Download Algebra Curriculum Guide – Unit 1 Expressions

Algebra Curriculum Guide – Unit 1 Expressions
2016 – 2017
Unit 1: Expressions
Time Frame: 11 – 14 days
Connections to Previous Learning:
Students use the properties of arithmetic learned in middle school to build and transform algebraic expressions of continued complexity. All exponent
rules with integer exponents were taught in 8th grade. Square roots and cube roots where taught in 8th grade.
Focus within the Grade Level:
Part A: Rational exponents are the new exponent learning. Connecting rational exponents to roots is a focus in algebra.
Part B: Students will work on addition, subtraction, and multiplying polynomial expressions. The vocabulary of polynomial expressions will be taught.
Students understand that complex expressions are built of the basic operations; sums of terms and products of factors. Students will give precise
attention to units when applying these skills to real world situations.
Connections to Subsequent Learning:
Students apply the properties of operations to algebraic expressions and extend these properties to functions such as square root, exponential, and
trigonometric. Factoring will occur in quadratic unit later in the year.
Unit 1
Clover Park School District 6/1/16
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Algebra Curriculum Guide – Unit 1 Expressions
2016 – 2017
Common Core Standards in this unit:
Extend the properties of exponents to rational exponents.
HSN.RN.A.1
Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to
those values, allowing for a notation for radicals in terms of rational exponents.
HSN.RN.A.2
Rewrite expressions involving radicals and rational exponents using the properties of exponents.
Interpret the structure of expressions.
HSA.SSE.A.1
Interpret expressions that represent a quantity in terms of its context.
HSA.SSE.A.1.A Interpret parts of an expression, such as terms, factors, and coefficients.
HSA.SSE.A.1.B Interpret complicated expressions by viewing one or more of their parts as a single entity.
HSA.SSE.B.3
Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the
expression.
HSA.SSE.B.3.C Use the properties of exponents to transform expressions for exponential functions.
Perform arithmetic operations on polynomials
HSA.APR.A.1 Understand that polynomials form a system analogous to the integers, namely they are closed under the operation of addition,
subtraction, and multiplication; add, subtract, multiply polynomials.
Mathematical Practices
1.
2.
3.
4.
5.
6.
7.
8.
Unit 1
Make sense of problems and persevere in solving them.
Reason abstractly and quantitatively.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
Use appropriate tools strategically.
Attend to precision.
Look for and make sure of structure.
Look for and express regularity in repeated reasoning.
Clover Park School District 6/1/16
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Algebra Curriculum Guide – Unit 1 Expressions
2016 – 2017
Stage 1 Desired Results
Transfer Goals
Students will be able to independently use their learning to…



Apply concepts and procedures involving expressions to solve to real world examples.
Reason quantitatively and use units to solve problems.
Interpret the structure of expressions.
Meaning Goals
UNDERSTANDINGS
Students will understand that…
 Every number has a decimal expansion.
 The value of any real number can be represented in relation to other real
numbers such as with decimals converted to fractions, scientific notation
and numbers written with exponents (8 = 23 ).
 Properties of operations with whole and rational numbers also apply to
all real numbers.
ESSENTIAL QUESTIONS





When is it advantageous to represent relationships between
quantities symbolically? numerically? graphically?
Why are procedures and properties necessary when
manipulating numeric or algebraic expressions?
How can the structure of expressions/equations/inequalities
help determine a solution strategy?
Why are quantities represented in multiple ways?
When are exponents used and why are they important?
Acquisition Goals
Students will know…

