# Mathematics Task Arcs

Save this PDF as:

Size: px
Start display at page:

## Transcription

2 mathematics Grade 7 Adding and Subtracting Positive and Negative Rational Numbers A SET OF RELATED S UNIVERSITY OF PITTSBURGH

3

5

6 mathematics Grade 7 Introduction Adding and Subtracting Positive and Negative Rational Numbers A SET OF RELATED S

7

9 8 Introduction Identified CCSSM and Essential Understandings CCSS for Mathematical Content: The Number System Essential Understandings Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers. 7.NS.A.1 7.NS.A.1a 7.NS.A.1b 7.NS.A.1c Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. Describe situations in which opposite quantities combine to make 0. For example, a hydrogen atom has 0 charge because its two constituents are oppositely charged. Understand p + q as the number located a distance q from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts. Understand subtraction of rational numbers as adding the additive inverse, p q = p + (-q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts. Addition and subtraction of rational numbers can be represented by movement on a number line, because the sum (or difference) is another rational number whose location is determined by its magnitude and sign. Two opposite numbers combine to make zero because they represent the same distance from zero on the number line. The sum of two numbers p and q is located q units from p on the number line, because addition can be modeled by movement along the number line. When q is a positive number, p + q is to the right of p. When q is a negative number, p + q is to the left of p. The sum of a number and its opposite, p + -p, is equal to zero because p and -p are the same distance from 0 in opposite directions. The difference of two numbers p q is equal to p + (-q) because both can be modeled by the same movement on the number line. That is, if q is positive, p q and p + (-q) are both located at the point q units to the left of p and if q is negative, both are located at a point q units to the right of p. The distance between a positive number p and negative number q is the sum of their absolute values because this represents each of their distances from zero and therefore their total distance from each other.

10 Introduction 9 CCSS for Mathematical Content: The Number System Essential Understandings 7.NS.A.1d 7.NS.A.3 Apply properties of operations as strategies to add and subtract rational numbers. Solve real-world and mathematical problems involving the four operations with rational numbers. Rational numbers can be decomposed and regrouped to efficiently add and subtract positive and negative integers. The differences b a and a b are opposites because they represent the same distance between two points on the number line. Subtraction of a lesser number minus a greater number will result in a negative difference, while subtraction of a greater number minus a lesser number will result in a positive difference. The order of the values being added does not affect the sum, but the order of the values being subtracted does affect the difference because a + b models the same movement on the number line as b + a, while a b and b a model movement in opposite directions on the number line. Many real-world situations can be modeled and solved using operations with positive and negative rational numbers. The CCSS for Mathematical Practice 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. *Common Core State Standards, 2010, NGA Center/CCSSO

12 Introduction 11 Task MP 1 MP 2 MP 3 MP 4 MP 5 MP 6 MP 7 MP 8 Task 1 Football Developing Understanding Task 2 Football Part 2 Developing Understanding Task 3 Fundraiser Developing Understanding Task 4 If A then B Solidifying Understanding Task 5 Choose Your Chips Wisely Developing Understanding Task 6 Traveling on the Number Line Developing Understanding Task 7 Cold We ather Developing Understanding Task 8 Keeping it Real Solidifying Understanding

14 Introduction 13 TASK 5 Choose Your Chips Wisely Developing Understanding TASK 6 Traveling on the Number Line Developing Understanding TASK 7 Cold Weather Developing Understanding TASK 8 Keeping it Real Solidifying Understanding Content Extend understanding of sums to analyze differences of positive and negative numbers. Understand subtraction as the opposite operation of addition. Develop understanding that subtraction is not communicative. Solidify an algorithm for subtracting integers. Strategy Represent the same value with different amounts of positive and negative chips using zero-sums. Compare movement on the number line in order to generalize. Write equations to represent differences in temperature. Compare positive and negative changes. Apply conceptual understandings of quantity and opposite values when subtracting integers. Representations Represent a context with a chip model. Use a number line to support this model. Start with an equation and construct number lines and chip representations. Use a number line to compare two equations where the order of the integers has been switched. Use number line and chips to support use of numeric strategies for subtracting integers.

15 14 Introduction

16 mathematics Grade 7 Tasks and Lesson Guides Adding and Subtracting Positive and Negative Rational Numbers A SET OF RELATED S

17

18 Tasks and Lesson Guides 17 Name Football TASK 1 The Mathletes have developed a new system for the yardage on a football field. The middle of their field is zero and the teams score touchdowns by crossing the 50 or the -50 yard line. The teams that play on the field are named the Positives and the Negatives. The Positives always move to the right to score in their end zone (50 yards) and the Negatives always move to the left to score in their end zone (-50 yards). Assume that when the first team starts in each problem, the ball is at zero. 1. Draw each scenario on the football field number line with arrows and determine the ball s final location. A. The Positives run 40 yards and then the Negatives get the ball and run 40 yards.

