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

Size: px
Start display at page:

Transcription

2 Which Shape? This problem gives you the chance to: identify and describe shapes use clues to solve riddles Use shapes A, B, or C to solve the riddles. A B C 1. I have 4 sides. My opposite sides are equal. I have 4 right angles. Which shape am I? 2. I have 4 sides. I have only 1 pair of parallel sides. Which shape am I? 3. I have 4 sides. My opposite sides are parallel. I do not have any right angles. a. Which shape am I? b. Draw lines that divide my shape into a rectangle and two right triangles. Copyright 2007 by Mathematics Assessment 74 Which Shape? Test 3

3 4. Write three different clues for shape D. D Clue 1: Clue 2: Clue 3: 5. Look closely at shapes E and F. E F Write a statement that tells how they are alike. Write a statement that tells how they are different. 9 Copyright 2007 by Mathematics Assessment 75 Which Shape? Test 3

4 Task 4: Which Shape? Rubric The core elements of performance required by this task are: identify and describe shapes use clues to solve riddles Based on these, credit for specific aspects of performance should be assigned as follows points section points 1. Gives correct answer: C or rectangle 1 2. Gives correct answer: B or trapezoid 1 3. Gives correct answer: A or parallelogram Draws lines that are correct. 4. Gives three correct statements such as: I have 4 sides. I have 4 right angles. All my sides are equal. 5. Gives two correct statements such as: They both have 4 sides. Shape F has a line of symmetry, and E does not. Shape F has four equal sides, and shape E does not ft 2 3x1 2x1 2 Total Points 9 3 Copyright 2007 by Noyce Foundation 76

5 Which Shape? Work the task. What are some of the attributes that you might expect students to use to describe the shapes in parts 4 and 5? What are some of the attributes or vocabulary that you think will give them difficulty? Mathematical literacy requires attention to details and constraints that is different from the level of detail needed to make sense of a story. Look at the first part of the task, identifying shapes from clues. In part one, approximately 11% of the students saw the 4 sides and picked shape A. How many of your students made this choice? In part two, students saw the parallel sides, but ignored the one pair. 23% picked shape A and 11% picked shape C. How did your students do? 30% of the students saw the no right angles, the last clue read, and picked shape B for part 3. 30% of the students did not attempt to draw lines for part 3b. What types of errors do you see in the student drawings? Which attributes confused students? (It might be helpful to draw a few examples, so that you can categorize mistakes or think how to set up a discussion about the errors with the class.) Look at the clues students used for part 4. List them into categories of correct or incorrect, incomplete. Students often think of mathematical ideas not anticipated by the rubric, so add those to the list as you find them. Correct Attributes Incorrect Attributes 4sides Equal sides 4 angles Right angles Parallel sides Line of symmetry Copyright 2007 by Noyce Foundation 77

7 Looking at Student Work on Which Shape? Student A is able to use the clues to identify the shapes being described and names the shapes. The student draws lines on shape A to meet the constraints or demands of the task. The student uses geometrical vocabulary to describe the attributes in parts 4 and 5. Student A Copyright 2007 by Noyce Foundation 79

8 Student A, part 2 Copyright 2007 by Noyce Foundation 80

9 Recognizing the Seeds of Mathematical Ideas Students sometimes come up with mathematical ideas not anticipated by the rubric or using imprecise language. How do we, as teachers, develop the flexibility to see mathematical thinking in student work? Look at the work of Student B. Notice that one scorer has given the student credit and one has not. Has the student noticed important characteristics about the shapes? Student B Look at the work of Student C. When taken alone, 2 right angles is not enough to describe shape D; neither is 4 sides or 4 equal sides. Clues need to be considered as a set. Can you make a shape with 4 sides and 2 right angles that is not a square? Can you make a shape with 4 equal sides and 2 right angles that is not a square? Student C Copyright 2007 by Noyce Foundation 81