Decimals that “terminate” actually repeat the digit zero. (2.5 =




2.500000….)
Numbers that repeat in their decimal form are called rational.
Numbers that do not repeat in their decimal form are called irrational.
Exponent operation properties.
Addition, subtraction, and multiplication of polynomials.
Unit 1
Students will be skilled at…
 Identify the different parts of the expression and explain their
meaning within context. (i.e. terms, factors, coefficients,
constants, exponents).
 Define, explain and describe the components of a
complicated expression using decomposition.
 Use exponent rules to rewrite expressions.
Clover Park School District 6/1/16
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Algebra Curriculum Guide – Unit 1 Expressions
2016 – 2017
Stage 1 Established Goals: Common Core State Standards for Mathematics
Students will be able to independently use their learning to…
Part A of unit
Interpret the structure of expressions
HSA.SSE.B.3
Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the
expression.
HSA.SSE.B.3.C Use the properties of exponents to transform expressions for exponential functions.
Extend the properties of exponents to rational exponents
HSN.RN.A.1
Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to
those values, allowing for a notation for radicals in terms of rational exponents.
HSN.RN.A.2
Rewrite expressions involving radicals and rational exponents using the properties of exponents.
Explanations, Examples, and Comments
Standards taught in 8th grade connected to these high school standards
8.NS.A.1 Know that numbers that are not rational are called irrational. Understand informally that every number has a
decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal
expansion that repeats eventually into a rational number.
8.NS.A.2 Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them
approximately on a number line diagram, and estimate the value of expressions.
8.EE.A.1 Know and apply the properties of integer exponents to generate equivalent numerical expressions.
8.EE.A.2 Use square root and cube root symbols to represent solutions to equations of the form 𝑥 2 = 𝑝 and 𝑥 3 = 𝑝, where p
is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes.
ALD
Target A: Extended the properties of exponents to rational exponents
Level 1 students should be able to rewrite expressions with rational exponents of the form (1/n) to radical form and vice
versa.
Level 2 students should be able to look for and use structure to extend the properties of integers exponents to multiply and
divide expressions with rational exponents that have common denominators.
Level 3 students should be able to rewrite expressions with rational exponents of the form (m/n) to radical form, and vice
versa, and look for and use structure to extend the properties of integer exponents to all laws of exponents on radical
expressions and expressions with rational exponents.
Vocabulary: Cards
Real Numbers (HS)
Rational Numbers (8th)
Irrational Numbers (8th)
Integers (7th)
Whole (4th)
Expand (7th)
Cube Root (8th)
Square Root (8th)
Base (8th)
Exponent (8th)
Radical Exponent (HS)
Item Specs Version 2.0
Target A
Target B
Item Specs Version 3.0
Target A
Target B
Target B: Use properties of rational and irrational numbers (only Level 1)
Unit 1
Clover Park School District 6/1/16
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Algebra Curriculum Guide – Unit 1 Expressions
2016 – 2017
Level 1 students should be able to identify the difference between a rational and irrational number.
Stage 1 Established Goals: Common Core State Standards for Mathematics
Students will be able to independently use their learning to…
Part B of unit
Interpret the structure of expressions.
HSA.SSE.A.1
Interpret expressions that represent a quantity in terms of its context.
HSA.SSE.A.1.A Interpret parts of an expression, such as terms, factors, and coefficients.
HAS.SSE.A.1.B Interpret complicated expressions by viewing one or more of their parts as a single entity.
Perform arithmetic operations on polynomials
HSA.APR.A.1 Understand that polynomials form a system analogous to the integers, namely they are closed under the operation of addition,
subtraction, and multiplication; add, subtract, multiply polynomials.
Explanations, Examples, and Comments
Vocabulary and Item Specs
ALD
Target D: Interpret the structure of expressions
Level 1 students should be able to identify parts of an expression, such as terms, factors, coefficients, exponents, etc.
Level 2 students should be able to interpret parts of an expression, such as terms, factors, coefficients, exponents, etc.,
and interpret simple compound expressions by viewing one or more of their parts as a single entity. They should be able
to recognize equivalent forms of linear expressions.
Level 3 students should be able to recognize equivalent forms of expressions and use the structure of an expression to
identify ways to rewrite it. They should be able to interpret complicated expressions by viewing one or more of their
parts as a single entity.
Vocabulary: Cards
Variable (6th)
Constant(7th)
Evaluate (5th)
Expression (6th)
Term
Like-Terms (HS)
Coefficient (6th)
Distribute (HS)
Polynomial (HS)
Squared Term (HS)
Linear (7th)
Quadratic (HS)
Monomial (HS)
Binomial (HS)
Trinomial (HS)
Factors (HS)
Target E: Write expressions in equivalent forms to solve problems
