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CCSS Algebra 1-2 Learning Targets with Rubric

This document is the product of a team of PPS teachers experienced in writing learning targets and using them in instruction. While it represents our best work, we know this document will act as a working draft, to be revisited and revised as we continue to hone our instruction around CCSS Algebra.

The intended audience of this document is teachers of mathematics. While this document will be especially helpful for teachers who are using proficiency-based grading, it should also be useful to all teachers of CCSS Algebra as a summary of the new content students are expected to master due to Oregon’s adoption of the Common Core State Standards for Mathematics. The learning targets are written in student-friendly language. We chose to further call out aspects of the learning target being assessed for teachers in the “apply” and “extend” columns.

Every student should be expected to show mastery of ALL of the learning targets at the C level. A higher grade reflects a higher level of mastery. Our desire when adding the grading rubric below each Learning Target is that there is some consistency of expectations amongst and within buildings for students in PPS.

Proficiency based grading can be a complex and difficult process. If you plan to use these Measurement Topics and Learning Targets to track student progress, one way to make tracking more manageable is to test at the Measurement Topic Level, in which case students would need to pass all Learning Targets at a C level in order to pass the Measurement Topic. Individual Learning Targets could still be assessed formatively and in cases of retesting.

Portland Public Schools CCSS Algebra 1-‐2 Learning Targets Revised June 2014

2 We modeled our work after Robert J. Marzano’s Measurement Topics (Formative Assessment & Standards-Based Grading, 2010). The structure is as follows:

The A stands for Algebra

Example Measurement Topic: A1: Solving Linear Equations A[#]. [Measurement Topic]

[CCSS covered under this measurement topic]

Learning Targets

I can apply…

I can extend…

A[#]a. [Learning Target Text]

This detail goes deeper into the more algorithmic type of problems students should be able to complete to demonstrate proficiency on this learning target.

This detail goes deeper into types of problem solving skills a student should be able to complete to demonstrate proficiency on this learning target.

C Students can do…

B Students can do…

A Students can do…

These questions are examples of the minimum level of knowledge students need to demonstrate by the end of the course in order to earn a C for this Learning Target.

These questions are examples of more than the minimum level of knowledge students need to demonstrate by the end of the course in order to earn a B for this Learning Target. Students at this level can demonstrate a deeper level of understanding than the minimum expectation.

These questions are examples of a student who is exceeding mastery for this Learning Target. Often these questions require students to put multiple parts of learning together to solve a task or may reflect something that was never directly taught in the classroom.

+ Throughout this document this symbol (+) indicates an area that students do not need to master during this course. Teachers could use this as an extension or differentiation lesson.


3 The Standards

The following Common Core State Standards for Mathematics are covered in the PPS CCSS Algebra course, including the recommended calendar and timeline (https://sites.google.com/site/ppshighschoolmath/algebra) and the Measurement Topics and Learning targets in this document. The standards covered are based on the recommendation in the CCSS Mathematics Appendix A Traditional Pathway. The complete set of standards and Appendix A are available for download at http://corestandards.org/the-standards. The following are the standards covered in CCSS Algebra:

• The Mathematical Practices • Number and Quantity

o The Real Number System: N-RN.1-3 o Quantity: N-Q.1-3

• Algebra o Seeing Structure in Expressions: A-SSE.1-3 o Arithmetic with Polynomials and Rational Expressions: A-APR.1 o Creating Equations: A-CDE.1-3 o Reasoning with Equations and Inequalities: A-REI.1, 3-7,10-12

• Functions o Interpreting Functions: F-IF.1-6, 7abe, 8, 9 o Building Functions: F-BF.1a, 2 o Linear, Quadratic, and Exponential Models: F-LE.2, 3, 5

• Statistics and Probability o Interpreting Categorical and Quantitative Data: S-ID.1-3, 5-9


4 Contents

Introduction …………………………………………………………………………………………………1-2 The Standards ………………………………………………………………………………………………... 3 A1. Solving Linear Equations ………………………………………………………………………………..5-6 A2. Linear Functions…………………………………………………………………………………………7-8 A3. Systems ………………………………………………………………………………………………….9-10 A4. Statistics ………………………………………………………………………………………………..11-12 A5. Quadratic Functions …………………………………………………………………………………..13-16 A6. Inequalities………………………………………………………………………………………...…...17-18 A7. Exponents & Exponential Functions …………………………………………………………………..19-20 A8. Sequences & Series……………………………………………………………………………………..21-22 A9. Functions …………………………………………………………………………..…………………..23-24


5 A1. Solving Linear Equations N-Q.1-3; A-SSE.1-3; A-REI.1, 3

Learning Targets

I can apply…

I can extend…

A1a. I can solve equations.

