remedial algebra - burlington-nj.net

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CITY OF BURLINGTON PUBLIC SCHOOL DISTRICT CURRICULUM

Remedial Algebra

Revision Date: 7/1/18

Submitted by: Cameron Heines

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Table of Contents: Course Overview ........................................................................................................................................................................................................... 3

Pacing Chart ................................................................................................................................................................................................................... 4

Unit 1: Relationships between Quantities and Reasoning with Equations Overview At-a-Glance ............................................................................... 5

Unit #1: Relationships between Quantities and Reasoning with Equations Targeted Instructional Planning to Address Central Unit Standards: ...... 9

Unit 2: Systems, Linear, and Exponential Relationships Overview At-a-Glance ............................................................................................... 13

Unit #2: Systems, and Linear and Exponential Relationships Targeted Instructional Planning to Address Central Unit Standards: ................. 18

Unit 3: Descriptive Statistics Overview At-a-Glance ..................................................................................................................................... 23

Unit #3: Descriptive Statistics Targeted Instructional Planning to Address Central Unit Standards: ............................................................ 27

Unit 4: Quadratic Functions and Modeling Overview At-a-Glance ................................................................................................................ 31

Unit #4: Investigate Bivariate Data Targeted Instructional Planning to Address Central Unit Standards: ..................................................... 35

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Course Overview The New Jersey Student Learning Standards provide a consistent, clear understanding of what students are expected to learn, so

teachers and parents know what they need to do to help them. The standards are designed to be robust and relevant to the real world,

reflecting the knowledge and skills that our young people need for success in college and careers. With American students fully

prepared for the future, our communities will be best positioned to compete successfully in the global economy.

The curriculum guide has been generated to not only help students achieve the New Jersey Student Learning Standards and

demonstrate proficiency on State assessments, but to also ensure that students will be prepared for college and career opportunities

following high school graduation.

Primary Resource(s)

Textbooks

Title: Envision Algebra 1; Publisher: Pearson Education Inc.; Copyright: 2018

Title: Algebra 1 Common Core; Publisher: Pearson Education Inc.; Copyright: 2012

Supplemental Materials (including various level of texts at each grade level)

Title: NJ Center for Teaching and Learning: Worksheets, Activities, and Assessments

www.njctl.org

Title: Desmos Labs

https://teacher.desmos.com/

Title: EdCite

https://www.edcite.com

Title: Mathematics Assessment Project – Mathematics Assessment Resource Services

http://map.mathshell.org/materials/tasks.php?taskid=381&subpage=apprentice

http://www.njctl.org/

http://www.njctl.org/

http://www.mathworksheetsland.com/

https://teacher.desmos.com/

https://www.edcite.com/

http://map.mathshell.org/materials/tasks.php?taskid=381&subpage=apprentice

4

Pacing Chart Unit # & Title Pacing

(must equal 165 days for full-year or

83 days for

half-year course)

Unit 1 – Relationships between Quantities and Reasoning with Equations 23 days

Unit 2 – Systems, and Linear and Exponential Relationships 25 days

Unit 3 – Descriptive Statistics 19 days

Unit 4 – Quadratic Functions and Modeling 16 days

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Unit 1: Relationships between Quantities and Reasoning with Equations

Overview At-a-Glance Unit #1 – Relationships between Quantities and Reasoning with Equations

Unit Description: By the end of Algebra, students have learned to solve linear equations in one variable and have applied graphical and

algebraic methods to analyze and solve systems of linear equations in two variables. This unit builds on these earlier experiences by

asking students to analyze and explain the process of solving an equation. Students develop fluency in writing, interpreting, and

translating between various forms of linear equations and inequalities, and using them to solve problems. They master the solution of

linear equations and apply related solution techniques and the laws of exponents to the creation and solution of simple exponential

equations. All of this work is grounded on understanding quantities and on relationships between them.

Essential Skills:

Interpret the structure of expressions.

Understand solving equations as a process of reasoning and explain the reasoning.

Solve equations and inequalities in one variable.

Create equations that describe numbers or relationships.

Reason quantitatively and use units to solve problems.

Standards Addressed within this Unit

Central Unit Standards- This unit will focus primarily on

learning goals aligned with the following standards:

Supporting Unit Standards- This unit will also include activities aligned

with the following standards:

A.SSE.1

A.REI.1

A.REI.3

N.Q.1

N.Q.2

N.Q.3

A.CED.1

A.CED.2

A.CED.3

A.CED.4

Math Standards

NJSLS 8.EE.B.5

NJSLS 8.EE.B.6

NJSLS 8.EE.C.7a

NJSLS 8.EE.C.7b

NGSS Standards

HS.PS2.A

HS.PS2.B

HS.ETS1.A

HS.ETS1.C

ELA Standards

RST.11-12.1

SL.11-12.5

WHST.11-12.7

WHST.11-12.8

WHST.11-12.9

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Unit Details

Modifications for Special Education Students, English

Language Learners, Students at Risk of Failure, and Gifted

Students- Modify instructional approach and/or assignments and

evaluations as needed based for students with IEPs, 504s, ELLs

and gifted and talented students including but not limited to:

Increased integration of higher order thinking processes,

creative and critical thinking activities, problem-solving,

and open-ended tasks

Advanced pacing levels Greater opportunities for freedom of choice and

independent study that encourage independent and intrinsic

learning The student is located close to where the teacher is

providing instruction, in addition to being able to receive

peer assistance.

Visual cues such as linear models are provided on the wall.

Teachers utilize concrete models such as Algebra tiles for

an extended period of time

Students verbalize what they are doing through words,

pictures, and numbers

Students are encouraged to justify their thinking using

targeted mathematical vocabulary

Students are encouraged to restate word problems in their

own words

Students are provided opportunities to teach the concept to

each other.

An abstract concept is represented in a variety of ways,

such as concrete examples, words, symbols, drawings, and

acting it out

Students are placed in heterogeneous groups for peer

assistance and modeling

Integration of 21st century skills through NJSLS 9 and Career

Education:

9.2.12.C.2

Career Ready Practice

CRP 1, 2, 4, 6, 8, 10, 11, 12

Lessons, activities, and assessments require creativity and

innovation on the part of the students. They are required to

create projects and products as examples of mastery in each

unit.

Critical thinking and problem-solving skills are a core

component of learning and assessment throughout this

curriculum. Students are required, in each unit, to advance

their learning through all levels of Bloom’s Taxonomy to

address the evaluation, synthesis, and creation of products

using learning at the highest levels. Problem-solving is a

recurring theme in the curriculum as students must seek

ways to creatively apply the concepts to solve problems

rather than simply remember the material.

