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HACKETTSTOWN PUBLIC SCHOOLS
HACKETTSTOWN, NEW JERSEY
MATHEMATICS
GRADE 7
CURRICULUM GUIDE
FINAL DRAFT
June 2012
Mr. Robert Gratz, Superintendent
Ms. Diane Pittenger, Assistant Superintendent for Curriculum and Instruction
Mr. Roy Huchel, Supervisor for Mathematics
Developed by:
Mrs. Donna Cohen
This curriculum may be modified through varying techniques,
strategies and materials, as per an individual student’s
Individualized Education Plan (IEP).
Approved by the Hackettstown Board of Education
At the regular meeting held on
8/8/2012
and
Aligned with the National Common Core Standards 2010
1
TABLE OF CONTENTS
Philosophy and Rationale:
3
Common Core Standards:
4-7
Course Proficiencies:
8
Student Proficiencies:
9
Methods of Evaluation:
10
Course Outline:
11 – 35
Ratios and Proportional Reasoning:
11 – 15
The Number System:
16 – 20
Expressions & Equations:
21 – 25
Geometry:
26 – 30
Statistics & Probability:
31 – 35
Resources and Materials:
36
2
PHILOSOPHY/RATIONALE
Through mathematics, students learn to identify, understand and solve real-world problems using abstract and
quantitative reasoning, existing structures and appropriate tools. Students also learn how to effectively
communicate, model, and critique connections with others.
3
NEW JERSEY COMMON CORE STATE STANDARDS
Topic:
Domain
CCSS
7.RP.1.
7.RP.2.
7.RP.3.
Topic:
Domain
CCSS
7.NS.1.
7.NS.2.
Common Core State Standard
Mathematics: Ratios & Proportional Relationships
Analyze proportional relationships and use them to solve real-world and mathematical
problems.
Core Content Statement
Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other
quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4
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.
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.
Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and
verbal descriptions of proportional relationships.
Represent proportional relationships by equations. For example, if total cost t is proportional to the
number n of items purchased at a constant price p, the relationship between the total cost and the
number of items can be expressed as t = pn.
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
Use proportional relationships to solve multistep ratio and percent problems. Examples: simple
interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and
decrease, percent error.
Mathematics: The Number System
Apply and extend previous understandings of operations with fractions to add, subtract,
multiply, and divide rational numbers.
Core Content Statement
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.
Describe situations in which opposite quantities combine to make 0. For example, a hydrogen
atom has 0 charge because its two constituents are oppositely charged.
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.
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.
Apply properties of operations as strategies to add and subtract rational numbers.
Apply and extend previous understandings of multiplication and division and of fractions to
multiply and divide rational numbers.
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.
Understand that integers can be divided, provided that the divisor is not zero, and every quotient
of integers (with non-zero divisor) is a rational number. If p and q are integers, then –(p/q) = (–
p)/q = p/(–q). Interpret quotients of rational numbers by describing real-world contexts.
4
7.NS.3.
Topic:
Domain
CCSS
7.EE.1.
7.EE.2.
Topic:
Domain
CCSS
7.EE.3.
7.EE.4.
Topic:
Domain
CCSS
7.G.1.
7.G.2.
7.G.3.
Apply properties of operations as strategies to multiply and divide rational numbers.
o 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.
Solve real-world and mathematical problems involving the four operations with rational numbers.1
Mathematics: Expressions & Equations
Use properties of operations to generate equivalent expressions.
Core Content Statement
Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions
with rational coefficients.
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. For example, a + 0.05a = 1.05a means that
“increase by 5%” is the same as “multiply by 1.05.”
Mathematics: Expressions & Equations
Solve real-life and mathematical problems using numerical and algebraic expressions and
equations.
Core Content Statement
Solve multi-step real-life and mathematical problems posed with positive and negative rational
numbers in any form (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. For example: If a woman making $25 an hour gets a 10% raise, she will make an
additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a
towel bar 9 3/4 inches long in the center of a door that is 27 1/2 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.
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
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. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?
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. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?
Common Core State Standard
Mathematics: Geometry
Draw construct, and describe geometrical figures and describe the relationships between
them.
Core Content Statement
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.
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
Describe the two-dimensional figures that result from slicing three-dimensional figures, as in
plane sections of right rectangular prisms and right rectangular pyramids.
5
Topic:
Domain
CCSS
7.G.4.
7.G.5.
7.G.6.
Topic:
Domain
CCSS
7.SP.1.
7.SP.2.
Topic:
Domain
CCSS
7.SP.3.
7.SP.4.
Topic:
Domain
CCSS
7.SP.5.
7.SP.6.
Mathematics: Geometry
Solve real-life and mathematical problems involving angle measure, area, surface area, and
volume.
Core Content Statement
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.
Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step
problem to write and solve simple equations for an unknown angle in a figure.
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.
Mathematics: Statistics & Probability
Use random sampling to draw inferences about a population.
Core Content Statement
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.
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. For 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.
Mathematics: Statistics & Probability
Draw informal comparative inferences about two populations.
Core Content Statement
Informally assess the degree of visual overlap of two numerical data distributions with similar
variability, measuring the difference between the centers by expressing it as a multiple of a
measure of variability. For example, the mean height of players on the basketball team is 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.
Use measures of center and measures of variability for numerical data from random samples to
draw informal comparative inferences about two populations. For example, decide whether the
words in a chapter of a seventh-grade science book are generally longer than the words in a
chapter of a fourth-grade science book.
Mathematics: Statistics & Probability
Investigate chance processes and develop, use, and evaluate probability models.
Core Content Statement
Understand that the probability of a chance event is a number between 0 and 1 that expresses the
likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0
indicates an unlikely event, a probability around 1/2 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. For 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.
6
7.SP.7.
7.SP.8.
Develop a probability model and use it to find probabilities of events. Compare probabilities from
a model to observed frequencies; if the agreement is not good, explain possible sources of the
discrepancy.
Develop a uniform probability model by assigning equal probability to all outcomes, and use the
model to determine probabilities of events. For 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.