19 18 Tasks and Lesson Guides TASK 1 B. The Negatives run the ball 12 yards and then another 8 yards. The Positives get the ball and run 20 yards. 2. The scorekeeper recorded the three plays represented by the expression shown below. The plus sign indicates that a new play has been added. (-18) + (-7) + 25 Describe the three plays and then determine the location of the ball at the end of the three plays. Justify your answer using a number line. 3. The scorekeeper records the following mathematical equations for a number of plays. Use the number line to determine the missing values. A (-30) + = 0 B (-10) + = 0 C = 0 D (-65) = 0 Summarize your strategy for determining the missing values

20 Tasks and Lesson Guides 19 Football Rationale for Lesson: Develop an understanding of how to use equations and the number line to calculate zero-sums. In this lesson, students explore the idea that opposite numbers have a zero-sum because they represent the same distance from zero on the number line. 1 Task: Football The Mathletes have developed a new system for the yardage on a football field. The middle of their field is zero and the teams score touchdowns by crossing the 50 or the -50 yard line. The teams that play on the field are named the Positives and the Negatives. The Positives always move to the right to score in their end zone (50 yards) and the Negatives always move to the left to score in their end zone (-50 yards). Assume that when the first team starts in each problem, the ball is at zero. See student paper for the complete task. Common Core Content Standards 7.NS.A.1 Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. 7.NS.A.1b Understand p + q as the number located a distance q from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts. 7.NS.A.3 Solve real-world and mathematical problems involving the four operations with rational numbers. Standards for Mathematical Practice Essential Understandings Materials Needed MP1 Make sense of problems and persevere in solving them. MP2 Reason abstractly and quantitatively. MP4 Model with mathematics. MP5 Use appropriate tools strategically. MP6 Attend to precision. MP7 Look for and make use of structure. MP8 Look for and express regularity in repeated reasoning. Addition and subtraction of rational numbers can be represented by movement on a number line, because the sum (or difference) is another rational number whose location is determined by its magnitude and sign. The sum of a number and its opposite, p + -p, is equal to zero because p and -p are the same distance from 0 in opposite directions. Task sheet. Additional paper. Calculator (optional).

23 22 Tasks and Lesson Guides 1 Application Summary Quick Write You are on a game show where you win money for answering questions correctly and lose money for answering questions incorrectly. The amount of money for each question varies. You have answered two questions incorrectly and have -\$45. But then you answer two questions correctly to get back to 0. What could the two questions have been worth? Why do opposite numbers add to zero? No quick write for students. Support for students who are English Learners (EL): 1. Students who are English Learners may be unfamiliar with the context. Demonstrate several examples of the movement of the game during the set-up so that the context is more concrete.

24 Tasks and Lesson Guides 23 Name Football Part 2 TASK 2 1. The statistician is calculating total yardage and organizes the plays into two groups according to a pattern. A. Determine the total yardage (sum) for each pair of plays. Set (-20) (-15) Set (-50) (-40) B. Describe how the plays were organized. 2. If a is a positive integer and b is a negative integer, make a conjecture about the conditions under which each of the statements true. A. a + b > 0 B. a + b < 0 C. a + b = 0 D. a + b = b + a

25 24 Tasks and Lesson Guides 2 Football Part 2 Rationale for Lesson: Recognize patterns involving magnitude and direction of positive and negative numbers. In this lesson, students learn methods for determining whether the sum of integers will be positive or negative. Task: Football Part 2 1. The statistician is calculating total yardage and organizes the plays into two groups according to a pattern. A. Determine the total yardage (sum) for each pair of plays. Set (-20) (-15) Set (-50) (-40) If a is a positive integer and b is a negative integer, make a conjecture about the conditions under which each of the statements true. A. a + b > 0 B. a + b < 0 C. a + b = 0 D. a + b = b + a Common Core Content Standards 7.NS.A.1b Understand p + q as the number located a distance q from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts. 7.NS.A.1d 7.NS.A.3 Apply properties of operations as strategies to add and subtract rational numbers. Solve real-world and mathematical problems involving the four operations with rational numbers. Standards for Mathematical Practice MP1 Make sense of problems and persevere in solving them. MP4 Model with mathematics. MP5 Use appropriate tools strategically. MP6 Attend to precision. MP7 Look for and make use of structure. MP8 Look for and express regularity in repeated reasoning.

