# Problem of the Month: Double Down

Save this PDF as:

Size: px
Start display at page:

## Transcription

2 In the first levels of the POM, students are presented with a task involving doubling values. The context of the task is finding the number of fleas on two dogs ears being walked by two teachers. In level B, students are presented with a family tree. They need to determine the difference in ages of family members and the year family members were certain ages. Students have to find the year a family member was twice as old as another family member. In level C, students are presented a dilemma on Facebook. A friend displays an embarrassing picture of you. The picture is spreading through the Internet. How many people will see the picture and how soon? In level D, students are given a geometrical figure of squares inside squares. The goal is to find the perimeters and areas of the sub squares in the figure. In the final level E, students are given information about population growth in terms of average birth, immigration, and death rates, and students must analyze and determine population growth estimates. The question involves growth in descendants of a family and the overall US population growth. Mathematical Concepts Some have defined mathematics as the science of patterns. Examining growing patterns is accessible to students. The question of how much or how fast a pattern is growing helps students focus on the difference between elements of a pattern. Many early patterns are linear. Patterns can be recognized as repeated addition. Students often begin to examine patterns with an informal recursive model. Patterns that grow by repeated multiplication are exponential patterns. Doubling is the most basic exponential pattern. Exponential patterns may be represented in tables, diagram, graphs and equations. The notation in an exponential equation or function will include either repeated multiplication of the same factor or exponents. CCSSM Alignment: Problem of the Month Double Down Silicon Valley Mathematics Initiative 2013.

3 Problem of the Month Double Down Level A Two students were walking to school one day when they saw two teachers each walking with two dogs. 1. Each dogs had two ears. How many dog ears were there in all? 2. On each dog s ear there were two fleas. How many fleas were there in all? Show your calculation. 3. Each flea called two more fleas to join them. How many fleas were there in all? Explain how you figured it out. Problem of the Month Double Down Page 1

4 Level B Alyssa s Family Look carefully at Alyssa s family tree. It shows the ages of the people in her family. Grandpa Lopez Age 66 Grandma Lopez Age 61 Grandpa Perez Age 71 Grandma Perez Age 68 Aunt Connie Age 32 Mom Age 35 Dad Age 37 Uncle Jesse Age 41 Brother Eric Age 14 Sister Alyssa Age 10 Sister Emily Age 7 1. How old was Eric when Alyssa was born? 2. What age was Grandpa Lopez when sister Emily was born? 3. How old was Grandma Perez when her son Jesse was born? Explain how you figured it out. 5. Find the total number of years that Alyssa s parents and grandparents have been alive. 6. Alyssa designed this family tree in the year In what year was her Grandma Perez born? In what year was her Grandpa Lopez born? Explain how you figured out these dates. 7. In what year was her Grandpa Lopez twice as old as her Dad? Show how you know. 8. In what year will Aunt Connie be twice as old as Eric? Show how you figured it out. Problem of the Month Double Down Page 2

5 Level C Saving Face on Facebook Your so called friend was able to obtain an embarrassing picture of you. Something you didn t want even your best friend to see. Without you knowing it, your friend sent the picture via Facebook to three other friends. Within an hour of receiving the picture, those friends sent the picture on to other people. Some sent them to just a couple of people, others sent them to four or five other people. You are not sure exactly who received and sent on pictures, put you re getting weird tweets from everywhere. You conservatively estimate that on average each person who received the picture sent it on to about three other people within one hour of receiving the picture. If this rate continues, how many people would have seen the picture in 5 hours and 12 hours? The world population is around 7 billion, how long before the image has been sent (or re sent) to more people than exist on earth? Problem of the Month Double Down Page 3

