Download Content Strand: Real Number System

Grade 9 Algebra 1, Q1
Content Strand: Real Number System
Standard: A1.NRNS.3 Explain why the sum or product of rational numbers is rational;
that the sum of a rational number and an irrational number is irrational; and that the
product of a nonzero rational number and an irrational number is irrational.
Related Standards:
CCSSM N.RN.3
Vocabulary: rational number, irrational number, sum, product, nonzero, real numbers,
whole numbers, integers, natural numbers, pi (not just 3.14), radical, square root, cube
root
Example: Explain why the number 2π must be irrational, given that π is irrational.
Answer: if 2π were rational, then half of 2π would also be rational, so π would have to
be rational as well.
Strategies/Activities:
http://mathequalslove.blogspot.com
Venn Diagram of real number system:
https://app.box.com/s/5e4ca1ed71280f1e3d7
http://cdn.kutasoftware.com/Worksheets/Alg1/Number%20Sets.
pdf
http://www.doe.virginia.gov/testing/solsearch/sol/math/8/mess_
8-2.pdf
http://www.mathworksheetsland.com/hsnumbersquan/3mul.htm
l
Partner work:
http://betterlesson.com/lesson/435707/operation-rationalirrational-numbers
Process Standards
1. Make sense of problems
and persevere in solving
them.
2. Reason both contextually
and abstractly.
3. Use critical thinking skills to
justify mathematical
reasoning and critique the
reasoning of others.
5. Use a variety of
mathematical tools effectively
and strategically.
6. Communicate
http://map.mathshell.org/lessons.php?unit=9110&collection=8&r mathematically and approach
edir=1
mathematical situations with
Grade 9 Algebra 1, Q1
precision.
Group activity: pull numbers from bag
7. Identify and utilize structure
and patterns.
Resources:
Text: Holt McDougal Algebra I Common Core Edition, pg. 431-432
Exemplar Lessons:
http://betterlesson.com/lesson/435707/operation-rational-irrational-numbers
Web Sites:
https://www.illustrativemathematics.org/content-standards/tasks/690
http://croitz.blogspot.com/search/label/Real%20Number%20System
Videos:
USATestPrep: Number System (2:25), Real Numbers and their Subsets (3:3), Subsets
of Real Numbers (4:24), The meaning of irrational numbers (3:38)
www.phschool.com, Web Code: ate-0775, Chapter 1, Lesson 3
https://learnzillion.com/lessonsets/647-identify-rules-for-adding-and-multiplying-rationaland-irrational-numbers
Sample Assessment-like Questions:
Assessments: Textbook assignments, Worksheet assignments, Quizzes, Tests, Oral
responses, Observations
http://mathbitsnotebook.com/Algebra1/RatIrratNumbers/RATPractice.html
Multiple Choice:
● What is the product of √17 and √2? Is the product rational or irrational?
A. 34; rational
C. √34; irrational
Grade 9 Algebra 1, Q1
B. √19; irrational
D. √291; rational
● Which word best describes the sum of √19 and √19?
A. rational
C. natural
B. imaginary
D. irrational
Open-Ended:
1. Let 𝑞 = √4 ⋅ 𝑝, where p is a rational number. What type of number is q? Explain
your reasoning.
2. How can you determine whether the product of
without multiplying?
2
7
9
and 11is rational or irrational
Grade 9 Algebra 1, Q1
Content Strand: Quantities
Standard: A1.NQ.1 Use units of measurement to guide the solution of multi-step
tasks. Choose and interpret appropriate labels, units, and scales when constructing
graphs and other data displays.
Related Standards:
SCCCR A1.ACE.1
SCCCR A1.AREI.3
CCSSM N.Q.1
Vocabulary: dimensional analysis, product, units of measurements (metric and
customary), conversion, rate, ratio, proportion, unit rate, scale factor, similar figures
Example: Include word problems where quantities are given in different units, which
must be converted to make sense of the problem. For example, a problem might have
an object moving 12 feet per second and another at 5 miles per hour. To compare
speeds, students convert 12 feet per second to miles per hour:
which is more than 5 miles per hour.
Strategies/Activities:
SREB Math Ready: Unit 1 Lesson 3 Task #4 and Unit 3
Measurement and Proportional Reasoning
http://map.mathshell.org/tasks.php?unit=HA24&collection
=9&redir=1
http://map.mathshell.org/tasks.php?unit=HA19&collection
=9&redir=1
http://mathequalslove.blogspot.com/2012/04/sugarpackets-and-proportions.html
http://mathequalslove.blogspot.com/2012/07/pre-algebraroad-trip-pr
http://mathequalslove.blogspot.com/2012/10/foldablelove.html
http://www.sciencewithmrjones.com/handouts.shtml#http
units
Process Standards
1. Make sense of problems and
persevere in solving them.
2. Reason both contextually and
abstractly.
3. Use critical thinking skills to
justify mathematical reasoning and
critique the reasoning of others.
4. Connect mathematical ideas
and real-world situations through
modeling.
5. Use a variety of mathematical
Grade 9 Algebra 1, Q1
Mr. Jones science class, Scroll down to “Units,
Measurements, and Conversions”, Look at Navigating
the Metric (ppt)” through “Challenging Problems Dimensional Analysis”
tools effectively and strategically.
6. Communicate mathematically
and approach mathematical
situations with precision.
7. Identify and utilize structure and
patterns.