¨ Variables on both sides of equation ¨ Combining like terms ¨ Using the distributive property ¨ Positive and negative terms ¨ Solutions that are rational numbers,

when there is no solution & when there are infinite solutions

¨ I can write answers in exact form, fractions or decimals when appropriate

¨ Model linear expressions and

equations using variables and solve problems using appropriate units

¨ +Determine the most efficient method and use it to rewrite and/or solve linear equations

¨ Identify and explain why some equations have one solution, no solution, and infinitely many solutions.


6x – 3x + 2 = 0 No solution type questions 6x + 9 = 4x + 2 All solution type questions

B

Students can do…

6 (x + 5) – 9 = 5x - 6( x – 5) = 10 6 ( x + 5) = 9x 4 – (x + 2) + 3x = 7

6 – 4( x + 3) = 10 !!!!= !

!


x ( x + 4) = x2 4x (2x + 5) = 8 (x + 1) (x – 1) (x + 5)(x + 4) = x2 – 9


6 A1. Solving Linear Equations N-Q.1-3; A-SSE.1-3; A-REI.1, 3 A1b. I can manipulate equations.

¨ Isolating a variable, manipulating linear

equations with more than one variable ¨ Rearranging an equation from standard

form into y = mx + b form (both where slope is a whole number & slope is a fraction) **teachers should note that this needs to be revisited in the context of graphing lines

¨ Positive & negative terms

¨ Model linear expressions and

equations using variables and solve problems using appropriate units

¨ Construct an argument to justify my solution process.

¨ Determine the most efficient method and use it to rewrite and/or solve linear equations


Solve for y: - 8x + 2y = 2


Solve for x: - 8x + 2y = 2


Solve for m: 4p = 4 + 2 (m – 𝑝)


7 A2. Linear Functions N-Q. 1-3; A-ASSE.1; A-CED.1-3; A-REI.6; F-IF.4, 6, 7abe, 9; F-LE.5

Learning Targets

I can apply…

I can extend…

A2a. I can model a linear function in multiple ways.

¨ Modeling in a table, graph, rule, and/or

situation ¨ Modeling with rules that include

positive, negative, and fraction slopes ¨ Calculating and interpreting the rate of

change (slope) and intercepts for a linear function represented as an equation, graph, or table (two points)

¨ Interpret and graph linear functions,

showing key features given an equation, table, or situation

¨ Given an x, find y or vice versa ¨ Compare the properties of two linear

functions when represented in multiple ways (i.e.: which has steeper slope)


Data table rule ( y = mx + b) Graph rule ( y = mx + b)


Convert data table into rule where data is not sequential

x 0 3 4 7 y

Given 2 points on graph write a rule Chapter 7 p. 197 graphs


Jumbled data write a rule

x 0 - 8 2 - 1 y


8 A2. Linear Functions N-Q. 1-3; A-ASSE.1; A-CED.1-3; A-REI.6; F-IF.4, 6, 7abe, 9; F-LE.5 A2b. I can determine the equation of a line.

¨ Given a point & slope (using Alg 1-2 as

a springboard to Alg 3-4 and point/slope formula as students work with transformations and manipulation)

¨ Given 2 points ¨ Given positive, negative, and fraction

slopes ¨ Find a line that is parallel ¨ Find a line that is perpendicular ¨ Rearranging an equation from standard

form into y = mx + b **this is revisited from A1

¨ Determine the x & y intercepts and

interpret their meanings ¨ Given a rule, calculate the intercepts

without graphing (including standard form)


Given (2, 4) and slope of – 3 find the equation of a line in y = mx + b form Given (- 6, 6) and slope of ½ find the equation of a line in y = mx + b form Given (0, 6) and (2, 10) find the equation of a line in y = mx + b form


Find the x & y intercepts of the line 2x + 3y = 6


Given the line y = - 3x + 7 find a line perpendicular to that line that passes through the point (6, 9)


9 A3: Systems A-CED.3; A-REI.5, 6, 11

Learning Targets

I can apply…

I can extend…

A3a. I can model systems in multiple ways.