28 Tasks and Lesson Guides 27 Support for students who are English Learners (EL): 1. Since the task is a continuation of the previous context that may have been unfamiliar to English Learners, demonstrate several examples of the movement of the game during the set-up so that the context is more concrete. 2. Have students who are English Learners demonstrate movement along the number line as they determine the sum. 2

29 28 Tasks and Lesson Guides TASK 3 Name Fundraiser You may recall that integers can be represented with chips as well as with a number line. Yellow chips represent positive numbers and red chips represent negative numbers. Renea and her business partner, Alicia, set up a business selling school supplies to raise money for their vacation. They use chips to model their expenses and their income. Expenses are the amount of money spent on supplies and income is the amount of money earned from selling the supplies. Profit is the amount of money a company makes. (Profit may be negative if a company has more expenses than income.) Renea and Alicia use negative (red) chips for their expenses and positive (yellow) chips for their income. 1. The chip diagram below represents their income and expenses for a given day. Calculate their profit. Use an equation and number line to support your calculation. 2. Model a second situation in which Renea and Alicia end the day having lost or made the same amount of money that they did in question 1. Explain your reasoning. 3. Renea and Alicia had \$15 in expenses and \$7 in income. Determine their profit. Justify your solution with chips as well as a number line.

35 34 Tasks and Lesson Guides TASK 4 Name If A then B 1. Determine the sum of each expression. A B C D E Summarize your strategy for calculating the sum of a positive and negative integer. 2. Determine whether each of the expressions below has a value that is positive, negative, or equal to 0. Explain your reasoning. a + 1 b + (-1) a + (-2) a+ (-a) a + b

38 Tasks and Lesson Guides 37 SHARE, DISCUSS, AND ANALYZE PHASE EU: The sum of two numbers p and q is located q units from p on the number line because addition can be modeled by movement along the number line. When q is a positive number, p + q is to the right of p. When q is a negative number, p + q is to the left of p. Walking around, I noticed groups using several different methods. Some groups used chips, others used a number line, while quite a few used a numeric strategy. Let s look first at this group s work. They used a number line. Then we will compare and contrast their strategy with the numeric strategy used by another group. Who can tell us how to determine whether the sum is going to be positive or negative for each of the methods? How can we determine the exact value using a number line? (Starting at the first number, I count spaces to the left or right. For , I start at -8 and count 18 spaces to the right. I ended up at 10.) As we compared the chip method, the number line method, or an algorithm, we saw that each method has strengths and weaknesses. Who can identify some of those strengths and weaknesses in their own words? - (The chip method lets us see at a glance whether the sum is negative or positive and I can see the zero pairs easily. It is hard to do with really big numbers though, because we don t have enough chips.) - (The number line method is nice because I can see why the sum is negative or positive. If I start at a negative and count right, I can see if I move across the zero or not. The number line is hard to use for really big numbers because I would need a big number line and it gets hard to count the spaces.) - (The rule of decomposing the numbers and looking for zero pairs works for all numbers, but sometimes it can be hard to know how to decompose the number or to know what is left over. If I had to add , I would have to subtract to figure out how to break up 42 into 8 and something else.) 4

40 Tasks and Lesson Guides 39 Name Choose Your Chips Wisely TASK 5 1. Red and yellow chips represent the sum of positive and negative numbers for two different equations shown below. A. Write the equation and the sum represented in each chip diagram. B. Explain why the expressions have the same sum. C. Write another equation that has the same sum. Justify your reasoning using chips. 2. Represent each number in two different ways using chips. Each representation must include positive and negative chips. Number Chip Representation 1 Chip Representation 2-3 2

41 40 Tasks and Lesson Guides TASK 5 3. Red and yellow chips represent the sum of positive and negative numbers. A. Explain why the diagram represents -2. B. Use the chip diagram above to answer the following subtraction problems. I II III IV V (-1) IV (-2) Describe any patterns that you notice.

### Mathematics Task Arcs

Overview of Mathematics Task Arcs: Mathematics Task Arcs A task arc is a set of related lessons which consists of eight tasks and their associated lesson guides. The lessons are focused on a small number

### Lesson Plan Warehouse Grade 7 Adding Integers

CCSSM: Grade 7 DOMAIN: The Number System Cluster: Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers. Standard: 7.NS.1: Apply

### Math Journal HMH Mega Math. itools Number

Lesson 1.1 Algebra Number Patterns CC.3.OA.9 Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. Identify and

### Math at a Glance for April

Audience: School Leaders, Regional Teams Math at a Glance for April The Math at a Glance tool has been developed to support school leaders and region teams as they look for evidence of alignment to Common

### First Grade Exploring Two-Digit Numbers

First Grade Exploring Two-Digit Numbers http://focusonmath.files.wordpress.com/2011/02/screen-shot-2011-02-17-at-3-10-19-pm.png North Carolina Department of Public Instruction www.ncdpi.wikispaces.net

### GRADE 6 MATH: SHARE MY CANDY

GRADE 6 MATH: SHARE MY CANDY UNIT OVERVIEW The length of this unit is approximately 2-3 weeks. Students will develop an understanding of dividing fractions by fractions by building upon the conceptual

### This lesson introduces students to decimals.

NATIONAL MATH + SCIENCE INITIATIVE Elementary Math Introduction to Decimals LEVEL Grade Five OBJECTIVES Students will compare fractions to decimals. explore and build decimal models. MATERIALS AND RESOURCES

### 2 Mathematics Curriculum

New York State Common Core 2 Mathematics Curriculum GRADE GRADE 2 MODULE 3 Topic E: Model Numbers Within 1000 with Place Value Disks 2.NBT.A Focus Standard: 2.NBT.A Understand place value. Instructional

### Factoring Quadratic Trinomials

Factoring Quadratic Trinomials Student Probe Factor x x 3 10. Answer: x 5 x Lesson Description This lesson uses the area model of multiplication to factor quadratic trinomials. Part 1 of the lesson consists

### Pre-Calculus Unit Plan: Vectors and their Applications. Dr. Mohr-Schroeder. Fall 2012. University of Kentucky. Jessica Doering.

