# Grade Level Year Total Points Core Points % At Standard %

Save this PDF as:

Size: px
Start display at page:

## Transcription

2 Marble Game This problem gives you the chance to: use probability in an everyday situation Linda has designed a marble game. Bag A Bag B 1. Bag A contains 3 marbles one red, one blue and one green. Bag B contains 2 marbles one red and one blue. G B R R B To play this game, a player draws one marble from each bag without looking. If the two marbles match (are the same color), the player wins a prize. What is the theoretical probability of winning a prize at a single try? Show your work. 2. Here are the results for the first 30 games. How do the results in this table and the theoretical probability you found compare? Win (Match) No Win (No Match) Explain any differences. Copyright 2009 by Mathematics Assessment Resource Service. Marble Game 44

3 3. Linda has designed a second game. The spinner has nine equal sections. To play the game, a player spins the spinner. Blue Red Gold If the spinner lands on a Gold section, the player wins a prize. Does the player have a better chance of winning with the bag game or the spinner game? Gold Red Gold Red Red Gold Explain your reasoning. 7 Copyright 2009 by Mathematics Assessment Resource Service. Marble Game 45

4 Marble Game Rubric The core elements of performance required by this task are: listed here Based on these, credit for specific aspects of performance should be assigned as follows points section points 1. Gives correct answer: 2 6 = 1 3 Lists all possibilities: RR, RB, BR, BB, GR, GB p(rr or BB) = 2/6 or 1/3 or Shows work such as: Probability R " R = 1 3 # 1 2 Probability B " B = 1 3 # or 1 1 Probability both same color = These results are quite close; 1 3 but the number of trials is not large enough to give an accurate estimate. or Explains that from these results the experimental probability = 9 30 = 3 10 = 0.3 The theoretical probability = 0.33 recurring 3. Gives correct answer: the spinner game Shows work such as: 1 the probability of winning on the spinner game is 4/9 = 0.44 recurring 2 Total Points 7 Copyright 2009 by Mathematics Assessment Resource Service. 46

5 Marble Game Work the task and look at the rubric. What are the key mathematical ideas being assessed in this task? What activities or experiences have students had with probability this year to help prepare them for the High School Exit Exam? How do you help students draw or define sample spaces? What models do they know? Look at student work on part 1. How many of your students put: 1/3 2/3 4/5 2/5 1/5 Red Other Make a list of models students used to figure out probability: Organized list Formula Now look at student work of part 2. How many students: Knew the probability was 9/30 or 30%? Did not compare to the two probabilities? Thought that winning was unlikely (nonnumerical)? Thought there were less wins than losses? Thought the probability was 9/21 or 3/7? What are some of the big ideas about quantifying probability that your students did not understand? Now look at student work on part 3, finding the probability of the spinner. How many of your students thought the spinner was better? the bag game was better? they were equal? How many of your students did not attempt to quantify the probability for winning the spinner? 47

6 Looking at Student Work on Marble Game Student A is able to make an organized list to show the sample space in part 1 and quantify the probability. The student does not how to convert the frequency table into a probability but recognizes that the total is important to the fraction. The student is able to quantify the probability on the spinner and compare it correctly to the bag game. Student A 48

7 Student B is able to get the correct probability, but from drawing the sample space incorrectly. What error has the student made? The student is able to calculate the experimental probability from the frequency table and understands that the denominators need to be the same to compare the two probabilities. However the student makes the wrong choice when comparing the two. The student has a complete explanation for part 3. Student B 49

8 Student C is able to draw a complete sample space and identify the winning choices, the student even gives the numerical probability. The student does not see the importance of the numerical probability with the idea of likely, unlikely, and certain, etc. dominating the thinking. Notice that in part 2 the student doesn t quantify the experimental probability. The student does give the correct numerical probability in part 3. Student C 50

9 Student D is not very explanatory and relies on numbers. In part 1 the student thinks about a variety of choices, but lands on the correct probability. In part 2 the student quantifies the probability, but makes no attempt to compare the probabilities. In part 3 the student finds the numerical probability. Student D 51

