Download Big Idea: Form and Function

Bellmore-Merrick Central High School District
7th Grade Mathematics Curriculum
Written by
Lauren Greco, Patricia Frenz, Julia Motley, Terrence Stamm
Supervised by Jane Boyd, Curriculum Developer
February 2011
Bellmore-Merrick Central High School District
7th Grade Mathematics Curriculum
This curriculum was created using an Understanding by Design format. Topics and content are organized
under Big Ideas to help students transfer understandings.
Contents of each unit:
Big Ideas, Big Questions, Topic, and Suggested Time
Goals as NYS standards
Common Misunderstandings and/or Confusing Concepts
Related Sixth-Grade Standards, Skills/Prior Knowledge
Vocabulary
Additional Resources
Understandings and Essential Questions
What students will know and be able to do
Corresponding Textbook Pages
Contents
Big Ideas and Big Questions
Interpretation – statistics
Prediction – probability
Identity – number theory
Order – order of operations and integers
Finding the Unknown – algebra
The Missing Piece – proportions
The World Around Us – geometry
Input/Output – functions
Textbook: Mathematics Course 2, Holt, Rinehart and Winston, 2008
2
Page
3
7
12
15
21
24
28
33
40
1.
Big Idea
Interpretation
Big Question
What happened?
What’s the best and why?
Topic
Content
2.
Big Idea
Prediction
Big Question
What are the chances?
What do you expect?
Topic
Experimental
Probability
Graphs and
extrapolations
Theoretical
Probability
Best Representation
Statistics
Central TendencyBest Measure
Range
Misleading Graphs
Sampling
Venn Diagram –
Set Theory
3
Content
Probability
Counting Principle
Tree Diagrams
Multiple Events
Compound Events
Independent Versus
Dependent
3.
Big Idea
4.
Identity
Big Idea
Order
Big Question
Where do I belong?
Who am I?
Topic
Content
Big Question
Does order matter?
Topic
Content
Number Sets –
Integers
Rational and Irrational
Primes and Composites
Number
Theory
Perfect Squares and
Roots
Order of
Operations
Integers
Order of
Operations
Evaluating
Expressions
Absolute Value
Least Common Multiple
Greatest Common
Factor
Exponents (beyond the
4 operations)
Scientific Notation
4
Operations with
Integers
(Properties
Without
Variables)
5.
Big Idea
Finding the Unknown
Big Question
Are you a detective?
What’s the “BIG” deal?
Topic
Content
6
Big Idea
The Missing Piece
Big Question
What do you have?
What do you need?
Topic
Content
Expressions
Ratios
Apply Properties
With Variables
Percents
Circle Graphs
Simplify
Algebra
Evaluate
Proportions
Currency
Map Scale
Balance
Conversions
Solving Equations
Solving Inequalities
Plotting Solutions on
a Number Line
Translating
5
Verbal Problems
7.
Big Idea
The World Around Us
8.
Big Idea
Input / Output
Big Question
Where am I going?
Who am I looking for?
How do I get there?
Topic
Content
Big Question
What comes Next?
Topic
Definitions
Coordinate Geometry
Elements of
Geometry
Geometry
Properties of
polygons,
quadrilaterals
Formulas: Area,
Perimeter, Volume,
Surface Area
Angles and
Relationships
Pythagorean
Theorem
6
Content
Functions
Relationships
Algebraic Patterns
Functions
Tables
Sequence
Interior Angles of
Polygon
Big Idea: Interpretation
Big Question: What happened? What’s the best and why?
Topic: Statistics
Suggested Time: 2+ Weeks
Goals (NYS Standards):
7.S.1
7.S.2
7.M.8
7.S.3
7.S.4
7.S.5
7.S.6
7.S.7
7.S.9
7.N.19
Identify and collect data using a variety of methods.
Display data in a circle graph.
Draw central angles in a given circle using a protractor (circle graphs.)
Convert raw data into double bar graphs and double line graphs.
Calculate the range for a given set of data.
Select the appropriate measure of central tendency.
Read and interpret data represented graphically (pictograph, bar graph, histogram, line graph, double line/bar graphs, or circle graph.)
Identify and explain misleading statistics and graphs.
Determine the validity of sampling methods to predict outcomes.
Justify the reasonableness of answers using estimation.
Common Misunderstandings and/or Confusing Concepts:




Students do not order numbers when finding median.
Students do not know when to add or subtract data in Venn Diagrams.
Students do not determine the most appropriate graph for data.
Range is not a measure of central tendency.
Additional Resources: http://www.jmap.org/
http://www.shodor.org/interactivate/lessons/IntroStatistics/
http://go.hrw.com/gopages/ma.html
http://www.kutasoftware.com/free.html
http://www.nysedregents.org/Grade7/Mathematics/home.html
7
Related Sixth-grade Standards
Skills/Prior Knowledge
6.N.21 Find multiple representations of rational numbers
(fractions, decimals, and percents 0 to 100)
6th May-June
6.S.1 Develop the concept of sampling when collecting
data from a population and decide the best method to
collect data for a particular question.
6.S.2 Record data in a frequency table.
6.S.3 Construct Venn diagrams to sort data
6.S.4 Determine and justify the most appropriate graph to
display a given set of data (pictograph, bar graph, line
graph, histogram, or circle graph.)
Vocabulary:
histogram, pictograph, bar graph, line graph, circle graph,
frequency table, mean, median, mode, range, outlier,
population, sample, estimation
Content
Goals
6th May-June:
6.S.1
Develop the
concept of
sampling when
collecting data
from a population
and decide the best
method to collect
data for a
particular question.
Understandings
Students will understand that:
There must be certain
validity to sampling.
A person’s opinion and/or
the results of collection data
could be swayed by how a
question is asked or data is
collected.
7.S.1
Identify and collect There must be a certain
validity to sampling to make
data using a
variety of methods. valid predictions.
Essential
Questions
Know
Do
Students will know:
Students will be able to:
What makes a survey What the best
valid?
representative sample for
a desired population
would be.
Where can you find
a representative
sample?
Is this a good
prediction?
Methods for collecting
data such as surveys and
counting.
What constitutes a valid
sample.
7.S.9
Determine the
validity of
sampling methods
to predict
outcomes.
6th May-June
6.S.2 Record data
in a frequency
table.
Frequency tables can be used
to organize and study data.
What advantages are
there to using a
frequency table?
412-415
Identify factors that
determine if a survey is
biased/unbiased.
Determine the validity of a
given sample.
Justify the validity of the
sampling method over
another.
How to organize data into Find patterns and make
a frequency table and how predictions using a frequency
to read the table.
table.
That frequency can be
represented in a fraction
form for comparison.
8
Conduct a survey that will
lead to a legitimate study.
Textbook:
Represent frequency in
fraction form to compare and
analyze.
376
Content
Goals
6th May-June
6.S.4
Determine and
justify the most
appropriate graph
to display a given
set of data
(pictograph, bar
graph, line graph,
histogram, or
circle graph.)
7.S.6
Read and interpret
data represented
graphically
(pictograph, bar
graph, histogram,
line graph, double
line/bar graphs, or
circle graph.)
7.S.3
Convert raw data
into double bar
graphs and double
line graphs.
Understandings
Students will understand that:
Essential
Questions
Know
Do
Students will know:
Students will be able to:
The type of graph used
depends on the data being
displayed.