Pre-Calculus Unit Plan: Vectors and their Applications Dr. Mohr-Schroeder Fall 2012 University of Kentucky Jessica Doering Andrea Meadors Stephen Powers Table of Contents Narrative and Overview of Unit

### Mathematics Curriculum Guide Precalculus 2015-16. Page 1 of 12

Mathematics Curriculum Guide Precalculus 2015-16 Page 1 of 12 Paramount Unified School District High School Math Curriculum Guides 2015 16 In 2015 16, PUSD will continue to implement the Standards by providing

### Factoring Quadratic Trinomials

Factoring Quadratic Trinomials Student Probe Factor Answer: Lesson Description This lesson uses the area model of multiplication to factor quadratic trinomials Part 1 of the lesson consists of circle puzzles

### Graphic Organizers SAMPLES

This document is designed to assist North Carolina educators in effective instruction of the new Common Core State and/or North Carolina Essential Standards (Standard Course of Study) in order to increase

### Grade 4 - Module 5: Fraction Equivalence, Ordering, and Operations

Grade 4 - Module 5: Fraction Equivalence, Ordering, and Operations Benchmark (standard or reference point by which something is measured) Common denominator (when two or more fractions have the same denominator)

### A Math Talk Community in Math Expressions Common Core

hmhco.com BUILDING A New Standard OF Success A Math Talk Community in Math Expressions Common Core Dr. Karen Fuson, Program Author of Math Expressions Common Core and Professor Emerita of Learning Sciences,

### Beads Under the Cloud

Beads Under the Cloud Intermediate/Middle School Grades Problem Solving Mathematics Formative Assessment Lesson Designed and revised by Kentucky Department of Education Mathematics Specialists Field-tested

### CAHSEE on Target UC Davis, School and University Partnerships

UC Davis, School and University Partnerships CAHSEE on Target Mathematics Curriculum Published by The University of California, Davis, School/University Partnerships Program 006 Director Sarah R. Martinez,

### Assignment #1: Spreadsheets and Basic Data Visualization Sample Solution

Assignment #1: Spreadsheets and Basic Data Visualization Sample Solution Part 1: Spreadsheet Data Analysis Problem 1. Football data: Find the average difference between game predictions and actual outcomes,

### Performance Level Descriptors Grade 6 Mathematics

Performance Level Descriptors Grade 6 Mathematics Multiplying and Dividing with Fractions 6.NS.1-2 Grade 6 Math : Sub-Claim A The student solves problems involving the Major Content for grade/course with

### A Second Course in Mathematics Concepts for Elementary Teachers: Theory, Problems, and Solutions

A Second Course in Mathematics Concepts for Elementary Teachers: Theory, Problems, and Solutions Marcel B. Finan Arkansas Tech University c All Rights Reserved First Draft February 8, 2006 1 Contents 25

### Teaching & Learning Plans. Arithmetic Sequences. Leaving Certificate Syllabus

Teaching & Learning Plans Arithmetic Sequences Leaving Certificate Syllabus The Teaching & Learning Plans are structured as follows: Aims outline what the lesson, or series of lessons, hopes to achieve.

### History of Development of CCSS

Implications of the Common Core State Standards for Mathematics Jere Confrey Joseph D. Moore University Distinguished Professor of Mathematics Education Friday Institute for Educational Innovation, College

### Title: Integers: Quick, Fun and Easy To Learn

Title: Integers: Quick, Fun and Easy To Learn Brief Overview Students will identify and understand positive and negative integers. Using this understanding, the students will use the number line, study

### Problem of the Month Pick a Pocket

The Problems of the Month (POM) are used in a variety of ways to promote problem solving and to foster the first standard of mathematical practice from the Common Core State Standards: Make sense of problems

### Balanced Assessment Test Algebra 2008

Balanced Assessment Test Algebra 2008 Core Idea Task Score Representations Expressions This task asks students find algebraic expressions for area and perimeter of parallelograms and trapezoids. Successful

### CORE Assessment Module Module Overview

CORE Assessment Module Module Overview Content Area Mathematics Title Speedy Texting Grade Level Grade 7 Problem Type Performance Task Learning Goal Students will solve real-life and mathematical problems