Develop a probability model (which may not be uniform) by observing frequencies in data
generated from a chance process. For 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?
Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.
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.
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 event.
Design and use a simulation to generate frequencies for compound events. For 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?
7
COURSE PROFICIENCIES
By the end of the course, this curriculum aims to:
1. Creating proportions to solve multistep ratio and percent problems.
2. Computing unit rates associated with ratios of fractions, including ratios of lengths, areas and other
quantities measured in like or different units.
3. Determining whether two quantities are in a proportional relationship.
4. Calculating the unit rate using tables, graphs, equations, diagrams and verbal descriptions of
proportional relationships.
5. Creating an equation that relates to a proportional relationship.
6. Explaining what a coordinate point on the graph of a proportional relationship means in terms of the
situation.
7. Using appropriate notation to indicate positive and negative numbers.
8. Locating rational numbers on a number line.
9. Comparing and ordering rational numbers.
10. Developing algorithms for all integer operations.
11. Writing mathematical sentences to show relationships.
12. Using fact families to solve simple equations with missing facts.
13. Using order of operations to make computational sequences clear.
14. Applying the Distributive Property to simplify expressions and solve problems.
15. Using positive and negative numbers to graph in four quadrants and to model questions.
16. Simplifying and rewriting linear expressions.
17. Representing linear relationships in tables, on graphs and as equations.
18. Converting between tables, graphs and linear equations.
19. Solving linear equations and inequalities algebraically.
20. Identifying the slope of a linear equation given a table, graph or equation.
21. Identifying the relationship between real-life problems and slope
22. Solving problems involving scale drawings
23. Drawing geometric shapes with given conditions
24. Using area and circumference of a circle to solve problems
25. Using supplementary, complimentary, vertical, and adjacent angles to solve problems
26. Solving problems involving area, volume and surface area of two- and three- dimensional objects
27. Using random samples to draw inferences about a general population
28. Developing and using probability models based on investigation
29. Finding the probability of simple and compound events
8
STUDENT PROFICIENCIES
Knowledge and skill proficiencies are indicated on the individual units found within this curriculum guide.
Students will be able to:
1. Use unit rates to compare values in similar in different measurements.
2. Recognize and analyze proportional relationships and use them to solve real-world and mathematical
problems.
3. Apply their understanding of addition, subtraction, multiplication and division to rational numbers.
4. Represent and solve real-life situations with rational numbers.
5. Solve linear equations including those with variables on both sides of the equation.
6. Relate tables, equations and graphs to each other.
7. Use linear equations to solve real-life problems.
8. Draw and describe geometrical figures and describe the relationships between them.
9. Solve real-life problems involving angle measure, area, surface area and volume
10. Use random samples to draw inferences about a general population
11. Find the probability of simple and compound events
9
METHODS OF EVALUATION
Based upon grade level and specific objectives, the students will be evaluated in a number of ways, which
include but are not limited to the following methods:
1.
2.
3.
4.
5.
6.
7.
8.
9.
Class work
Homework
Study Island
SuccessMaker
Unit Quizzes
Partner Quizzes
Unit Tests
NJ Ask Mathematics
Unit Project
10
Hackettstown School District
Mathematics
7th Grade
Mission Statement: Through mathematics, students learn to identify, understand and solve real-world problems
using abstract and quantitative reasoning, existing structures and appropriate tools. Students also learn how to
effectively communicate, model, and critique connections with others.
Stage 1: Desired Results
Topic: Ratios and Proportional Reasoning
Core Content Curriculum Number & Strands
Domain
Analyze proportional relationships and use them to solve real-world and mathematical
problems.
CCSS
CCSS Content Statement
Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other
quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4
7.RP.1.
hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2miles per
hour.
7.RP.2.
Recognize and represent proportional relationships between quantities.
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.
Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal
descriptions of proportional relationships.
Represent proportional relationships by equations. For example, if total cost t is proportional to the
number n of items purchased at a constant price p, the relationship between the total cost and the
number of items can be expressed as t = pn.
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.
Use proportional relationships to solve multistep ratio and percent problems. Examples: simple
7.RP.3.
interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and
decrease, percent error.
Essential Questions
Enduring Understandings
1. When quantities have different measurements, Students will understand that:
how can they be compared?
1. Proportions are a good way to solve linear
2. How can a unit rate be used to find the total
problems by scaling ratios up or down.
cost of something?
2. Unit rates make it easy to find any number of
3. Why is a ratio a good means of comparison?
solutions.
4. What is the relationship between ratios and
3. Ratios make it easy to compare two quantities.
similar figures?
4. A straight line on a graph represents a
5. How can ratios be used in daily life to find
proportional relationship.
unknown quantities or inaccessible
measurements?
6. How can we use proportions to solve
problems?
11
Knowledge and Skills: (Focus of Instruction)
Students will be instructed on:
1. Creating proportions to solve multistep ratio and percent problems
2. Computing unit rates associated with ratios of fractions, including ratios of lengths, areas and other
quantities measured in like or different units.
3. Determining whether two quantities are in a proportional relationship.
4. Calculating the unit rate using tables, graphs, equations, diagrams and verbal descriptions of
proportional relationships.