Resources:
Text:
Holt McDougal Algebra I Common Core Edition, Section 1-8 and 1-9
Exemplar Lessons:
http://betterlesson.com/lesson/614611/dimensional-analysis
https://www.engageny.org/resource/algebra-i-module-1-topic-c-lesson-18
https://www.engageny.org/resource/algebra-i-module-1-topic-d-lesson-25
Web Sites:
Videos:
http://my.hrw.com/tabnav/controller.jsp?isbn=9780547708508
USATestPrep: Ratios and Proportions (0:50), Using Indirect Measurement (1:22 sec),
Dimensional Analysis (2:4)
www.phschool.com, Web Code: ate-0775, Chapter 3, Lessons 4, 5
For fun: https://www.youtube.com/watch?v=ZfcHMwh8Ujs
Sample Assessment-like Questions:
Assessments: Textbook assignments, Worksheet assignments, Quizzes, Tests, Oral
responses, Observations
Grade 9 Algebra 1, Q1
Holt Algebra 1 Test Prep: p. 67-68; 73-74
http://mathbitsnotebook.com/Algebra1/Units/UNUnitsPractice.html
Multiple Choice:
A pipe is leaking at the rate of 8 fluid ounces per minute. Use dimensional analysis to
find out how many gallons the pipe is leaking per hour.
A. 3,840 gal/h
C. 3.75 gal/h
B. 0.02 gal/h
D. 17.07 gal/h
Open Ended:
Express 75 kilometers per hour in meters per second.
Grade 9 Algebra 1, Q1
Content Strand: Quantities
Standard: A1.NQ.3* Choose a level of accuracy appropriate to limitations on
measurement when reporting quantities in context.
Related Standards:
SCCCR A1.NQ.2
CCSSM N.Q.1
Vocabulary: accuracy, precision, tolerance, units of measurements (metric and
customary)
Example:
Determining price of gas by estimating to the nearest cent is appropriate because you
will not pay in fractions of a cent but the cost of gas is
.
Strategies/Activities:
http://www.thirteen.org/edonline/ntti/resources/lessons/si
gnificant/c.html
http://tinyurl.com/ng42rh5
http://www.mathsisfun.com/accuracy-precision.html
Process Standards
1. Make sense of problems and
persevere in solving them.
2. Reason both contextually and
abstractly.
3. Use critical thinking skills to
justify mathematical reasoning
and critique the reasoning of
others.
4. Connect mathematical ideas
and real-world situations through
modeling.
5. Use a variety of mathematical
tools effectively and
strategically.
6. Communicate mathematically
Grade 9 Algebra 1, Q1
and approach mathematical
situations with precision.
7. Identify and utilize structure
and patterns.
Resources:
Text:
Holt McDougal Algebra I Common Core Edition, Sections 1-10
Exemplar Lessons:
http://betterlesson.com/lesson/627899/precision-vs-accuracy
Web Sites:
https://www.illustrativemathematics.org/content-standards/HSN/Q/A/3
Videos:
http://my.hrw.com/tabnav/controller.jsp?isbn=9780547708508
USATestPrep: Sets of Numbers and Appropriate Units (2:12)
https://learnzillion.com/lessonsets/399-choose-a-level-of-accuracy-appropriate-tolimitations-on-measurement
Sample Assessment-like Questions:
Assessments: Textbook assignments, Worksheet assignments, Quizzes, Tests, Oral
responses, Observations
Holt Algebra 1 Test Prep: p.81-82
http://mathbitsnotebook.com/Algebra1/Units/UNUnitsPractice.html
Multiple Choice:
● Four students calculated the volume of a 12.8 oz container. Their results are
shown in the table. Whose calculation is the most accurate?
Grade 9 Algebra 1, Q1
Student
Volume (oz)
Wally
12.546
Rex
12.59
Amanda
12.69
Joni
12.75
A. Wally’s
C. Amanda’s
B. Rex’s
D. Joni’s
●
Which of these measurements is the most precise?
A. 4 m
C. 1.3 km
B. 127 mm
D. 5.14 cm
Open Ended:
Write the possible range for the measurement 47 cm ± 2.2%. Round to
the nearest hundredth if necessary.
Grade 9 Algebra 1, Q1
Content Strand: Structure and Expressions
Standard: A1.ASE.1* Interpret the meanings of coefficients, factors, terms, and
expressions based on their real-world contexts. Interpret complicated expressions as
being composed of simpler expressions. (Limit to linear; quadratic; exponential.)
Related Standards:
SCCCR A1.NQ.1
CCSSM A.SSE.1
Vocabulary: coefficient, factors, variable, terms, expressions, numerical expression,
algebraic expression, verbal expression, evaluate, substitute, sum, difference, product,
quotient, squared, square root, cubed, cube root, less than, more than, is (equal),
double, triple, half, third, reduced by, increased by, decreased by, twice, in groups of,
power, exponent, per, ratio, order of operations
Example:
1. Suppose the cost of cell phone service for a month is represented by the expression
0.40s + 12.95. Students can analyze how the coefficient of 0.40 represents the cost of
one minute (40¢), while the constant of 12.95 represents a fixed, monthly fee, and s
stands for the number of cell phone minutes used in the month. Similar real-world
examples, such as tax rates, can also be used to explore the meaning of expressions.
2. A box of chocolates at Rhebb’s is computed by charging for each kind of chocolate.
Caramels cost $0.40 each.
Butter Creams cost $0.30 each.
Chocolate Covered Cherries cost $0.60 each.
For a particular sale this equation describes the cost of purchase.
0.40a + 0.30b + 0.60c = 8.00
A. What does each of the variables in the equation represent?
B. What are the coefficients and what do they represent?
C. What does the 8.00 represent?
3. A company uses two different-sized trucks to deliver sand. The first truck can
transport x cubic yards, and the second x cubic yards. The first truck makes S trips to a
job site, while the second makes T trips. What do the following expressions represent?