Learning advocates for health literacy as a critical

component of a healthy lifestyle and the ability to make

good health-related decisions.

Students explore areas that support environmental literacy,

including society’s impact on the environment and what can

be done to support environmental solutions.

Lessons, where appropriate, incorporate multiple

perspectives to infuse cultural and global awareness.

Students must be information literate, i.e. they must be able

to find and use information effectively, in order to succeed

in class as learning activities require independent research

of relevant information outside of the provided textbook

and/or resources.

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Assessments- including benchmarks, formative, summative,

and alternative assessments

Formative

Fluency Practice Activities

EDCITE Lesson Quizzes

Topic Readiness Assessment

Mid-Topic Assessment

Mid-Topic Performance Task

(ExamView®) Lesson and Checkpoint Quizzes

PARCC Review Questions

Summative

Modified PARCC Review Questions

STEM Project

Topic Assessment

Topic Performance Task

Suggested Interdisciplinary Activities for this Unit

Career Education- On a business trip, you rent a car. The rental

company charges $24.95 plus $.05 per mile for each mile you

drive. Write a function rule to describe the relationship between

the cost of the rental, r, and the number of miles you drove, m.

Health/PE – Use mathematical formulas to justify the concept of

an efficient diet.

English Language Arts & Literacy – Daily warm-ups and journal

entries will integrate writing and will reinforce prewriting, editing,

and self-evaluating.

Art – Students model fraction multiplication by creating shaded

grids representing fractional values and overlapping with another

grid. The resulting area will illustrate the product of the two

fractions.

Science – Balance chemical equations by applying the law of

conservation of mass.

History/Social Studies – Utilize the Work Backward strategy to

solve problems that only give a final result and ask students to find

the initial value. This can be related to reverse map reading when

directions are given to a location and must be followed in reverse

to find the original starting point.

Technical Subjects- Students interpret linear and exponential

equations that model simple and compound interest investments.

Students will be able to explain the difference between simple

interest and compound interest. They will also be able to

understand multiple representations of the same model, including

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descriptive, algebraic and tabular data, and graphical

representations of the equations.

World Languages- Using a map of Spain, find the coordinates to

three major cities.

Unit Resources

Teachers should utilize school resources available in our Media Center to infuse alternate sources, perspectives, and approaches.

Resources should include textual support but also span multimedia options to engage multiple modalities. In addition, to support

struggling readers and increase rigor for advanced readers, the coursework may also draw on additional developmentally appropriate

resources to facilitate challenging levels of work for all students.

Leveled Supplemental Materials and Media/School Library

Resources

Various leveled texts available via text, supplemental text, and

in the appendices of the curriculum document

Additional supplemental resources: Learnzillion, Khan

Academy, Math TV, BetterLesson, Kuta Software, Math

Worksheets Land

Informational Text resources from EdHelper, Scholastic Math

Digital Resources: CC Stations, CSI Math Projects, and CCSS

Mathematics Warm-ups

Integration of the Technology Standard

8.1.12.A.3

8.1.12.D.5

Use of Microsoft Excel spreadsheets

Graphing Calculators

Google Classroom to share assignments, problems, explanations

Desmos activities to communicate and collaborate on math tasks

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Unit #1: Relationships between Quantities and Reasoning with Equations

Targeted Instructional Planning to Address Central Unit Standards: Central Unit

Standard

and Student

Learning

Objective

Suggested Instructional Activities Suggested Student Output Formative Assessments

(Portfolios, Projects,

Tasks, Evaluations, &

Rubrics)

A.SSE.1

A.REI.1

A.REI.3

MARS Tasks: Solving Equation in One Variable

SWBAT solve linear equations in one variable

with rational number coefficients, collect like

terms, expand expressions using the distributive

property, and categorize linear equations in one

variable as having one, none, or infinitely many

solutions. It also aims to encourage discussion

on some common misconceptions about

algebra.

Sorting Equations and Identities

SWBAT interpret exponential and linear

functions and, in particular, to identify and help

students who have the following difficulties:

Translating between descriptive, algebraic,

tabular, and graphical representation of the

functions.

Recognizing how and why a quantity changes

per unit interval.

Defining Regions of Inequalities

SWBAT use linear inequalities to create a set of

solutions.

Teaching Channel: Using Stations to Explore Algebra Expressions

Solving Linear Equations in One

Variable

Students will solve linear equations in one

variable. Given a linear equation in one

variable, students will determine if it has

one, none, or infinitely many solutions.

Students will collaboratively create posters

displaying their justifications and they will

critique each other’s reasoning.

Calling Plans

Students will explore a real-world problem

to determine which is the best deal on a cell

phone plan. Students will create a table,

draw a graph, and write an equation to

model the situation and to assist them in

finding the best deal.

Reasoning with Linear Inequalities

Students will critique a peer’s solution to a

linear inequality and find the mathematical

errors the student made. Students will

explain why some of the steps in the

solution are mathematically incorrect.

Formative

Fluency Practice

Activities

EDCITE Lesson

Quizzes

Topic Readiness

Assessment

Mid-Topic

Assessment

Mid-Topic

Performance Task

(ExamView®)

Lesson and

Checkpoint

Quizzes

PARCC Review

Questions

Summative

Modified PARCC

Review Questions

STEM Project

Topic Assessment

Topic Performance

Task

http://map.mathshell.org/materials/lessons.php?taskid=442



http://map.mathshell.org/materials/lessons.php?taskid=426#task426

http://map.mathshell.org/materials/lessons.php?taskid=426#task426

http://map.mathshell.org/materials/lessons.php?taskid=219&subpage=concept


https://www.teachingchannel.org/videos/high-school-algebra-lesson?fd=1




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Student groups rotate among tasks to make

sense of expressions

Collaborate to Solve Compound

Inequalities

Transform students into teachers using a jigsaw

to solve inequalities

Algebra Tiles

Use tiles to represent variables and constants,

learn how to represent and solve algebra

problem. Solve equations, substitute in variable

expressions, and expand and factor. Flip tiles,

remove zero pairs, copy and arrange, and make

your way toward a better understanding of

algebra.

Mathematics Vision Project: Module 1: Getting Ready

In preparation for back to school, the school

administration has planned to replace the tile in

the cafeteria. They would like to have a

checkerboard pattern of tiles two rows wide as a

surrounding frame for the tables and serving

carts.

Notebooks will have notes on one side of

the page and visual representations of the

material on the other

Journal entries written about the usage of

linear equations in the real world

Open-ended responses to questions

involving the usage of linear equations for

real world data

Student-led discussion of key points of

linear equations and their transformations

Presentations using technology for a

children’s storybook

Collected Homework

Notebook Checks

N.Q.1

N.Q.2

N.Q.3

MARS TASK: Leaky Faucet

How much water might a dripping faucet waste

in a year?