### VISUAL ALGEBRA FOR COLLEGE STUDENTS. Laurie J. Burton Western Oregon University

VISUAL ALGEBRA FOR COLLEGE STUDENTS Laurie J. Burton Western Oregon University VISUAL ALGEBRA FOR COLLEGE STUDENTS TABLE OF CONTENTS Welcome and Introduction 1 Chapter 1: INTEGERS AND INTEGER OPERATIONS

### INDIANA ACADEMIC STANDARDS. Mathematics: Grade 6 Draft for release: May 1, 2014

INDIANA ACADEMIC STANDARDS Mathematics: Grade 6 Draft for release: May 1, 2014 I. Introduction The Indiana Academic Standards for Mathematics are the result of a process designed to identify, evaluate,

### The GMAT Guru. Prime Factorization: Theory and Practice

. Prime Factorization: Theory and Practice The following is an ecerpt from The GMAT Guru Guide, available eclusively to clients of The GMAT Guru. If you would like more information about GMAT Guru services,

### 6 Mathematics Curriculum

New York State Common Core 6 Mathematics Curriculum GRADE Table of Contents 1 Rational Numbers GRADE 6 MODULE 3 Module Overview... 3 Topic A: Understanding Positive and Negative Numbers on the Number Line

### High School Algebra Reasoning with Equations and Inequalities Solve equations and inequalities in one variable.

Performance Assessment Task Quadratic (2009) Grade 9 The task challenges a student to demonstrate an understanding of quadratic functions in various forms. A student must make sense of the meaning of relations

### Tasks in the Lesson. Mathematical Goals Common Core State Standards. Emphasized Standards for Mathematical Practice. Prior Knowledge Needed

Mathematical Goals Common Core State Standards Emphasized Standards for Mathematical Practice Prior Knowledge Needed Vocabulary Lesson 2.4 Five Numbers Bingo Overview and Background Information By the

### Probabilistic Strategies: Solutions

Probability Victor Xu Probabilistic Strategies: Solutions Western PA ARML Practice April 3, 2016 1 Problems 1. You roll two 6-sided dice. What s the probability of rolling at least one 6? There is a 1

### Change Number Stories Objective To guide children as they use change diagrams to help solve change number stories.

Number Stories Objective To guide children as they use change diagrams to help solve change number stories. www.everydaymathonline.com epresentations etoolkit Algorithms Practice EM Facts Workshop Game

### Fourth Grade Fractions

Fourth Grade Fractions http://upload.wikimedia.org/wikibooks/en/9/92/fractions_of_a_square.jpg North Carolina Department of Public Instruction www.ncdpi.wikispaces.net Overview The implementation of the

### DESCRIPTIVE STATISTICS. The purpose of statistics is to condense raw data to make it easier to answer specific questions; test hypotheses.

DESCRIPTIVE STATISTICS The purpose of statistics is to condense raw data to make it easier to answer specific questions; test hypotheses. DESCRIPTIVE VS. INFERENTIAL STATISTICS Descriptive To organize,

### Differentiated Instruction Strategies

Miss Taylor Brooke Stancil s Differentiated Instruction Strategies Choral Response: Choral response is a very simple technique in which the teacher asks questions to the class as a whole and the students

### Grade 6 Mathematics Assessment. Eligible Texas Essential Knowledge and Skills

Grade 6 Mathematics Assessment Eligible Texas Essential Knowledge and Skills STAAR Grade 6 Mathematics Assessment Mathematical Process Standards These student expectations will not be listed under a separate

### 4 G: Identify, analyze, and synthesize relevant external resources to pose or solve problems. 4 D: Interpret results in the context of a situation.

MAT.HS.PT.4.TUITN.A.298 Sample Item ID: MAT.HS.PT.4.TUITN.A.298 Title: College Tuition Grade: HS Primary Claim: Claim 4: Modeling and Data Analysis Students can analyze complex, real-world scenarios and

### Tennessee Mathematics Standards 2009-2010 Implementation. Grade Six Mathematics. Standard 1 Mathematical Processes

Tennessee Mathematics Standards 2009-2010 Implementation Grade Six Mathematics Standard 1 Mathematical Processes GLE 0606.1.1 Use mathematical language, symbols, and definitions while developing mathematical

### Acing Math (One Deck At A Time!): A Collection of Math Games. Table of Contents

Table of Contents Introduction to Acing Math page 5 Card Sort (Grades K - 3) page 8 Greater or Less Than (Grades K - 3) page 9 Number Battle (Grades K - 3) page 10 Place Value Number Battle (Grades 1-6)

### Wentzville School District Algebra 1: Unit 8 Stage 1 Desired Results

Wentzville School District Algebra 1: Unit 8 Stage 1 Desired Results Unit Title: Quadratic Expressions & Equations Course: Algebra I Unit 8 - Quadratic Expressions & Equations Brief Summary of Unit: At