10 Student D has the seeds for the mathematical idea of rotational symmetry, but doesn t have the mathematical language to name the property. How do we encourage students to think about important ideas, which might not be introduced formally until much later grades? How do we keep them looking for and discovering relationships? Student D What s wrong with this picture? Students had difficulty drawing in the lines to make a rectangle and two right triangles. For each piece of student work, try to identify the attributes that they overlooked or incomplete definitions about a shape. Student E makes two triangles and a four-sided shape. What is the student not understanding or focusing on? Now look at part 4. The student comes up with for mathematical ideas about the square, but then uses none of those ideas in thinking about shapes E and F. What might be a next instructional move for this child? Student E Copyright 2007 by Noyce Foundation 82

11 Shape E, part 3 Copyright 2007 by Noyce Foundation 83

12 Student F has trouble with the drawing in part 3. What is the student forgetting? Examine the student s description of differences. The student is probably noticing the reflex angle in E, but does not know how to talk about it and leaves the description vague. We sometimes want students to have precise language. When encountering a new idea, students need to rely on everyday language and some mathematical language used in new ways. What are some ways that we might hope third graders would describe this angle? What are the attributes from part 4 that might help the student in thinking about the differences between the two shapes? What could the student build on? Student F Copyright 2007 by Noyce Foundation 84

13 What are each of these students understanding and not understanding? Student G Student H Copyright 2007 by Noyce Foundation 85

14 Do you think Student I is only asked to draw lines when looking for symmetry? Student I What are the important attributes of shape that we want students to pay attention to? How do we help them develop their sense of what to pay attention to? Look at the work of Student J. Does the student only think about angles as acute shapes? Notice that the student in part 5 is thinking about the shape as a totality, rather than comparing parts. How is this student thinking about the reflex angle? Student J Copyright 2007 by Noyce Foundation 86

15 Thinking about the angle in E is difficult for students. While we don t want students to memorize formal language about the angle, students should have opportunities to encounter and think about these types of big mathematical ideas and try to describe them. What questions might you want to ask Student K to probe his thinking? Copyright 2007 by Noyce Foundation 87

16 Student K Look at the descriptions by Student L. Would you have given them credit? Why are why not? Are the attributes accurate? Relevant? Student L Copyright 2007 by Noyce Foundation 88

17 Some students struggled with just counting the sides and angles for the two shapes. See some typical responses by Students M and N. Student M Student N Copyright 2007 by Noyce Foundation 89

18 Finally some students, like Student O, are still operating at the lowest van Hiele level. They are thinking of what the shape looks like and how it can be subdivided. Student O Copyright 2007 by Noyce Foundation 90

19 3 rd Grade Task 4 Which Shape? Student Task Core Idea 4 Geometry and Measurement Identify and describe shapes, using key attributes. Use clues to solve riddles. Identify how shapes are alike and different using geometric attributes. Recognize and use characteristics, properties, and relationships of two-dimensional geometric shapes. Identify and compare attributes of two-dimensional shapes and develop vocabulary to describe the attributes. Use visualization, spatial reasoning, and geometric modeling to solve problems. Recognize geometric ideas and relationships and apply them to problems. Mathematics in this task: Understanding geometric attributes, such as angle size, number of angles, number of sides, parallel sides. Sorting and describing shapes using attributes. Comparing and contrasting shapes on geometric attributes. Composing and decomposing shapes. Based on teacher observations, this is what third graders know and are able to do: Identify shapes by their attributes Describe attributes of a square, particularly 4 sides and 4 angles Areas of difficulty for third graders: Drawing in lines to decompose a shape into a rectangle and two triangles Describing similarities and differences for E and F Correct vocabulary o Students used point or corner for angle o Closed shape, open shape o How to classify angles o They confused side and face and side and edge o Parallel sides Copyright 2007 by Noyce Foundation 91

20 The maximum score available on this task is 9 points. The minimum score needed for a level 3 response, meeting standards, is 4 points. Most students, 88%, could give 3 clues for describing a rectangle. 77% could also identify the shape with 4 right angles and opposite sides equal. Almost half the students, 47%, could identify all 3 shapes and give 3 clues for describing a rectangle. 30% could also draw in lines for subdividing a shape into a rectangle and two right triangles. 5% could meet all the demands of the task including comparing and contrasting shapes E and F, using geometric attributes. About 2% of the students scored no points on the task. Half of these students attempted the task. Copyright 2007 by Noyce Foundation 92