Leaky Faucet Dan Meyer Extension

Achieve the Core: Yogurt Packing

Use and interpret appropriate units of

measurement, estimation and the

appropriate level of precision for

applications

Journal entries written about the usage of

data in the real world and how to represent

data in algebra

https://www.teachingchannel.org/videos/middle-school-lesson-idea




http://illuminations.nctm.org/Activity.aspx?id=3482

http://illuminations.nctm.org/Activity.aspx?id=3482

https://www.mathematicsvisionproject.org/uploads/1/1/6/3/11636986/sec1_mod1_getready_se_80713.pdf

https://www.mathematicsvisionproject.org/uploads/1/1/6/3/11636986/sec1_mod1_getready_se_80713.pdf

http://www.map.mathshell.org/materials/download.php?fileid=786

http://threeacts.mrmeyer.com/leakyfaucet/

http://threeacts.mrmeyer.com/leakyfaucet/

http://www.achieve.org/files/CCSS-CTE-Yogurt-Packaging-FINAL.pdf

http://www.achieve.org/files/CCSS-CTE-Yogurt-Packaging-FINAL.pdf

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Students works to solve a real-life problem

involving money made from packaging and

selling tubs of yogurt.

Illustrative Mathematics: How Much is a penny worth

Pennies have a monetary face value of one cent,

but they are made of material that has a market

value that is usually different.

Traffic Jam

Last Sunday, an accident caused traffic jam 12

miles long on a straight stretch of a two-lane

freeway. How many vehicles do you think were

in the traffic jam? Explain your thinking and

show all calculations.

Open-ended responses to real-world

problems talking about data and

measurement

Student-led discussion of key points of

measurement

Presentations using technology on physical

fitness and the measurement of related

formulas

Collected Homework

Notebook Checks

A.CED.1

A.CED.2

A.CED.3

A.CED.4

MARS Tasks: Building and Solving Equations

SWBAT create and solve linear equations.

Optimization Problems: Boomerangs

SWBAT Interpret a situation and represent the

constraints and variables mathematically, select

appropriate mathematical methods to use,

explore the effects of systematically varying the

constraints, interpret and evaluate generated

data and identify the optimum case, and

checking it for confirmation.

Lines and Linear Equations

SWBAT interpret speed as the slope of a linear

graph, and translate between the equation of a

line and its graphical representation.

Students use hands-on techniques to

investigate the meaning of linear equations.

Students will write the equation of line that

models the height of the cups and they will

interpret the meaning of the slope and y-

intercept in relation to the number and size

of the cups.

Students can find the unit rate or ratio in

real-life situations.

Determine the viability of solutions to a

linear equation or inequality in a real world

context

https://www.illustrativemathematics.org/content-standards/tasks/473






http://map.mathshell.org/materials/download.php?fileid=1241






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Illustrative Mathematics: Dimes and Quarters

This task does not actually require that the

student solve the system but that they recognize

the pairs of linear equations in two variables

that would be used to solve the system.

Equations and Formulas

SWBAT rewrite formulas and solve for a given

variable in a literal equation.

Rewriting Equations

The goal of this task is to manipulate equations

in order to solve for a specified variable.

Teaching Channel Reviewing Linear Equations in

Two Variables

SW Review understanding of linear equations


http://s3.amazonaws.com/illustrativemathematics/attachments/000/000/168/original/public_task_220.pdf?1427851185





https://www.teachingchannel.org/videos/linear-equation-misconceptions-ccssmdc




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Unit 2: Systems, Linear, and Exponential Relationships

Overview At-a-Glance Unit #2 – Systems, Linear, and Exponential Relationships

Unit Description: Students will learn function notation and develop the concepts of domain and range. They move beyond viewing

functions as processes that take inputs and yield outputs and start viewing functions as objects in their own right. They explore many

examples of functions, including sequences; they interpret functions given graphically, numerically, symbolically, and verbally, translate

between representations, and understand the limitations of various representations. They work with functions given by graphs and tables,

keeping in mind that, depending upon the context, these representations are likely to be approximate and incomplete. Their work

includes functions that can be described or approximated by formulas as well as those that cannot. When functions describe relationships

between quantities arising from a context, students reason with the units in which those quantities are measured. Students explore

systems of equations and inequalities and they find and interpret their solutions. Students build on, and informally extend their

understanding of, integer exponents to consider exponential functions. They compare and contrast linear and exponential functions,

distinguishing between additive and multiplicative change. They interpret arithmetic sequences as linear functions and geometric

sequences as exponential functions.

Essential Skills:

Extend the properties of exponents to rational exponents.

Build a function that models a relationship between two quantities.

Build new functions from existing functions.

Understand the concept of a function notation.

Interpret functions that arise in applications in terms of a context.

Analyze functions using different representations.

Solve systems of equations.

Represent and solve equations and inequalities graphically.

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Supporting Unit Standards- This unit will also include activities

aligned with the following standards:

N.RN.1

N.RN.2

F.BF.1

F.BF.2

F.BF.3

F.IF.1

F.IF.2

F.IF.3

F.IF.4

F.IF.7

F.IF.9

A.REI.5

A.REI.6

A.REI.10

A.REI.11

A.REI.12

Math Standards

8.EE.C.8a

8.EE.C.8b

8.EE.C.8c

8.SP.A.3

8.F.B.4

NGSS Standards

HS.LS4.A

HS.LS4.B

HS.LS4.C

ELA Standards

RST.11-12.1

RST.11-12.8

SL.11-12.4

WHST.11-12.9

WHST.9-12.2

Unit Details






ELL support materials (eDictionaries, native language

prompts, etc.)



and open-ended tasks CSI Projects to integrate higher-order thinking skills and

creativity

Create portfolios and Peer Lessons

Graphic organizers

Visual Vocabulary

Use real-word context examples to demonstrate the

meaning of the parts of a system of equations for the

students

Use of visual interactive websites that through the

manipulation of graphs represent inequalities


Education:

9.2.12.C.2


CRP 1, 2, 4, 6, 8, 10, 11, 12




unit.










Lessons, where appropriate, incorporate multiple

perspectives to infuse cultural and global awareness.