### Performance Assessment Task Which Shape? Grade 3. Common Core State Standards Math - Content Standards

Performance Assessment Task Which Shape? Grade 3 This task challenges a student to use knowledge of geometrical attributes (such as angle size, number of angles, number of sides, and parallel sides) to

### GMAT SYLLABI. Types of Assignments - 1 -

GMAT SYLLABI The syllabi on the following pages list the math and verbal assignments for each class. Your homework assignments depend on your current math and verbal scores. Be sure to read How to Use

### Fundamentals of Probability

Fundamentals of Probability Introduction Probability is the likelihood that an event will occur under a set of given conditions. The probability of an event occurring has a value between 0 and 1. An impossible

### DENTAL IMPRESSIONS TARGET COMMON CORE STATE STANDARD(S) IN MATHEMATICS: N-Q.1:

This task was developed by high school and postsecondary mathematics and health sciences educators, and validated by content experts in the Common Core State Standards in mathematics and the National Career

### Task: Representing the National Debt 7 th grade

Tennessee Department of Education Task: Representing the National Debt 7 th grade Rachel s economics class has been studying the national debt. The day her class discussed it, the national debt was \$16,743,576,637,802.93.

### Considerations for Using STAR Data with Educator Evaluation: Ohio

Considerations for Using STAR Data with Educator Evaluation: Ohio Purpose Renaissance Learning has developed this document in response to customer requests for information on how to use the data generated

### A Concrete Introduction. to the Abstract Concepts. of Integers and Algebra using Algebra Tiles

A Concrete Introduction to the Abstract Concepts of Integers and Algebra using Algebra Tiles Table of Contents Introduction... 1 page Integers 1: Introduction to Integers... 3 2: Working with Algebra Tiles...

### Executive Summary Principles and Standards for School Mathematics

Executive Summary Principles and Standards for School Mathematics Overview We live in a time of extraordinary and accelerating change. New knowledge, tools, and ways of doing and communicating mathematics

### Linked Core Abilities

Courtesy of Army JROTC U2C4L3 Negotiating Key Words: Negotiation Principled Negotiation What You Will Learn to Do Negotiate a win/win solution for a given situation Linked Core Abilities Communicate using

### Operations and Supply Chain Management Prof. G. Srinivasan Department of Management Studies Indian Institute of Technology Madras

Operations and Supply Chain Management Prof. G. Srinivasan Department of Management Studies Indian Institute of Technology Madras Lecture - 41 Value of Information In this lecture, we look at the Value

### Unit #3: Investigating Quadratics (9 days + 1 jazz day + 1 summative evaluation day) BIG Ideas:

Unit #3: Investigating Quadratics (9 days + 1 jazz day + 1 summative evaluation day) BIG Ideas: Developing strategies for determining the zeroes of quadratic functions Making connections between the meaning

### Problem of the Month Through the Grapevine

The Problems of the Month (POM) are used in a variety of ways to promote problem solving and to foster the first standard of mathematical practice from the Common Core State Standards: Make sense of problems

### Voyager Sopris Learning Vmath, Levels C-I, correlated to the South Carolina College- and Career-Ready Standards for Mathematics, Grades 2-8

Page 1 of 35 VMath, Level C Grade 2 Mathematical Process Standards 1. Make sense of problems and persevere in solving them. Module 3: Lesson 4: 156-159 Module 4: Lesson 7: 220-223 2. Reason both contextually

### Indiana Academic Standards Mathematics: Algebra I

Indiana Academic Standards Mathematics: Algebra I 1 I. Introduction The college and career ready Indiana Academic Standards for Mathematics: Algebra I are the result of a process designed to identify,

### USING ALGEBRA TILES EFFECTIVELY

MATHEMATICS USING ALGEBRA TILES EFFECTIVELY TOOLS FOR UNDERSTANDING by Bettye C. Hall Reviewers James Gates, Ed.D. Yvonne S. Gentzler, Ph.D. AUTHOR Bettye C. Hall is the former Director of Mathematics

### Tennessee Department of Education. Task: Sally s Car Loan

Tennessee Department of Education Task: Sally s Car Loan Sally bought a new car. Her total cost including all fees and taxes was \$15,. She made a down payment of \$43. She financed the remaining amount

### Mathematics Curriculum

New York State Common Core 3 G R A D E Mathematics Curriculum GRADE 3 MODULE 1 Topic B Division as an Unknown Factor Problem 3.OA.2, 3.OA.6, 3.OA.3, 3.OA.4 Focus Standard: 3.OA.2 Interpret whole-number

### Fractions Packet. Contents

Fractions Packet Contents Intro to Fractions.. page Reducing Fractions.. page Ordering Fractions page Multiplication and Division of Fractions page Addition and Subtraction of Fractions.. page Answer Keys..

### Near Optimal Solutions

Near Optimal Solutions Many important optimization problems are lacking efficient solutions. NP-Complete problems unlikely to have polynomial time solutions. Good heuristics important for such problems.

