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Common Core Learning Standards for MathematicsHigh School Algebra 1

Relationships Between Quantities and Reasoning with Equations

Common Core Learning Standards Concepts Embedded Skills Vocabulary

Reason quantitatively and use units to solve problems.Working with quantities and the relationships between them provides grounding for work with expressions, equations, and functions.

Units of measurement

in data

Units of measure in

solving problems

Appropriate scales and units for

descriptive modeling

N.Q.1 create and translate units consistently with data and graphs

Create a reasonable and appropriate scale for graphs and data displays (charts)

AccuracyMeasurementQuantitiesLimitationsUnitsFormulasScaleOriginData displaysGraphsSolutionModelingConversionsTableChart

N.Q.1 Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.

N.Q.2 create appropriate units for multi-step problems

Create appropriate units to write an equation for a real world situation

Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Alignment Project for Mathematics— Permission to use (not alter) and reproduce for educational purposes only.

N.Q.2 Define appropriate quantities for the purpose of descriptive modeling.N.Q.3 Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.

Limiting data for

measurement

N.Q.3 identify variable quantities, choose a level of accuracy based on the problem situation

SAMPLE TASKS


I.) a.) You are purchasing jeans and T-shirts. Jeans cost $35 and T-shirts cost $15. You only have $115 to spend and plan on purchasing a total of 5 items. Graph the system 35 x+15 y=115 and x+ y=5 on the grid below. Show appropriate scale and label axis appropriately.

b.) What variable represents the number of jeans purchased?

c.) What variable represents the number of T-shirts purchased?

d.) How many pairs of jeans and how many T-shirts can you buy?

e.) Explain why a point in the fourth quadrant does not satisfy the system.


II.) You have a jar of pennies and quarters. You want to choose 15 coins that are worth exactly $4.35. a.) Write a system of equations that models this situation.

b.) Solve the system graphically. Show appropriate scale and label axis appropriately.

c.) Is your solution reasonable in terms of the original problem? Explain.


Graph will appear on Key document.III.) By comparing and contrasting the graphs, explain why they appear different?



Interpret the structure of expressions.Limit to linear expressions and to exponential expressions with integer exponents.

Identify terms and coefficients in an algebraic expression

Identify parts of multi-term expressions and formulas by breaking them up into their parts

A.SSE.1 Identify parts of an expression, including its terms, factors and coefficients.

Identify the factors within a term

Identify the difference between monomials, binomials, trinomials, and polynomials

Translate a complex expression by dissecting it into its individual parts

Terms Expression Monomial Binomial Trinomial Polynomial Factor Coefficient

A.SSE.1 Interpret expressions that represent a quantity in terms of itscontext.★a. Interpret parts of an expression, such as terms, factors, and coefficients.b. Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret p(1+r )n as the product of P and a factor not depending on P.

SAMPLE TASKSI.) Match the following with their classification

_____ 1.) 3 x2+6x A.) Monomial _____2.) x2−2 x+1 B.) Binomial _____ 3.) 5 x3 C.) Trinomial _____ 4.) −2 x4−5 x3+6 x−1 D.) Polynomial


II.) a.) Simplify the following: 2 x(3x2+4−2 x)

b.) When in standard form what is the leading coefficient?

III.) In the expression 6a2−5ab+3b−12

a.) List the term(s)

b.) List the coefficient(s)

c.) List the constant(s)


Common Core Learning Standards Concepts Embedded Skills VocabularyCreate equations that describe numbers or relationships.Limit A.CED.1 and A.CED.2 to linear and exponential equations, and, in the case of exponential equations, limit to situations requiring evaluation of exponential functions at integer inputs.Limit A.CED.3 to linear equations and inequalities. Limit A.CED.4 to formulas which are linear in the variable of interest.

Creating equations,

inequalities, and exponential equations

Solve equations, inequalities,

and exponential equations

Graphing equations and inequalities in two variables

A.CED.1 create and solve a linear equation or inequality from a word problem

Create and solve an exponential equation from a word problem

linearexponential

equation inequality

systems of equations

systems of inequalities

solution set of equations and inequalities

A.CED.2 Write linear equations using two variables (y= form)

Identify parts of the coordinate plane (axes and quadrants)

Graph linear with correct labels and scales from a word problem

Write exponential equation using two variables(y= form)

Graph an exponential equation from a table of values

VariableCoordinate planeAxesQuadrantsLabelsScalesStandard formAppropriateTable of valuesGrowth and decay


Finding the solution to the

system of equations and

inequalities

Constraints on equations and inequalities

Solving literal equations

with an appropriate scale from a word problemA.CED.1 Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.A.CED.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.A.CED.3 Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods.A.CED.4 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm’s law V = IR to highlight resistance R.