A. S + T
B. x + y
C. xS + yT
Strategies/Activities:
http://cdn.kutasoftware.com/Worksheets/PreAlg/Evaluatin
Process Standards
Grade 9 Algebra 1, Q1
g%20Variable%20Expressions.pdf
1. Make sense of problems and
http://cdn.kutasoftware.com/Worksheets/Alg1/Variable%2 persevere in solving them.
0and%20Verbal%20Expressions.pdf
2. Reason both contextually and
http://cdn.kutasoftware.com/Worksheets/Alg1/Evaluating abstractly.
%20Expressions.pdf
http://mathequalslove.blogspot.com/2012/08/a-peek-at- 3. Use critical thinking skills to
justify mathematical reasoning and
my-algebra-1-interactive.html
critique the reasoning of others.
http://www.math-play.com/Algebraic-Expressions4. Connect mathematical ideas
Millionaire/algebraic-expressions-millionaire.html
and real-world situations through
http://teachers.henrico.k12.va.us/math/hcpsalgebra1/mo modeling.
dule1-1.html
6. Communicate mathematically
http://teachers.henrico.k12.va.us/math/hcpsalgebra1/mo and approach mathematical
dule1-2.html
situations with precision.
http://www.math-drills.com/algebra.shtml#translating
7. Identify and utilize structure
and patterns.
http://illuminations.nctm.org/Lesson.aspx?id=2583
https://itunes.apple.com/us/app/5-dice-order-operationsgame/id572774867?ls=1&mt=8
Resources:
Text:
Holt McDougal Algebra I Common Core Edition, Section 1-1
SREB Math Ready: Unit 1 Lesson 6 Task 11 and Task 13
Exemplar Lessons:
https://commoncorealgebra1.wikispaces.hcpss.org/file/detail/A.SSE.A.1%20Lesson%20
Interpreting%20Expressions.docx
http://betterlesson.com/lesson/resource/1988596/do-now-problem-docx
http://betterlesson.com/lesson/541540/linear-expressions-and-word-problems
https://www.engageny.org/resource/algebra-i-module-1-topic-b-lesson-6
https://www.engageny.org/resource/algebra-i-module-1-topic-b-lesson-7
Web Sites:
Grade 9 Algebra 1, Q1
Interpreting Expressions https://commoncorealgebra1.wikispaces.hcpss.org/Unit+1
Videos:
http://my.hrw.com/tabnav/controller.jsp?isbn=9780547708508
USATestPrep: Evaluate Algebraic Expressions, Simplifying Expressions
www.phschool.com, Web Code: ate-0775, Chapter 1, Lessons 1, 2
Sample Assessment-like Questions:
Assessments: Textbook assignments, Worksheet assignments, Quizzes, Tests, Oral
responses, Observations
Holt Algebra 1 Test Prep: p. 10-11
http://mathbitsnotebook.com/Algebra1/AlgebraicExpressions/AEexpressPractice.html
Multiple Choice:
● At the zoo, a child pays c dollars for a ticket and an adult pays g dollars. Explain
in words the meaning of 𝑔 = 2𝑐.
A. An adult ticket costs twice as much as a child ticket.
B. An adult ticket costs half as much as a child ticket.
C. Twice as many child tickets as adult tickets are sold.
D. Half as many adults as children go to the zoo.
● A clothing store is having a sale where all T-shirts are $10. The sales tax is
5%.Dan buys n T-shirts during this sale, the total cost of his purchase will be 10n
+ 0.05(10n). Interpret the meaning of 0.05(10n) in this context.
A. The expression 0.05(10n) represents the price of each T-shirt.
B. The expression 0.05(10n) represents the cost of Dan’s purchase before tax.
C. The expression 0.05(10n) represents the total tax on Dan’s purchase.
D. The expression 0.05(10n) represents the total cost of Dan’s purchase.
Open Ended:
1. Explain the meaning of the exponent 3 in the algebraic expression (𝑥 + 𝑦)3.
2. Hana makes beaded bracelets for sale. The materials for each bracelet cost
$2.00 and she sells the bracelets for $7.25 each. To find her profits, she writes
the equation p =7.25x - 2.00x. Explain what the variable x represents.
Grade 9 Algebra 1, Q1
Grade 9 Algebra 1, Q1
Content Strand: Reasoning with Equations and Inequalities
Standard: A1.AREI.3* Solve linear equations and inequalities in one variable,
including equations with coefficients represented by letters.
Related Standards:
SCCCR A1.AREI.1
SCCCR A1.ASE.1
SCCCR A1.ACE.1
CCSSM A.REI.1
Vocabulary: equation, variable, constant, inverse operation, order of operations,
coefficient, solution, properties of equality, no solution, infinitely many solutions, identity,
multiplicative inverse (reciprocal), like terms
Example:
●
● ax + 7 = 12
●
Strategies/Activities:
Process Standards
https://commoncorealgebra1.wikispaces.hcpss.org/file/de
tail/A.CED.A.1%20Task%20Setting%20the%20Table.doc 1. Make sense of problems and
persevere in solving them.
http://mathequalslove.blogspot.com/2013/11/algebra-1inb-pages-solving-equations.html
2. Reason both contextually and
abstractly.
http://www.quia.com/mc/540939.html
3. Use critical thinking skills to
http://www.quia.com/cc/540939.html
http://www.math-play.com/One-Step-Equation-Game.html justify mathematical reasoning
and critique the reasoning of
http://www.quia.com/cb/77775.html
others.
http://cdn.kutasoftware.com/Worksheets/Alg1/One4. Connect mathematical ideas
Step%20Equations.pdf
and real-world situations through
http://cdn.kutasoftware.com/Worksheets/Alg1/Twomodeling.