6 Level D Shrinking Squares Consider the shaded squares. Write a sequence showing the perimeter of each square in the sequence. 1. What is the perimeter of each shaded square? 2. What is the area of each shaded square? 3. Discuss the different patterns you can find in the diagram. 4. Suppose there are twelve terms in the sequence. What is the perimeter of the 12 th square? Show how you figured it out. 5. How can you find the area of the 20 th shaded square without having to find all of the ones before it? 6. At what rate do the different patterns change from term to term? How do you know? 7. How can you determine any terms in any of the patterns? Explain. Problem of the Month Double Down Page 4

7 Level E Family Tree In the United States, the average female gives birth to 2.6 children. The average life span is 65 years. The average age a female bears children is when she is 28 years old. Explore these statistics and determine a model for population growth. Suppose a female is born the year you were born. Create a family tree to understand the growth in number of descendants. Use mathematics to answer the following questions. How many descendants would the female have in 60 years? How many of the descendants would be female in 100 years? When would the total number of descendants ever born be greater than 20? When would the number of actually living descendants exceed 30? Explain the functions you used to answer these questions. If currently a baby in the U.S. is born every 5 seconds, a person in the U.S. dies every 45 seconds, and a new immigrant comes to the U.S. every 25 seconds, what is the rate of growth in our country? Look up our current population in the United States. Create a function to generate future growth based upon this data. Determine future populations. Explain how fast our country s population will grow. Problem of the Month Double Down Page 5

8 Problem of the Month Double Down Primary Version Level A Materials: For the teacher: Picture of one person walking two dogs and a picture of two people walking each with two dogs. For each student: paper and pencil. Discussion on the rug: (Teacher shows picture #1 of the person walking the dogs.) Look at this picture very closely. What do you see? (Students volunteer what they see.) How many dogs do you see, and how do you know? (Students respond, and one shows how they counted them.) Teacher asks, How many dog ears do you think there are? (Teacher calls on students to demonstrate and explain.) (Teacher shows picture #2 of two people each with two dogs.) How many dogs do we have? How many dog ears do we have now? (Class explores these ideas). In small groups: (Students work in pairs.) (Teacher passes out to each pair picture #3 with four people each with two dogs.) The teacher says to the class, You have a set of counters on your table that you can use to help you figure your answer. Now look at the picture. How many dogs are there now? How many dog ears do you think there are? (At the end of the investigation, have students either discuss or dictate a response to this summary question.) Tell me how many dogs and how many dog ears could there be in the picture. Tell me how you figured it out. Problem of the Month Double Down Page 6

9 Picture 1 Problem of the Month Double Down Page 7

10 Picture 2 Problem of the Month Double Down Page 8

11 Picture 3 Problem of the Month Double Down Page 9

13 Problem of the Month Double Down Task Description Level B This task challenges a student to use multiplicative thinking to solve problems involving unknowns. The students are presented with a family tree. They need to determine the difference in ages of family members and what year family members were certain ages. Students have to find the year a family member was twice as old as another family member. Common Core State Standards Math Content Standards Operations and Algebraic Thinking Represent and solve problems involving addition and subtraction. 2.OA.1. Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. Represent and solve problems involving multiplication and division. 3.OA.4. Determine the unknown whole number in a multiplication or division equation relating three whole numbers. Common Core State Standards Math Standards of Mathematical Practice MP.2 Reason abstractly and quantitatively. Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects. MP.7 Look for and make use of structure. Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 x 8 equals the well-remembered 7 x x 3, in preparation for learning about the distributive property. In the expression x 2 + 9x + 14, older students can see the 14 as 2 x 7 and the 9 as They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 3(x y) 2 as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers x and y. CCSSM Alignment: Problem of the Month Double Down Silicon Valley Mathematics Initiative 2013.