What graph would
best display a set
data?
The criteria to determine
the appropriate graph to
display a set of data.
Data can be represented in
various ways.
Do you like to read
or look at pictures?
How to convert data into
and read various types of
graphs.
The relationships
represented graphically help
to read and interpret data.
Data can be organized and
represented in the form of a
double line/bar graph.
What information
can you get from
looking at a picture?
Can you make a
picture of this data
set?
How to read and interpret
various graphs including
understanding keys, the
information given in titles
and labels, and how to
accurately read scales.
Steps to converting a set
of data onto a graph.
The process of
constructing a graph
starting at 0 with an
appropriate scale and
include a key.
The criteria which
determines that a graph is
double line or double bar.
9
Convert data into and read
various types of graphs.
Textbook:
386,402
408-411
Choose and transform a data
set into an appropriate graph.
Justify the type of graph used
to represent data.
Draw conclusions based upon
analyzing different graphs.
386-387,
403,408
Extrapolate statistics from a
graph in response to specific
questions asked in a verbal
problem.
Construct a graph starting at 0 388,
given a data set.
402-405
Content
Goals
6th May-June
6.S.3
Construct Venn
diagrams to sort
data
“Circle Graphs”
can be taught here
or with “The
World Around
Us”
7.S.2
Display data in a
circle graph.
Understandings
Students will understand that:
A Venn Diagram is a method
of organizing data to
compare and contrast.
10
Why would one use
a Venn Diagram to
display data?
Data in the form of percents
is best displayed using a
circle graph.
What graph would
best display a set
data?
Proportions are used to
convert data to percents and
organize the data using a
circle graph.
Can a circle graph be
used when data is
not in percent form?
7.M.8
Draw central
angles in a given
circle using a
protractor (circle
graphs.)
7.S.4
Calculate the
range for a given
set of data.
Essential
Questions
Know
Do
Students will know:
Students will be able to:
The meaning of the
components of a Venn
Diagram and strategies
for interpreting a Venn
Diagram.
A method for organizing
data in a Venn Diagram.
A circle graph is used to
show percents.
Strategies for reading and
drawing conclusions from
a circle graph.
A procedure for
converting raw data to a
percent.
To find the percent of
360º for each central
angle.
Organize a given data set into
a Venn Diagram and draw
conclusions from the results.
Textbook:
398-399
Solve verbal problems using
data from a Venn Diagram.
Make decisions based upon
data represented in the form
of a circle graph.
408-411
Construct a circle graph with
data given in the form of
percents, fractions, or raw
data.
464
Calculate range and use range
to draw conclusions about a
sample.
381
The proper use of a
protractor to create a
circle graph.
The concept of range helps
to visualize the spread of the
data.
Is range a measure of The definition of range
central tendency?
and how it is calculated.
What range means in
relation to understanding
a set of data.
Content
Goals
7.S.5
Select the
appropriate
measure of central
tendency.
7.S.7
Identify and
explain misleading
statistics and
graphs.
Understandings
Students will understand that:
Determining central
tendency helps to analyze
data.
Essential
Questions
Is there a “best”
measure of central
tendency?
One means of determining
central tendency may give a
truer picture of the data than
another.
How statistics can be used to
manipulate what you want
others to perceive / believe.
That graphs can misrepresent
information.
Know
Do
Students will know:
Students will be able to:
The meaning of “central
tendency.”
Calculate mean, median, and
mode.
The meaning of each of
the measures of central
tendency.
Draw conclusions from the
measures of central tendency.
Methods to calculate
mean, median, and mode.
Do you believe
everything you read?
How an outlier affects
data.
Can you believe
everything you see?
The reasoning necessary
to determine the measure
that best describes the
data set.
The characteristics of
misleading graphs and
why they are inaccurate.
7.N.19
Justify the
reasonableness of
answers using
estimation.
11
Estimating first helps to
determine the validity of
calculations.
Does this make
sense?
To make estimations
based upon statistics
before calculating
Textbook:
382
Defend a decision when
choosing the most appropriate
measure of central tendency.
Choose an appropriate
measure of central tendency
for a given data set and
justify the decision.
383
Analyze misleading graphs
422
and be able to determine what
characteristic made it
misleading.
Discuss when society may
use a graph that is actually
misleading.
Validate or disregard
estimations.
385
Idea: Predictions
Big Question: What are the chances? What do you expect?
Topic: Probability
Suggested Time: 5-7 Days
Goals (NYS Standards):
7.S.8
7.S.9
7.S.10
7.S.11
7.S.12
7.N.19
Interpret data to provide the basis for predictions and to establish experimental probabilities.
Determine the validity of sampling methods to predict outcomes.
Predict the outcome of an experiment.
Design and conduct an experiment to test predictions.
Compare actual results to predicted results.
Justify the reasonableness of answers using estimation.
Common Misunderstandings and/or Confusing Concepts:





If I flip a coin 50 times, I will get heads 25 times and tails 25 times.
Probability is measured between 1 and 100.
Students will add fractions when they are supposed to multiply them and vice versa.
Students cannot distinguish between single and multiple events.
Students lack pre-requisite understanding of fractions.
Related Sixth-grade Standards
Skills/Prior Knowledge
6. N.16 Add and subtract fractions with unlike
denominators.
6.N.17 Multiply and divide fractions with unlike
denominators.
6.S.9 List possible outcomes for compound events.
6.S.10 Determine the probability of dependent events
6.S.11 Determine the number of possible outcomes for a
compound event by using the fundamental counting
principle and use this to determine the probabilities of
events when the outcomes have equal probability.
Additional Resources:
Vocabulary:
http://www.jmap.org/
http://www.nysedregents.org/Grade7/Mathematics/home.html
http://www.kutasoftware.com/free.html
http://go.hrw.com/gopages/ma.html
Probability, dependent events, independent events,
experiment, experimental probability, outcome, sample
space, theoretical probability
12
Content
Goals
7.S.8
Interpret data to
provide the basis
for predictions and
to establish
experimental
probabilities.
7.S.9
Determine the
validity of
sampling methods
to predict
outcomes.
7.S.10
Predict the
outcome of an
experiment.
7.S.11
Design and
conduct an
experiment to test
predictions.
Continue with
7.S.12 on next
page
13
Understandings
Students will understand that:
The experimental probability
of an event is not always
what is theoretically
expected.
Essential
Questions
What makes a
prediction more
reliable?
Know
Do
Students will know:
Students will be able to:
Past experiences are
useful in predicting
future outcomes.
Use probability to calculate a
prediction.
Textbook:
632, 644
Draw reasonable conclusions
from valid sample spaces.
That creating a sample space
will allow them to visualize
all of the possible outcomes.
What makes a
sample space valid?
What constitutes a
valid sample space and
make predictions from
the sample space.
The experimental probability
of an event is not always
what is theoretically
expected.
How is your
expectation different
from the actual
result?
How to use
experimental
probability to make
reasonable predictions.
Is it possible to flip 5
heads in a row?
A strategy to make
reasonable predictions
based upon the patterns
of results from an
experiment.
Over time, the “law of large
numbers” will prevail
(experimental probability
approaches theoretical
probability with a trial
increase).
How does theoretical
and experimental
probability compare
and contrast?
The probability of
multiple events can be
predicted. (and / or)
Specific outcomes
and/or the total number
of outcomes can be
determined.