5. Creating an equation that relates to a proportional relationship.
6. Explaining what a coordinate point on the graph of a proportional relationship means in terms of the
situation
Learning Expectations/Objectives
st
Integration of 21 Century Skills
Integration of 21st Century Learning
FLEXIBILITY AND ADAPTABILITY
Information Literacy
Adapt to Change
• Access and Evaluate Information
• Adapt to varied roles, jobs responsibilities,
• Access information efficiently (time) and
schedules and context
effectively (sources)
• Work effectively in a climate of ambiguity and
• Evaluate information critically and
changing priorities
competently
Be Flexible
Use and Manage Information
• Incorporate feedback effectively
• Use information accurately and creatively for
• Deal positively with praise, setbacks and
the issue or problem at hand
criticism
• Manage the flow of information from a wide
• Understand, negotiate and balance diverse
variety of sources
views and beliefs to reach workable solutions,
• Apply a fundamental understanding of the
particularly in multi-cultural environments
ethical/legal issues surrounding the access and
INITIATIVE AND SELF-DIRECTION
use of information
Manage Goals and Time
Media Literacy
• Set goals with tangible and intangible success
Analyze Media
criteria
• Understand both how and why media messages
• Balance tactical (short-term) and strategic
are constructed, and for what purposes
(long-term) goals
• Examine how individuals interpret messages
• Utilize time and manage workload efficiently
differently, how values and points of view are
Work Independently
included or excluded, and how media can
• Monitor, define, prioritize and complete tasks
influence beliefs and behaviors
without direct oversight
• Apply a fundamental understanding of the
Be Self-directed Learners
ethical/legal issues surrounding the access and
• Go beyond basic mastery of skills and/or
use of media
curriculum to explore and expand one’s own
Create Media Products
learning and opportunities to gain expertise
• Understand and utilize the most appropriate
• Demonstrate initiative to advance skill levels
media creation tools, characteristics and
towards a professional level
conventions
• Demonstrate commitment to learning as a
• Understand and effectively utilize the most
lifelong process
appropriate expressions and interpretations in
• Reflect critically on past experiences in order
diverse, multi-cultural environments
to inform future progress
SOCIAL AND CROSS-CULTURAL SKILLS
Interact Effectively with Others
• Know when it is appropriate to listen and when
to speak
12
•
Conduct themselves in a respectable,
professional manner
Work Effectively in Diverse Teams
• Respect cultural differences and work
effectively with people from a range of social
and cultural backgrounds
• Respond open-mindedly to different ideas and
values
• Leverage social and cultural differences to
create new ideas and increase both innovation
and quality of work
PRODUCTIVITY AND ACCOUNTABILITY
Manage Projects
• Set and meet goals, even in the face of
obstacles and competing pressure
• Prioritize, plan and manage work to achieve
the intended result
Produce Results
• Demonstrate additional attributes associated
with producing high quality products including
the abilities to:
- Work positively and ethically
- Manage time and projects
effectively
- Multi-task
- Participate actively, as well as be
reliable and punctual
- Present oneself professionally and
with proper etiquette
- Collaborate and cooperate
effectively with teams
- Respect and appreciate team
diversity
- Be accountable for results
LEADERSHIP AND RESPONSIBILITY
Guide and Lead Others
• Use interpersonal and problem-solving skills to
influence and guide others toward a goal
• Leverage strengths of others to accomplish a
common goal
• Inspire others to reach their very best via
example and selflessness
• Demonstrate integrity and ethical behavior in
using influence and power
Be Responsible to Others
• Act responsibly with the interests of the larger
community in mind
13
Stage 2: Evidence of Understanding
Hackettstown Benchmarks: (Do or Say)
Students will be able to:
1. Use unit rates to compare values in similar in different measurements.
2. Recognize and analyze proportional relationships and use them to solve real world and mathematical
problems.
3. Represent proportional relationships as equations.
Assessment Methods:
Formative: (On-going)
• Class work
• Homework
• Study Island
• SuccessMaker
• Unit Quizzes
• Partner Quizzes
• Unit Tests
• NJ Ask Mathematics
Summative: (Culminating)
• Unit Project – Monster Project – enlarge/shrink an image using ratios`
Other Evidence and Student Self-Assessment:
• Student Self-Assessment
o Mathematical Reflections
• Interdisciplinary
o Social Studies – Map Creation
Stage 3: Learning Plan
To show evidence students may complete the following assessment:
A
• All-Similar Shapes Project – use ratios and proportions to draw conclusions about similar
shapes
Instructor will provide differentiated instruction through any and all of the following strategies:
B
• Readiness/ability
• Adjusting questions
• Compacting Curriculum
• Tiered Assignments
• Acceleration/Deceleration
• Peer teaching
Students will reflect, rethink, revise, and refine by:
C
• Unit self-assessment
• Preparation reflection form
• Work corrections
Resources:
Student Materials:
• Connected Mathematics 2
• Teacher created material
• Graph paper
• Construction paper
• Crayons
• Colored pencils
• Rulers
14
• Calculator
Technology:
• SmartBoard
• Calculators
• Internet websites
Teaching Materials:
• Connected Mathematics 2
• Teacher created material
• SuccessMaker
Teaching Resources:
• Connected Mathematics 2 resource pack
• Teacher created material
• SmartBoard
• Calculator
• SuccessMaker
• Internet websites
15
Hackettstown School District
Mathematics
7th Grade
Mission Statement: Through mathematics, students learn to identify, understand and solve real-world problems
using abstract and quantitative reasoning, existing structures and appropriate tools. Students also learn how to
effectively communicate, model, and critique connections with others.
Stage 1: Desired Results
Topic: The Number System
Domain
CCSS
7.NS.1.
7.NS.2.
Core Content Curriculum Number & Strands
Apply and extend previous understandings of operations with fractions to add, subtract,
multiply, and divide rational numbers.
CCSS Content Statement
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.
Describe situations in which opposite quantities combine to make 0. For example, a hydrogen atom
has 0 charge because its two constituents are oppositely charged.
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.
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.
Apply properties of operations as strategies to add and subtract rational numbers.
Apply and extend previous understandings of multiplication and division and of fractions to multiply
and divide rational numbers.
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.
Understand that integers can be divided, provided that the divisor is not zero, and every quotient of
integers (with non-zero divisor) is a rational number. If p and q are integers, then –(p/q) = (–p)/q
=p/(–q). Interpret quotients of rational numbers by describing real world contexts.
Apply properties of operations as strategies to multiply and divide rational numbers.
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.NS.3.
Solve real-world and mathematical problems involving the four operations with rational numbers.1
Essential Questions
Enduring Understandings
1. How do negative and positive numbers help in Students will understand that:
describing the situation?
1. Positive or negative numbers and their
2. What will integer operations tell about a
opposites are additive inverses.
problem?