10 Student E is able to define the sample space and give a definition for finding probability. The student can t turn the definition into a numerical expression. Instead the student quantifies the number of wins. In part 2 the student is also concerned with winning or losing rather than a numerical expression. The student subtracts wins from losses with the frequency table, rather than comparing the probability in 1 with the probability in 2. The student could find the numerical probability for the spinner. How do we help students to see the relevance for the numerical probability when their focus is on the importance of winning? What would make this important to them? Student E 52

11 Student F gets the correct probability, but for the wrong reasons. The student seems to think about 2 bags, so 50% and 50% to get 100. Then the student divides by the 3 marbles in the first bag. The student does calculate correctly the experimental probability. In part 3 the student incorrectly counts the number of sections on the spinner. The student doesn t combine the winning choices. Student F 53

12 Student G is able to make a list for the sample space, but doesn t know how to use it to write a correct probability. The student does not use the total in either part 1 or part 2. The student doesn t understand how to set up the probability for the spinner, and instead seems to compare the reds from the two games. Student G 54

13 Student H attempts to draw the sample space, but uses the first bag twice. The student seems to think that games should be fair, have a 50% chance of winning in part 2. The student is able to identify the winning spaces on the spinner, but then compares chances to chances rather than probability. Student H 55

14 Student I identifies the winning combinations in part 1, but sets up the probability with total marbles instead of total possibilities. What experiences help students to understand the distinction between the two? In part 2 the student seems to compare the winning to not winning rather than set up a probability. In part 3 the student doesn t quantify the fraction for winning on the spinner. Student I 56

15 8 th Grade Task 3 Marble Game Student Task Use probability in an everyday situation. Core Idea 2 Probability Apply and deepen understanding of theoretical and empirical probability. Determine theoretical and experimental probabilities and use these to make predictions about events. Represent probabilities as ratios, proportions, decimals or percents. Represent the sample space for a given event in an organized way. Mathematics of this task: Define a sample space for a game Identify winning combinations Express theoretical probability numerically Convert data from a frequency table to an experimental probability Compare probabilities by finding commonality (percents, common denominator) Find simple probability for a spinner Based on teacher observation, this is what eighth graders know and are able to do: Determine the game with the best probability of winning Identify the probability on a spinner Areas of difficulty for eighth graders: Understanding the difference between marbles and the total possibilities in setting up the probabilities Defining a sample space for a compound event Still thinking about likely/ unlikely or wining/losing instead of in terms of numerical probabilities Comparing colors in the bag game and spinner instead of the probabilities Using numbers to quantify the probability in the frequency table and spinner 57

16 The maximum score available for this task is 7 points. The minimum score for a level 3 response, meeting standards, is 4 points. More than half the students, 60%, could identify the winning game. Some students, 28%, could also give the numerical probability for winning the spinner game. About 7% of the students could find the probability for winning the bag game (their reasoning may not have been correct). Less than 1% of the students could meet all the demands of the task including defining the sample space for the bag game and giving the theoretical and experimental probability and noticing that they were close in value. 40% of the students scored no points on this task. 92% of the students in the sample with this score attempted the task. 58

17 Marble Game Points Understandings Misunderstandings 0 40% of the students in the sample got this score. 92% of them attempted the task. 18% of the students thought the chances of winning the bag game were better. 10% thought the chances were the same for both games. 20% made no attempt to quantify the probability on the spinner game. Some students subtracted winning outcomes (4-1 Students could select the game with the highest probability of winning. 2 Students could give the probability of winning on the spinner and knew it was a higher probability than the bag game. 3 Students could work with the spinner game and find the probability for the bag game. 4 Students could find the correct probability for the bag game with correct reasoning, give the correct probability for the spinner game, and compare the two values. 7 Students could reason about a compound event, define the sample space, and write a probability. Students could convert a frequency table into an experimental probability. Students could compare probabilities by converting them to decimals, percents or fractions with common denominators. Students could give a probability for a simple event like a spinner. 2). Students could not support their reasoning by quantifying the probability on the spinner. Students could not find the probability for winning the bag game. 8% thought the probability was 4/5. 8% thought the probability was 2/3. 8% thought the probability was 2/5. Students could not give convincing or correct justification for their probability. Many students arrived at a probability of 1/3 using incorrect logic. Students could not write the experimental probability or compare it to the probability for the bag game. 13% used the word unlikely instead of giving a numerical value. 13% did not attempt this part of the task. 8% of the students compared winning to losing in the frequency table instead of comparing the frequency table to the theoretical probability in part 1. 59