15 Problem of the Month: Double Down Task Description Level D This task challenges a student to investigate a problem involving a geometric sequence. The students are given a geometrical figure of squares inside squares with rational dimensions. The goal is to find the perimeters and areas of the sub-squares in the figure. Common Core State Standards Math Content Standards The Number System Apply and extend previous understandings of multiplication and division to divide fractions by fractions. 6.NS.1. Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. Expressions and Equations Apply and extend previous understandings of arithmetic to algebraic expressions. 6.EE.1. Write and evaluate numerical expressions involving whole-number exponents. Geometry Solve real-world and mathematical problems involving area, surface area, and volume. 6.G.1. Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems. Solve real-life and mathematical problems involving angle measure, area, surface area, and volume. 7.G.6. Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. Common Core State Standards Math Standards of Mathematical Practice MP.2 Reason abstractly and quantitatively. Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects. MP.4 Model with mathematics. Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose. CCSSM Alignment: Problem of the Month Double Down Silicon Valley Mathematics Initiative 2013.

16 Problem of the Month Double Down Task Description Level E This task challenges a student to investigate a real-life problem involving exponential growth rates. The students are given information about population growth in terms of average birth, immigration, and death rates, and students must analyze and determine population growth estimates. The question involves growth in descendants of a family and the overall US population growth. Common Core State Standards Math Content Standards High School Functions - Linear and Exponential Models Construct and compare linear and exponential models and solve problems F-LE.1. Distinguish between situations that can be modeled with linear functions and with exponential functions. b. Recognize situations in which one quantity changes at a constant rate per unit interval relative to another. F-LE.2. Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). High School Functions - Building Functions Build a function that models a relationship between two quantities F-BF.1. Write a function that describes a relationship between two quantities. Common Core State Standards Math Standards of Mathematical Practice MP.2 Reason abstractly and quantitatively. Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects. MP.7 Look for and make use of structure. Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 x 8 equals the well-remembered 7 x x 3, in preparation for learning about the distributive property. In the expression x 2 + 9x + 14, older students can see the 14 as 2 x 7 and the 9 as They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 3(x y) 2 as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers x and y. MP.8 Look for and express regularity in repeated reasoning. Mathematically proficient students notice if calculations are repeated, and look both for general methods and for shortcuts. Upper elementary students might notice when dividing 25 by 11 that they are repeating the same calculations over and over again, and conclude they have a repeating decimal. By paying attention to the calculation of slope as they repeatedly check whether points are on the line through (1, 2) with slope 3, middle school students might abstract the equation (y 2)/(x 1) = 3. Noticing the regularity in the way terms cancel when expanding (x 1)(x + 1), (x 1)(x2 + x + 1), and (x 1)(x3 + x2 + x + 1) might lead them to the general formula for the sum of a geometric series. As they work to solve a problem, mathematically proficient students maintain oversight of the process, while attending to the details. They continually evaluate the reasonableness of their intermediate results. CCSSM Alignment: Problem of the Month Double Down Silicon Valley Mathematics Initiative 2013.

17 Problem of the Month Double Down Task Description Primary Level This task challenges students to represent and determine a quantity. The students are presented with the task of interpreting a picture and applying their understanding of quantity to determine an unknown amount. The context of the task is finding the number of ears on two dogs being walked by two teachers. Not all the ears are seen in the picture, but they are implied. Common Core State Standards Math Content Standards Operations and Algebraic Thinking Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from. K.OA.1. Represent addition and subtraction with objects, fingers, mental images, drawings, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations. K.OA.2. Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem. K.OA.3. Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = and 5 = 4 + 1). Common Core State Standards Math Standards of Mathematical Practice MP.2 Reason abstractly and quantitatively. Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects. MP.7 Look for and make use of structure. Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 x 8 equals the well-remembered 7 x x 3, in preparation for learning about the distributive property. In the expression x 2 + 9x + 14, older students can see the 14 as 2 x 7 and the 9 as They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 3(x y) 2 as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers x and y. CCSSM Alignment: Problem of the Month Double Down Silicon Valley Mathematics Initiative 2013.