2. Commutative Property, Distributive Property
3. What models would help in showing the
and the order of operations makes solving
relationships in the problem situation?
expressions easier.
3. Algorithms for integer operations explain the
relationships between positive and negative
numbers.
16
Knowledge and Skills: (Focus of Instruction)
Students will be instructed on:
1. Using appropriate notation to indicate positive and negative numbers
2. Locating rational numbers on a number line.
3. Comparing and ordering rational numbers.
4. Developing algorithms for all integer operations.
5. Writing mathematical sentences to show relationships.
6. Using fact families to solve simple equations with missing facts.
7. Using order of operations to make computational sequences clear.
8. Applying the Distributive Property to simplify expressions and solve problems.
9. Using positive and negative numbers to graph in four quadrants and to model questions
Learning Expectations/Objectives
st
Integration of 21 Century Skills
Integration of 21st Century Learning
FLEXIBILITY AND ADAPTABILITY
Information Literacy
Adapt to Change
• Access and Evaluate Information
• Adapt to varied roles, jobs responsibilities,
• Access information efficiently (time) and
schedules and context
effectively (sources)
• Work effectively in a climate of ambiguity and
• Evaluate information critically and
changing priorities
competently
Be Flexible
Use and Manage Information
• Incorporate feedback effectively
• Use information accurately and creatively for
• Deal positively with praise, setbacks and
the issue or problem at hand
criticism
• Manage the flow of information from a wide
• Understand, negotiate and balance diverse
variety of sources
views and beliefs to reach workable solutions,
• Apply a fundamental understanding of the
particularly in multi-cultural environments
ethical/legal issues surrounding the access and
INITIATIVE AND SELF-DIRECTION
use of information
Manage Goals and Time
Media Literacy
• Set goals with tangible and intangible success
Analyze Media
criteria
• Understand both how and why media messages
• Balance tactical (short-term) and strategic
are constructed, and for what purposes
(long-term) goals
• Examine how individuals interpret messages
• Utilize time and manage workload efficiently
differently, how values and points of view are
Work Independently
included or excluded, and how media can
• Monitor, define, prioritize and complete tasks
influence beliefs and behaviors
without direct oversight
• Apply a fundamental understanding of the
Be Self-directed Learners
ethical/legal issues surrounding the access and
• Go beyond basic mastery of skills and/or
use of media
curriculum to explore and expand one’s own
learning and opportunities to gain expertise
• Demonstrate initiative to advance skill levels
towards a professional level
• Demonstrate commitment to learning as a
lifelong process
• Reflect critically on past experiences in order
to inform future progress
SOCIAL AND CROSS-CULTURAL SKILLS
Interact Effectively with Others
• Know when it is appropriate to listen and when
to speak
17
•
Conduct themselves in a respectable,
professional manner
Work Effectively in Diverse Teams
• Respect cultural differences and work
effectively with people from a range of social
and cultural backgrounds
• Respond open-mindedly to different ideas and
values
• Leverage social and cultural differences to
create new ideas and increase both innovation
and quality of work
PRODUCTIVITY AND ACCOUNTABILITY
Manage Projects
• Set and meet goals, even in the face of
obstacles and competing pressure
• Prioritize, plan and manage work to achieve
the intended result
Produce Results
• Demonstrate additional attributes associated
with producing high quality products including
the abilities to:
- Work positively and ethically
- Manage time and projects
effectively
- Multi-task
- Participate actively, as well as be
reliable and punctual
- Present oneself professionally and
with proper etiquette
- Collaborate and cooperate
effectively with teams
- Respect and appreciate team
diversity
- Be accountable for results
LEADERSHIP AND RESPONSIBILITY
Guide and Lead Others
• Use interpersonal and problem-solving skills to
influence and guide others toward a goal
• Leverage strengths of others to accomplish a
common goal
• Inspire others to reach their very best via
example and selflessness
• Demonstrate integrity and ethical behavior in
using influence and power
Be Responsible to Others
• Act responsibly with the interests of the larger
community in mind
18
Stage 2: Evidence of Understanding
Hackettstown Benchmarks: (Do or Say)
Students will be able to:
1. Compare rational numbers
2. Apply their understanding of addition, subtraction, multiplication and division to rational numbers.
3. Use order of operations and the distributive property to simplify expressions with rational numbers.
4. Graph coordinates in all four quadrants.
5. Represent and solve real-life situations with rational numbers.
Assessment Methods:
Formative: (On-going)
• Class work
• Homework
• Study Island
• SuccessMaker
• Unit Quizzes
• Partner Quizzes
• Unit Tests
• NJ Ask Mathematics
Summative: (Culminating)
• Unit Project – Dealing Down- Develop strategies to use in a card game using rational numbers
Other Evidence and Student Self-Assessment:
• Student Self-Assessment
o Mathematical Reflections
• Interdisciplinary
o Social Studies – time lines
o Finance – income/debt
o Science - temperature
Stage 3: Learning Plan
To show evidence students may complete the following assessment:
A
• Story creation
Instructor will provide differentiated instruction through any and all of the following strategies:
B
• Readiness/ability
• Adjusting questions
• Compacting Curriculum
• Tiered Assignments
• Acceleration/Deceleration
• Peer teaching
Students will reflect, rethink, revise, and refine by:
C
• Unit self-assessment
• Preparation reflection form
• Work corrections
Resources:
Student Materials:
• Connected Mathematics 2
• Teacher created material
• Graph paper
• Construction paper
• Crayons
19
• Colored pencils
• Rulers
• Calculator
Technology:
• SmartBoard
• Calculators
• Internet websites
Teaching Materials:
• Connected Mathematics 2
• Teacher created material
• SuccessMaker
Teaching Resources:
• Connected Mathematics 2 resource pack
• Teacher created material
• SmartBoard
• Calculator
• SuccessMaker
• Internet websites
20
Hackettstown School District
7TH Grade Mathematics
Mission Statement: Through mathematics, students learn to identify, understand and solve real-world problems
using abstract and quantitative reasoning, existing structures and appropriate tools. Students also learn how to
effectively communicate, model, and critique connections with others.