18 Implications for Instruction Students need more exposure to probability. While in elementary school, students learn about probability in terms of likelihood, in middles school students should start to make progress on quantifying probability. Students need to see the difference between odds (favorable outcomes to unfavorable outcomes) and probability (favorable outcomes to total possible outcomes). Before any of this can be determined, students need to be able to develop sample space. The spinner is easy because all of the spaces were equal size and could be added together. Students understand generally how to determine probability on a single number cube. They have trouble with compound events: rolling a die and then rolling a second die or spinning a spinner; drawing from two different bags. Students need to practice with strategies like making an organized list or drawing a tree diagram to help them develop all the possible outcomes. Some students still have trouble distinguishing between the actual objects used in the event (marbles in the bag) and the outcome of drawing the red marble. Some students need to understand that probability is the chance of something happening rather than winning. Many students were only focused on winning the game. Students need to think about the difference between theoretical probability and experimental probability. While many students could quantify the size of the experimental probability, there was little evidence about the difference between chance and expected values. Ideas for Action Research With 40% of the students scoring no points on this task, students need to do some serious work with the idea of probability. While this isn t an eighth grade standard, it is tested on the High School Exit exam. Probability is also an interesting way to help students review ideas about fractions and decimals, making them feel like they are studying a new topic. Before trying to formalize the information, students just need to build up some experiential knowledge. They need lots of experiences with games of chance. Some interesting tasks can be found in Chance Encounters by Education Development Center, Inc. One group of activities involves describing probabilities as fractions, percents, decimals and ratios. It is called Designing Mystery Spinner Games. See a part of the activity on the next page. A different set of activities is to decide if games are Fair. See examples on following pages. A problem of the month on Fair Games is also available on the SVMI website: 60

19 How does this activity press students to practice skills such as using fractions, decimals, and percentages? How does it help students use justification and mathematical reasoning? 61

20 62

21 In this game, students are asked to help Terry decide which is the better game to play. How does this help students practice basic skills? What strategies do you think students might use to rank the games? 63

22 64

### A REI.2 Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.

Performance Assessment Task Hexagons Grade 7 task aligns in part to CCSSM HS Algebra The task challenges a student to demonstrate understanding of the concepts of relations and functions. A student must

### 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

### Performance Assessment Task Fair Game? Grade 7. Common Core State Standards Math - Content Standards

Performance Assessment Task Fair Game? Grade 7 This task challenges a student to use understanding of probabilities to represent the sample space for simple and compound events. A student must use information

### High School Functions Building Functions Build a function that models a relationship between two quantities.

Performance Assessment Task Coffee Grade 10 This task challenges a student to represent a context by constructing two equations from a table. A student must be able to solve two equations with two unknowns

### Grade Level Year Total Points Core Points % At Standard %

Performance Assessment Task Vincent s Graphs This task challenges a student to use understanding of functions to interpret and draw graphs. A student must be able to analyze a graph and understand the

### Performance Assessment Task Peanuts and Ducks Grade 2. Common Core State Standards Math - Content Standards

Performance Assessment Task Peanuts and Ducks Grade 2 The task challenges a student to demonstrate understanding of concepts involved in addition and subtraction. A student must be fluent with addition

### Performance Assessment Task Bikes and Trikes Grade 4. Common Core State Standards Math - Content Standards

Performance Assessment Task Bikes and Trikes Grade 4 The task challenges a student to demonstrate understanding of concepts involved in multiplication. A student must make sense of equal sized groups of

### Performance Assessment Task Picking Fractions Grade 4. Common Core State Standards Math - Content Standards

Performance Assessment Task Picking Fractions Grade 4 The task challenges a student to demonstrate understanding of the concept of equivalent fractions. A student must understand how the number and size

