and distinguish
between linear and area measures.
Reason with shapes and their attributes.
•
•
•
•
•
•
•
•
•
Convert like measurement units within a given
measurement system.
Represent and interpret data.
Geometric measurement: understand concepts of
volume and relate volume to multiplication and
to addition.
Graph points on the coordinate plane to solve
real-world and mathematical problems.
Classify two-dimensional figures into categories
based on their properties.
Curriculum Guide 2014-2015
Expressions
and
Equations
The Number
System
Ratios and
Proportional
Reasoning
Domain
Grade 6
Grade 7
Grade 8
•
Understand ratio concepts and use ratio
reasoning to solve problems.
•
Analyze proportional relationships and use them
to solve real-world and mathematical problems.
•
Know that there are numbers that are not
rational, and approximate them by rational
numbers.
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Apply and extend previous understandings of
multiplication and division to divide fractions by
fractions.
Compute fluently with multi-digit numbers and
find common factors and multiples.
Apply and extend previous understandings of
numbers to the system of rational numbers.
Apply and extend previous understandings of
arithmetic to algebraic expressions.
Reason about and solve one-variable equations
and inequalities.
Represent and analyze quantitative relationships
between dependent and independent variables.
Solve real-world and mathematical problems
involving area, surface area and volume.
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Apply and extend previous understandings of
operations with fractions to add, subtract,
multiply and divide rational numbers.
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Use properties of operations to generate
equivalent expressions.
Solve real-life and mathematical problems using
numerical and algebraic expressions and
equations.
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Work with radicals and integer exponents.
Understand the connections between
proportional relationships, lines and linear
equations.
Analyze and solve linear equations and pairs of
simultaneous linear equations.
Develop understanding of statistical variability.
Summarize and describe distributions.
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Geometry
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Statistics
and
Probability
Poudre School District
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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
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volume.
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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.
Define, evaluate and compare functions.
Use functions to model relationships between
quantities.
Understand congruence and similarity using
physical models, transparencies or geometry
software.
Understand and apply the Pythagorean Theorem.
Solve real-world and mathematical problems
involving volume of cylinders, cones and spheres.
Investigate patterns of association in bivariate
data.
Curriculum Guide 2014-2015
Conceptual
Category
Algebra 1
Number and Quantity
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Geometry
The Real Number System
Extend the properties of exponents to rational
exponents.
Use properties of rational and irrational
numbers.
Reason quantitatively and use units to solve
problems.
Quantities
The Complex Number System
Algebra 2
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Extend the properties of exponents to rational
exponents.
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Reason quantitatively and use units to solve
problems.
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Algebra
Poudre School District
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Vector Quantities and Matrices
**Reserved for the fourth course.
Seeing Structure in Expressions
Interpret the structure of expressions.
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Write expressions in equivalent forms to solve
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problems.
Arithmetic with Polynomials and Rational Expressions
Perform arithmetic operations on polynomials.
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Understand the relationship between zeros
and factors of polynomials.
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Creating Equations
Create equations that describe numbers or
relationships.
Understand solving equations as a process of
reasoning and explain the reasoning.
Solve equations and inequalities in one
variable.
Solve systems of equations.
Represent and solve equations and
inequalities graphically.
Reasoning with Equations and Inequalities
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Perform arithmetic operations with complex
numbers.
Use complex numbers in polynomial identities
and equations.
Interpret the structure of expressions.
Write expressions in equivalent forms to solve
problems.
Perform arithmetic operations on
polynomials.
Understand the relationship between zeros
and factors of polynomials.
Use polynomial identities to solve problems.
Rewrite rational expressions.
Create equations that describe numbers or
relationships.
Understand solving equations as a process of
reasoning and explain the reasoning.
Solve equations and inequalities in one
variable.
Solve systems of equations.
Represent and solve equations and
inequalities.
Curriculum Guide 2014-2015
Conceptual
Category
Algebra 1
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Functions
Poudre School District
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Geometry
Interpreting Functions
Understand the concept of a function and use
function notation.
Interpret functions that arise in applications in
terms of the context.
Analyze functions using different
representations.
Build a function that models a relationship
between two quantities.
Build new functions from existing functions.
Construct and compare linear, quadratic, and
exponential models and solve problems.
Interpret expressions for functions in terms of
the situation they model.
Algebra 2
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Building Functions
Linear, Quadratic, and Exponential Models
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Trigonometric Functions
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Understand the concept of a function and use
function notation.
Interpret functions that arise in applications
in terms of the context.
Analyze functions using different
representations.
Build a function that models a relationship
between two quantities.
Build new functions from existing functions.
Construct and compare linear, quadratic, and
exponential models and solve problems.
Interpret expressions for functions in terms of
the situation they model.
Extend the domain of trigonometric functions
using the unit circle.
Model periodic phenomena with
trigonometric functions.
Prove and apply trigonometric identities.
Curriculum Guide 2014-2015
Geometry
Conceptual
Category
Poudre School District
Algebra 1
Geometry
Congruence
• Experiment with transformation in the plane.
• Understand congruence in terms of rigid motions.
• Prove geometric theorems.
• Make geometric constructions.
Similarity, Right Triangles, and Trigonometry
• Understand similarity in terms of similarity
transformations.
• Prove theorems using similarity.
• Define trigonometric ratios and solve problems
involving right triangles.
• Apply trigonometry to general triangles.
Circles
• Understand and apply theorems about circles.
• Find arc lengths and areas of sectors of circles.
Expressing Geometric Properties with Equations
• Translate between the geometric description and
the equation of a conic section.
• Use coordinates to prove simple geometric
theorems algebraically.
Geometric Measurement and Dimension
• Explain volume formulas and use them to solve
problems.
• Visualize relationships between two-dimensional
and three-dimensional objects.
Modeling Geometry
• Apply geometric concepts in modeling situations.
Algebra 2
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Translate between the geometric
description and the equation for a conic
section.
Curriculum Guide 2014-2015
Conceptual
Category
Algebra 1
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Statistics and Probability
Poudre School District
Geometry
Interpreting Categorical and Quantitative Data
Summarize, represent, and interpret data on a
single count or measurement variable.
Summarize, represent, and interpret data on
two categorical and quantitative variables.
Interpret linear models.
Algebra 2
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Making Inferences and Justifying Conclusions
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Conditional Probability and the Rules of Probability
• Understand independence and conditional
probability and use them to interpret data.
• Use the rules of probability to compute
probabilities of compound events in a uniform
probability model.
Using Probability to Make Decisions
• Use probability to evaluate outcomes of decisions.
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Summarize, represent, and interpret data
on a single count or measurement variable.
Summarize, represent and interpret data
on two categorical and quantitative
variables.
Understand and evaluate random
processes underlying statistical
experiments.
Make inferences and justify conclusions
from sample surveys, experiments and
observational studies.
Understand independence and conditional
probability and use them to interpret data.
Use the rules of probability to compute
probabilities of compound events in a
uniform probability model.
Use probability to evaluate outcomes of
decisions.