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Students find it useful through technology to recognize

functions that represents the same relationship

Provide a situation that uses Desmos to demonstrate how to

build a function to model a relationship between two

quantities

Students will design a word problem that reflects the use of

graphing inequalities

Students will write a real-life scenario and explain the

process needed to solve a system of linear equations with

two variables

Student will create a real world problem where students

will build a function that model a relationship between two

quantities

Students will explain the relationship of properties of

exponents to exponential functions

Students will compare and contrast the properties of a

linear equation and linear inequality equation

Students discuss the following question: Which quantity

will grow more rapidly - one that is increasing

exponentially, one that is increasing quadratically or one

that is increasing linearly?

Learning and assessment activities support the push to

make students media literate, as they are often required to

analyze, evaluate, and create messages in a wide variety of

media modes, genres, and formats.

In order to succeed in this course, students must be able to

use technology as a tool in order to research, organize,

evaluate, and communicate information.

Activities in the curriculum help develop life and career

skills in all students by promoting flexibility and

adaptability, requiring initiative and self-direction in the

learning process, supporting social and cross-cultural skills

in both content and teamwork efforts, and measuring

productivity and accountability through independent and

group assignment completion.



Formative









Career Education – Students use linear functions to analyze and

compare the weekly income for the allowances and summer jobs

for two high schools students. They determine under which

circumstances each student will make the most income and explain

what happens to the functions when hourly rates or allowances are

changed.

Health/PE – Find the amount of heartbeats in 10 seconds.

Estimate the amount of heartbeats in one minute

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Summative


STEM Project

Topic Assessment


English Language Arts & Literacy – Jack has already typed 3

pages for a report. Jill hasn’t even started yet. Jack writes ½ page

a day. Jill can write 1 page per day. After how many days will

they have the same number of pages written?

Science – A staff gauge measures the height of the water level in a

river compared to the average water level. At one gauge the river

is 1 ft. below its average water level of 10 ft. it begins to rise by a

constant rate of 1.5 f.t per hour. Graph the linear function to show

the change in water level over time.

History/Social Studies – Find a recursive formula for the height

above the ground of the nth step of the pyramid for Machu Pichu.

Technical Subjects – A fashion designer is designing a patterned

fabric. Complete a table for the amount of rows of squares of

alternating colors and the amount of each color.

World Languages – Find the highest and lowest point in France.

Create inequalities to represent those points and shade the area that

they overlap. What does the overlap represent?

Unit Resources






Resources

Various leveled texts available via text, supplemental text,

and in the appendices of the curriculum document


8.1.12.A.2

8.1.12.F.1


17



Worksheets Land

Informational Text resources from EdHelper, Scholastic

Math

Digital Resources: CC Stations, CSI Math Projects, and

CCSS Mathematics Warm-ups




18

Unit #2: Systems, and Linear and Exponential Relationships


Standard and

Student

Learning

Objective

Suggested Instructional Activities Suggested Student

Output

Formative Assessments


Tasks, Evaluations, &

Rubrics)

N.RN.1

N.RN.2

Mars Tasks:

Applying Properties of Exponents

SWBAT Recall and use the properties of exponents to generate

equivalent numeric expressions.

Giantburgers

Every day 7% of Americans eat at Giantburger restaurants!

Your task is to decide whether this newspaper headline can be

true.

Multiplying Cells

Students in a science lab observe cells multiplying. Your task is to

use their observation to work out how the number of cells

increases over time.

The Real Number System

A set of 4 short questions on rational and irrational numbers

Manipulating Radicals

SWBAT use the properties of exponents, including rational

exponents and manipulate algebraic statements involving radicals.

Discriminate between equations and identities.

Desmos Activities:

Lawnmower Math

In this activity, students will learn how math can give them the

power to quickly mow dozens of lawns without breaking a sweat.

They'll first estimate the correct radius for a pole that'll guide a

lawnmower in a spiral around a lawn. Eventually they'll create an

Comparing Investments –

Students interpret

exponential and linear

functions given a real-

world context including

modeling simple and

compound interest

investments. Students

determine how and why a

quantity changes per unit

interval, discovering that

linear functions grow by

equal distances and

exponential functions grow

by equal factors over equal

intervals. They understand

multiple representations of

the same model, including

descriptive, algebraic and

tabular data, and graphical

representations of the

equations.

The Penny Problem –

Students will evaluate a

context where one quantity

is growing exponentially

Formative

Fluency Practice

Activities

EDCITE Lesson

Quizzes

Topic Readiness

Assessment

Mid-Topic

Assessment

Mid-Topic

Performance

Task

(ExamView®)

Lesson and

Checkpoint

Quizzes

PARCC Review

Questions

Summative

Modified

PARCC Review

Questions

STEM Project








http://map.mathshell.org/materials/tasks.php?taskid=289&subpage=novice

http://map.mathshell.org/materials/tasks.php?taskid=289&subpage=novice


https://teacher.desmos.com/activitybuilder/custom/5873db71ae798052084222cb

19

algebraic expression and see how it helps them mow lots of lawns

very quickly.

Pool Boarder Problem

In this Desmos-ified treatment of a classic math problem, students

will first construct expressions with numbers to determine the

number of tiles that border a pool. Then they'll use those numerical

expressions to help them write an expression with VARIABLES.

Then they'll put the algebraic expression to the test, and see if it

helps them find the tiles for lots of pools very quickly.

Pentomino Puzzles

In this activity, students work through a series of "pentomino sum"

puzzles. They begin informally (and rather inefficiently). But later,

they'll develop and apply an algebraic approach, demonstrating the

power and efficiency of mathematics along the way.

and the other is linear.

Students will determine

that a quantity that is

increasing exponentially

will eventually exceed a

quantity that is increasing

linearly.

Topic

Assessment

Topic

Performance

Task

F.BF.1

F.BF.2

F.BF.3

MARS Tasks:

A Golden Crown

Archimedes famously solved a problem for a king who thought his

crown might be a fake. In this task, you must work out whether the

crown is pure gold.

Modeling Situations with Linear Equations

SWBAT find relationships between pairs of unknowns and

express these as tables and graphs. Find general relationships

between several variables and express these in different ways by

rearranging formulas.

Illustrative Mathematics:

Skeleton Tower - This problem is a quadratic function example

A Sum of Functions - The intent of this problem is to have

students think about how function addition works on a

fundamental level

Lake Algae - The purpose of this task is to introduce students to

exponential growth.

Arithmetic and

Geometric Sequences –

Students investigate

arithmetic and geometric

sequences by creating

functions for the two types

of sequences. Students link

arithmetic sequences to

linear functions and

geometric sequences to

exponential functions.

Notebooks will have notes

on one side of the page and

visual representations of

the material on the other

Journal entries written

about how to set up

https://teacher.desmos.com/activitybuilder/custom/58798fc7e338613f05a42feb

https://teacher.desmos.com/activitybuilder/custom/57b4e4d1d10935cb09ad667b

http://map.mathshell.org/tasks.php?unit=HE10&collection=9










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Kim and Jordan - In this task, students may choose a

representation that suits them and then reason from within that

representation.