### 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:

### 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

### 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

### 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: 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 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

### 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

### 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:

### 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

### Problem of the Month: Once Upon a Time

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: On Balance

Problem of the Month: On Balance 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

### 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

### 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

### 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

### 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:

### 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

### 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

### 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

### 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

### 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.

### 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:

### 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

### 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

### 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

### 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

### Grade 4 Mathematics, Quarter 4, Unit 4.3 Using Place Value to Add and Subtract Whole Numbers to the Millions. Overview

Whole Numbers to the Millions Overview Number of instruction days: 7 9 (1 day = 90 minutes) Content to Be Learned Round multi-digit whole numbers using understanding of place value. Recognize that the

### Problem of the Month: Cutting a Cube

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 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

### Georgia Department of Education. Calculus

K-12 Mathematics Introduction Calculus The Georgia Mathematics Curriculum focuses on actively engaging the students in the development of mathematical understanding by using manipulatives and a variety

### Pearson Algebra 1 Common Core 2015

A Correlation of Pearson Algebra 1 Common Core 2015 To the Common Core State Standards for Mathematics Traditional Pathways, Algebra 1 High School Copyright 2015 Pearson Education, Inc. or its affiliate(s).

### 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

### Describing and Solving for Area and Perimeter

Grade 3 Mathematics, Quarter 2,Unit 2.2 Describing and Solving for Area and Perimeter Overview Number of instruction days: 8-10 (1 day = 90 minutes) Content to Be Learned Distinguish between linear and

### 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

### 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

### 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

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

### 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

### 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

### Polynomial Operations and Factoring

Algebra 1, Quarter 4, Unit 4.1 Polynomial Operations and Factoring Overview Number of instructional days: 15 (1 day = 45 60 minutes) Content to be learned Identify terms, coefficients, and degree of polynomials.

### Problem of the Month The Shape of Things

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:

### 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 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

### 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

### 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

### Campbellsport School District Understanding by Design (UbD) Template

Campbellsport School District Understanding by Design (UbD) Template Class Curriculum/Content Area: Math Course Length: 1 year Course Title: 6 th Grade Math Date last reviewed: April 24, 2015 Prerequisites:

### Overview. Essential Questions. Precalculus, Quarter 4, Unit 4.5 Build Arithmetic and Geometric Sequences and Series

Sequences and Series Overview Number of instruction days: 4 6 (1 day = 53 minutes) Content to Be Learned Write arithmetic and geometric sequences both recursively and with an explicit formula, use them

### 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

### 1 ST GRADE COMMON CORE STANDARDS FOR SAXON MATH

1 ST GRADE COMMON CORE STANDARDS FOR SAXON MATH Calendar The following tables show the CCSS focus of The Meeting activities, which appear at the beginning of each numbered lesson and are taught daily,

### Overview. Essential Questions. Grade 8 Mathematics, Quarter 4, Unit 4.3 Finding Volume of Cones, Cylinders, and Spheres

Cylinders, and Spheres Number of instruction days: 6 8 Overview Content to Be Learned Evaluate the cube root of small perfect cubes. Simplify problems using the formulas for the volumes of cones, cylinders,

### CORE Assessment Module Module Overview

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

### Common Core State Standards - Mathematics Content Emphases by Cluster Grade K

Grade K Not all of the content in a given grade is emphasized equally in the standards. Some clusters require greater emphasis than the others based on the depth of the ideas, the time that they take to

### 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

### 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

### 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

### 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

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

Performance Assessment Task Marble Game task aligns in part to CCSSM HS Statistics & Probability Task Description The task challenges a student to demonstrate an understanding of theoretical and empirical

### Overview. Essential Questions. Grade 4 Mathematics, Quarter 1, Unit 1.1 Applying Place Value Up to the 100,000s Place

to the 100,000s Place Overview Number of instruction days: 8 10 (1 day = 90 minutes) Content to Be Learned Compare whole numbers within 1,000,000 using >,