636, 412
Use experiments to calculate
reasonable predictions.
Conduct valid experiments to
test predictions.
633
644
Content
Goals
Understandings
Students will understand that:
7.S.12
Compare actual
results to predicted
results.
Actual results can vary from
predicted results.
7.N.19
Justify the
reasonableness of
answers using
estimation
The answer they get should
be reasonable.
14
Probability is not an “exact
science.”
Essential
Questions
Know
Do
Students will know:
Students will be able to:
Textbook:
How is your
expectation different
from the actual
result?
Events can be certain,
impossible, likely,
unlikely or as likely as
not.
Make inferences based upon
their expected and actual results.
632, 648
What is going on?
Answers should be
logical based on their
estimated answer.
Estimate to come up with a
reasonable answer.
633
Does this make
sense?
Big Idea: Identity
Big Question: Where do I belong? Who am I?
Topic: Number Theory
Suggested Time: 3 ½ weeks
Goals (NYS Standards):
7.N.1 Distinguish between the various subsets of real numbers (counting/natural numbers, whole, integers, rational numbers, and irrational
numbers)
7.N.2 Recognize the difference between rational and irrational numbers (e.g., explore different approximations of  )
7.N.3 Place rational and irrational numbers (approximations) on a number line and justify the placement of the numbers
7.N.4 Develop the laws of exponents for multiplication and division
7.N.5 Write numbers in scientific notation
7.N.6 Translate numbers from scientific notation into standard form
7.N.7 Compare numbers written in scientific notation
7.N.8 Find the common factors and greatest common factor of two or more numbers
7.N.9 Determine multiples and least common multiple of two or more numbers
7.N.10 Determine the prime factorization of a given number and write in exponential form
7.N.14 Develop a conceptual understanding of negative and zero exponents with a base of ten and relate to fractions and decimals
(e.g., 10-2 = .01 = 1/100)
7.N.15 Recognize and state the value of the square root of a perfect square (up to 225)
7.N.16 Determine the square root of non-perfect squares using a calculator
7.N.17 Classify irrational numbers as non-repeating/non-terminating decimals
7.N.18 Identify the two consecutive whole numbers between which the square root of a non-perfect square, whole number less than 225 lies
(with and without the use of a number line)
7.N.19 Justify the reasonableness of answers using estimation
15
Common Misunderstandings and/or Confusing Concepts:








16
Square roots vs. perfect square
Factors vs. multiples
3.14 is 
3.14 is irrational
A negative exponent yields a negative number
The exponent in scientific notation is the amount of zeros in the number
Last decimal place on the calculator is always right.
Estimation is rounding the answer
Related Six-grade Standards
Skills/Prior Knowledge

Recognizing place value (Fifth-grade Standard)
6.N.1 Read and write whole numbers to trillions
6.N.14 Locate rational numbers on a number line
(including positive and negative)
6.N.15 Order rational numbers (including positive and
negative)
6.N.20 Represent fractions as terminating or repeating
decimals
6.N.21 Find multiple representations of rational
numbers (fractions, decimals, and percents 0 – 100)
6.N.23 Represent repeated multiplication in exponential
form
6.N.24 Represent exponential form as repeated
multiplication
6.N.27 Justify the reasonableness of answers using
estimation (including rounding)
Additional Resources:
Vocabulary:
http://www.purplemath.com/modules/factnumb.htm
www.coolmath.com/prealgebra/04-exponents/index.html (Exponent games)
http://www.mathplayground.com/howto_gcflcm.html (GCF LCM Video)
http://www.quia.com/pop/37541.html (rational and irrational quiz)
Compare, Composite Numbers, Consecutive, Counting
Numbers, Difference, Equivalent, Exponent, Exponential
form, Factor, GCF, Integers, Irrational, LCM, Multiple,
Natural number, Non-perfect square , Non-terminating
decimal, Number line Order, Perfect Square, Pi, Prime
Numbers, Prime Factorization, Product, Rational
Numbers, Real Numbers, Repeating decimal, Scientific
Notation, Square root, Subset, Sum, Standard form,
Terminating decimal, Translate, Whole Numbers.
Content
Goals
7.N.1
Distinguish between
the various subsets of
real numbers
(counting/natural
numbers, whole
numbers, integers,
rational numbers, and
irrational numbers)
7.N.2
Recognize the
difference between
rational and irrational
numbers (e.g., explore
different
approximations of  )
Understandings
Students will understand that:
A number can be classified
in more than one way.
Essential
Questions
7.N.3
Place rational and
irrational numbers
(approximations) on a
number line and
justify the placement
of the numbers
17
Do
Students will be able to:
Textbook
Can a number have
multiple identities?
The difference between
the subsets of real
numbers.
Classify numbers into the
appropriate subset of real
numbers and give reasoning.
Skills
Bank: 779
Can an irrational
number be placed on
a finite number line?
The difference between
rational and irrational.
Identify a number as rational
or irrational and explain why.
129
562
Mathematics is a language
which allows us to
communicate more
precisely and effectively.
A rational number can be
expressed as a fraction.
Skills
Bank: 779
7.N.17
Classify irrational
numbers as nonrepeating/nonterminating decimals
Know
Students will know:
Irrational numbers go on
forever.
Irrational numbers are
unpredictable – you never
know what comes next.
How far can
numbers go?
That an irrational number
cannot be written as a
fraction.
Recognize irrational numbers.
Where rational and
irrational numbers are
located on the number
line.
Properly place rational and
irrational numbers on the
number line.
Content
Goals
Understandings
Students will understand that:
Essential
Questions
Know
Do
Students will know:
Students will be able to:
Textbook
7.N.15
Recognize and state the
value of the square root
of a perfect square (up
to 225)
7.N.16
Determine the square
root of non-perfect
squares using a
calculator
There is a relationship
between squaring a number
and taking it’s square root.
What makes a square The square roots of
“perfect?”
perfect squares up to 225.
7.N.18
The square root of nonperfect squares is an
irrational number that is
not finite.
7.N.4
Develop the laws of
exponents for
multiplication and
division
Rules are used for
consistency in math.
18
Exponent rules can be
discovered through
understanding of
mathematical
abbreviations.
550
The calculator strokes for
finding the square root of
a non-perfect square.
The square root of nonperfect squares lie between
two consecutive whole
numbers.
Identify the two
consecutive whole
numbers between which
the square root of a nonperfect square, whole
number less than 225
lies (with and without
the use of a number
line)
Find the square root of a nonperfect square using a
calculator.
Is there a difference
between finding the
square of a number
and finding its
square root?
Can numbers be
represented multiple
ways?
Which 2 whole numbers
non-perfect squares fall
between.
Use perfect squares to
estimate the square roots of
non-perfect squares.
How to find and estimate
square roots of numbers.
The basis for the laws of
exponents and use them
to simplify expressions.
Discover and create the laws
of exponents for
multiplication and division.
Multiply and divide
exponents with the same base
and be able to express them
in exponential form,
expanded and standard form.
Skills
Bank: 780
Content
Goals
7.N.14
Develop a conceptual
understanding of
negative and zero exp.
with a base of ten
7.N.5
Write numbers in
scientific notation
7.N.6
Translate numbers from
scientific notation into
standard form
Understandings
Students will understand that:
Negative and zero
exponents relate to what
happens when the laws of
exponents are applied.