### N Q.3 Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.

Performance Assessment Task Swimming Pool Grade 9 The task challenges a student to demonstrate understanding of the concept of quantities. A student must understand the attributes of trapezoids, how to

### 2012 Noyce Foundation

Performance Assessment Task Hexagons in a Row Grade 5 This task challenges a student to use knowledge of number patterns and operations to identify and extend a pattern. A student must be able to describe

### Performance Assessment Task Parking Cars Grade 3. Common Core State Standards Math - Content Standards

Performance Assessment Task Parking Cars Grade 3 This task challenges a student to use their understanding of scale to read and interpret data in a bar graph. A student must be able to use knowledge of

### Performance Assessment Task Cindy s Cats Grade 5. Common Core State Standards Math - Content Standards

Performance Assessment Task Cindy s Cats Grade 5 This task challenges a student to use knowledge of fractions to solve one- and multi-step problems with fractions. A student must show understanding of

### Performance Assessment Task Leapfrog Fractions Grade 4 task aligns in part to CCSSM grade 3. Common Core State Standards Math Content Standards

Performance Assessment Task Leapfrog Fractions Grade 4 task aligns in part to CCSSM grade 3 This task challenges a student to use their knowledge and understanding of ways of representing numbers and fractions

### Performance Assessment Task Baseball Players Grade 6. Common Core State Standards Math - Content Standards

Performance Assessment Task Baseball Players Grade 6 The task challenges a student to demonstrate understanding of the measures of center the mean, median and range. A student must be able to use the measures

### 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

### Performance Assessment Task Gym Grade 6. Common Core State Standards Math - Content Standards

Performance Assessment Task Gym Grade 6 This task challenges a student to use rules to calculate and compare the costs of memberships. Students must be able to work with the idea of break-even point to

### Operations and Algebraic Thinking Represent and solve problems involving multiplication and division.

Performance Assessment Task The Answer is 36 Grade 3 The task challenges a student to use knowledge of operations and their inverses to complete number sentences that equal a given quantity. A student

### Common Core State Standards. Standards for Mathematical Practices Progression through Grade Levels

Standard for Mathematical Practice 1: Make sense of problems and persevere in solving them. Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for

### Problem of the Month. Squirreling it Away

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

### Statistics and Probability Investigate patterns of association in bivariate data.

Performance Assessment Task Scatter Diagram Grade 9 task aligns in part to CCSSM grade 8 This task challenges a student to select and use appropriate statistical methods to analyze data. A student must

### Problem of the Month: Calculating Palindromes

Problem of the Month: 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:

### Problem of the Month: Fair Games

Problem of the Month: 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:

### Overview. Essential Questions. Grade 7 Mathematics, Quarter 4, Unit 4.2 Probability of Compound Events. Number of instruction days: 8 10

Probability of Compound Events Number of instruction days: 8 10 Overview Content to Be Learned Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. Understand

### Solving Equations with One Variable

Grade 8 Mathematics, Quarter 1, Unit 1.1 Solving Equations with One Variable Overview Number of Instructional Days: 15 (1 day = 45 minutes) Content to Be Learned Solve linear equations in one variable

### PA Common Core Standards Standards for Mathematical Practice Grade Level Emphasis*

Habits of Mind of a Productive Thinker Make sense of problems and persevere in solving them. Attend to precision. PA Common Core Standards The Pennsylvania Common Core Standards cannot be viewed and addressed

### Measurement with Ratios

Grade 6 Mathematics, Quarter 2, Unit 2.1 Measurement with Ratios Overview Number of instructional days: 15 (1 day = 45 minutes) Content to be learned Use ratio reasoning to solve real-world and mathematical

### Students have to guess whether the next card will have a higher or a lower number than the one just turned.

Card Game This problem gives you the chance to: figure out and explain probabilities Mrs Jakeman is teaching her class about probability. She has ten cards, numbered 1 to 10. She mixes them up and stands

### High School Functions Interpreting Functions Understand the concept of a function and use function notation.

Performance Assessment Task Printing Tickets Grade 9 The task challenges a student to demonstrate understanding of the concepts representing and analyzing mathematical situations and structures using algebra.