Campus Flu - The purpose of this problem is to have students

compose functions using tables of values only.

Teaching Channel:

Conjecturing About Functions - Analyze patterns and represent

functions

YouCubed.org:

Patterns and Functions

The goal of this unit is to show students the importance of looking

for patterns and why there is a need to generalize them, especially

if there is a very large figure number.

Desmos Activities:

Charge!

In this activity, students use linear modeling to predict how long it

will take for a smartphone to reach full charge. Students will also

interpret the parameters of their equation in context.

Penny Circle

In this activity, students gather data, build a model, and then use

that model to answer the question, "How many pennies fit in a

large circle?"

Opening Weekend Sales

In this activity, students use previous iPhone sales data to make

predictions about the number of iPhone 6s units sold during its

opening weekend in September 2015. Students choose from linear,

quadratic, or exponential models, or build their own based on a

different function of their choosing.

functions and what purpose

they have in the real world

Open-ended responses to

questions involving

functions and how to enter

them into technology

Student-led discussion

on setting up functions

Technology-based

presentation based around

a game they created:

The students will need to

use google sheets as part of

their game creation

Collected Homework and Notebook Checks

https://www.illustrativemathematics.org/content-standards/HSF/BF/A/1/tasks/241



https://www.teachingchannel.org/videos/conjecture-lesson-plan

https://www.teachingchannel.org/videos/conjecture-lesson-plan

https://www.youcubed.org/tasks/patterns-and-products/

https://teacher.desmos.com/activitybuilder/custom/563a59893f80f2fd0b7c77f0

https://teacher.desmos.com/activitybuilder/custom/586ab17c2f8cd5bc3bcaf259

https://teacher.desmos.com/activitybuilder/custom/561d6a780784861e06c3a6d5

21

F.IF.1

F.IF.2

F.IF.3

F.IF.4

F.IF.7

F.IF.9

Illustrative Mathematics

Foxes and Rabbits

This task emphasizes the importance of the "every input has

exactly one output" clause in the definition of a function, which is

violated in the table of values of the two populations.

Interpreting the Graph

The purpose of this task is to help students learn to read

information about a function from its graph, by asking them to

show the part of the graph that exhibits a certain property of the

function.

Mathematics Vision Project:

Module 5 Features of Functions

This task is designed to develop the ideas of features of functions

using a situation.

Desmos Activities:

Graphing Stories

This activity will help students make the transition from one-

variable representations (eg. number lines) to the TWO-variable

representation of the coordinate plane. Students will watch 15-

second videos and translate them into graphs with your help.

Commuting Times

This activity illustrates the relationship between a dataset (which

is usually not a function) and a model of the data (which—in

algebra—is a function).

Marbleslides: Lines

In this delightful and challenging activity, students will transform

lines so that the marbles go through the stars. Students will test

their ideas by launching the marbles, and have a chance to revise

before trying the next challenge.



visual representations of

the material on the other


about how to set up

functions and what purpose

they have in the real world

Open-ended responses

involving functions and

how to enter them into

technology

Student-led discussion of

key points of functions

Technology based

presentation about the

length of time to say

tongue twisters. Data will

be recorded and presented

using google slides

Collected Homework and

Notebook Checks



https://www.illustrativemathematics.org/content-standards/HSF/IF/A/tasks/636

https://www.illustrativemathematics.org/content-standards/HSF/IF/A/tasks/636

https://www.mathematicsvisionproject.org/uploads/1/1/6/3/11636986/sec1_mod5_features_tn_71713.pdf




https://teacher.desmos.com/activitybuilder/custom/58797d35d81a612605304b1f

https://teacher.desmos.com/activitybuilder/custom/575f221e56a5e3a7573ddd0e

https://teacher.desmos.com/activitybuilder/custom/566b31734e38e1e21a10aac8

22

A.REI.5

A.REI.6

A.REI.10

A.REI.11

A.REI.11

Mars Tasks:

Defining Regions Using Inequalities

Students will use linear inequalities to create a set of solutions.

Desmos Activities:

Systems of Linear Equations

In this activity, students write and solve a system of two linear

equations to explore the numerical and graphical meaning of

"solution." The activity closes by asking students to apply what

they've learned to similar situations.

Playing Catch-Up

Students will develop their understanding of systems of equations,

particularly as they're represented as tables, equations, and graphs.

They'll apply that understanding to the question, "Will one racer

catch another?”

Wafers and Crème

In this activity, students predict which pack of cookies contains

more calories. Students then learn the number of calories in each

pack and use this new information to calculate the number of

calories in a new pack of cookies.

Polygraph: Linear Systems

This Custom Polygraph is designed to spark vocabulary-rich

conversations about systems of linear equations. Key vocabulary

that may appear in student questions includes: parallel, intersect,

solution, quadrant, axis, vertical, horizontal, slanted, increasing,

and decreasing.


real-world problems

involving systems of linear

equations


the different methods of

solving systems of linear

equations

Presentations using

technology for a Student

Council dinner. Students

will be given different

variables to consider and

they will solve a system of

linear equations to

determine the course of

action that should be

followed

Collected Homework

Notebook Checks





https://teacher.desmos.com/activitybuilder/custom/5807d7306ef115e7053a142a

https://teacher.desmos.com/activitybuilder/custom/5818fb314e762b653c3bf0f3

https://teacher.desmos.com/activitybuilder/custom/56d74abe3df0d04006f0cb97

https://teacher.desmos.com/polygraph/custom/560aa8dc58fd074d156181c3

23

Unit 3: Descriptive Statistics

Overview At-a-Glance Unit #3 – Descriptive Statistics

Unit Description: Experience with descriptive statistics began as early as Grade 6. Students were expected to display numerical data

and summarize it using measures of center and variability. By the end of middle school, they were creating scatterplots and recognizing

linear trends in data. This unit builds upon that prior experience, providing students with more formal means of assessing how a model

fits data. Students use regression techniques to describe approximately linear relationships between quantities. They use graphical

representations and knowledge of the context to make judgments about the appropriateness of linear models. With linear models, they

look at residuals to analyze the goodness of fit.