Very large or very small
numbers are commonly
written in scientific
notation for ease of use.
Essential
Questions
Can you see a
pattern?
Can the same
number have a
different look?
5
What does 10
actually mean?
7.N.7
7.N.10
Determine the prime
factorization of a given
number and write in
exponential form
19
Do
Students will be able to:
How to rewrite numbers
with negative exponents.
Evaluate negative exponents
by
 By rewriting them
When a whole number
using a fraction with a
has a negative exponent,
positive exponent
the value of the power is
 As a decimal.
less than 1.
The format of a number
written in scientific
notation.
A strategy to translate
numbers from scientific
notation and standard
form and vise versa.
Know the meaning of the
exponents to compare
numbers written in
scientific notation.
Compare numbers
written in scientific
notation
Divisibility Rules/Prime
& Composite # Review
Know
Students will know:
Any composite number can How do you prove a
be expressed as the product number’s prime?
of its prime factors.
How do you know a
number is factored
completely?
How to break a number
down into its factors
using a tree or other
method.
What is meant by
exponential form (number
expressed as a product of
prime factors)
Translate numbers from
scientific notation and
standard form and vise versa.
Textbook
134
18
Compare and order numbers
written in scientific notation.
Analyze and work with
numbers in scientific notation
within verbal problems and/or
charts.
Express a number as the
product of prime factors in
exponential form.
Skills
Bank: 767
106
Content
Goals
Understandings
Students will understand that:
A number has a limited
Find the common factors amount of factors.
7.N.8
Essential
Questions
Can a number have
unlimited factors?
and greatest common
factor of two or more
numbers
Know
Do
Students will know:
Students will be able to:
How to find the common
factors of two or more
numbers using methods
such as: rainbow listing,
cake method, or prime
factorization.
A common factors is a
number that “goes into”
the original numbers
7.N.9
Determine multiples
and least common
multiple of two or more
numbers
7.N.19
Justify the
reasonableness of
answers using
estimation
20
A number has an unlimited
amount of multiples.
For estimation to work, it
must be done before the
actual answer is calculated.
The calculated answer
should be reasonable when
compared t the estimate.
Can a number have
unlimited multiples?
Does this make
sense?
Determine the greatest
common factor of two or
more numbers
Textbook:
110
Describe the difference
between a factor and a
multiple.
A strategy for finding the
multiples of numbers.
Determine the least common
multiple of two or more
numbers.
A multiple starts with the
original number and
expands.
Describe the difference
between a factor and a
multiple.
To estimate before they
calculate.
Estimate to come up with a
reasonable answer.
Answers should be logical Compare their original
based on their estimated
estimated answer with the
answer.
calculation to determine
reasonableness.
114
Big Idea: Order
Big Question: Does order matter?
Topic: Order of Operations and Integers
Suggested Time: 7-10 days
Goals (NYS Standards):
7.N.11 Simplify expressions using order of operations
Note: Expressions may include absolute value and/or integral exponents greater than 0.
7.N.12 Add, subtract, multiply, and divide integers
7.N.13 Add and subtract two integers
(with and without the use of a number line)
7.N.19 Justify the reasonableness of answers using estimation
Common Misunderstandings and/or Confusing
Concepts:





Multiplication always comes before division when
evaluating expressions.
Absolute value is the opposite (inverse) of the value.
Larger negative digits have a greater value than lower negative
digits (-5> -1).
Parentheses designate the distributive property.
Students see parenthesis and try to do something with them
first even if there is no operation inside of them (-5).
Related Sixth-grade Standards
Skills/Prior Knowledge
6.N.2 Define and identify the commutative and associative properties of
addition and multiplication
6.N.3 Define and identify the distributive property of multiplication over
addition
6.N.4 Define and identify the identity and inverse properties of addition
and multiplication
6.N.5 Define and identify the zero property of multiplication
6.N.13 Define absolute value and determine the absolute value of rational
numbers (including positive and negative)
6.N.19 Identify the multiplicative inverse (reciprocal) of a number
6.N.22 Evaluate numerical expressions using order of operations (may
include exponents of two and three)
Additional Resources:
Vocabulary:
Integer PowerPoint website: http://math.pppst.com/integers.html
Website for worksheets:
http://math.about.com/
Order of Operation Games:
http://www.shodor.org/interactivate/activities/
Textbook online: http://my.hrw.com Chapter 2 Integers
SMART Notebook – Search: Number line
Absolute value, Difference, Integers, Justify, Order of Operations, Product,
Quotient, Simplify, Sum, Evaluate, Opposites, Inverses, Multiplicative
Inverse, Reciprocal
21
Content
Goals
7.N.12
Add, subtract,
multiply, and
divide integers
7.N.13
Add and subtract
two integers
(with and without
the use of a
number line)
7.N.11
Simplify
expressions using
order of operations
Note: Expressions
may include
absolute value
and/or integral
exponents greater
than 0.
Understandings
Students will understand that:
Specific rules can be
developed and applied for
integer operations.
There are multiple
representations for integers
and operations.
The number line can be used
to conceptualize adding and
subtracting integers.
The set of rules, the order of
operations, allows you to
evaluate an expression in a
logical manner.
Each property (identity,
commutative, associative,
zero, inverse, and
distributive) serves a specific
purpose when evaluating an
expression.
The product of multiplicative
inverses (reciprocals) will
always be one.
The sum of additive inverses
will always be zero.
22
Essential
Questions
Know
Do
Students will know:
Students will be able to:
Vocabulary related to
Does money grow on the representation of
trees?
integers. Ex: below,
gain, profit, loss,
withdraw decrease,
Do good things
deposit, exceed…
always happen to
good people?
The application of the
integer rules to the
correct operations in
the expressions.
Does your calculator
follow the rules for
the order of
operations?
What difference do
parentheses make?
Can you put on your
shoes before your
socks?
What happens if you
don’t follow a
logical order?
The number line and
other representations
can be used to add and
subtract integers.
The specific order that
expressions must be
evaluated in.
Absolute value of an
integer is the distance
from zero.
Each term inside the
parenthesis can be
multiplied by the
coefficient.
The properties
(identity, commutative,
associative, zero,
inverse, and
distributive).
Apply the rules of integer
operations.
Recognize the additive inverse
in a given problem.
Textbook:
82
88
94
Use the number line to add and
subtract integers.
Add and subtract integers using
the rules they develop from the
number line.
Justify the procedure to perform
operations with integers.
Evaluate an expression using
the correct order of operations.
Find the absolute value of an
integer.
Compare integers.
Compare absolute values of
integers.
Apply properties to manipulate
an expression.
23
28
Content
Goals
7.N.19
Justify the
reasonableness of
answers using
estimation
23
Understandings
Students will understand that:
The answer they get should
be reasonable.
Essential
Questions
What is going on?
Does this make
sense?
Know
Do
Students will know:
Students will be able to:
Answers should be
logical based on their
estimated answer.
Estimate to come up with a
reasonable answer.
Textbook:
163
389
Big Idea: Finding the Unknown
Big Question: Are you a detective? What’s the BIG deal?