Stage 1: Desired Results
Topic: Expressions and Equations
Core Content Curriculum Number & Strands
Domain Use properties of operations to generate equivalent expressions.
CCSS
7.EE.1.
7.EE.2.
Domain
CCSS
7.EE.3.
7.EE.4.
CCSS Content Statement
Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions
with rational coefficients.
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. For example, a + 0.05a = 1.05a means that
“increase by 5%” is the same as “multiply by 1.05.”
Core Content Curriculum Number & Strands
Solve real-life and mathematical problems using numerical and algebraic expressions and
equations.
CCSS Content Statement
Solve multi-step real-life and mathematical problems posed with positive and negative rational
numbers in any form (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. For example: If a woman making $25 an hour gets a 10% raise, she will make an
additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a
towel bar 9 3/4 inches long in the center of a door that is 27 1/2 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.
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.
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.
For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?
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. For 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.
21
Essential Questions
1. What relationships are linear?
2. How can a linear relationship be represented?
3. How do you find solutions of linear equations?
Enduring Understandings
Students will understand that:
1. Linear relationships can be modeled by a table,
graph or equation
2. Linear equations can be solved algebraically or
by analyzing a table or graph.
3. Slope of a line represents the rate of change.
Knowledge and Skills: (Focus of Instruction)
Students will be instructed on:
1. Simplifying and rewriting linear expressions.
2. Representing linear relationships in tables, on graphs and as equations.
3. Converting between tables, graphs and linear equations.
4. Solving linear equations and inequalities algebraically.
5. Identifying the slope of a linear equation given a table, graph or equation.
6. Identifying the relationship between real-life problems and slope
Learning Expectations/Objectives
st
Integration of 21 Century Skills
Integration of 21st Century Learning
FLEXIBILITY AND ADAPTABILITY
Information Literacy
Adapt to Change
• Access and Evaluate Information
• Adapt to varied roles, jobs responsibilities,
• Access information efficiently (time) and
schedules and context
effectively (sources)
• Work effectively in a climate of ambiguity and
• Evaluate information critically and
changing priorities
competently
Be Flexible
Use and Manage Information
• Incorporate feedback effectively
• Use information accurately and creatively for
• Deal positively with praise, setbacks and
the issue or problem at hand
criticism
• Manage the flow of information from a wide
• Understand, negotiate and balance diverse
variety of sources
views and beliefs to reach workable solutions,
• Apply a fundamental understanding of the
particularly in multi-cultural environments
ethical/legal issues surrounding the access and
INITIATIVE AND SELF-DIRECTION
use of information
Manage Goals and Time
Media Literacy
• Set goals with tangible and intangible success
Analyze Media
criteria
• Understand both how and why media messages
• Balance tactical (short-term) and strategic
are constructed, and for what purposes
(long-term) goals
• Examine how individuals interpret messages
• Utilize time and manage workload efficiently
differently, how values and points of view are
Work Independently
included or excluded, and how media can
• Monitor, define, prioritize and complete tasks
influence beliefs and behaviors
without direct oversight
• Apply a fundamental understanding of the
Be Self-directed Learners
ethical/legal issues surrounding the access and
• Go beyond basic mastery of skills and/or
use of media
curriculum to explore and expand one’s own
Create Media Products
learning and opportunities to gain expertise
• Understand and utilize the most appropriate
• Demonstrate initiative to advance skill levels
media creation tools, characteristics and
towards a professional level
conventions
• Demonstrate commitment to learning as a
• Understand and effectively utilize the most
lifelong process
appropriate expressions and interpretations in
diverse, multi-cultural environments
22
•
Reflect critically on past experiences in order to ICT Literacy
inform future progress
Apply Technology Effectively
• Use technology as a tool to research, organize,
SOCIAL AND CROSS-CULTURAL SKILLS
evaluate and communicate information
Interact Effectively with Others
• Know when it is appropriate to listen and when
• Use digital technologies (computers, PDAs,
to speak
media players, GPS, etc.),
• Conduct themselves in a respectable,
communication/networking tools and social
professional manner
networks appropriately to access, manage,
integrate, evaluate and create information to
Work Effectively in Diverse Teams
• Respect cultural differences and work
successfully function in a knowledge economy
effectively with people from a range of social
• Apply a fundamental understanding of the
ethical/legal issues surrounding the access and
and cultural backgrounds
• Respond open-mindedly to different ideas and
use of information technologies
values
• Leverage social and cultural differences to
create new ideas and increase both innovation
and quality of work
PRODUCTIVITY AND ACCOUNTABILITY
Manage Projects
• Set and meet goals, even in the face of obstacles
and competing pressure
• Prioritize, plan and manage work to achieve the
intended result
Produce Results
• Demonstrate additional attributes associated
with producing high quality products including
the abilities to:
- Work positively and ethically
- Manage time and projects effectively
- Multi-task
- Participate actively, as well as be
reliable and punctual
- Present oneself professionally and
with proper etiquette
- Collaborate and cooperate
effectively with teams
- Respect and appreciate team
diversity
- Be accountable for results
LEADERSHIP AND RESPONSIBILITY
Guide and Lead Others
• Use interpersonal and problem-solving skills to
influence and guide others toward a goal
• Leverage strengths of others to accomplish a
common goal
• Inspire others to reach their very best via
example and selflessness
• Demonstrate integrity and ethical behavior in
using influence and power
23
Be Responsible to Others
• Act responsibly with the interests of the larger
community in mind
Stage 2: Evidence of Understanding
Hackettstown Benchmarks: (Do or Say)
Students will be able to:
1. Solve linear equations including those with variables on both sides of the equation.
2. Relate tables, equations and graphs to each other.
3. Use linear equations to solve real-life problems.
4. Identify slope and y-intercept given a table, graph, equation or real-life scenario
Assessment Methods:
Formative: (On-going)
• Class work
• Homework
• Study Island
• SuccessMaker
• Unit Quizzes
• Partner Quizzes
• Unit Tests
• NJ Ask Mathematics
Summative: (Culminating)
• Unit Project Ball-bounce project – Collect & analyze data, represent the data on a graph, as a linear
equation, etc
Other Evidence and Student Self-Assessment:
• Student Self-Assessment
o Mathematical Reflections
• Interdisciplinary
o Finance
o Science
o Business
o Entrepreneurism
Stage 3: Learning Plan
To show evidence students may complete the following assessment:
A
• Research linear relationships in life, analyze and compile research
Instructor will provide differentiated instruction through any and all of the following strategies:
B
• Readiness/ability
• Adjusting questions
• Compacting Curriculum
• Tiered Assignments
• Acceleration/Deceleration
• Peer teaching
Students will reflect, rethink, revise, and refine by:
C
• Unit self-assessment
• Preparation reflection form
• Work corrections
24
Resources:
Student Materials:
• Connected Mathematics 2
• Teacher created material
• Graph paper
• Construction paper
• Crayons
• Colored pencils
• Rulers
• Calculator
Technology:
• SmartBoard
• Calculators
• Internet websites
Teaching Materials:
• Connected Mathematics 2
• Teacher created material
• SuccessMaker
Teaching Resources:
• Connected Mathematics 2 resource pack
• Teacher created material
• SmartBoard
• Calculator
• SuccessMaker
• Internet websites
25
Hackettstown School District
Mathematics
7th Grade
Mission Statement: Through mathematics, students learn to identify, understand and solve real-world problems
using abstract and quantitative reasoning, existing structures and appropriate tools. Students also learn how to
effectively communicate, model, and critique connections with others.
Stage 1: Desired Results
Topic: Geometry
Core Content Curriculum Number & Strands
Draw, construct, and describe geometrical figures and describe the relationships between
them.
CCSS
CCSS Content Statement
Solve problems involving scale drawings of geometric figures, including computing actual lengths
7.G.1.
and areas from a scale drawing and reproducing a scale drawing at a different scale.
Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given
7.G.2.
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.
Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane
7.G.3.
sections of right rectangular prisms and right rectangular pyramids.
Core Content Curriculum Number & Strands
Domain
Solve real-life and mathematical problems involving angle measure, area, surface area, and
volume.
CCSS
CCSS Content Statement
Know the formulas for the area and circumference of a circle and use them to solve problems; give
7.G.4.
an informal derivation of the relationship between the circumference and area of a circle.
Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step
7.G.5.
problem to write and solve simple equations for an unknown angle in a figure.
Solve real-world and mathematical problems involving area, volume and surface area of two- and
7.G.6.
three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.
Essential Questions
Enduring Understandings
1. How can real-world situations be represented
Students will understand that:
by scale drawings?
1. Scale drawings can be used to solve real-world
problems
2. How do two- and three-dimensional figures
relate?
2. Formulas can be used to find circumference,
area, volume & surface area of many realworld shapes.
Knowledge and Skills: (Focus of Instruction)
Students will be instructed on:
1. Solving problems involving scale drawings
2. Drawing geometric shapes with given conditions
3. Using area and circumference of a circle to solve problems
4. Using supplementary, complimentary, vertical, and adjacent angles to solve problems
5. Solving problems involving area, volume and surface area of two- and three- dimensional objects
Domain
26
Learning Expectations/Objectives
Integration of 21 Century Skills
Integration of 21st Century Learning
FLEXIBILITY AND ADAPTABILITY
Information Literacy
Adapt to Change
• Access and Evaluate Information
• Adapt to varied roles, jobs responsibilities,
• Access information efficiently (time) and
schedules and context
effectively (sources)
• Work effectively in a climate of ambiguity and
• Evaluate information critically and
changing priorities
competently
Be Flexible
Use and Manage Information
• Incorporate feedback effectively
• Use information accurately and creatively for
• Deal positively with praise, setbacks and
the issue or problem at hand
criticism
• Manage the flow of information from a wide
• Understand, negotiate and balance diverse
variety of sources
views and beliefs to reach workable solutions,
• Apply a fundamental understanding of the
particularly in multi-cultural environments
ethical/legal issues surrounding the access and
INITIATIVE AND SELF-DIRECTION
use of information
Manage Goals and Time
Media Literacy
• Set goals with tangible and intangible success
Analyze Media
criteria
• Understand both how and why media messages
• Balance tactical (short-term) and strategic
are constructed, and for what purposes
(long-term) goals
• Examine how individuals interpret messages
• Utilize time and manage workload efficiently
differently, how values and points of view are
Work Independently
included or excluded, and how media can
• Monitor, define, prioritize and complete tasks
influence beliefs and behaviors
without direct oversight
• Apply a fundamental understanding of the
Be Self-directed Learners
ethical/legal issues surrounding the access and
• Go beyond basic mastery of skills and/or
use of media
curriculum to explore and expand one’s own
Create Media Products
learning and opportunities to gain expertise
• Understand and utilize the most appropriate
• Demonstrate initiative to advance skill levels
media creation tools, characteristics and
towards a professional level
conventions
• Demonstrate commitment to learning as a
• Understand and effectively utilize the most
lifelong process
appropriate expressions and interpretations in
• Reflect critically on past experiences in order
diverse, multi-cultural environments
to inform future progress
ICT Literacy
SOCIAL AND CROSS-CULTURAL SKILLS
Apply Technology Effectively
Interact Effectively with Others
• Use technology as a tool to research, organize,
• Know when it is appropriate to listen and when
evaluate and communicate information
to speak
• Use digital technologies (computers, PDAs,
• Conduct themselves in a respectable,
media players, GPS, etc.),
professional manner
communication/networking tools and social
Work Effectively in Diverse Teams
networks appropriately to access, manage,
• Respect cultural differences and work
integrate, evaluate and create information to
effectively with people from a range of social
successfully function in a knowledge economy
and cultural backgrounds
• Apply a fundamental understanding of the
• Respond open-mindedly to different ideas and
ethical/legal issues surrounding the access and
values
use of information technologies
• Leverage social and cultural differences to
create new ideas and increase both innovation
and quality of work
27
st
PRODUCTIVITY AND ACCOUNTABILITY
Manage Projects
• Set and meet goals, even in the face of
obstacles and competing pressure
• Prioritize, plan and manage work to achieve
the intended result
Produce Results
• Demonstrate additional attributes associated
with producing high quality products including
the abilities to:
- Work positively and ethically
- Manage time and projects
effectively
- Multi-task
- Participate actively, as well as be
reliable and punctual
- Present oneself professionally and
with proper etiquette
- Collaborate and cooperate
effectively with teams
- Respect and appreciate team
diversity
- Be accountable for results
LEADERSHIP AND RESPONSIBILITY
Guide and Lead Others
• Use interpersonal and problem-solving skills to
influence and guide others toward a goal
• Leverage strengths of others to accomplish a
common goal
• Inspire others to reach their very best via
example and selflessness
• Demonstrate integrity and ethical behavior in
using influence and power
Be Responsible to Others
• Act responsibly with the interests of the larger
community in mind
Stage 2: Evidence of Understanding
Hackettstown Benchmarks: (Do or Say)
Students will be able to:
1. Draw and describe geometrical figures and describe the relationships between them.
2. Solve real-life problems involving angle measure, area, surface area and volume
3. Find supplementary, complementary, vertical and adjacent angles.
Assessment Methods:
Formative: (On-going)
• Class work
• Homework
• Study Island
• SuccessMaker
• Unit Quizzes
28
• Unit Tests
• NJ Ask Mathematics
Summative: (Culminating)
• Unit Project: Package Design Contest – students will create packaging that meets criteria, including a
design that uses angles
Other Evidence and Student Self-Assessment:
• Student Self-Assessment
o Mathematical Reflections
• Interdisciplinary
o Business
o Marketing
o Science
Stage 3: Learning Plan
To show evidence students may complete the following assessment:
A
• Evaluate given packaging to minimize surface area and cost
Instructor will provide differentiated instruction through any and all of the following strategies:
B
• Readiness/ability
• Adjusting questions
• Compacting Curriculum
• Tiered Assignments
• Acceleration/Deceleration
• Peer teaching
Students will reflect, rethink, revise, and refine by:
C
• Unit self-assessment
• Preparation reflection form
• Work corrections
Resources:
Student Materials:
• Connected Mathematics 2
• Teacher created material
• Graph paper
• Crayons
• Colored pencils
• Rulers
• Calculator
• Cartoons
• Compasses
• Protractors
• Geometers Sketchpad
• 3-Dimensional Shape Sets
Technology:
• SmartBoard
• Geometers Sketchpad
• Calculators
• Internet websites
29
Teaching Materials:
• Connected Mathematics 2
• Geometers Sketchpad
• Teacher created materials
• SuccessMaker
Teaching Resources:
• Connected Mathematics 2 resource pack
• Teacher created material
• SmartBoard
• Calculator
• SuccessMaker , internet websites
30
Hackettstown School District
Mathematics
7th Grade
Mission Statement: Through mathematics, students learn to identify, understand and solve real-world problems
using abstract and quantitative reasoning, existing structures and appropriate tools. Students also learn how to
effectively communicate, model, and critique connections with others.
Stage 1: Desired Results
Topic: Statistics & Probability
Core Content Curriculum Number & Strands
Domain
Use random sampling to draw inferences about a population.
CCSS
CCSS Content Statement
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
7.SP.1.
sample is representative of that population. Understand that random sampling tends to produce
representative samples and support valid inferences.
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
7.SP.2.
gauge the variation in estimates or predictions. For 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.
Core Content Curriculum Number & Strands
Domain
Draw informal comparative inferences about two populations.
CCSS
CCSS Content Statement
Informally assess the degree of visual overlap of two numerical data distributions with similar
variability, measuring the difference between the centers by expressing it as a multiple of a
measure of variability. For example, the mean height of players on the basketball team is 10 cm
7.SP.3.
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.
Use measures of center and measures of variability for numerical data from random samples to
draw informal comparative inferences about two populations. For example, decide whether the
7.SP.4.
words in a chapter of a seventh-grade science book are generally longer than the words in a
chapter of a fourth-grade science book.
Common Core State Standards
Domain
Investigate chance processes and develop, use, and evaluate probability models.
CCSS
CCSS Content Statement
Understand that the probability of a chance event is a number between 0 and 1 that expresses the
likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near
7.SP.5.
0 indicates an unlikely event, a probability around 1/2 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
7.SP.6.
frequency given the probability. For 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.
31
Develop a probability model and use it to find probabilities of events. Compare probabilities from
7.SP.7.
a model to observed frequencies; if the agreement is not good, explain possible sources of the
discrepancy.
Develop a uniform probability model by assigning equal probability to all outcomes, and use the
model to determine probabilities of events. For 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.
Develop a probability model (which may not be uniform) by observing frequencies in data
generated from a chance process. For 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?
Find probabilities of compound events using organized lists, tables, tree diagrams, and
7.SP.8.
simulation.
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.
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 event.
Design and use a simulation to generate frequencies for compound events. For 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?
Essential Questions
Enduring Understandings
1. What is a random sample and how does it
Students will understand that:
represent a population?
1. Random samples can be used to draw
2. How does the probability of an event occurring
conclusions about a general population.
effect the decisions that we make?
2. Probability is the chance that an event will
occur.