Level 1 students should be able to write a quadratic expression with integer coefficients and a leading coefficient of 1 in
an equivalent form by factoring. They should be able to use properties of exponents to expand a single variable
(coefficient of 1) with a positive integer exponent into an equivalent form and vice versa.
Level 2 students should be able to write a quadratic expression with integer coefficients in an equivalent form by
factoring or by completing the square. They should be able to use properties of exponents to expand a repeated single
variable (coefficient of 1) with a nonnegative integer exponent into an equivalent form and vice versa.
Level 3 students should be able to write a quadratic expression with rational coefficients in an equivalent form by
factoring and by completing the square. They should be able to identify and use the zeros to solve or explain familiar
problems, and they should be able to use properties of exponents to write equivalent forms of exponential functions
with one or more variables, integer coefficients, and nonnegative rational exponents involving operations of addition,
subtraction, and multiplication, including distributing an exponent across terms within parentheses.
Unit 1
Clover Park School District 6/1/16
Item Specs Version 3.0
Target D
Target E
Target F
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Algebra Curriculum Guide – Unit 1 Expressions
2016 – 2017
Level 4 students should be able to find the maximum or minimum values of a quadratic function. They should be able to
choose an appropriate equivalent form of an expression in order to reveal a property of interest when solving problems.
Target F: perform arithmetic operations on polynomials
Level 1 students should be able to add, subtract, and multiply single-variable polynomials of degree 2 or less.
Level 2 students should be able to add, subtract, and multiply multi-variable polynomials made up of monomials of
degree 2 or less. They should understand that polynomials are closed under addition.
Level 3 students should be able to add, subtract, and multiply multi-variable polynomials of any degree and understand
that polynomials are closed under subtraction and multiplication.
Stage 2 - Evidence
SAMPLE Assessment Evidence
CLASSROOM/PERFORMANCE TASK(S):
Evaluative Criteria:
Common Assessment
See Sample Assessments for Unit 1.
Generating Polynomials from Patterns Lesson and PowerPoint
Washington State: Materials to help districts and others understand the
OTHER ASSESSMENT EVIDENCE:
organization and content of the standards and the content and evidence
base used to support the standards:
http://mathpractices.edc.org/pdf/Rational_Exponents.pdf
Washington State: Instructional materials, Resources and Course
Support: http://www.k12.wa.us/Mathematics/Resources.aspx
Washington State: Professional Learning Support:
http://www.k12.wa.us/Mathematics/profdev.aspx
Washington State: General Assessment Resources:
http://www.k12.wa.us/Mathematics/Assessment.aspx
SBA Sample Items
F-BF.2 (N.276)
A-REI.3 (I.088)
Stage 3 – Learning Plan Sample
Summary of Key Learning Events and Instruction that serves as a guide to a detailed lesson planning
LEARNING ACTIVITIES:
Additional Resources
Teacher should use assessment data to determine which of the
A suggested guide to layout of unit by days if teaching every other day in a block
Part A: HSA.SSE.B.3, HSA.SSEB.3.C, HSN.RN.A.1, and HSN.RN.A.2 Rational Exponents
Unit 1
Clover Park School District 6/1/16
materials below best meet student instructional needs. All materials
listed may not be needed.
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Algebra Curriculum Guide – Unit 1 Expressions
2016 – 2017
Stage 3 – Learning Plan Sample
Day 1: Holt Algebra 1: 7-1 Integer Exponents (review from 8th grade)
Day 2: Holt Algebra 1: 7-3 Multiplication Properties of Exponents (review from 8th grade)
Day 3: Holt Algebra 1: 7-4 Division properties of Exponents (review from 8th grade)
Day 4: Holt Algebra 1: Chapter 11 Extension Rational Exponents
Day 5: Holt Algebra 2: 8-6 Radical Expressions and Rational Exponents
Part A:
HSA.SSE.B.3, HSA.SSEB.3.C, HSN.RN.A.1, and HSN.RN.A.2
Rational Exponents
Fractional Exponents Lesson
Exploring Rational Exponents
Algebraic Expression Card Match
Exploring Exponents TI Activity
- Student papers
- Teacher papers
Exponent Rules TI Activity
- Student papers
- Teacher papers
Part B: HSA.SSE.A.1, HSA.SSE.A.1.A, HSA.SSE.A.1.B, and HSA.APR.A.1 Algebraic Expressions
Day 6: Holt Algebra 1: 7-5 Polynomials
Day 7: Holt Algebra 1: 7-6 Add/Subtract Polynomials
Day 8: Simplify Algebraic Expressions with Some Geometry: Worksheets
Day 9: Holt Algebra 1: 7-7 Multiplying Polynomials
Day 10: Algebraic Expressions with Some Geometry: Lesson and Worksheets
Day 11: Holt Algebra 1: 7-8 Special Products of Binomials
Common Assessment
Unit 1
Clover Park School District 6/1/16
Part B: HSA.SSE.A.1, HSA.SSE.A.1.A, HSA.SSE.A.1.B, and
HSA.APR.A.1 Algebraic Expressions
Holt Algebra 2: 1-5 Properties of Exponents
Checkerboard Borders: Develop Understanding Task pg. 4
(multiply polynomials)
Building More Checkerboard Borders: Develop
Understanding Task pg. 9
(multiply polynomials)
Algebraic Expressions with Some Geometry: Worksheets
Generating Polynomials from Patterns: Lesson and
PowerPoint
Interpreting Algebraic Expressions: Lesson and
PowerPoint
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