¨ Interpreting a table, graph, rules,

situation and solutions ¨ Graphing systems of linear equations by

hand or using a graphing calculator ¨ Finding exact or approximate solutions

(as a coordinate pair or both variables in context)

¨ Positive, negative, and fraction slopes

¨ Model situations in any form (solve

using substitution or elimination) ¨ Solve using multiple representations ¨ Make connections between

representations (slope, intercepts…) ¨ Identify the solution in each

representation



Pizza problem from Essential Skills 3p + 4s = 80.70 5p + 2s = $75.75 From graph to rules


The perimeter of a triangle is 51cm. the longest side is 2cm and the shortest side is 3cm. Third side is 3 cm longer than the shortest side. Write a system of equations and solve for all three sides


10 A3: Systems A-CED.3; A-REI.5, 6, 11

A3b. I can solve systems using algebra.

¨ Substitution including equal values

method (include distributive property with positive and negative coefficients)

¨ Elimination – including multiplying one equation by a positive or negative number – including coefficients greater than one

¨ Solve a system of linear equations using elimination where I have to multiply both equations, can include a decimal and/or fraction multipliers or coefficients

¨ Identify and explain why some linear

systems have one solution, no solution, and infinitely many solutions

¨ Round appropriately for the given information


Solve by substitution Solve by elimination Solve by equal values x = y + 4 2x + 3y = 10 y = 6x + 2 2x + 3y = -12 4x – 3y = -4 y = 4x - 10


Solve by substitution Solve by equal values Solve by elimination y = x + 5 x = - 5y + 2 where you have to 4x – 6y = 12 x = 3y - 2 multiply both equations


Solve by substitution Having all solution/no solution answers 3x = y – 2 6x = 4 – 2y Solve using an inefficient method or looking at student work and do it a different way


11 A4: Statistics S-ID.1-3; S-ID.5-9

Learning Targets

I can apply…

I can extend…

A4a. I can determine the line of best fit.

¨ Graphing a line of best fit by hand and

using a graphing calculator ¨ Interpreting slope and intercept in

context ¨ Correlation (positive, negative, none) vs.

causation ¨ Continuous vs. discrete ¨ +Finding the line of best fit using

correlation coefficient and residuals

¨ Determine if statements of causation seem

reasonable or unreasonable and defend my opinion

¨ Use my line of best fit to make predictions and analyze the reasonableness of the solutions

¨ Discuss other models – if linear model does not work, can it still be modeled?

¨ +Plot and analyze the residuals, relate them to the correlation coefficient, and use both to describe how well the equation fits the data


Given a data set, graph it by hand and find the equation for the line of best fit Given a data set use the TI-84 to find the line of best fit for a data set Interpret the slope and y-intercept from a graph and make connections in context


Use a line of best fit to make predictions (extrapolate) - predict y given x a. School funding & homicide rates (both over time) b. Rates of dog ownership over time comparing cities, countries c. Stop & search events vs. crime rate (I know NYC has the data) d. Median income of a school, district, etc. vs. college graduation rate e. Gun ownership & crime rate (both over time) f. How much students sleep and their scores on a test compared to how much students study and their scores on a test


Use a line of best fit to make predictions (extrapolate) - predict x given y Compare two data sets and their slope and make predictions Ex: given how much students sleep and their scores on a test compared to how much students study and their scores on a test, what is OPTIMAL and justify your thinking


12 A4: Statistics S-ID.1-3; S-ID.5-9 A4b. I can represent one variable data.

¨ Create & interpret dot plots ¨ Create & interpret histograms ¨ Create & interpret box plots

¨ Use appropriate statistics for the shape

of the data distribution to compare center (median & mean) and spread (IQR & SD) of two or more data sets

¨ Interpret differences in shape, center and spread in context, accounting for possible effects of outliers


Basic creating and interpretation of multiple representations of data


Comparing two sets of data Using data that isn’t “clean”, has outliers or is missing pieces


Data analysis Analysis of outliers and their effect on data behavior


13 A5: Quadratic Functions N-RN.3; A-SSE.1, 3; A-CED.1-3; A-REI.1, 4, 7, 11; F-IF.4, 7a, 8, 9

Learning Targets

I can apply…

I can extend…

A5a. I can rewrite quadratic expressions.