Step%20Equations.pdf
5. Use a variety of mathematical
http://cdn.kutasoftware.com/Worksheets/Alg1/Multi-
Grade 9 Algebra 1, Q1
Step%20Equations.pdf
http://cdn.kutasoftware.com/Worksheets/Alg1/Absolute%
20Value%20Equations.pdf
tools effectively and strategically.
6. Communicate mathematically
and approach mathematical
situations with precision.
7. Identify and utilize structure
and patterns.
Resources:
Text:
Holt McDougal Algebra I Common Core Edition, Section 1-2, 1-3, 1-4, 1-5, 1-7
SREB Math Ready Unit 2 Equations
Exemplar Lessons:
https://commoncorealgebra1.wikispaces.hcpss.org/file/detail/A.CED.A.1%20Lesson%20
Solving%20Equations%20with%20Algebra%20Tiles.docx
https://www.engageny.org/resource/algebra-i-module-1-topic-c-lesson-11
https://www.engageny.org/resource/algebra-i-module-1-topic-c-lesson-12
https://www.engageny.org/resource/algebra-i-module-1-topic-c-lesson-13
http://betterlesson.com/lesson/537089/two-step-equations
http://betterlesson.com/lesson/521026/solving-multi-step-equations-comparingprocesses-day-2-of-4
Web Sites:
Videos:
http://my.hrw.com/tabnav/controller.jsp?isbn=9780547708508
USATestPrep: Solve 1-variable Equations (2:19), Solve Two-Step Equations (2:00),
Solve Multi-step Equations (2:18)
www.phschool.com, Web Code: ate-0775, Chapter 2: Lessons 4, 5; Chapter 3: Lesson
1, 2, 3, 6
http://www.onlinemathlearning.com/solving-two-step-equations-integers.html
Sample Assessment-like Questions:
Assessments: Textbook assignments, Worksheet assignments, Quizzes, Tests, Oral
responses, Observations
Grade 9 Algebra 1, Q1
Holt Algebra 1 Test Prep: p. 21-22, 29, 37-38, 44-45, 58-60
http://mathbitsnotebook.com/Algebra1/LinearEquations/LEPracEquations.html
Multiple Choice:
● Solve 50q - 43 = 52q - 81.
A. q = 38
C. q = -38
B. q = -19
D. q = 19
Open Ended:
1. Solve the equation.
3(x + 4) - 1 = 3x + 2
2. Solve 7b + 3 - 4b = 3 - 3(b + 4).
Grade 9 Algebra 1, Q1
Content Strand: Reasoning with Equations and Inequalities
Standard: A1.AREI.1* Understand and justify that the steps taken when solving simple
equations in one variable create new equations that have the same solution as the
original.
Related Standards:
SCCCR A1.AREI.3
SCCCR A1.ACE.1
CCSSM A.REI.1
Vocabulary: equation, variable, constant, order of operations, inverse operations,
multiplicative inverse (reciprocal), equivalent, like terms, properties: commutative,
associative, distributive, reflexive, identity, equality, substitution
Example:
● Explain why the equation x/2 + 7/3 = 5 has the same solutions as the equation 3x
+ 14 = 30. Does this mean that x/2 + 7/3 is equal to 3x + 14?
● Show that x = 2 and x = -3 are solutions to the equation x^2 + x = 6. Write the
equation in a form that shows these are the only solutions, explaining each step
in your reasoning.
● Transform 2x – 5 = 7 to 2x = 12 and tell what property of equality was used.
Strategies/Activities:
http://mathequalslove.blogspot.com/2013/11/algebra-1inb-pages-solving-equations.html
http://map.mathshell.org/lessons.php?unit=8245&collecti
on=8&redir=1
http://schoolhouseteachers.com/wpcontent/uploads/2013/03/March-Through-Equations.pdf
https://tusd.haikulearning.com/abrown/mrs.../cms.../3543
1149.doc?t…
http://www.corwin.com/upmdata/18260_Gregory_ActDiffClssrm_MSMath_Pages_3
0_31.pdf
Process Standards
1. Make sense of problems and
persevere in solving them.
2. Reason both contextually and
abstractly.
3. Use critical thinking skills to
justify mathematical reasoning and
critique the reasoning of others.
4. Connect mathematical ideas and
real-world situations through
modeling.
Grade 9 Algebra 1, Q1
http://teachers.henrico.k12.va.us/math/HCPSalgebra1/A4d1.html
http://teachers.henrico.k12.va.us/math/HCPSalgebra1/A4d-2.html
6. Communicate mathematically
and approach mathematical
situations with precision.
7. Identify and utilize structure and
patterns.
Resources:
Text:
Holt McDougal Algebra I Common Core Edition, Section 1-2, 1-3, 1-4, 1-5, 1-7
SREB Math Ready Unit 2 Equations
Exemplar Lessons:
https://commoncorealgebra1.wikispaces.hcpss.org/file/detail/A.REI.A.1%20Lesson%20
Scales%20of%20Equality.doc
http://betterlesson.com/lesson/526370/justifying-the-solutions-to-linear-equations
http://betterlesson.com/lesson/517050/solving-equations-by-constructing-argumentsday-1-of-2
Web Sites:
Videos:
http://my.hrw.com/tabnav/controller.jsp?isbn=9780547708508
USATestPrep: Solve 1-variable Equations (2:19), Solve Two-Step Equations (2:00),
Solve Multi-step Equations (2:18)
www.phschool.com, Web Code: ate-0775, Chapter 2: Lessons 4, 5; Chapter 3: Lesson
1, 2, 3, 6
Sample Assessment-like Questions:
Assessments: Textbook assignments, Worksheet assignments, Quizzes, Tests, Oral
responses, Observations
Holt Algebra 1 Test Prep: p. 21-22, 29, 37-38, 44-45, 58-60
Grade 9 Algebra 1, Q1
http://mathbitsnotebook.com/Algebra1/LinearEquations/LEJustifyPractice.html
Multiple Choice:
Solve the equation 4x - 6 = 34. Write a justification for each step.