Knowledge and Skills: (Focus of Instruction)
Students will be instructed on:
1. Using random samples to draw inferences about a general population
2. Developing and using probability models based on investigation
3. Finding the probability of simple and compound events
Learning Expectations/Objectives
st
Integration of 21 Century Skills
Integration of 21st Century Learning
FLEXIBILITY AND ADAPTABILITY
Information Literacy
Adapt to Change
• Access and Evaluate Information
• Adapt to varied roles, jobs responsibilities,
• Access information efficiently (time) and
schedules and context
effectively (sources)
• Work effectively in a climate of ambiguity and
• Evaluate information critically and
changing priorities
competently
Be Flexible
Use and Manage Information
• Incorporate feedback effectively
• Use information accurately and creatively for
• Deal positively with praise, setbacks and
the issue or problem at hand
criticism
• Manage the flow of information from a wide
• Understand, negotiate and balance diverse
variety of sources
views and beliefs to reach workable solutions,
• Apply a fundamental understanding of the
particularly in multi-cultural environments
ethical/legal issues surrounding the access and
use of information
32
INITIATIVE AND SELF-DIRECTION
Manage Goals and Time
• Set goals with tangible and intangible success
criteria
• Balance tactical (short-term) and strategic
(long-term) goals
• Utilize time and manage workload efficiently
Work Independently
• Monitor, define, prioritize and complete tasks
without direct oversight
Be Self-directed Learners
• Go beyond basic mastery of skills and/or
curriculum to explore and expand one’s own
learning and opportunities to gain expertise
• Demonstrate initiative to advance skill levels
towards a professional level
• Demonstrate commitment to learning as a
lifelong process
• Reflect critically on past experiences in order
to inform future progress
SOCIAL AND CROSS-CULTURAL SKILLS
Interact Effectively with Others
• Know when it is appropriate to listen and when
to speak
• Conduct themselves in a respectable,
professional manner
Work Effectively in Diverse Teams
• Respect cultural differences and work
effectively with people from a range of social
and cultural backgrounds
• Respond open-mindedly to different ideas and
values
• Leverage social and cultural differences to
create new ideas and increase both innovation
and quality of work
PRODUCTIVITY AND ACCOUNTABILITY
Manage Projects
• Set and meet goals, even in the face of
obstacles and competing pressure
• Prioritize, plan and manage work to achieve
the intended result
Produce Results
• Demonstrate additional attributes associated
with producing high quality products including
the abilities to:
- Work positively and ethically
- Manage time and projects
effectively
- Multi-task
Media Literacy
Analyze Media
• Understand both how and why media messages
are constructed, and for what purposes
• Examine how individuals interpret messages
differently, how values and points of view are
included or excluded, and how media can
influence beliefs and behaviors
• Apply a fundamental understanding of the
ethical/legal issues surrounding the access and
use of media
Create Media Products
• Understand and utilize the most appropriate
media creation tools, characteristics and
conventions
• Understand and effectively utilize the most
appropriate expressions and interpretations in
diverse, multi-cultural environments
ICT Literacy
Apply Technology Effectively
• Use technology as a tool to research, organize,
evaluate and communicate information
• Use digital technologies (computers, PDAs,
media players, GPS, etc.),
communication/networking tools and social
networks appropriately to access, manage,
integrate, evaluate and create information to
successfully function in a knowledge economy
• Apply a fundamental understanding of the
ethical/legal issues surrounding the access and
use of information technologies
33
- Participate actively, as well as be
reliable and punctual
- Present oneself professionally and
with proper etiquette
- Collaborate and cooperate
effectively with teams
- Respect and appreciate team
diversity
- Be accountable for results
LEADERSHIP AND RESPONSIBILITY
Guide and Lead Others
• Use interpersonal and problem-solving skills to
influence and guide others toward a goal
• Leverage strengths of others to accomplish a
common goal
• Inspire others to reach their very best via
example and selflessness
• Demonstrate integrity and ethical behavior in
using influence and power
Be Responsible to Others
• Act responsibly with the interests of the larger
community in mind
Stage 2: Evidence of Understanding
Hackettstown Benchmarks: (Do or Say)
Students will be able to:
1. Use random samples to draw inferences about a general population
2. Find the probability of simple and compound events
3. Determine probability of an outcome based on an experiment
Assessment Methods:
Formative: (On-going)
• Class work
• Homework
• Study Island
• SuccessMaker
• Unit Quizzes
• Unit Tests
• NJ Ask Mathematics
Summative: (Culminating)
• Unit Project Carnival Game project – create a carnival game that meets given criteria, evaluating the
probability of all outcomes
Other Evidence and Student Self-Assessment:
• Student Self-Assessment
o Mathematical Reflections
• Interdisciplinary
o Genetics
o Game Play
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Stage 3: Learning Plan
To show evidence students may complete the following assessment:
A
• Game Evaluation-evaluate the probability of all outcomes of a known game
Instructor will provide differentiated instruction through any and all of the following strategies:
B
• Readiness/ability
• Adjusting questions
• Compacting Curriculum
• Tiered Assignments
• Acceleration/Deceleration
• Peer teaching
Students will reflect, rethink, revise, and refine by:
C
• Unit self-assessment
• Preparation reflection form
• Work corrections
Resources:
Student Materials:
• Connected Mathematics 2
• Teacher created material
• Graph paper
• Crayons
• Colored pencils
• Rulers
• Calculator
• Dice
• Spinners
• Color-coded cubes
• Coins
• Paper cups
Technology:
• SmartBoard
• Calculators
• Internet websites
Teaching Materials:
• Connected Mathematics 2
• Teacher created material
• SuccessMaker
Teaching Resources:
• Connected Mathematics 2 resource pack
• Teacher created material
• SmartBoard
• Calculator
• SuccessMaker
• Internet websites
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Resources:
Student Materials:
• 3-Dimensional Shape Sets
• Calculator
• Cartoons
• Coins
• Color-coded cubes
• Colored pencils
• Compasses
• Connected Mathematics 2
• Construction paper
• Crayons
• Dice
• Geometers Sketchpad
• Graph paper
• Paper cups
• Protractors
• Rulers
• Spinners
• Teacher created material
Technology:
• Calculators
• Geometers Sketchpad
• Internet websites
• SmartBoard
Teaching Materials:
• Connected Mathematics 2
• Geometers Sketchpad
• SuccessMaker
• Teacher created materials
Teaching Resources:
• Calculator
• Connected Mathematics 2 resource pack
• Internet websites
• SmartBoard
• SuccessMaker ,
• Internet websites
• Teacher created material
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