Topic: Algebra
Suggested Time: 2-3 Weeks
Goals (NYS Standards):
7.A.1 Translate two-step verbal expressions into algebraic expressions
7.A.2 Add and subtract monomials with exponents of one
7.A.3 Identify a polynomial as an algebraic expression containing one or more terms
7.A.4 Solve multi-step equations by combining like terms, using the distributive property, or moving variables to one side of the equation
7.A.5 Solve one-step inequalities (positive coefficients only)
7.A.6 Evaluate formulas for given input values (surface area, rate, and density problems)
7.G.10 Graph the solution set of an inequality (positive coefficients only) on a number line
Common Misunderstandings and/or Confusing Concepts:








Minus and negative are two different things
Solving equations by trial and error (substitution)
Expressions can be solved
Distribute only to the first term
Meaning of operation keywords (difference, quotient, “from”, etc)
Application of inverse operations
Meaning of inequality symbols
Typical multi-step error:
2x - 5 - 7x = 13
+7x
+ 7x
9x - 5 = 13
Additional Resources:
http://www.bbc.co.uk/education/mathsfile/shockwave/games/equationma
tch.html
24
Related Sixth-grade Standards
Skills/Prior Knowledge
6.N.1 Understand the multiplicative inverse (reciprocal) of a number
6.A.2 Use substitution to evaluate algebraic expressions (may
include exponents of one, two and three
6.A.3 Translate two-step verbal sentences into algebraic equations
6.A.4 Solve and explain two-step equations involving whole
numbers using inverse operations
Vocabulary:
Additive Inverse, Multiplicative Inverse, Algebra, Algebraic
Expression, Algebraic Equations, Algebraic Inequality, Algebraic
Relationship, Coefficient, Combining Like Terms, Equation,
Expression, Evaluate, Inequality, Solution, Term, Verbal Expression,
Constant, Variable, Substitute, Solve, One-Step Equation, Two-Step
Equation, Multi-Step Equation, Simplify, Order of Operations
Content
Goals
7.A.1
Translate two-step
verbal expressions
into algebraic
expressions
7.A.2
Add and subtract
monomials with
exponents of one
7.A.3
Identify a polynomial
as an algebraic
expression containing
one or more terms
Understandings
Students will understand that:
Vocabulary is essential to
communicating.
There are many words that
mean add, subtract, multiply
or divide.
Terms can take different
forms within an expression
or equation.
The concept of “like terms”
allows for terms to be
manipulated and/or
combined within
expressions and equations.
An expression is in simplest
form when there are no like
terms left to be combined.
Essential
Questions
Is Math a language?
or
How is Math a
language?
Know
Do
Students will know:
Students will be able to:
Verbal – operation
equivalents and how to
translate verbal phrases
into algebraic expressions.
That an expression is a
mathematical phrase that
contains operations,
numbers, and/or variables.
Like terms are terms with
How are they “like”? the same variable raised to
the same exponent or terms
with no variable at all.
That to simplify an
expression is to combine
like terms.
A polynomial is an
algebraic expression
containing one or more
terms.
The vocabulary related to
classifying a polynomial by
the number of terms.
Combining like terms
means to add or subtract
coefficients.
25
Translate a verbal phrase
into an algebraic
expression.
Identify terms that are
“like”.
Simplify expressions by
combining like terms.
Classify given
polynomials.
Textbook
38, 75
42, 781
Content
Goals
7.A.4
Solve multi-step
equations by
combining like terms,
using the distributive
property, or moving
variables to one side
of the equation
Understandings
Students will understand that:
Essential
Questions
There is a difference
between an expression and
an equation.
What role does
balance play in
solving equations?
Algebra is not done by trial
and error but by a logical set
of steps.
What is a solution?
Mathematical properties are
necessary for solving
equations (e.g. distributive,
inverse, identity, etc).
The distributive property
changes the order of
operations when solving
equations (“breaks the
power” of the parenthesis).
How do we know if
we have the right
solution?
Is there more than
one way to solve an
equation?
Know
Do
Students will know:
Students will be able to:
To evaluate expressions
using substitution.
The order for solving
multi-step equations could
include distributing,
combining like terms, using
inverse properties to
manipulate the terms, and
finally solving for the
variable.
Equations have a finite
solution set.
Does order matter?
The solution is the value of
the variable that makes the
equation true.
“Evaluate formulas” Equations must maintain
can be taught here or balance.
with “The World
Around Us” geometry
To use substitution to
verify the truth of the
solution.
7.A.6
Evaluate formulas for
given input values
(surface area, rate,
and density problems)
To recognize the correct
values for formula
substitution.
26
Explain the difference
between an expression and
an equation.
Textbook
676, 682,
686
Demonstrate the algebraic
process necessary to arrive
at a solution.
Solve multi-step equations
by following a logical set
of steps.
Explain the process used to
solve any given multi-step
equation.
Evaluate equation for the
solution.
Formulas
Evaluate any formula given 711
certain values.
Content
Goals
7.A.5
Solve one-step
inequalities (positive
coefficients only)
7.G.10
Graph the solution set
of an inequality
(positive coefficients
only) on a number
line
Understandings
Students will understand that:
Essential
Questions
Inequalities are solved in the
same manner as solving an
equation.
How do inequalities
and equations
compare?
That there are an infinite
number of solutions to an
inequality.
Is there ever a time
where you can have
more than one
solution?
What role does
balance play in
solving inequalities?
Know
Do
Students will know:
Students will be able to:
To apply inverse
properties to solving
one-step inequalities
(positive coefficients
only).
Graph the solution set of
inequalities and justify.
That whatever is done
to one side of the
Choose appropriate numbers
inequality must be done within and outside the solution
to the other side in
set to check for truth.
order to maintain truth.
The solutions are the
values of the variable
that make the
inequality true.
Inequalities have an
infinite solution set.
The solution set of an
inequality can be
represented on a line
graph with the use of
arrows and open/closed
points.
The relationship
between the symbols,
>, <, ≤, and ≥ , and
their representation on
a line graph.
27
Solve one-step inequalities
(positive coefficients only).
Explain why an inequality has
more than one solution.
Explain the process used to
solve any given inequality.
Textbook
692
Big Idea: The Missing Piece
Big Question: What do you have? What do you need?
Topic: Proportions
Suggested Time: 8 – 10 Days
May-June Suggested Time: 8 Days
Goals (NYS Standards):
7.M.2
7.M.3
7.M.4
7.M.9
Convert capacities and volumes within a given system
Identify customary and metric units of mass
Convert mass within a given system
Determine the tool and technique to measure with an appropriate
level of precision: mass
7.M.10 Identify the relationship between relative error and magnitude
when dealing with large numbers (e.g., money, population)
7.M.12 Determine personal references for customary/metric units of mass
7.M.13 Justify the reasonableness of the mass of an object
Common Misunderstandings and/or Confusing Concepts:







28
The best buy is the one with the most units
Rounding to the cents place means rounding to the hundredths place, not
the tenths place
A proportion has to be organized in a specific way
How the information is presented in the problem is not necessarily the
order it is placed in the proportion
Divide units by cost
A big unit equals a big measurement
Kilo means big!