4x - 6 = 34
+6
4x
4𝑥
4
+6
= 40
=
40
4
x = 10
Given equation
[1]
Simplify.
[2]
Simplify.
A. [1] Substitution Property of Equality; C. [1] Division Property of Equality;
[2] Division Property of Equality
[2] Subtraction Property of Equality
B. [1] Addition Property of Equality;
[2] Division Property of Equality
D. [1] Addition Property of Equality;
[2] Reflexive Property of Equality
Open Ended:
Solve 3(a + 3) – 6 = 21. Write a reason for each step.
Grade 9 Algebra 1, Q1
Grade 9 Algebra 1, Q1
Content Strand: Creating Equations
Standard: A1.ACE.1* Create and solve equations and inequalities in one variable that
model real-world problems involving linear, quadratic, simple rational, and exponential
relationships. Interpret the solutions and determine whether they are reasonable. (Limit
to linear; quadratic; exponential with integer exponents.)
Related Standards:
SCCCR A1.AREI.1
SCCCR A1.ARE.3
CCSSM A.CED.1
Vocabulary: coefficient, factors, variable, terms, expressions, numerical expression,
algebraic expression, verbal expression, equation, evaluate, substitute, sum, difference,
product, quotient, squared, square root, cubed, cube root, less than, more than, is
(equal), double, triple, half, third, reduced by, increased by, decreased by, twice, in
groups of, power, exponent, per, ratio, absolute value, order of operations, constant,
inverse operation, solution, properties of equality, no solution, infinitely many solutions,
identity, multiplicative inverse (reciprocal), like terms, reasonable, interpret
Example:
● Lava coming from the eruption of a volcano follows a parabolic path. The height
h in feet of a piece of lava t seconds after it is ejected from the volcano is given
by
. After how many seconds does the lava reach its maximum height
of 1000 feet?
●
Given that the following trapezoid has area 54 cm 2, set up an equation to find
the length of the base, and solve the equation.
Strategies/Activities:
http://teachers.henrico.k12.va.us/math/HCPSalgebra1/A-
Process Standards
Grade 9 Algebra 1, Q1
4d-1.html
http://mathequalslove.blogspot.com/2013/11/algebra-1inb-pages-solving-equations.html
http://mathequalslove.blogspot.com/2012/09/algebra-1inb-pages-over-multi-step.html
http://teachers.henrico.k12.va.us/math/HCPSalgebra1/A4d-2.html
http://www.superteachertools.us/jeopardyx/jeopardyreview-game.php?gamefile=61123#.VYMOgVVViko
http://map.mathshell.org/lessons.php?unit=8245&collecti
on=8&redir=1
https://www.nsa.gov/academia/_files/collected_learning/
middle_school/algebra/deciphering_world_problems.pdf
1. Make sense of problems and
persevere in solving them.
2. Reason both contextually and
abstractly.
3. Use critical thinking skills to
justify mathematical reasoning
and critique the reasoning of
others.
4. Connect mathematical ideas
and real-world situations through
modeling.
5. Use a variety of mathematical
tools effectively and strategically.
http://cdn.kutasoftware.com/Worksheets/PreAlg/OneStep%20Word%20Problems.pdf
6. Communicate mathematically
and approach mathematical
situations with precision.
http://cdn.kutasoftware.com/Worksheets/PreAlg/TwoStep%20Word%20Problems.pdf
7. Identify and utilize structure
and patterns.
Resources:
Text:
Holt McDougal Algebra I Common Core Edition, Section 1-2, 1-3, 1-4, 1-5, 1-7
SREB Math Ready Unit 2 Equations
Exemplar Lessons:
http://betterlesson.com/lesson/443652/more-solving-problems-with-equations
http://betterlesson.com/lesson/528877/creating-linear-equations-in-one-variable
Web Sites:
Relationships in One Variable
https://commoncorealgebra1.wikispaces.hcpss.org/Unit+1
Grade 9 Algebra 1, Q1
http://calculator.tutorvista.com/solving-equations-with-variables-on-both-sidescalculator.html
Videos:
http://my.hrw.com/tabnav/controller.jsp?isbn=9780547708508
https://learnzillion.com/lessons/1249-writing-algebraic-equations-addition-subtraction
USATestPrep: Solve 1-variable Equations (2:19), Solve Two-Step Equations (2:00),
Solve Multi-step Equations (2:18), Word Problems into Equations (2:11)
www.phschool.com, Web Code: ate-0775, Chapter 2: Lessons 4, 5; Chapter 3:
Lesson 1, 2, 3, 6, 9; Chapter 4: Lesson 6
Sample Assessment-like Questions:
Assessments: Textbook assignments, Worksheet assignments, Quizzes, Tests, Oral
responses, Observations
Holt Algebra 1 Test Prep: p. 21-22, 29, 37-38, 44-45, 58-60
http://mathbitsnotebook.com/Algebra1/LinearEquations/LEAPPS.html
Multiple Choice:
Paolo can mow the lawn at his family’s home in 2 hours. His younger sister Roberta
needs 3 hours to mow the lawn. Paolo and Roberta would like to have 2 lawnmowers
so they both can mow at the same time. The siblings need to know how much time
working together would save to help convince their parents to get another lawnmower.