### Problem of the Month The Wheel Shop

Problem of the Month The Wheel Shop The Problems of the Month (POM) are used in a variety of ways to promote problem solving and to foster the first standard of mathematical practice from the Common Core

### Mathematics Assessment Collaborative Tool Kits for Teachers Looking and Learning from Student Work 2009 Grade Eight

Mathematics Assessment Collaborative Tool Kits for Teachers Looking and Learning from Student Work 2009 Grade Eight Contents by Grade Level: Overview of Exam Grade Level Results Cut Score and Grade History

### Representing Data 1: Using Frequency Graphs

CONCEPT DEVELOPMENT Mathematics Assessment Project CLASSROOM CHALLENGES A Formative Assessment Lesson Representing Data 1: Using Graphs Mathematics Assessment Resource Service University of Nottingham

### For example, estimate the population of the United States as 3 times 10⁸ and the

CCSS: Mathematics The Number System CCSS: Grade 8 8.NS.A. Know that there are numbers that are not rational, and approximate them by rational numbers. 8.NS.A.1. Understand informally that every number

### Herzog Keyboarding Grades 3 through 5. Overarching Essential Questions

Herzog Keyboarding Grades 3 through 5 Overarching Essential Questions How will learning to keyboard help me with my academics today and my career tomorrow? Introduction The lessons in the Herzog Keyboarding

### Number Sense and Numeration, Grades 4 to 6

Number Sense and Numeration, Grades 4 to 6 Volume 3 Multiplication A Guide to Effective Instruction in Mathematics, Kindergarten to Grade 6 2006 Every effort has been made in this publication to identify

### Representing Data Using Frequency Graphs

Lesson 25 Mathematics Assessment Project Formative Assessment Lesson Materials Representing Data Using Graphs MARS Shell Center University of Nottingham & UC Berkeley Alpha Version If you encounter errors

### Intended Use of the document: Teachers who are using standards based reporting in their classrooms.

Standards Based Grading reports a student s ability to demonstrate mastery of a given standard. This Excel spread sheet is designed to support this method of assessing and reporting student learning. Purpose

### Developing Base Ten Understanding: Working with Tens, The Difference Between Numbers, Doubling, Tripling, Splitting, Sharing & Scaling Up

Developing Base Ten Understanding: Working with Tens, The Difference Between Numbers, Doubling, Tripling, Splitting, Sharing & Scaling Up James Brickwedde Project for Elementary Mathematics jbrickwedde@ties2.net

### GRADE 6 MATH: GROCERY SHOPPING AND THE QUILT OF A MATH TEACHER

GRADE 6 MATH: GROCERY SHOPPING AND THE QUILT OF A MATH TEACHER UNIT OVERVIEW This unit contains a curriculum- embedded Common Core aligned task and instructional supports. The task is embedded in a 2 3

### YOU CAN COUNT ON NUMBER LINES

Key Idea 2 Number and Numeration: Students use number sense and numeration to develop an understanding of multiple uses of numbers in the real world, the use of numbers to communicate mathematically, and

### Base-Ten and Place Value

1 Base-Ten and Place Value Jumping Jelly Beans Hundred Board-O Order Up! Number Neighborhood Stretching Numbers Place Value Pause Place Value Bingo 1 2 BRAIN-COMPATIBLE ACTIVITIES FOR MATHEMATICS, GRADES

### Dynamic Programming Problem Set Partial Solution CMPSC 465

Dynamic Programming Problem Set Partial Solution CMPSC 465 I ve annotated this document with partial solutions to problems written more like a test solution. (I remind you again, though, that a formal

### Discrete Mathematics and Probability Theory Fall 2009 Satish Rao, David Tse Note 10

CS 70 Discrete Mathematics and Probability Theory Fall 2009 Satish Rao, David Tse Note 10 Introduction to Discrete Probability Probability theory has its origins in gambling analyzing card games, dice,

### Lesson 8 Setting Healthy Eating & Physical Activity Goals

Lesson 8 Setting Healthy Eating & Physical Activity Goals Overview In this lesson, students learn about goal setting. They review the activity sheets they filled out earlier to log their eating and activity

### 6th Grade Lesson Plan: Probably Probability

6th Grade Lesson Plan: Probably Probability Overview This series of lessons was designed to meet the needs of gifted children for extension beyond the standard curriculum with the greatest ease of use

### That s Not Fair! ASSESSMENT #HSMA20. Benchmark Grades: 9-12

That s Not Fair! ASSESSMENT # Benchmark Grades: 9-12 Summary: Students consider the difference between fair and unfair games, using probability to analyze games. The probability will be used to find ways

### Problem of the Month: Digging Dinosaurs

: The Problems of the Month (POM) are used in a variety of ways to promote problem solving and to foster the first standard of mathematical practice from the Common Core State Standards: Make sense of