May-June
7.M.1
7.M.5
7.M.6
7.M.7
Calculate distance using a map scale
Calculate unit price using proportions
Compare unit prices
Convert money between different currencies with the use
of an exchange rate table and a calculator
Related Sixth-grade Standards
Skills/Prior Knowledge
 Using a ruler to measure distances
 Choosing an appropriate scale for a situation
6.N.6 Understand the concept of rate
6.N.7 Express equivalent ratios as a proportion
6.N.8 Distinguish the difference between rate and
ratio
6.N.9 Solve proportions using equivalent fractions
6.A.5 Solve simple proportions within context
6.M.2 Identify customary units of capacity (cups,
pints, quarts, and gallons)
6.M.3 Identify equivalent customary units of capacity
(cups to pints, pints to quarts, quarts to gal)
6.M.4 Identify metric units of capacity (l and ml)
6.M.5 Identify equivalent metric units of capacity
(milliliter to liter and liter to milliliter
Additional Resources:
Vocabulary:
Sites:
http://en.wikipedia.org/wiki/Approximation_error
http://en.widipedia.org/wiki/Large_numbers#Large_numbers_in_the_everyday_
world
http://www.x-rates.com/calculator.html (Foreign currency calculator)
Algebra, Algebraic Solution, Calculate,
Equation, Equivalent ratios, Equivalent Fractions, Evaluate,
Exchange rates, Extremes, Magnitude, Map scale, Mathematical
solutions, Means of a proportion, Proportion, Proportional
reasoning, Ratio, Relative Error, Scale Drawing
29
Content
Goals
Understandings
Students will understand that:
Essential
Questions
Know
Do
Students will know:
Students will be able to:
Textbook
7.M.12
Determine
personal
references for
customary/metric
units of mass
Real life references can be
used for metric and
customary conversions.
Can any part of you
be used as a
reference for a unit
of measurement?
The personal references
for customary/metric units
of mass.
Use personal references to
approximate
customary/metric units of
mass.
14
292
7.M.2
Convert capacities
and volumes with
a given system
Equal does not always look
the same.
When do we use a
proportion?
Recognize when a
comparison is made in a
word problem.
14-17
Proportions can organize
information in a meaningful
way.
Is there only one
way to solve a
proportion?
How to write ratios in
three different ways
( :, fraction, “to”) and
when a fourth way is
appropriate,
e.g. … out of.
7.M.3
Identify
customary and
metric units of
mass
7.M.4
Convert mass
within a given
system
Capacities, volumes and mass Is there more than
can be expressed in multiple
one way to state a
units with a given system.
measurement?
To know to write a ratio in
words that describes the
units being compared.
Are elephants and
babies weighed in
the same units?
To use the verbal ratio
when writing a proportion
to convert within a given
system.
U.S. system of
measurement differs from
the rest of the world
30
Write a verbal ratio.
Use a proportion to convert
capacities, volumes and mass
within a given system.
292-296
Content
Goals
Essential
Questions
Know
Do
Students will know:
Students will be able to:
Tools and techniques will
7.M.9
Determine the tool measure mass with an
and technique to
appropriate level of precision.
measure with an
appropriate level
of precision: mass
Do you think that a
bathroom scale is a
good tool to measure
the mass of a grape?
Which tool or technique is
the best choice to measure
mass with an appropriate
level of precision.
Choose the best tool to
measure the mass of an
object and explain why.
7.M.10
Identify the
relationship
between relative
error and
magnitude when
dealing with large
numbers (e.g.
money,
population)
A number can be calculated
that relates to the significance
of an error.
When does an error
in a count or
measurement matter
most?
The formula used to
determine relative error.
Express the relative error
with large numbers.
What is meant by relative
error.
Describe when an error will
have an affect on the
reliability of the data.
7.M.13
Justify the
reasonableness of
the mass of an
object
The mass of an object should
be reasonable.
31
Understandings
Students will understand that:
Textbook
Do you think that a
truck scale is a good
tool to measure a
person’s mass
When an error will have
an significant impact.
Can the mass of your
math book be 16
mg?
How to recognize the
reasonableness of their
answers.
Determine the
reasonableness of their
answer.
783
May-June
Content
Goals
7.M.1
Calculate
distance using a
map scale
7.M.5
Calculate unit
price using
proportions
7.M.6
Compare unit
prices
Understandings
Students will understand that:
The map scale creates a
visual representation of an
actual distance.
Proportion is the technique
used to find unit price
because it is a comparison.
Unit price is the best way to
compare prices.
Essential
Questions
Know
Do
Students will know:
Students will be able to:
How far do you
live from school?
Where to find a map scale on
a map.
How could you
determine this
distance?
How do you
determine the cost
of a blank CD if
you purchase a
package of 25?
The map scale is used to
determine actual distances.
Unit means one item.
Unit price is how much it
costs for one item.
32
One US dollar is not worth
one unit of currency in
another country.
Exchange rates can fluctuate
daily.
Use the map scale to
determine actual distances
and vice-versa.
14
292
Use proportions to find unit
prices.
274
Unit prices always have
money on the top of the rate.
How to set up a proportion to
Which is the better determine the unit price of an
buy?
item.
How to compare unit prices
to determine the better buy.
7.M.7
Convert money
between
different
currencies with
the use of an
exchange rate
table and a
calculator
Textbook
How many US
dollars will you
need to buy 1
Euros?
Money values change by the
minute.
To create a proportion to
convert money between
different currencies.
What an exchange rate is.
How to read an exchange rate
table.
Given prices and quantities,
determine the better buy.
Convert between different
currencies using proportions
along with an exchange rate
table and a calculator.
782
Big Idea: The World Around Us
Big Question: What Do I Need? What am I Looking For?
Topic: Geometry
Suggested Time: 3 Weeks
Goals (NYS Standards):
7.G.1
7.G.2
7.G.3
Calculate the radius or diameter, given the circumference or area of a circle
Calculate the volume of prisms and cylinders, using a given formula and a calculator
Identify the two-dimensional shapes that make up the faces and bases of three-dimensional shapes
(prisms, cylinders, cones, and pyramids)
7.G.4 Determine the surface area of prisms and cylinders, using a calculator and a variety of methods
7.G.5 Identify the right angle, hypotenuse, and legs of a right triangle
7.G.6 Explore the relationship between the lengths of the three sides of a right triangle to develop the Pythagorean Theorem
7.G.7 Find a missing angle when given angles of a quadrilateral
7.G.8 Use the Pythagorean Theorem to determine the unknown length of a side of a right triangle
7.G.9 Determine whether a given triangle is a right triangle by applying the Pythagorean Theorem and using a calculator
7.A.6 Evaluate formulas for given input values (surface area, rate, and density problems)
7.M.11 Estimate surface area
7.M.8 Draw central angles in a given circle using a protractor (circle graphs)
7.S.2 Display data in a circle graph
7.N.19 Justify the reasonableness of answers using estimation
May-June
7.A.9 Build a pattern to develop a rule for determining the sum of the interior angles of polygons
33
Common Misunderstandings and/or Confusing
Concepts:






When to use the circumference and area formula
Confusion with surface area and volume
When to round
Difference between estimating and rounding
3.14 is pi
Try to use Pythagorean theorem with angles
Related Sixth-grade Standards
Skills/Prior Knowledge:
 Rounding
 Identify various types of angles
 Identify various types of triangles
 Square roots and perfect squares
 Substitution
6.A.6 Evaluate formulas for given input values (circumference, area, volume,
distance, temperature, interest, etc.)