A.CED.3 Graph systems of equations and or inequalities with correct labels and scales from a word problem

explain whether solutions to a given problem are valid

Explain what the solution to a problem represents

Solve inequalities and identify the correct domain for the solution within the constraints of the word problem

Domain

Constraints

Solution set

A.CED.4 rewrite equations in terms of a different variable

Rewrite equations in terms of a different variable with squared variables

Literal equations

SAMPLE TASKS


I.)a.) Sue’s total cell phone bill was $56.60. If her plan includes $50 for 1000 minutes a month plus $0.30 for every minute over 1000, how many extra minutes did Sue use this month? Write and solve a linear equation to prove your answer. Only an algebraic solution will be accepted.

b.) Explain why 18 minutes is not a solution to the equation.

II.)The volume of a rectangular solid is K cm3, the height is represented by M cm, and the length is represented by N cm. Solve for the width in terms of K, M, and N.


III.)a.) A new museum had 7500 visitors this year. The museum expects the number of visitors to grow by 5% each year. The function

y=7500∗1.05x models the predicted number of visitors each year after x years. Graph the function for the domain 0≤ x≤5.

b.) Predict the number of visitors in year 7.

c.) How many years would it take for the museum to reach 20,000 visitors? Explain how you arrived at your answer.


IV.)Write a system of linear inequalities with the given characteristic.

a.) All solutions are in Quadrant III. b.) Graph to prove your work


V.)Graph the system of linear inequalities: x≥2 , y≥−3 ,∧x+ y≤ 4a.) Describe the shape of the solution region

b.) Find the vertices of the solution region

c.) Find the area of the solution region



Understand solving equations as a process of reasoning and explain the reasoning. Students should focus on and master A.REI.1 for linear equations and be able to extend and apply their reasoning to other types of equations in future courses. Students will solve exponential equations with logarithms in Algebra II.

Explain steps to solving an

equation

A.REI.1Assuming an equation has a solution, create a convincing argument that justifies each step in the solution process. Justifications may include the associative, commutative, and division properties, combining like terms, multiplication by 1

Explain the steps in solving an equation from another students work

Describe the reasonableness of a solution

Describe the method used to solve an equation

Properties Method Reasonable Solution Justify

A.REI.1 Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.

SAMPLE TASKS


I.) Use properties of equality and other properties to justify the solution below

Equation Property Reasons 4 ( x+7 )−16=44 4 x+28−16=44 ____________________

4 x+12=44 ____________________ -12 -12 4x = 32 ____________________ 4 4 x = 8 ____________________

I.) Two students solved the same inequality for x. Explain which student solved the inequality correctly and describe where the error occurred.

Student A Student B 12−3 x ≤6 12−3 x ≤6 −3 x≤−6 −3 x≤−6 x≥2 x≤2



Solve equations and inequalities in one variable. Extend earlier work with solving linear equations to solving linear inequalitiesin one variable and to solving literal equations that are linear in the variable being solved for. Include simple exponential equations that rely only on application of the

laws of exponents, such as 5x=125 or 2x=116 .

Solve linear equations

Solve simple exponential equations

Solve literal equations

Solve linear inequalities

A.REI.3Construct a solution to a linear equation in one variable

Solve simple exponential equations that use the laws of exponents

Construct a solution to an equation with variable coefficients

Construct Coefficients Variables Exponential Literal Solution set

A.REI.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

SAMPLE TASKSI.) Solve for x: 4 x=640

II.) Solve for x: 3x=274


III.) Solve for p in the equation 3 p+m=r , in terms of m and r.

IV.) Solve for x: 10 x+12=2(5 x+6) and explain why your solution is unique.


V.) Solve for m: 9m−4=−3m+5+12m and explain why your solution is unique.

VI.) Is the point (5, -2) a solution to 2 x+ y>10, justify your answer.



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commoncoremath.wikispaces.comcommoncoremath.wikispaces.com/file/vie… · Web view · 2012-06-06Limit A.CED.3 to linear equations and inequalities. Limit A.CED.4 to formulas which