What equation can the siblings use to determine the time t, in hours, needed to mow
the lawn when they work together?
A.
𝒕 𝒕
+ =𝟏
𝟐 𝟑
C.
B.
𝟐𝒕 + 𝟑𝒕 = 𝟏
D.
𝒕 𝒕 𝟏
+ =
𝟐 𝟑 𝟐
𝟐𝒕 + 𝟑𝒕 =
𝟏
𝟐
Open Ended:
Jeremy receives a base salary of $25,000 plus 5% commission on his
sales. Jeremy received a total salary of $45,000 last year. How much
were his total sales?
Grade 9 Algebra 1, Q1
Content Strand: Creating Equations
Standard: A1.AREI.11* Solve an equation from f(x) = g(x) graphically by identifying the
x-coordinate(s) of the point(s) of intersection of the graphs of �= �(�) and � = g(�).
(Limit to linear; quadratic; exponential.)
Related Standards:
SCCCR A1.ACE.1
SCCCR A1.ACE.2
SCCCR A1.AREI.3
CCSSM A.REI.11
Vocabulary: equation, variable, constant, inverse operation, order of operations,
coefficient, solution, properties of equality, no solution, infinitely many solutions, identity,
multiplicative inverse (reciprocal), like terms, graphically, intersection, x-coordinate
Example:
Strategies/Activities:
SREB Math Ready Unit 2 Equations, Lesson 2
Process Standards
1. Make sense of problems and
persevere in solving them.
2. Reason both contextually and
abstractly.
3. Use critical thinking skills to
justify mathematical reasoning
and critique the reasoning of
others.
4. Connect mathematical ideas
and real-world situations through
modeling.
5. Use a variety of mathematical
tools effectively and strategically.
6. Communicate mathematically
Grade 9 Algebra 1, Q1
and approach mathematical
situations with precision.
7. Identify and utilize structure and
patterns.
Resources:
Text:
Holt McDougal Algebra I Common Core Edition, Section 1-5 Technology Lab
Exemplar Lessons:
http://mathbits.com/MathBits/TISection/Algebra1/SolveEquations.htm
Web Sites:
Relationships in One Variable
https://commoncorealgebra1.wikispaces.hcpss.org/Unit+1
Videos:
http://my.hrw.com/tabnav/controller.jsp?isbn=9780547708508
Sample Assessment-like Questions:
Assessments: Textbook assignments, Worksheet assignments, Quizzes, Tests, Oral
responses, Observations
Holt Algebra 1 Test Prep: p. 21-22, 29, 37-38, 44-45, 58-60
http://mathbitsnotebook.com/Algebra1/LinearEquations/LEPracEquations.html
Multiple Choice:
Lila graphed two linear functions, y = f(x) and y = g(x). Use a graphing
utility to graph f(x)= 0.9x - 2.1 and g(x) = -1.8x + 1.5. Then use the graph
to find the approximate solution to the equation f(x) = g(x).
A. 2.2
C. 0.8
B. 1.3
D. -0.9
Open Ended:
Grade 9 Algebra 1, Q1
Find the x-coordinates of the points of intersection, if any, of the graphs
of the following functions.
f(x) = -3x + 12
g(x) = 2x - 3
Grade 9 Algebra 1, Q1
Content Strand: Creating Equations
Standard: A1.ACE.4* Solve literal equations and formulas for a specified variable
including equations and formulas that arise in a variety of disciplines.
Related Standards:
SCCCR A1.AREI.3
SCCCR A1.NQ.1
CCSSM A.CED.4
Vocabulary: variable, inverse operations, literal, formula, coefficient, factors, terms,
expressions, numerical expression, algebraic expression, verbal expression, equation,
evaluate, substitute, sum, difference, product, quotient, squared, square root, cubed,
cube root, less than, more than, is (equal), double, triple, half, third, reduced by,
increased by, decreased by, twice, in groups of, power, exponent, per, ratio, order of
operations, constant, inverse operation, solution, properties of equality, no solution,
infinitely many solutions, identity, multiplicative inverse (reciprocal), like terms,
reasonable, interpret
Example:
● The Pythagorean Theorem expresses the relation between the legs a and b of a
right triangle and its hypotenuse c with the equation a2 + b2 = c2.
○ Why might the theorem need to be solved for c?
○ Solve the equation for c and write a problem situation where this form of
the equation might be useful.
○ Solve
for radius r.
● Motion can be described by the formula below, where t = time elapsed, u=initial
velocity, a = acceleration, and s = distance traveled
s = ut+½at2
● Why might the equation need to be rewritten in terms of a?
● Rewrite the equation in terms of a.
Strategies/Activities:
http://mathequalslove.blogspot.com/2013/06/literal-
Process Standards
Grade 9 Algebra 1, Q1
equations-scavenger-hunt.html
https://www.mangahigh.com/enus/math_games/algebra/rearranging_forumulas_/literal_e
quations
1. Make sense of problems and
persevere in solving them.