Essential Skills:

Summarize, represent, and interpret data on a single count or measurement variable

Summarize, represent, and interpret data on two categorical and quantitative variables

Interpret linear models






S.ID.1

S.ID.2

S.ID.3

S.ID.5

S.ID.6

S.ID.7

S.ID.8

S.ID.9

Math Standards

NJSLS 8.SP.A.1

NJSLS 8.SP.A.2

NJSLS 8.SP.A.3

NJSLS 8.SP.A.4

NJSLS 8.F.A.3

NJSLS 8.F.B.4

NGSS Standards

HS.ESS1.B

HS.ESS2.A HS.ESS2.D

HS-ESS3.D

ELA Standards

RST.11-12.1

RST.11-12.2 RST.11-12.7

SL.11-12.5

http://www.corestandards.org/ELA-Literacy/RST/6-8/1/









24

Unit Details






Have the students work in groups to generate data from the

internet, such as the CST scores and other data. Have them

construct a table based on the pattern and then graph the

values and explain the relationship observed on the graph

(association). Example: Certain students took two different

tests (Test A and Test B). In the scatter diagram, each

square represents one student and shows the scores that

student got in the two tests.

Use graphs of experiences that are familiar to students to

increase accessibility and supports understanding and

interpretation of proportional relationship. Students are

expected to both sketch and interpret graphs including

scatter plot

Students will explore how the residuals, the differences

between the corresponding coordinates on the least squares

line and the actual data values for each age, reveal

additional information. Students should be able to sketch

each distribution and answer questions about it just from

knowledge of these three facts (shape, center, and spread)

Have students design an experiment (project) where they

would collect data from different sources, make a scatter

plot of the data, and draw a line of best fit modeling the

data. From the plot, students would write the regression

coefficient and the residual to explain the strength of the

association


Education:

9.2.12.C.2


CRP 1, 2, 4, 6, 8, 10, 11, 12




unit.













Lessons integrate a focus on civic literacy so that student can

better understand the rights and obligations of citizenship.




Communication and collaboration is crucial for student

success as learners. Throughout this curriculum, students

must be able to communicate deep understanding through

open ended responses (both orally and in writing). In

addition, students are often required to work collaboratively

25

with their peers, which promotes the ability to succeed in

the area of social cooperative work, increases

communication skills, and promotes leadership and

responsibility.



Formative








Summative


STEM Project

Topic Assessment



Career Education- A pollster selects 100 people from each town

in a certain candidate’s district to see if they support the candidate.

Decide whether the sampling is random, systematic, or stratified.

Health/PE – Students study historical Super Bowl data to reflect

on average (mean, median, and mode) losing scores, winning

scores, and range of scores. They are asked to judge which of these

central measurements seem the most meaningful and explain their

reasoning.

English Language Arts & Literacy- Create a Venn diagram

comparing traits of two novels by the same author.

Art - Students create three dimensional graphs of survey data

(such as favorite food, movie, sport, etc.).

Science – Students experiment with line of best fit using technology

or an applet. Students will use a scatter graph to investigate a

possible connection between length and width of bird’s eggs. They

will create a scatter plot to compare team salary with team wins and

analyze data in this timely activity. Students can use this data to see

if there is a statistically significant correlation between team salary

and wins.

History/Social Studies–Collect data from various resources about

the population of all countries in South America, calculate both

26

mean and median and use this information as a comparison to

determine which country is the “most popular.”

Technical Subjects – Create PowerPoint presentations to display

data collected about rainfall amounts in NJ over the past 10 years.

World Languages – What is the distribution of languages

throughout the world in terms of population and/or countries?

How is it changing?

Unit Resources






Resources





Worksheets Land


Math




8.1.12.A.5

8.2.12.A.2





27

Unit #3: Descriptive Statistics


Standard

and Student

Learning

Objective

Suggested Instructional Activities Suggested Student

Output

Formative

Assessments


Tasks, Evaluations,

& Rubrics)

S.ID.1

S.ID.2

S.ID.3

MARS Tasks:

Using Frequency Graphs

SWBAT use frequency graphs to identify a range of measures and

make sense of this data in a real-world context.

Using Box Plots

SWBAT interpret data using frequency graphs and box plots. In

particular, this unit aims to identify and help students who have

difficulty figuring out the data points and spread of data from

frequency graphs and box plots.


Haircut Costs

This problem could be used as an introductory lesson to present group

comparisons and to engage students in a question they may find

amusing and interesting.

Speed Trap

SWBAT demonstrate an ability to construct boxplots and to use

boxplots as the basis for comparing distributions.

Understanding the Standard Deviation

SWBAT understand the standard deviation as a measure of variability

in a data distribution. The task is conceptual rather than computational

and does not require students to calculate the standard deviation.

Measuring Variability in a Data Set

Create a scatterplot

from given data and

explain how the two

sets of data are related

and what the trend

appears to be Describe the positive or

negative correlation

between bivariate data

by modeling data with

line. Observe and

explain any outliers. Produce frequency table

of collected bivariate data Make logical

conjectures and

predictions from

scatterplot data

Formative

Fluency Practice

Activities

EDCITE Lesson

Quizzes

Topic Readiness

Assessment

Mid-Topic

Assessment

Mid-Topic

Performance

Task

(ExamView®)

Lesson and

Checkpoint

Quizzes

PARCC Review

Questions

Summative

Modified

PARCC Review

Questions





https://www.illustrativemathematics.org/content-standards/HSS/ID/A/1/tasks/942












28

The purpose of this task is to develop students’ understanding of

standard deviation


Module 8-Modeling Data

In this task, students will use prior knowledge to interpret data using a

histogram, and then represent the same data with a box plot. Students

will also discuss the similarities/differences of these representations

and surface ideas relating to effects of extreme data points (outliers)

and data that is bimodal.

Journal entries (from

teacher provided prompts) Notebook activities Open-ended responses Practice Worksheets

STEM Project

Topic

Assessment

Topic

Performance

Task

S.ID.5

S.ID.6

MARS Tasks:

Interpreting and Using a Graph: Taxi Fares

SWBAT select and use mathematical ideas to solve a problem and

then compare and critique alternative approaches. The lesson presents

students with a distance-time scatter plot representing journeys made

by a taxi cab. They use this to decide upon a suitable rate at which the

driver should charge passengers.

Devising a Measure for Correlation

SWBAT understand the notion of positive correlation. In particular,

this unit aims to identify and help students who have difficulty in

understanding correlation as the degree of fit between two variables and making a mathematical model of a situation.


Musical Preference

The basic idea is for students to demonstrate that they know what it

means for two variables to be associated: that if we knew someone

were in one group (for example, they like rap), we now know more

about their preferences for rock than if we knew nothing at all.