### 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

### 5 th Grade Common Core State Standards. Flip Book

5 th Grade Common Core State Standards Flip Book This document is intended to show the connections to the Standards of Mathematical Practices for the content standards and to get detailed information at

### Glencoe. correlated to SOUTH CAROLINA MATH CURRICULUM STANDARDS GRADE 6 3-3, 5-8 8-4, 8-7 1-6, 4-9

Glencoe correlated to SOUTH CAROLINA MATH CURRICULUM STANDARDS GRADE 6 STANDARDS 6-8 Number and Operations (NO) Standard I. Understand numbers, ways of representing numbers, relationships among numbers,

### 8 th Grade Math Curriculum/7 th Grade Advanced Course Information: Course 3 of Prentice Hall Common Core

8 th Grade Math Curriculum/7 th Grade Advanced Course Information: Course: Length: Course 3 of Prentice Hall Common Core 46 minutes/day Description: Mathematics at the 8 th grade level will cover a variety

### PowerTeaching i3: Algebra I Mathematics

PowerTeaching i3: Algebra I Mathematics Alignment to the Common Core State Standards for Mathematics Standards for Mathematical Practice and Standards for Mathematical Content for Algebra I Key Ideas and

### 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.

### Domain Essential Question Common Core Standards Resources

Middle School Math 2016-2017 Domain Essential Question Common Core Standards First Ratios and Proportional Relationships How can you use mathematics to describe change and model real world solutions? How

### 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,

### 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

### 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,

### Mathematics Interim Assessment Blocks Blueprint V

6-7 Blueprint V.5.7.6 The Smarter Balanced Interim Assessment Blocks (IABs) are one of two distinct types of interim assessments being made available by the Consortium; the other type is the Interim Comprehensive

### 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

### #1 Make sense of problems and persevere in solving them.

#1 Make sense of problems and persevere in solving them. 1. Make sense of problems and persevere in solving them. Interpret and make meaning of the problem looking for starting points. Analyze what is

### California Common Core State Standards Comparison- FOURTH GRADE

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. Standards

K-12 Louisiana Student Standards for Mathematics: Table of Contents Introduction Development of K-12 Louisiana Student Standards for Mathematics... 2 The Role of Standards in Establishing Key Student Skills

### Mathematics. Mathematical Practices

Mathematical Practices 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

### Greater Nanticoke Area School District Math Standards: Grade 6

Greater Nanticoke Area School District Math Standards: Grade 6 Standard 2.1 Numbers, Number Systems and Number Relationships CS2.1.8A. Represent and use numbers in equivalent forms 43. Recognize place

### Math Foundations IIB Grade Levels 9-12

Math Foundations IIB Grade Levels 9-12 Math Foundations IIB introduces students to the following concepts: integers coordinate graphing ratio and proportion multi-step equations and inequalities points,

### Unit 1, Review Transitioning from Previous Mathematics Instructional Resources: McDougal Littell: Course 1

Unit 1, Review Transitioning from Previous Mathematics Transitioning from previous mathematics to Sixth Grade Mathematics Understand the relationship between decimals, fractions and percents and demonstrate

### Math Common Core Standards Fourth Grade

Operations and Algebraic Thinking (OA) Use the four operations with whole numbers to solve problems. OA.4.1 Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 7 as a statement

### CCGPS Curriculum Map. Mathematics. 7 th Grade

CCGPS Curriculum Map Mathematics 7 th Grade These materials are for nonprofit educational purposes only. Any other use may constitute copyright infringement. Unit 1 Operations with Rational Numbers a b

### AERO/Common Core Alignment 3-5

AERO/Common Core Alignment 3-5 Note: In yellow are the AERO Standards and inconsistencies between AERO and Common Core are noted by the strikethrough ( eeeeee) notation. AERO Common Core Mapping 1 Table