### Decimals in the Number System

Grade 5 Mathematics, Quarter 1, Unit 1.1 Decimals in the Number System Overview Number of Instructional Days: 15 (1 day = 45 minutes) Content to Be Learned Recognize place value relationships. In a multidigit

### Overview. Essential Questions. Algebra I, Quarter 1, Unit 1.2 Interpreting and Applying Algebraic Expressions

Algebra I, Quarter 1, Unit 1.2 Interpreting and Applying Algebraic Expressions Overview Number of instruction days: 6 8 (1 day = 53 minutes) Content to Be Learned Write and interpret an expression from

### 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

### Pythagorean Theorem. Overview. Grade 8 Mathematics, Quarter 3, Unit 3.1. Number of instructional days: 15 (1 day = minutes) Essential questions

Grade 8 Mathematics, Quarter 3, Unit 3.1 Pythagorean Theorem Overview Number of instructional days: 15 (1 day = 45 60 minutes) Content to be learned Prove the Pythagorean Theorem. Given three side lengths,

### Overview. Essential Questions. Grade 4 Mathematics, Quarter 3, Unit 3.3 Multiplying Fractions by a Whole Number

Multiplying Fractions by a Whole Number Overview Number of instruction days: 8 10 (1 day = 90 minutes) Content to Be Learned Understand that a fraction can be written as a multiple of unit fractions with

### Problem of the Month: Perfect Pair

Problem of the Month: 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:

### Expressions and Equations Understand the connections between proportional relationships, lines, and linear equations.

Performance Assessment Task Squares and Circles Grade 8 The task challenges a student to demonstrate understanding of the concepts of linear equations. A student must understand relations and functions,

### Problem of the Month Diminishing Return

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

### Tom wants to find two real numbers, a and b, that have a sum of 10 and have a product of 10. He makes this table.

Sum and Product This problem gives you the chance to: use arithmetic and algebra to represent and analyze a mathematical situation solve a quadratic equation by trial and improvement Tom wants to find

### 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

### Problem of the Month: Double Down

Problem of the Month: Double Down 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

### Unit 1: Place value and operations with whole numbers and decimals

Unit 1: Place value and operations with whole numbers and decimals Content Area: Mathematics Course(s): Generic Course Time Period: 1st Marking Period Length: 10 Weeks Status: Published Unit Overview Students

### 2012 Noyce Foundation

Performance Assessment Task Carol s Numbers Grade 2 The task challenges a student to demonstrate understanding of concepts involved in place value. A student must understand the relative magnitude of whole

### 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

### Problem of the Month: William s Polygons

Problem of the Month: William s Polygons 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

### Standards for Mathematical Practice: Commentary and Elaborations for 6 8

Standards for Mathematical Practice: Commentary and Elaborations for 6 8 c Illustrative Mathematics 6 May 2014 Suggested citation: Illustrative Mathematics. (2014, May 6). Standards for Mathematical Practice:

### Operations and Algebraic Thinking Represent and solve problems involving addition and subtraction. Add and subtract within 20. MP.

Performance Assessment Task Incredible Equations Grade 2 The task challenges a student to demonstrate understanding of concepts involved in addition and subtraction. A student must be able to understand

### Total Student Count: 3170. Grade 8 2005 pg. 2

Grade 8 2005 pg. 1 Total Student Count: 3170 Grade 8 2005 pg. 2 8 th grade Task 1 Pen Pal Student Task Core Idea 3 Algebra and Functions Core Idea 2 Mathematical Reasoning Convert cake baking temperatures

### Understand the Concepts of Ratios and Unit Rates to Solve Real-World Problems

Grade 6 Mathematics, Quarter 2, Unit 2.1 Understand the Concepts of Ratios and Unit Rates to Solve Real-World Problems Overview Number of instructional days: 10 (1 day = 45 60 minutes) Content to be learned

### Gary School Community Corporation Mathematics Department Unit Document. Unit Number: 8 Grade: 2

Gary School Community Corporation Mathematics Department Unit Document Unit Number: 8 Grade: 2 Unit Name: YOU SEE IT!!! (2D & 3D Shapes) Duration of Unit: 18 days UNIT FOCUS Students describe and analyze

### CCSS: Mathematics. Operations & Algebraic Thinking. CCSS: Grade 5. 5.OA.A. Write and interpret numerical expressions.