Support for a Longer School Day

Notebooks will have

notes on one side of the

page and visual




about how to data and

where it can be found in

the real world.


to questions involving

data and how to enter it

into technology


on the different ways to

present data

Technology-based

presentation about

gathered data. The

https://www.mathematicsvisionproject.org/uploads/1/1/6/3/11636986/sec1_mod8_data_tn_71713.pdf














https://www.illustrativemathematics.org/content-standards/HSS/ID/B/5/tasks/123






29

The purpose of this task is to provide students with an opportunity to

calculate and interpret joint, marginal and relative frequencies using

data in a two-way table

Coffee and Crime

This task addresses many standards regarding the description and

analysis of bivariate quantitative data, including regression and

correlation.

Laptop Battery Charge

This task uses a situation that is familiar to students to solve a problem

they probably have all encountered before: How long will it take until

an electronic device has a fully charged battery? A linear model can

be used to solve this problem.

Restaurant Bill and Party Size

The purpose of this task is to assess student understanding of residuals

and residual plots (S.ID.6). Students see a residual plot in a context

where a linear model is appropriate and also see a residual plot in a

context where a linear model is not appropriate.

Desmos Activities:

Scatter Plot Capture

In this activity, students use observations about scatterplot

relationships to make predictions about future points in the plot. In

particular, students focus on linear vs nonlinear association, strong vs weak association, and increasing vs decreasing plots.

Polygraph: Scatter Plots

This Custom Polygraph is designed to spark vocabulary-rich conversations about scatter plots.

Line of Best Fit

In this activity, students visualize a line to fit a data set, then graph that line with sliders, and use it to make a prediction.

students will determine

what information they

would like to gather

from other students and

then they will go collect

it. They will also need

to present the data and

analysis to the class.

Collected Homework

and Notebook Checks

Student-constructed

written summaries of

key points and

applications of

essential topics and/or

essential questions









https://teacher.desmos.com/activitybuilder/custom/58cc26d4c722f106146a8310

https://teacher.desmos.com/polygraph/custom/560aa8c858fd074d1561808f

https://teacher.desmos.com/activitybuilder/custom/56fab6bc1ab86b1f0600369d

30

S.ID.7

S.ID.8

S.ID.9


Texting and Grades II

The purpose of this task is to assess ability to interpret the slope and intercept of the line of best fit in context.

Olympic Men’s 100meter Dash

The task asks students to identify when two quantitative variables

show evidence of a linear association, and to describe the strength and

direction of that association. Students then utilize a least-squares

regression line to make predictions, and to make conjectures about the

limitations of the model.

Golf and Divorce

This is a simple task addressing the distinction between correlation

and causation. Students are given information indicating a correlation

between two variables, and are asked to reason out whether or not a

causation can be inferred.

High Blood Pressure

The purpose of this task is to assess understanding of how study

design dictates whether a conclusion of causation is warranted.

Math Test Grades

The goal of this task is twofold. For part (a) since we are not given

how large each of the groups in the table are, the best we can do is to

apply reasoning about ratios (in the form of percents) to give a range

of possible answers. For part (b), the goal is to recognize a misuse of

statistical reasoning. Of the three groups, the one with the highest

percentage of A's is the group whose studies were limited to less than

3 hours a week.

Desmos Activities:

Alligator Investigation

An enormous alligator lurks in the swamp. Can scatterplots and least-

squares regression tell you if you have enough animal tranquilizer to

stay safe?

Notebooks will have

notes on one side of the

page and visual




about how to data and

where it can be found in

the real world


to questions involving

data and how to enter it

into technology


on the different ways to

present data

Technology-based

presentation about

gathered data. The

students will determine

what information they

would like to gather

from other students and

then they will go collect

it. They will also need

to present the data and

analysis to the class.

Collected Homework

and Notebook Checks

https://www.illustrativemathematics.org/content-standards/HSS/ID/C/7/tasks/1028










https://teacher.desmos.com/activitybuilder/custom/5670aca10255cd610798be54

31

Unit 4: Quadratic Functions and Modeling

Overview At-a-Glance Unit #4 – Quadratic Functions and Modeling

Unit Description: In preparation for work with quadratic relationships, students explore distinctions between rational and irrational

numbers. They consider quadratic functions, comparing the key characteristics of quadratic functions to those of linear and

exponential functions. They select from among these functions to model phenomena. Students learn to anticipate the graph of a

quadratic function by interpreting various forms of quadratic expressions. In particular, they identify the real solutions of a quadratic

equation as the zeros of a related quadratic function.

Essential Skills:

Use properties of rational and irrational numbers.

Interpret functions that arise in applications in terms of a context.

Analyze functions using different representations.

Build a function that models a relationship between two quantities.

Build new functions from existing functions.

Construct and compare linear, quadratic, and exponential models and solve problems.

Interpret expressions for functions in terms of the situation they model.






F.IF.4

F.IF.5

F.IF.6

F.IF.7

F.IF.8

F.IF.9

F.BF.1

F.BF.3

F.BF.4

Math Standards

N.RN.3

F.LE.1

F.LE.2

F.LE.3

F.LE.5

NGSS Standards

HS.PS1.A HS.PS1.B

HS.ETS1.C

ELA Standards

RST.11-12.1 SL.11-12.5 WHST.11-12.7

WHST.9-12.2







32

Unit Details






Advance/Guided Notes Teacher Modeling (non-verbal teacher communication in

addition to spoken instructions)

Simplified written and verbal instructions ELL support materials (eDictionaries, native language

prompts, etc.)



and open-ended tasks Advanced pacing levels CSI Projects to integrate higher-order thinking skills and

creativity

Create portfolios and Peer Lessons

Reteaching worksheets

Graphic organizers

Visual Vocabulary

Graph paper to produce visual representations of

transformations

Have students evaluate different functions (linear,

quadratics, and exponential) for a given variable. Then

engage the students in identifying appropriate domain for

the functions.

Help students take the "function machine" that they learned

in the earlier grades and turn it into a deeper understanding

of relating the situation, table, and rule (formula) of


Education:

9.2.12.C.2


CRP 1, 2, 4, 6, 8, 10, 11, 12




unit.













In order to succeed in this course, students must be able to

use technology as a tool in order to research, organize,

evaluate, and communicate information.

Learning incorporates skills focusing on financial,

economic, business, and entrepreneurial literacy.

Students must be information literate, i.e. they must be able

to find and use information effectively, in order to succeed

in class as learning activities require independent research

of relevant information outside of the provided textbook

and/or resources.

33

functions. The goal here is to help students make the

connections

Understanding and use the formal mathematical language

of functions

Provide students an opportunity to compare two functions

(quadratic and exponential), represented in different ways

(table, graph, or situation)

Provide the students several opportunities to collect data to

model different situations related to linear, quadratic,

exponential functions, and trigonometric functions






Formative








Summative


STEM Project

Topic Assessment


Unit 1-4 Cumulative/Benchmark Assessment


Career Education – A cell phone company sells about 500 phones

each week when it charges $75 per phone. It sells 20 more phones

per week for each $1 decrease in price. The company’s revenue is

the product of the number of phones sold and the price of each

phone. What price should the company charge to maximize its

revenue?