2. Reason both contextually and
abstractly.
http://www.regentsprep.org/Regents/math/ALGEBRA/AE4 3. Use critical thinking skills to
/indexAE4.htm
justify mathematical reasoning
and critique the reasoning of
http://handsonmathinhighschool.blogspot.com/2012/07/m others.
ade4math-3-literal-equations.html
4. Connect mathematical ideas
http://teachers.henrico.k12.va.us/math/hcpsalgebra1/mod and real-world situations through
ule3-5.html
modeling.
http://teachers.henrico.k12.va.us/math/HCPSalgebra1/A4a.html
5. Use a variety of mathematical
tools effectively and strategically.
6. Communicate mathematically
and approach mathematical
situations with precision.
7. Identify and utilize structure
and patterns.
Resources:
Text:
Holt McDougal Algebra I Common Core Edition, Section 1-6
SREB Math Ready Unit 2 Lesson 4 Task 11 and 12
Exemplar Lessons:
https://commoncorealgebra1.wikispaces.hcpss.org/file/detail/A.CED.A.4%20Lesson%20
Homecoming.doc
http://betterlesson.com/lesson/443648/solving-literal-equations
Web Sites:
https://www.engageny.org/resource/algebra-i-module-1-topic-c-lesson-19
http://betterlesson.com/lesson/443648/solving-literal-equations
Grade 9 Algebra 1, Q1
Videos:
http://my.hrw.com/tabnav/controller.jsp?isbn=9780547708508
USATestPrep: Solving Formulas for Specified Variables (2:59)
https://learnzillion.com/lessons/3321-solve-literal-equations
Sample Assessment-like Questions:
Assessments: Textbook assignments, Worksheet assignments, Quizzes, Tests, Oral
responses, Observations
Holt Algebra 1 Test Prep: p. 52-53
http://mathbitsnotebook.com/Algebra1/LinearEquations/LELiteralEquationPractice.html
Multiple Choice:
5
Solve 𝑦 = 8 𝑏 + 10 for b.
8
𝑏 = − 𝑦 + 16
5
A.
B.
𝑏=
8
𝑦 − 16
5
C.
D.
𝑏=
5
𝑦 − 10
8
5
𝑏 = − 𝑦 + 10
8
Open Ended:
1. Solve P = 2(l + w) for l.
2. Use the distance formula to find the unknown value.
d = 171 mi, r = 19 mi/min, t = ?
Grade 9 Algebra 1, Q1
Content Strand: Real Number System
Standard: A1.AREI.3* Solve linear equations and inequalities in one variable,
including equations with coefficients represented by letters.
Related Standards:
SCCCR A1.ACE.1
SCCCR A1.AREI.1
CCSSM A.REI.3
Vocabulary: coefficient, factors, variable, terms, expressions, numerical expression,
algebraic expression, verbal expression, inequality, evaluate, substitute, sum,
difference, product, quotient, less than, more than, double, triple, half, third, reduced by,
increased by, decreased by, twice, in groups of, power, exponent, per, ratio, order of
operations, constant, inverse operation, solution, properties of equality, no solution,
infinitely many solutions, identity, multiplicative inverse (reciprocal), like terms, greater
than, greater than or equal to, less than, less than or equal to, is more than, is less than,
no more than, no less than, at most, at least, maximum, minimum, compound, and, or,
open/closed circle, inclusive, not inclusive, intersection, union, reasonable, interpret
Example:
● 3x > 9
● Solve for x: 2/3x + 9 < 18
Strategies/Activities:
http://misscalculate.blogspot.com/search/label/Algebra%
20I%20Lessons
http://teachers.henrico.k12.va.us/math/hcpsalgebra1/A5a.html
http://mathequalslove.blogspot.com/2013/11/onevariable-inequalities-inb-pages.html
http://mathequalslove.blogspot.com/2012/09/algebra-1inb-pages-over-multi-step.html
Process Standards
1. Make sense of problems and
persevere in solving them.
2. Reason both contextually and
abstractly.
http://tinyurl.com/nuualln
3. Use critical thinking skills to
justify mathematical reasoning and
critique the reasoning of others.
http://www.quia.com/rr/521133.html?AP_rand=52840854
8
4. Connect mathematical ideas and
real-world situations through
Grade 9 Algebra 1, Q1
https://www.mangahigh.com/enus/math_games/algebra/inequalities/inequalities
modeling.
5. Use a variety of mathematical
tools effectively and strategically.
https://www.mangahigh.com/enus/math_games/algebra/inequalities/two_inequality_sign
s
6. Communicate mathematically
and approach mathematical
situations with precision.
https://campus.mangahigh.com/en-us/px/213/0/0
http://www.regentsprep.org/Regents/math/algebra/AE8/p
artnerResource.htm
7. Identify and utilize structure and
patterns.