¨ In standard, factored, or vertex form

(completing the square)

¨ +Isolate a specific variable in a given

quadratic formula with coefficients represented by letters

¨ +Derive by completing the square ¨ Compare/contrast multiple

representations of two quadratic functions

¨ Explain sum & product rules for rational and irrational numbers


(x +5)(x +2) x2 + 7x + 10 (x + 3)2 + 9 x2 + 6x + 18


Find x. (x + ? )(x +2) x2 + 7x + 10 Are the two following forms of a quadratic equivalent? Justify your answer. (x + 3)2 + 8 x2 + 6x + 18


Without factoring, predict which quadratic expressions below may have more than one factored form. Explain your reasoning for each.

a. 3x2 – 27x + 12 b. x2 – 11x + 111 c. – 4x2 – 12x – 4 d. 3x2 + 3x - 13



A5b. I can solve quadratic equations.

¨ By looking at a graph (including

systems with linear/quadratic or quadratic/quadratic)

¨ Using square roots ¨ Using the Zero Product Property ¨ Using the Quadratic Formula ¨ Using a calculator to check (from a

table and by calculating the zeros) ¨ Appropriate rounding & use of

approximation

¨ Give both exact and approximate

answers ¨ Solve systems of linear/quadratic or

quadratic/quadratic by graphing ¨ Solve a system of equations that

includes one or more quadratic equations algebraically

¨ Classify and give an example of rational and irrational numbers




Explain/Justify why examples of student work is incorrect. Solve for x: (X + 3)(x2 + 6x – 5) = 0 For the quadratic function use the idea of completing the square to write it in vertex form. Then state the vertex of the parabola. y = x2 - 4x + 9


15 A5: Quadratic Functions N-RN.3; A-SSE.1, 3; A-CED.1-3; A-REI.1, 4, 7, 11; F-IF.4, 7a, 8, 9 A5c. I can graph quadratic functions.

¨ Identify the x- and y-intercepts, line of

symmetry, vertex, “mirror” point, and use substitution to find another pair of points




Investigate the function: y = x2 + 2x – 8 Given the vertex and intercepts of a parabola, generate a quadratic function with a stretch factor of 1. Given x-intercepts create a quadratic equation in any two forms.



A5d. I can model quadratic functions.

¨ Given the zeros and vertex, write the

equation in factored and vertex form (a≠1)

¨ Continuous and discrete

¨ Identify and interpret parts of

quadratics (term, factor, coefficient, vertex, intercepts) in terms of its situation

¨ Answer questions about a modeled equation and interpret the reasonableness of the solutions

¨ +Include scatterplot and line of best fit


Amelia launched her science fair rocket and then backed away. The path of the rocket is given by h = - 10x2 + 100x – 160 where h is the height and x is the distance from Amelia. • How long is the rocket in the air? • At what time does the rocket stop going up and start coming

down? What is the maximum height of the rocket?


Zoe likes to make pancakes. She can flip a pancake in the air and have it land in the frying pan. The motion of the pancake is represented by the equation y= - 9x2 + 9.8x, where x represents the number of seconds after Zoe flips the pancake in the air, and y represents the height of the pancake above the frying pan. How high is the pancake at the top of its flight?


A 5.6 feet tall woman is shooting a free throw. The path of the basketball is parabolic in shape and the ball reaches its maximum height of 11.5 feet when the ball is 10 feet from the player. Find the equation for the path of the ball. Let x be the horizontal distance from the shooter, and y be the height of the ball. The ball hits the front of the rim, which is 10 feet high. How far is the shooter from the rim?


17 A6: Inequalities N-Q. 1-3; A-SSE.2, 3; A-CED, 1-3; A-REI. 3, 12

Learning Targets

I can apply…

I can extend…

A6a. I can solve inequalities and represent them in multiple ways.