Health/PE – What function can be used to track a ball in flight?

Students compare properties of two functions represented in

different ways - algebraically, graphically, or in numerical tables.

Using tables and graphs, students determine which function has the

greatest maximum and the greatest non-negative root.

English Language Arts & Literacy – How can you use the

discriminant to write a quadratic equation and to determine the

number of solutions? Write an instruction set that could be used

by a non- mathematician. Art – Either create a bowl or bring a bowl in. Measure three

coplanar points on the inside of the bowl. Then create an equation

34

for the parabola on the inside of the bowl by using those three

points.

Science – Temperature Conversions - Students write a function

that describes a relationship between two quantities. They explore

unit conversion as composition of two functions (when several

successive conversions are required) and the inverses of those

functions (units can always be converted in either of two

directions).

History/Social Studies – Population and Food Supply – Students

construct linear/ exponential functions from verbal descriptions

and explore the idea of the dominance of exponential over linear

functions. They construct/ compare linear and exponential

functions and find the intersections of their graphs. Using graphs

and tables students observe that an exponential increase eventually

exceeds a linear or quadratic increase in quantities.

Technology – Use Excel to generate quadratic lines of best fit.

Discuss correlation coefficients. Using phone data from prior

activities, use a spreadsheet to find a line of best fit. Compare this

to the line of best fit from a graphing utility.

World Language – Translate the key words: parabola, vertex,

point, curve, quadratic, and polynomial. Then write a brief

explanation of each word in [insert world language].

Unit Resources





35


Resources





Worksheets Land


Math




8.1.12.C.1 8.1.12.A.1





Unit #4: Investigate Bivariate Data


Standard

and Student

Learning

Objective

Suggested Instructional Activities Suggested Student Output Formative

Assessments


Tasks, Evaluations,

& Rubrics)

F.IF.4

F.IF.5

F.IF.6


Influenza Epidemic

The principal purpose of this task is to probe students' ability to

correlate symbolic statements about a function using function

notation with a graph of the function, and to interpret their

answers in terms of the quantities between which the function

describes a relationship.

Warming and Cooling

This task is meant to be a straight-forward assessment task of graph reading and interpreting skills.

How is the Weather?



visual representations of the


Journal entries written about

how to find the domain and

range of a quadratic

function


questions involving the

Formative

Fluency Practice

Activities

EDCITE Lesson

Quizzes

Topic Readiness

Assessment

Mid-Topic

Assessment







36

Match each graph to the corresponding description of

the weather during the day.

Logistic Growth Model, Explicit Version

This problem introduces a logistic growth model in the concrete

setting of estimating the population of the U.S.

The Canoe Trip, Variation 1

The purpose of this task is to give students practice constructing

functions that represent a quantity of interest in a context, and

then interpreting features of the function in the light of that

context.

The High School Gym

Calculate and interpret the average rate of change of a function

(presented symbolically or as a table) over a specified interval.

Estimate the rate of change from a graph.

Temperature Change

This task gives an easy context to introduce the idea of average

rate of change.

Average Cost

John makes DVDs of his friend’s shows. He has realized that,

because of his fixed costs, his average cost per DVD depends

on the number of DVDs he produces. The cost of producing x

DVDs is given by a function.

different parts of a quadratic

and their purposes


key points of quadratic

graphs

Technology-based

presentation about the

different parts of a

quadratic. Students will be

split into groups and each

group will be given a

different part of a quadratic

graph. Students will report

out the importance of their

part.


Notebook Checks

Mid-Topic

Performance

Task

(ExamView®)

Lesson and

Checkpoint

Quizzes

PARCC Review

Questions

Summative

Modified

PARCC Review

Questions

STEM Project

Topic

Assessment

Topic

Performance

Task

Unit 1-4

Cumulative /

Benchmark

Assessment

F.IF.7

F.IF.8

F.IF.9

MARS Tasks:

Functions and Everyday Situations

This lesson is intended to help you assess how well students are

able to articulate verbally the relationships between variables

arising in everyday contexts.


Identifying Graphs of Functions






how to find the vertex of a

quadratic when given in

standard form









https://www.illustrativemathematics.org/content-standards/HSF/IF/B/4/tasks/387

https://www.illustrativemathematics.org/content-standards/HSF/IF/B/4/tasks/387






37

The goal of this task is to get students to focus on the shape of the graph of the equation y=e^x and how this changes depending on the sign of the exponent Which Function? The task addresses knowledge related to interpreting forms of

functions derived by factoring or completing the square.

Throwing Baseballs

This task allows the students to compare characteristics of two

quadratic functions that are each represented differently, one as

the graph of a quadratic function and one written out

algebraically.


questions involving

quadratic functions and

their different parts


key parts of a quadratic

function and how to find

them

F.BF.1

F.BF.3

F.BF.4

Mars Task:

Patchwork

In this task, you must investigate number patterns and to find a

rule, or a formula, that will help Kate figure out the number of

squares she needs for cushions of different sizes.

Sidewalk Patterns

In this task, you will look for rules which let you work out how

many blocks of different colors are needed to make different

sized patterns.

Modeling: Having Kittens

This lesson is intended to help you assess how well students can

interpret a situation and represent the constraints and variables

mathematically; and investigate an exponentially increasing

sequence.

Sorting Functions

You are given four graphs, four equations, four tables, and four

rules. Your task is to match each graph with an equation, a table

and a rule.

Linear and Exponential Models

A set of 3 short questions on linear and exponential models






transforming a function


questions involving

transformation of functions


key points of transforming

functions


Notebook Checks









http://map.mathshell.org/materials/lessons.php?taskid=407&subpage=problem

http://map.mathshell.org/materials/lessons.php?taskid=407&subpage=problem





38


Arithmetic and Geometric Sequence

The purpose of this task is to develop representations for

arithmetic sequences that

students can draw upon throughout the unit.

Linear and Exponential Functions

This task builds upon students’ experiences with arithmetic and

geometric sequences to extend to the broader class of linear and

exponential functions with continuous domains.

https://www.mathematicsvisionproject.org/uploads/1/1/6/3/11636986/sec1_mod3_sequences_tn_71713.pdf




https://www.mathematicsvisionproject.org/uploads/1/1/6/3/11636986/sec1_mod4_lef_tn_71713.pdf




remedial algebra - burlington-nj.net

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