### CORRELATED TO THE SOUTH CAROLINA COLLEGE AND CAREER-READY FOUNDATIONS IN ALGEBRA

We Can Early Learning Curriculum PreK Grades 8 12 INSIDE ALGEBRA, GRADES 8 12 CORRELATED TO THE SOUTH CAROLINA COLLEGE AND CAREER-READY FOUNDATIONS IN ALGEBRA April 2016 www.voyagersopris.com Mathematical

### DRAFT. New York State Testing Program Grade 8 Common Core Mathematics Test. Released Questions with Annotations

DRAFT New York State Testing Program Grade 8 Common Core Mathematics Test Released Questions with Annotations August 2014 Developed and published under contract with the New York State Education Department

### Ten Strategies to Encourage Academic Integrity in Large Lecture Classes

Ten Strategies to Encourage Academic Integrity in Large Lecture Classes Brian Udermann and Karrie Lamers Introduction Academic integrity has been and continues to be a lively topic of discussion on most

### Grade 6 Mathematics Common Core State Standards

Grade 6 Mathematics Common Core State Standards Standards for Mathematical Practice HOW make sense of problems, persevere in solving them, and check the reasonableness of answers. reason with and flexibly

### Terminology and Scripts: what you say will make a difference in your success

Terminology and Scripts: what you say will make a difference in your success Terminology Matters! Here are just three simple terminology suggestions which can help you enhance your ability to make your

### DRAFT. New York State Testing Program Grade 7 Common Core Mathematics Test. Released Questions with Annotations

DRAFT New York State Testing Program Grade 7 Common Core Mathematics Test Released Questions with Annotations August 2014 Developed and published under contract with the New York State Education Department

### Gaming the Law of Large Numbers

Gaming the Law of Large Numbers Thomas Hoffman and Bart Snapp July 3, 2012 Many of us view mathematics as a rich and wonderfully elaborate game. In turn, games can be used to illustrate mathematical ideas.

### Representing Data with Frequency Graphs

CONCEPT DEVELOPMENT Mathematics Assessment Project CLASSROOM CHALLENGES A Formative Assessment Lesson Representing Data with Graphs Mathematics Assessment Resource Service University of Nottingham & UC

### Math Board Games. For School or Home Education. by Teresa Evans. Copyright 2005 Teresa Evans. All rights reserved.

Math Board Games For School or Home Education by Teresa Evans Copyright 2005 Teresa Evans. All rights reserved. Permission is given for the making of copies for use in the home or classroom of the purchaser

### South Carolina College- and Career-Ready (SCCCR) Algebra 1

South Carolina College- and Career-Ready (SCCCR) Algebra 1 South Carolina College- and Career-Ready Mathematical Process Standards The South Carolina College- and Career-Ready (SCCCR) Mathematical Process

### Computing Unit Planner: Year 5 Unit 1 Quiz and Game

Computing Unit Planner: Year 5 Unit 1 Quiz and Game National Curriculum Computing Content design, write and debug programs that accomplish specific goals, including controlling or simulating physical systems;

### Personal Financial Literacy

Personal Financial Literacy 7 Unit Overview Being financially literate means taking responsibility for learning how to manage your money. In this unit, you will learn about banking services that can help

### Unit 12: Introduction to Factoring. Learning Objectives 12.2

Unit 1 Table of Contents Unit 1: Introduction to Factoring Learning Objectives 1. Instructor Notes The Mathematics of Factoring Teaching Tips: Challenges and Approaches Additional Resources Instructor

### Network Planning and Analysis

46 Network Planning and Analysis 1. Objective: What can you tell me about the project? When will the project finish? How long will the project take (project total duration)? 2. Why is this topic Important

### Using the Area Model to Teach Multiplying, Factoring and Division of Polynomials

visit us at www.cpm.org Using the Area Model to Teach Multiplying, Factoring and Division of Polynomials For more information about the materials presented, contact Chris Mikles mikles@cpm.org From CCA

### Whitnall School District Report Card Content Area Domains

Whitnall School District Report Card Content Area Domains In order to align curricula kindergarten through twelfth grade, Whitnall teachers have designed a system of reporting to reflect a seamless K 12

### This document contains Chapter 2: Statistics, Data Analysis, and Probability strand from the 2008 California High School Exit Examination (CAHSEE):

This document contains Chapter 2:, Data Analysis, and strand from the 28 California High School Exit Examination (CAHSEE): Mathematics Study Guide published by the California Department of Education. The

### Rational Number Project

Rational Number Project Initial Fraction Ideas Lesson : Overview Students observe with circles that as the unit is divided into more and more equal parts, the unit parts become smaller. Materials Fraction

### Lesson 9: Radicals and Conjugates

Student Outcomes Students understand that the sum of two square roots (or two cube roots) is not equal to the square root (or cube root) of their sum. Students convert expressions to simplest radical form.