¨ One variable (number line; open/closed

circle, shade which way?) ¨ Linear and quadratic ¨ Inequality; number line; sentence

¨ Model from situation; inequality,

number line ¨ Solve compound one-variable

inequalities ¨ Round appropriately for the given

information


Draw the graph of the solution region for the system of inequalities below.

𝑦 > 𝑥 − 4 𝑦 ≤ ! !! 𝑥 + 6

Write an inequality that represents the solutions shown on the number line below.


Sketch the graph for the following inequality. Test and verify a point in the solution region.

3 ≤ 𝑥 + 5 ≥ 7


Write the equations for a series of inequalities that make a regular pentagon (shaded on the inside) with vertices at L(0,4) I(4,7) G(11,4) H(8,0) T(3,0)


18 A6: Inequalities N-Q. 1-3; A-SSE.2, 3; A-CED, 1-3; A-REI. 3, 12

A6b. I can graph inequalities and identify the solution region.

¨ Two-variable (coordinate grid:

dotted/solid line, shade which side?) ¨ Single linear inequalities ¨ Systems of linear inequalities ¨ Quadratic inequalities

¨ Model from situation; system of

inequalities, graph ¨ Graph systems of inequalities including

linear/quadratic and quadratic/quadratic and special cases

¨ Determine whether a given point is a solution

¨ Model a system of linear, quadratic, and/or exponential inequalities using a graphing calculator and use the model to answer questions

¨ Identify a solution region


Graph the inequalities below on graph paper. 𝑦 ≤ −𝑥 + 5 To honor 50 years in business, All Strikes Bowling is having an anniversary special. Shoes rent for $1.25 and each game is $0.75. If Charlie has $20 and needs to rent shoes, how many games can he bowl?


Janet and Eric decided to plant tomatoes and corn on their farm. They can use up to 20 acres of land. Since Janet really likes corn, they have decided to plan more than twice as many acres of corn as tomatoes. Eric would like to have a minimum of 5 acres of tomatoes. • Write and graph a system of inequalities for this situation. Let x = acres of tomatoes and y = acres of corn • Name three possible combinations of acreage and indicate the corresponding points in the solution region.


Write two inequalities for the system below. Choose a point in the shaded region and verify your solution to both equations.


19 A7: Exponents & Exponential Functions N-RN. 1-2; N-Q.1-3; A-SSE. 1-3; A-CED. 1-3; F-IF. 4, 7abe, 8, 9; F-LE.5

Learning Targets

I can apply…

I can extend…

A7a. I can apply the properties of exponents.

¨ Simplify or rewrite algebraic

expressions with positive, zero, negative, and fractional exponents

¨ No negative or zero exponents allowed in final answers

¨ Difficulty: One variable/one law One variable/two laws Two variables/one law

¨ Apply multiple laws and/or variables ¨ +Extend the properties of exponents to

explain why negative, zero and fractional exponents work



Which of the expressions below are equivalent to -2x2? Make sure you find all of the correct answers. Justify your solution.

a. − 4𝑥! b. – ! !!

!!! c. !

!!! d. ! !

!!! !!

e. (2x)2 f. −2𝑥!


Simplify. Justify your thinking.

4𝑚! ∙ 𝑚!

− 8 𝑚!! 1𝑥!

! !

∙ 𝑥 ∙ 𝑥! Use of fractional exponents, use of multiple exponent rules Looking at student work


20 A7: Exponents & Exponential Functions N-RN. 1-2; N-Q.1-3; A-SSE. 1-3; A-CED. 1-3; F-IF. 4, 7abe, 8, 9; F-LE.5

A7b. I can model exponential functions in multiple ways.

¨ Model from situation: table, graph

(sketch) rule – continuous vs. discrete ¨ Interpret key features (intercepts,

asymptotes, intervals where increasing/decreasing and positive/negative)

¨ Identify and interpret parts of an exponential expression (initial value, base/common multiplier, exponent) in terms of its situation

¨ Classify the function as growth or decay

¨ Distinguish between situations that are

linear and those that are exponential ¨ Solve and model problems using

appropriate units and interpret the reasonableness of the solutions

¨ (+) Using a scatterplot and line of best fit

¨ Compare properties of two exponential functions when represented in multiple ways



Dinner at your grandfather’s favorite restaurant now costs $25.25 and has been increasing steadily at 4% per year. How much did it cost 35 years ago when he was dating your grandmother?