http://cdn.kutasoftware.com/Worksheets/Alg1/Graphing%
20Inequalities.pdf
http://cdn.kutasoftware.com/Worksheets/Alg1/OneStep%20Inequalities.pdf
http://cdn.kutasoftware.com/Worksheets/Alg1/TwoStep%20Inequalities.pdf
http://cdn.kutasoftware.com/Worksheets/Alg1/MultiStep%20Inequalities.pdf
http://cdn.kutasoftware.com/Worksheets/Alg1/Compound
%20Inequalities.pdf
http://cdn.kutasoftware.com/Worksheets/Alg1/Absolute%
20Value%20Inequalities.pdf
Resources:
Text:
Holt McDougal Algebra I Common Core Edition, section 2-1, 2-2, 2-3, 2-4, 2-5, 2-6, 2-7
Exemplar Lessons:
http://betterlesson.com/lesson/573860/solving-linear-inequalities
Grade 9 Algebra 1, Q1
https://commoncorealgebra1.wikispaces.hcpss.org/file/detail/A.REI.B.3%20Lesson%20
Solving%20Inequalities.docx
Web Sites:
Videos:
http://my.hrw.com/tabnav/controller.jsp?isbn=9780547708508
USATestPrep: Graphing Solutions to Inequalities (2:49), Interpret Solutions:
Inequalities (1:18), Solve 1-Variable Inequalities I (1:24), Solve 1-Variable Inequalities II
(1:53), Solve Multistep Inequalities (2:18), Solving Linear Inequalities (2:43), Word
Problems: Linear Inequalities (2:58)
www.phschool.com, Web Code: ate-0775, Chapter 4: Lessons 1, 2, 3, 4, 5
Sample Assessment-like Questions:
Assessments: Textbook assignments, Worksheet assignments, Quizzes, Tests, Oral
responses, Observations
Holt Algebra 1 Test Prep: p. 104-105, 110-111, 116-118, 124-125, 130-131, 139-140,
146-148
http://mathbitsnotebook.com/Algebra1/Inequalities/IQinequalityPractice.html
http://mathbitsnotebook.com/Algebra1/Inequalities/IQCompoundPractice.html
http://mathbitsnotebook.com/Algebra1/Inequalities/IQAppliedPractice.html
Multiple Choice:
Solve -5h + 3 < -7.
A.
h>2
C. h < 2
B.
h > -2
D.
Open Ended:
h < -2
Grade 9 Algebra 1, Q1
Solve 2x + 7 > x + x + 1.
Grade 9 Algebra 1, Q1
Content Strand: Real Number System
Standard: A1.ACE.1* Create and solve equations and inequalities in one variable that
model real-world problems involving linear, quadratic, simple rational, and exponential
relationships. Interpret the solutions and determine whether they are reasonable. (Limit
to linear; quadratic; exponential with integer exponents.)
Related Standards:
SCCCR A1.AREI.1
SCCCR A1.AREI.3
CCSSM A.CED.1
Vocabulary: coefficient, factors, variable, terms, expressions, numerical expression,
algebraic expression, verbal expression, inequality, evaluate, substitute, sum,
difference, product, quotient, squared, square root, cubed, cube root, less than, more
than, double, triple, half, third, reduced by, increased by, decreased by, twice, in groups
of, power, exponent, per, ratio, absolute value, order of operations, constant, inverse
operation, solution, properties of equality, no solution, infinitely many solutions, identity,
multiplicative inverse (reciprocal), like terms, greater than, greater than or equal to, less
than, less than or equal to, is more than, is less than, no more than, no less than, at
most, at least, maximum, minimum, compound, and, or, open/closed circle, inclusive,
not inclusive, intersection, union, reasonable, interpret
Example:
A total of 66 people attended a field trip to a chocolate factory for a tour. A maximum of
15 people are allowed to tour at one time. Create an inequality to describe how many
tour groups to organize? (Let g = the number of groups.)
Strategies/Activities:
Process Standards
https://www.khanacademy.org/math/prealgebra/applying-math-reasoning-topic/greater-than-lessthan/e/inequalities-in-one-variable-1
http://teachers.henrico.k12.va.us/math/hcpsalgebra1/A5a.html
http://www.algebra-class.com/solving-word-problems-inalgebra-practice.html
1. Make sense of problems and
persevere in solving them.
2. Reason both contextually and
abstractly.
3. Use critical thinking skills to
justify mathematical reasoning and
Grade 9 Algebra 1, Q1
http://www.doe.state.la.us/lde/uploads/5629.pdf
critique the reasoning of others.
4. Connect mathematical ideas and
real-world situations through
modeling.
5. Use a variety of mathematical
tools effectively and strategically.
6. Communicate mathematically
and approach mathematical
situations with precision.
7. Identify and utilize structure and
patterns.
Resources:
Text:
Holt McDougal Algebra I Common Core Edition, sections 2-1, 2-2, 2-3, 2-4, 2-5, 2-6, 2-7
Exemplar Lessons:
http://betterlesson.com/lesson/443651/creating-inequalities-to-solve-problems
Web Sites:
http://www.shmoop.com/common-core-standards/ccss-hs-a-ced-1.html
Videos:
http://my.hrw.com/tabnav/controller.jsp?isbn=9780547708508
USATestPrep: Graphing Solutions to Inequalities (2:49), Interpret Solutions:
Inequalities (1:18), Solve 1-Variable Inequalities I (1:24), Solve 1-Variable Inequalities II
(1:53), Solve Multi-step Inequalities (2:18), Solving Linear Inequalities (2:43), Word
Problems: Linear Inequalities (2:58)
www.phschool.com, Web Code: ate-0775, Chapter 4: Lessons 1, 2, 3, 4, 5, 6
Sample Assessment-like Questions:
Assessments: Textbook assignments, Worksheet assignments, Quizzes, Tests, Oral
responses, Observations
Grade 9 Algebra 1, Q1
Holt Algebra 1 Test Prep: p. 104-105, 110-111, 116-118, 124-125, 130-131, 139-140,
146-148
http://mathbitsnotebook.com/Algebra1/Inequalities/IQAppliedPractice.html
Multiple Choice:
Mrs. Nelson is buying folding chairs that are on sale for $10. She has
$50. Which inequality can be solved to show the number of chairs c Mrs.
Nelson can buy?
A. 10c < 50
B. 10c > 50
Open Ended
1. A store manager is accepting applications for part-time workers. He can hire no
more than 14 people. So far, he has hired 9 people. Write and solve an inequality
to determine how many more people the manager can hire.
2. An essay must be at least 500 words long to be accepted. Define a variable and
write an inequality for the acceptable number of words in an essay. Graph the
solutions.