### 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 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

### A Correlation of. to the. Common Core State Standards for Mathematics Grade 4

A Correlation of to the Introduction envisionmath2.0 is a comprehensive K-6 mathematics curriculum that provides the focus, coherence, and rigor required by the CCSSM. envisionmath2.0 offers a balanced

### 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

### Math Content

2012-2013 Math Content PATHWAY TO ALGEBRA I Unit Lesson Section Number and Operations in Base Ten Place Value with Whole Numbers Place Value and Rounding Addition and Subtraction Concepts Regrouping Concepts

### Mathematics. Mathematical Practices

Mathematical Practices 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

### Course: Math 7. engage in problem solving, communicating, reasoning, connecting, and representing

Course: Math 7 Decimals and Integers 1-1 Estimation Strategies. Estimate by rounding, front-end estimation, and compatible numbers. Prentice Hall Textbook - Course 2 7.M.0 ~ Measurement Strand ~ Students

### Operations and Algebraic Thinking. K.NBT Number and Operations in Base Ten

KINDERGARTEN K.CC K.OA Counting and Cardinality Know number names and the count sequence. Count to tell the number of objects. Compare numbers. Operations and Algebraic Thinking Understand addition as

### Prentice Hall: Middle School Math, Course 1 2002 Correlated to: New York Mathematics Learning Standards (Intermediate)

New York Mathematics Learning Standards (Intermediate) Mathematical Reasoning Key Idea: Students use MATHEMATICAL REASONING to analyze mathematical situations, make conjectures, gather evidence, and construct

### 3rd Grade Texas Mathematics: Unpacked Content

3rd Grade Texas Mathematics: Unpacked Content What is the purpose of this document? To increase student achievement by ensuring educators understand specifically what the new standards mean a student must

### Common Core State Standards for Mathematics for California Public Schools Kindergarten Through Grade Twelve

Common Core State Standards for Mathematics for California Public Schools Kindergarten Through Grade Twelve Adopted by the California State Board of Education August 2010 Updated January 2013 Prepublication

### 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

### Vocabulary, Signs, & Symbols product dividend divisor quotient fact family inverse. Assessment. Envision Math Topic 1

1st 9 Weeks Pacing Guide Fourth Grade Math Common Core State Standards Objective/Skill (DOK) I Can Statements (Knowledge & Skills) Curriculum Materials & Resources/Comments 4.OA.1 4.1i Interpret a multiplication

### Fourth Grade. Operations & Algebraic Thinking. Use the four operations with whole numbers to solve problems. (4.OA.A)

Operations & Algebraic Thinking Use the four operations with whole numbers to solve problems. (4.OA.A) 4.OA.A.1: Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 7 as a statement

### DLM Mathematics Year-End Assessment Model Blueprint

DLM Mathematics Year-End Assessment Model 2014-15 Blueprint In this document, the blueprint refers to the range of Essential Elements (s) that will be assessed during the spring 2015 assessment window.

### Chapter 111. Texas Essential Knowledge and Skills for Mathematics. Subchapter A. Elementary

Elementary 111.A. Chapter 111. Texas Essential Knowledge and Skills for Mathematics Subchapter A. Elementary Statutory Authority: The provisions of this Subchapter A issued under the Texas Education Code,

### Fourth Grade Common Core State Standard (CCSS) Math Scope and Sequence

I= Introduced R=Reinforced/Reviewed Fourth Grade Math Standards 1 2 3 4 Operations and Algebraic Thinking Use the four operations with whole numbers to solve problems. 4.0A.1 - Interpret a multiplication

### 4 th Grade. Math Common Core I Can Checklists

4 th Grade Math Common Core I Can Checklists Math Common Core Operations and Algebraic Thinking Use the four operations with whole numbers to solve problems. 1. I can interpret a multiplication equation

### Such As Statements, Kindergarten Grade 8

Such As Statements, Kindergarten Grade 8 This document contains the such as statements that were included in the review committees final recommendations for revisions to the mathematics Texas Essential