Compare and contrast an exponential function and a linear function.


21 A8: Sequences & Series F-IF.3; F-BF. 1a, 2; F-LE.2; A.SSE.4

Learning Targets

I can apply…

I can extend…

A8a. I can write sequences.

¨ Arithmetic and geometric sequences ¨ Explicit and recursive expressions ¨ A table, graph, situation or set of points

¨ Distinguish and explain the difference

between recursive and explicit, and arithmetic and geometric

¨ Differentiate between continuous and discrete

¨ Extend or complete an incomplete sequence

¨ Convert a list of numbers (sequence) into multiple representations of a function


Write a rule given the table

- 3

- 2

- 1

0

1

16

8

4

2

1 Given the rule, fill in the table below.


Trixie wants an arithmetic sequence with a common difference of –17 and a16th term of 93. (In other words, t (15) = 93.) Is it possible to create an arithmetic sequence to fit her information? If it is possible, find the rule. If it is not possible, explain why not.


Trixie is at it again. This time she wants an arithmetic sequence that has a graph with a slope of 22. She also wants t (8) =164 and the 13th term to have a value of 300. Is it possible to create an arithmetic sequence to fit her information? If it is possible, find the rule. If it is not possible, explain why not.


22 A8: Sequences & Series F-IF.3; F-BF. 1a, 2; F-LE.2; A.SSE.4

Learning Targets

I can apply…

I can extend…

A8b. I can evaluate series.

¨ Derive a series and the common ratio ¨ Express the sum of a finite geometric

series ¨ Calculate the sum of a finite geometric

series

¨ Recognize real world scenarios that

model geometric series (i.e. mortgage payments)

¨ Calculate the sum of a finite geometric series for a real world problem


Drought-conscious Darcy is collecting rainwater in order to water her garden through the hot, dry summer. During the last big rainstorm she filled 12 buckets full to the rim. She plans to use one bucket of water each week. However, Darcy did not count on evaporation. In the sun, each uncovered bucket loses 0.35 gallons of its water volume each week. If each bucket starts with 15 gallons in it, how many gallons will be in each of the unused buckets after 2 weeks in the sun? After 7 weeks? At the end of the 12th week, how many total gallons of water will Darcy have poured on her plants?


Lucy is working with a series that has 12 as its first term and is generated by the expression t(n) = - 9 + 21n. The sum of her series is 3429. How many terms are in her series?



23 A9. Functions A-REI.10; F-IF.1-3, 5, 6, 7abe; F-BF.1a, 2; F-LE.1-3

Learning Targets

I can apply…

I can extend…

A9a. I can use function notation to evaluate and interpret functions.

¨ Input/output: determine f (2) ¨ If f (x) = 7, solve for x

¨ Explain and verify with examples that

every point on the graph of an equation makes the equation true.

¨ Compare properties of two non-similar functions (linear, quadratic, exponential) when represented in multiple ways

¨ Graph a step or piecewise function from its equation and show key features


Evaluate f (5) for the function f (x) = x2 + 5x – 9


For the function f(x) = x2 + 5x + 13 if f(x) = 7, solve for x


Compare properties of quadratic and exponential functions when represented in multiple ways Graph a step or piece-wise function


24 A9. Functions A-REI.10; F-IF.1-3, 5, 6, 7abe; F-BF.1a, 2; F-LE.1-3

A9b. I can determine if a representation is a function and state its domain and range.

¨ Given a situation, table, graph or rule ¨ Vertical line test ¨ Using inequality notation (set notation

optional)

¨ Defend my choice of domain and range ¨ Demonstrate understanding of the

concepts: function, relation, domain and range as they relate to each other

¨ Create multiple representation of a function


Is this a function? Defend your reasoning.


Is this a function? Defend your reasoning. x2 + 9x - 5


Sonny graphed the equation f x = −0.5 𝑥 and made the summary statements listed below. Which of her statements are accurate? Explain to Sonny the reasons why her other statements are incorrect.

a. The graph looks like half of a parabola on its side b. The graph has no symmetry c. The values for y are both positive and negative d. The graph has no y-intercepts e. As x gets larger, y gets smaller

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