6.G.2 Determine the area of triangles and quadrilaterals (squares, rectangles,
rhombi, and trapezoids) and develop formulas
6.G.3 Use a variety of strategies to find the area of regular and irregular
polygons
6.G.5 Identify radius, diameter, chords and central angles of a circle
6.G.6 Understand the relationship between the diameter and radius of a circle
6.G.7 Determine the area and circumference of a circle, using the appropriate
formula
6.G.9 Understand the relationship between the circumference and the diameter
of a circle
6.G.11 Calculate the area of basic polygons drawn on a coordinate plane
(rectangles and shapes composed of rectangles having sides with integer lengths)
Additional Resources:
Vocabulary:
Interactive 3D Shapes:
http://www.learner.org/interactives/geometry/index.html
All of Geometry:
http://www.mathsisfun.com/geometry/index.html
Pythagorean Theorem:
http://www.mathsnet.net/dynamic/pythagoras/index.html
Lessons from NCTM: http://illuminations.nctm.org
Textbook Online http://my.hrw.com Chapters 8,9,10
Teacher Resources Power Presentation NY-10
Pythagorean Theorem
SMART Notebook: Packaging Explorer, Interactive
Protractor, Mathematical Toolkit 2D Shape Creation
Acute, Adjacent, Angle, Arc, Area, Central, Chord, Circle, Circumference, Cone,
Cube, Cubic Unit, Cylinder, Decagon, Degree, Diagonal, Diameter, Dimension,
Equilateral Triangle, Face, Geometry, Heptagon, Hexagon, Hypotenuse, Interior
Angle, Isosceles Triangle, Legs, Line, Line Segment, Measure, Measurement,
Net, Nonagon, Obtuse, Octagon, Parallel, Parallelogram, Pentagon, Perpendicular,
Perimeter, Point, Polygon, Prisms, Protractor, Pythagorean Theorem,
Quadrilateral, Radius, Right, Rectangle, Regular Polygon, Rhombus, Scalene
Triangle, Straight, Trapezoid, Triangle, Vertex
34
Content
Goals
“Circle Graphs”
can be taught here
or with “Interpretation”- statistics
7.M.8
Draw central
angles in a given
circle using a
protractor (circle
graphs)
7.S.2
Display data in a
circle graph
7.G.1
Calculate the
radius or diameter,
given the
circumference or
area of a circle
7.G.7
Find a missing
angle when given
angles of a
quadrilateral
35
Understandings
Students will understand that:
The basis of geometry is
undefined.
The central angle of a circle
graph is used to display the
angle measurement (degree)
of the data.
There is a relationship
between the percent of data
and the percent of a circle.
There is a relationship
between the diameter or
radius and circumference or
area of a circle.
Wholes are just a sum of
their parts.
Essential
Questions
What makes a point,
line or plane
undefined?
How does what I
measure change how
I measure?
Know
Do
Students will know:
Students will be able to:
The classification of
angles.
The correct tool to use
when constructing a circle
graph is the protractor.
Central angles are used to
display the percent of
data.
Calculate percents given raw
data.
460
Calculate percent of 360 to
determine the measure of
central angles.
Construct an accurate circle
graph of data given a protractor.
A procedure to align and
measure with a protractor
to calculate or create
angles.
Which is more
A strategy to recognize
accurate: using 3.14, which formula
leaving the answer in (circumference or area) is
appropriate for a given
terms of  , or the
situation.
calculator readout?
Place data in the correct
segments of a given circle
graph.
What’s missing from
your day to make it
perfect?
Calculate the missing angle of a
quadrilateral when given its
other angles.
The sum of the angles of
a quadrilateral is 3600.
Textbook:
Calculate the radius or
524
diameter, given the
538
circumference or area of a circle
and explain their process.
478
Content
Goals
7.G.3
Identify the twodimensional
shapes that make
up the faces and
bases of threedimensional
shapes (prisms,
cylinders, cones,
and pyramids)
7.G.2
Calculate the
volume of prisms
and cylinders,
using a given
formula and a
calculator
Understandings
Students will understand that:
Each geometric shape has its
own distinct characteristics.
There is a blueprint for every
three-dimensional shape.
Essential
Questions
What would a
blueprint of your
house/room/yourself
look like?
Know
Do
Students will know:
Students will be able to:
Three-dimensional
shapes are made up of
two-dimensional faces.
The characteristics of
the faces of a solid
shape.
580
596
Identify the shapes that make up
the faces of three-dimensional
solids.
How to name threedimensional shapes
based on their faces.
The volume of a threedimensional object is the
space inside of the object.
How can you fill an
object?
What objects can
you fill?
What’s on the
inside?
How to recognize
which formula
(perimeter, area,
volume or surface area)
is appropriate for a
given situation (word
problems).
The meaning for each
variable in a given
formula.
The difference between
perimeter, area, surface
area and volume.
36
Recognize nets.
Textbook:
Calculate the volume of prisms
and cylinders by using given
formulas.
Justify the use of the appropriate
formula.
Identify the appropriate unit of
measurement for volume.
586
Content
Goals
7.G.4
Determine the
surface area of
prisms and
cylinders, using a
calculator and a
variety of methods
Understandings
Students will understand that:
The surface area of a threedimensional object is the
space outside of the object.
Formulas can be used to
calculate various problems.
Essential
Questions
How do you wrap a
present?
Know
Do
Students will know:
Students will be able to:
How to recognize
which formula
(perimeter, area,
volume or surface area)
is appropriate for a
given situation (word
problems).
Calculate the surface area of
prisms and cylinders by using
given formulas.
The difference between
perimeter, area, surface
area and volume.
Justify the use of the appropriate
formula.
“Evaluate
formulas” can be
taught here or with
“Finding the
Unknown” –
algebra
How to recognize the
correct values for the
surface area formula.
Evaluate any formula given
certain values.
7.A.6
Evaluate formulas
for given input
values (surface area,
rate, and density
problems)
37
597
Apply the appropriate unit of
measurement for surface area.
7.M.11
Estimate surface
area
The vocabulary that
prompts estimating
surface area rather than
calculating surface
area.
Textbook:
Formulas
711
Content
Goals
7.G.5
Identify the right
angle, hypotenuse,
and legs of a right
triangle
7.G.6
Explore the
relationship between
the lengths of the
three sides of a right
triangle to develop
the Pythagorean
Theorem
7.G.8
Use the Pythagorean
Theorem to
determine the
unknown length of a
side of a right
triangle
7.G.9
Determine whether a
given triangle is a
right triangle by
applying the
Pythagorean
Theorem and using a
calculator
7.N.19
Justify the
reasonableness of
answers using
estimation
38
Understandings
Students will understand that:
Patterns can be developed
into formulas.
Essential
Questions
What patterns have
you noticed today?
The Pythagorean Theorem
mathematically describes
the relationship of the sides
of a right triangle.
Know
Do
Students will know:
Students will be able to:
The characteristics of
the various parts of a
right triangle.
There is a relationship
between the lengths of
the sides of a right
triangle (a2 + b2 = c2).
Label the legs and the
hypotenuse of a right triangle.
Textbook:
556
Use the relationship between the
sides of the right triangle to
develop the Pythagorean
Theorem.
The hypotenuse is the
longest side of the
triangle, across from
the right angle.
The Pythagorean Theorem
is a tool that when used
correctly will help them to
figure out any unknown
side of a right triangle.
Are directions
necessary?
To use the Pythagorean
Theorem to find the
missing side of a right
triangle.