CCSS: Mathematics Operations & Algebraic Thinking CCSS: Grade 5 5.OA.A. Write and interpret numerical expressions. 5.OA.A.1. Use parentheses, brackets, or braces in numerical expressions, and evaluate

### Problem of the Month: Game Show

Problem of the Month: 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:

### Modeling in Geometry

Modeling in Geometry Overview Number of instruction days: 8-10 (1 day = 53 minutes) Content to Be Learned Mathematical Practices to Be Integrated Use geometric shapes and their components to represent

### Comparing Fractions and Decimals

Grade 4 Mathematics, Quarter 4, Unit 4.1 Comparing Fractions and Decimals Overview Number of Instructional Days: 10 (1 day = 45 60 minutes) Content to be Learned Explore and reason about how a number representing

### G C.3 Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle.

Performance Assessment Task Circle and Squares Grade 10 This task challenges a student to analyze characteristics of 2 dimensional shapes to develop mathematical arguments about geometric relationships.

### Creating, Solving, and Graphing Systems of Linear Equations and Linear Inequalities

Algebra 1, Quarter 2, Unit 2.1 Creating, Solving, and Graphing Systems of Linear Equations and Linear Inequalities Overview Number of instructional days: 15 (1 day = 45 60 minutes) Content to be learned

### Performance Assessment Task Symmetrical Patterns Grade 4. Common Core State Standards Math - Content Standards

Performance Assessment Task Symmetrical Patterns Grade 4 The task challenges a student to demonstrate understanding of the concept of symmetry. A student must be able to name a variety of two-dimensional

### Overview. Essential Questions. Grade 5 Mathematics, Quarter 3, Unit 3.1 Adding and Subtracting Decimals

Adding and Subtracting Decimals Overview Number of instruction days: 12 14 (1 day = 90 minutes) Content to Be Learned Add and subtract decimals to the hundredths. Use concrete models, drawings, and strategies

### Problem of the Month: Circular Reasoning

Problem of the Month: Circular Reasoning 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

### Overview. Essential Questions. Grade 4 Mathematics, Quarter 4, Unit 4.1 Dividing Whole Numbers With Remainders

Dividing Whole Numbers With Remainders Overview Number of instruction days: 7 9 (1 day = 90 minutes) Content to Be Learned Solve for whole-number quotients with remainders of up to four-digit dividends

### Gary School Community Corporation Mathematics Department Unit Document. Unit Number: 3 Grade: 4

Gary School Community Corporation Mathematics Department Unit Document Unit Number: 3 Grade: 4 Unit Name: Measurement with Angles and Rectangles Duration of Unit: 20 Days UNIT FOCUS In this unit, students

### Evaluation Tool for Assessment Instrument Quality

REPRODUCIBLE Figure 4.4: Evaluation Tool for Assessment Instrument Quality Assessment indicators Description of Level 1 of the Indicator Are Not Present Limited of This Indicator Are Present Substantially

### Grade Level Year Total Points Core Points % At Standard 9 2003 10 5 7 %

Performance Assessment Task Number Towers Grade 9 The task challenges a student to demonstrate understanding of the concepts of algebraic properties and representations. A student must make sense of the

### 0.75 75% ! 3 40% 0.65 65% Percent Cards. This problem gives you the chance to: relate fractions, decimals and percents

Percent Cards This problem gives you the chance to: relate fractions, decimals and percents Mrs. Lopez makes sets of cards for her math class. All the cards in a set have the same value. Set A 3 4 0.75

### Division with Whole Numbers and Decimals

Grade 5 Mathematics, Quarter 2, Unit 2.1 Division with Whole Numbers and Decimals Overview Number of Instructional Days: 15 (1 day = 45 60 minutes) Content to be Learned Divide multidigit whole numbers