The Pythagorean Theorem
must be applied to
determine if a triangle is a
right triangle given three
sides of a triangle.
How can looks be
deceiving?
That Pythagorean
Prove whether or not a triangle
Theorem can be used to is a right triangle using the
prove a triangle is a
Pythagorean Theorem.
right triangle.
The answer they get should
be reasonable.
What is going on?
Should our
judgments be based
on what we see?
Does this make
sense?
Answers should be
logical based on their
estimated answer.
Apply the Pythagorean Theorem 556
to determine the unknown
length of a side of a right
triangle and explain.
Estimate to come up with a
reasonable answer.
558 #15
Content
Goals
Understandings
Students will understand that:
May – June
Can be taught
within “The
World Around
Us” or “Input/
Output”
7.A.9
Build a pattern to
develop a rule for
determining the sum
of the interior angles
of polygons
39
Patterns can be developed
into formulas.
Essential
Questions
Know
Do
Students will know:
Students will be able to:
The sum of the
What can the number measures of the angles
of sides of a polygon in a triangle is 180º.
predict?
By dividing any figure
What patterns have
into triangles, you can
you noticed today?
find the sum of its
angle measures.
There is a relationship
between the number of
sides of a polygon and
the sum of the interior
angles of the same
polygon.
Every polygon has a
different angle sum that
can be determined
based on a single
formula.
Textbook:
Identify polygons up to ten
sides.
478
Divide polygons into triangles
to find the sum of its angle
measures.
Use this process to create a
pattern.
Write a formula (rule) for
finding the sum of the interior
angles in a polygon with n sides.
Apply the rule to find the sum
of the angles for any given
polygon.
Big Idea: Input/Output
Big Question: What Comes Next?
Topic: Functions
Suggested Time: 1 ½ weeks
Goals (NYS Standards):
7.A.7
Draw the graphic representation of a pattern from an equation or from a table of data
7.A.8 Create algebraic patterns using charts/tables, graphs, equations, and expressions
7.A.10 Write an equation to represent a function from a table of values (May-June)
7.PS.6 Represent problem situations verbally, numerically, algebraically, and graphically
May-June:
7.A.9 Build a pattern to develop a rule for determining the sum of the interior angles of polygons
Common Misunderstandings and/or Confusing Concepts:





Reversing the order of the x and y-coordinates
Points on a linear equation do not always form a pattern or are straight
Lines have a beginning and an end
Quadrant I begins in upper left corner and goes clockwise
Dependent vs. Independent variables
Additional Resources:
http://www.math.com/school/subject2/practice
40
Related Sixth Grade Standards
Skills/Prior Knowledge
6.G.10
6.G.11
Identify and plot points in all four quadrants
Calculate the area of basic polygons drawn on a
coordinate plane (rectangles and shapes
composed of rectangles having sides with integer
lengths)
Vocabulary:
Algebraic expressions, Algebraic Equations, Algebraic
Pattern, Algebraic Term, Angle, Arithmetic Sequence,
Axes, Coefficient, Constant, Coordinates, Coordinate
Plane, Decagon, Dependent Variables, Equation, Formula,
Function, Geometric Sequence, Horizontal, Independent
Variables, Input, Interior angles, Linear Equation, Linear
function, Ordered Pairs, Origin, Output, Pattern, Pentagon,
Plot, Point, Polygon, Quadrant, Quadratic Equation,
Regular Polygon, Sequence, Slope, Slope-Intercept Form,
Sum, Table of Values, Term, Vertical, X-axis, Y-axis, Yintercept
Content
Goals
Review:
6.G.10
Identify and plot
points in all 4
quadrants
Understandings
Students will understand that:
An ordered pair (coordinates) represents a
location.
Essential
Questions
Know
Do
Students will know:
Students will be able to:
Where can I be An ordered pair can be plotted
found?
on a coordinate plane.
The components of a coordinate
plane (axes, quadrants,
negative/positive integers).
The location of the quadrants.
Textbook
Plot ordered pairs on a
coordinate plane.
Construct a coordinate
plane.
224
Identify the x and y
coordinates within an
ordered pair.
Locate a point on a
coordinate plane.
7.A.7
Draw the
graphic
representation
of a pattern
from an
equation or
from a table of
data
A set (table) of values is
directly related to a set of
points on a coordinate plane.
A line is an infinite set of
points and contains an
infinite number of solutions.
Tables are used to organize
and display the input and
output values of a function.
How many
points lie on a
line?
Where do I
begin / end?
What is the
pattern?
A function can be represented Can I make
in multiple forms.
predictions
based on a
pattern?
41
That a line is an infinite set of
points.
A first degree equation is a
straight line when graphed on
the coordinate plane.
The procedure for creating a
table of values.
That a table of values contains
ordered pairs.
A function rule can be stated as
an equation.
One variable represents the
input and the other represents
the output.
Only two points are needed to
draw the graph of a linear
function.
Graph the equation of a
line on a coordinate plane.
Create a table of values
given an expression or
equation.
228
Find the output for each
input.
248
Use a graph to find the
output value of a linear
function for a given input
value.
Formulate the ordered pairs
from a table of values.
238
Content
Goals
Understandings
Students will understand that:
7.A.8
Create
algebraic
patterns using
charts/tables,
graphs,
equations, and
expressions
That relationships exist
between the independent
and dependent variables, x
and y , respectively.
7.A.10 (Post)
Write an
equation to
represent a
function from
a table of
values
The relationships within the
table of values can be written
as an equation.
7.PS.6
Represent
problem
situations
verbally,
numerically,
algebraically,
and
graphically
42
Essential
Questions
How are the
values related?
Know
Do
Students will know:
Students will be able to:
To look for patterns within a
table to determine the rule.
What’s next in
line?
Textbook:
Create and identify patterns
using tables, graphs and
equations.
228
238
Write and graph ordered
242
pairs from tables.
248
Intro. or extension:
Describe a sequence as
arithmetic or geometric.
What pattern
do I follow?
That a function can be written
as an equation to describe a set
or ordered pairs.
Write a function/equation
that describes a set of
ordered pairs/table of
values.
That functions follow rules.
Graphs show relationships.
Examine patterns and
sequences.
How are
graphs
interpreted?
To relate graphs to real-life
situations.
Determine which equation
fits a table of values.
Describe situations that fit
a graph.
Interpret graphs.
242
248
232
Content
Goals
Understandings
Students will understand that:
Essential
Questions
May – June
Can be taught Patterns can be developed
into formulas.
within “The
World Around
Us” or “Input/
Output”
7.A.9
Build a pattern to
develop a rule for
determining the
sum of the
interior angles of
polygons
43
What can the
number of
sides of a
polygon
predict?
What patterns
have you
noticed today?
Know
Do
Students will know:
Students will be able to:
The sum of the measures of the
angles in a triangle is 180º.
Identify polygons up to ten
sides.
By dividing any figure into
triangles, you can find the sum
of its angle measures.
Divide polygons into
triangles to find the sum of
its angle measures.
There is a relationship between
the number of sides of a
polygon and the sum of the
interior angles of the same
polygon.
Use this process to create a
pattern.
Textbook:
478
Every polygon has a different
angle sum that can be
determined based on a single
formula.
Write a formula (rule) for
finding the sum of the
interior angles in a polygon
with n sides.
Apply the rule to find the
sum of the angles for any
given polygon.
44