### 2012 Noyce Foundation

Performance Assessment Task Granny s Balloon Trip Grade 5 This task challenges a student to use knowledge of scale to organize and represent data from a table on graph. A student must understand scale

### Problem of the Month: Fractured Numbers

Problem of the Month: 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:

### SGO Example: Mathematics, Grade 6

SGO Example: Mathematics, Grade 6 Overview This Student Growth Objective (SGO) was created by a 6th grade mathematics teacher to focus on Mathematical Practice 4 (MP4) Model with mathematics as articulated

### Marie has a winter hat made from a circle, a rectangular strip and eight trapezoid shaped pieces. y inches. 3 inches

Winter Hat This problem gives you the chance to: calculate the dimensions of material needed for a hat use circle, circumference and area, trapezoid and rectangle Marie has a winter hat made from a circle,

### a) Three faces? b) Two faces? c) One face? d) No faces? What if it s a 15x15x15 cube? How do you know, without counting?

Painted Cube (Task) Imagine a large 3x3x3 cube made out of unit cubes. The large cube falls into a bucket of paint, so that the faces of the large cube are painted blue. Now suppose you broke the cube

### 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

### Integer Operations. Overview. Grade 7 Mathematics, Quarter 1, Unit 1.1. Number of Instructional Days: 15 (1 day = 45 minutes) Essential Questions

Grade 7 Mathematics, Quarter 1, Unit 1.1 Integer Operations Overview Number of Instructional Days: 15 (1 day = 45 minutes) Content to Be Learned Describe situations in which opposites combine to make zero.

### Cindy s Cats. Cindy has 3 cats: Sammy, Tommy and Suzi.

Cindy s Cats This problem gives you the chance to: solve fraction problems in a practical context Cindy has 3 cats: Sammy, Tommy and Suzi. 1. Cindy feeds them on Cat Crunchies. Each day Sammy eats 1 2

### Problem of the Month: First Rate

Problem of the Month: First Rate 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

Algebra II, Quarter 1, Unit 1.3 Quadratic Functions: Complex Numbers Overview Number of instruction days: 12-14 (1 day = 53 minutes) Content to Be Learned Mathematical Practices to Be Integrated Develop

### Discovering Math: Intermediate Probability Teacher s Guide

Teacher s Guide Grade Level: 6 8 Curriculum Focus: Mathematics Lesson Duration: 2 3 class periods Program Description Discovering Math: Intermediate Probability From theoretical models to simulations and

### A REI.2 Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.

Performance Assessment Task Magic Squares Grade 9 The task challenges a student to demonstrate understanding of the concepts representing and analyzing mathematical situations and structures with algebraic

### High School Algebra Reasoning with Equations and Inequalities Solve systems of equations.

Performance Assessment Task Graphs (2006) Grade 9 This task challenges a student to use knowledge of graphs and their significant features to identify the linear equations for various lines. A student

### Overview. Essential Questions. Precalculus, Quarter 2, Unit 2.5 Proving Trigonometric Identities. Number of instruction days: 5 7 (1 day = 53 minutes)

Precalculus, Quarter, Unit.5 Proving Trigonometric Identities Overview Number of instruction days: 5 7 (1 day = 53 minutes) Content to Be Learned Verify proofs of Pythagorean identities. Apply Pythagorean,

### Activities/ Resources for Unit V: Proportions, Ratios, Probability, Mean and Median

Activities/ Resources for Unit V: Proportions, Ratios, Probability, Mean and Median 58 What is a Ratio? A ratio is a comparison of two numbers. We generally separate the two numbers in the ratio with a

### 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

### Understanding Place Value

Grade 5 Mathematics, Quarter 1, Unit 1.1 Understanding Place Value Overview Number of instructional days: 7 (1 day = 45 minutes) Content to be learned Explain that a digit represents a different value

### Grades K-6. Correlated to the Common Core State Standards

Grades K-6 Correlated to the Common Core State Standards Kindergarten Standards for Mathematical Practice Common Core State Standards Standards for Mathematical Practice Kindergarten The Standards for

### Geometry Solve real life and mathematical problems involving angle measure, area, surface area and volume.

Performance Assessment Task Pizza Crusts Grade 7 This task challenges a student to calculate area and perimeters of squares and rectangles and find circumference and area of a circle. Students must find

### Core Idea Task Score Properties and

Balanced Assessment Test 2009 Core Idea Task Score Properties and Soup and Beans Representations This task asks students write equation to describe objects on a scale. Students need to use proportional

### Preview of Common Core State Standards Sample EAGLE Items Grade 7 Mathematics

Preview of Common Core State Standards Sample EAGLE Items Grade 7 Mathematics July 11, 2012 Grade 7 Technology enabled, multiple part, constructed response item types use a common context and contain several

### Shape Hunting This problem gives you the chance to: identify and describe solid shapes

Shape Hunting This problem gives you the chance to: identify and describe solid shapes Detective Sherlock Shapehunter tracks down solid shapes using clues provided by eyewitnesses. Here are some eyewitness

### a. Assuming your pattern continues, explain how you would build the 10 th figure.

Tile Patterns 1. The first 3 s in a pattern are shown below. Draw the 4 th and 5 th s. 1 st Figure 2 nd Figure 3 rd Figure 4 th Figure 5 th Figure a. Assuming your pattern continues, explain how you would

### Overall Frequency Distribution by Total Score

Overall Frequency Distribution by Total Score Grade 8 Mean=17.23; S.D.=8.73 500 400 Frequency 300 200 100 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34

### 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

### Chapter 15. Definitions: experiment: is the act of making an observation or taking a measurement.

MATH 11008: Probability Chapter 15 Definitions: experiment: is the act of making an observation or taking a measurement. outcome: one of the possible things that can occur as a result of an experiment.

### Common Core Standards Mission Statement

Common Core Standards Mission Statement http://www.corestandards.org/the-standards/mathematics/introduction/how-to-read-thegrade-level-standards/ The Common Core State Standards provide a consistent, clear

### Deal or No Deal Lesson Plan

Deal or No Deal Lesson Plan Grade Level: 7 (This lesson could be adapted for 6 th through 8 th grades) Materials: Deck of Playing Cards Fair Coin (coin with head and tail sides) for each pair of students

### Laws of Sines and Cosines and Area Formula

Precalculus, Quarter 3, Unit 3.1 Laws of Sines and Cosines and Area Formula Overview Number of instructional days: 8 (1 day = 45 minutes) Content to be learned Derive and use the formula y = 1 2 absin

Chance deals with the concepts of randomness and the use of probability as a measure of how likely it is that particular events will occur. A National Statement on Mathematics for Australian Schools, 1991

### Understanding Place Value of Whole Numbers and Decimals Including Rounding

Grade 5 Mathematics, Quarter 1, Unit 1.1 Understanding Place Value of Whole Numbers and Decimals Including Rounding Overview Number of instructional days: 14 (1 day = 45 60 minutes) Content to be learned

### Overview. Essential Questions. Precalculus, Quarter 3, Unit 3.4 Arithmetic Operations With Matrices

Arithmetic Operations With Matrices Overview Number of instruction days: 6 8 (1 day = 53 minutes) Content to Be Learned Use matrices to represent and manipulate data. Perform arithmetic operations with

### LESSON PLAN. Unit: Probability Lesson 6 Date: Summer 2008

LESSON PLAN Grade Level/Course: Grade 6 Mathematics Teacher(s): Ms. Green & Mr. Nielsen Unit: Probability Lesson 6 Date: Summer 2008 Topic(s): Playing Carnival Games Resources: Transparencies: Worksheets:

### Math, Grades 6-8 TEKS and TAKS Alignment

111.22. Mathematics, Grade 6. 111.23. Mathematics, Grade 7. 111.24. Mathematics, Grade 8. (a) Introduction. (1) Within a well-balanced mathematics curriculum, the primary focal points are using ratios

### Overview. Essential Questions. Precalculus, Quarter 1, Unit 1.4 Analyzing Exponential and Logarithmic Functions

Analyzing Exponential and Logarithmic Functions Overview Number of instruction days: 5 7 (1 day = 53 minutes) Content to Be Learned Rewrite radical expressions using the properties of exponents. Rewrite