21 Which Shape? Points Understandings Misunderstandings 0 Half the students with this score attempted the task. They had difficulty describing attributes for a square. They gave information, such as: no angles or no right angle, looks like a box or piece of paper or a rectangle, or 3 Students could give 3 clues about a square. 4 Students could identify the rectangle from clues and give 3 clues for a square. 6 Students could identify rectangle, parallelogram, and trapezoid from their attributes and give attributes for a square. 7 Students could identify shapes from attributes and describe attributes of shapes. Students could decompose a shape into rectangle and two right triangles. its pointy. They had difficulty matching a set of clues to a shape. For part 1 (4 sides, 4 right angles) 11% of the students picked the parallelogram. For part 2 (4 sides, only 1 pair of parallel sides) 23% picked the parallelogram and 11% picked the rectangle. For part 3 (4 sides, no right Angles, opposite sides parallel) 30% picked the trapezoid. 30% of all students did not draw lines to subdivide a shape into a rectangle and 2 right angles. Students did not usually think carefully about angle size. Students had difficulty describing the similarities and differences between two shapes. 31% described the shapes as sharp or pointy.16% just noted that the shapes were different. 16% thought that E had only 3 angles or 3 sides. 7% tried to describe the concave angle with words like indent or goes in and goes out. 9 Students could identify shapes from attributes and describe attributes of a square. They could decompose shapes into component parts by attributes. They could also compare and contrast shapes based on geometric attributes. Implications for Instruction Students should be able to think about the geometric attributes of shapes: number of sides, number of angles, types of angles, length of sides, and parallel sides. Students should be able to both identify a shape from its attributes and describe the attributes of a shape. Copyright 2007 by Noyce Foundation 93

22 Students need experiences with a rich variety of 2- and 3- dimensional shapes. Students should be pressed to describe how shapes are the same or different. This helps them become of aware of a variety of attributes and lays the foundation for understanding formal definitions at a later time. Ideas for Action Research The Logic of Classifying and Sorting Look at the lesson below (from Teaching Student-Centered Mathematics, Grades K-3 by John Van de Walle). How might this lesson be modified to help students think about 3- dimensional shapes? Can you design your own set of shapes? Make sure you think carefully about the question posed by the Stop Sign. Copyright 2007 by Noyce Foundation 94

23 Copyright 2007 by Noyce Foundation 95

### 1. I have 4 sides. My opposite sides are equal. I have 4 right angles. Which shape am I?

Which Shape? This problem gives you the chance to: identify and describe shapes use clues to solve riddles Use shapes A, B, or C to solve the riddles. A B C 1. I have 4 sides. My opposite sides are equal.

### 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.

### 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

### 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

### 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.

### 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 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

### 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

### 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

### 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

### 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

### 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,

### 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

### 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

### How To Be A Mathematically Proficient Person

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

### 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:

### 3. Relationship between this Unit and the Principles and Standards for School Mathematics (NCTM 2000). This Unit

4 th Grade Mathematics Lesson Plan April 16-18, 2002 Brewer Island School, San Mateo, CA Instructor: Akihiko Takahashi 1. Title of Unit: Finding the Area of Shapes 2. Goal: a. To deepen students understanding

### How Old Are They? This problem gives you the chance to: form expressions form and solve an equation to solve an age problem. Will is w years old.

How Old Are They? This problem gives you the chance to: form expressions form and solve an equation to solve an age problem Will is w years old. Ben is 3 years older. 1. Write an expression, in terms of

### 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

### 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

### Number Factors. Number Factors Number of factors 1 1 1 16 1, 2, 4, 8, 16 5 2 1, 2 2 17 1, 17 2 3 1, 3 2 18 1, 2, 3, 6, 9, 18 6 4 1, 2, 4 3 19 1, 19 2

Factors This problem gives you the chance to: work with factors of numbers up to 30 A factor of a number divides into the number exactly. This table shows all the factors of most of the numbers up to 30.

### 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

### 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:

### Grade 8 Mathematics Geometry: Lesson 2

Grade 8 Mathematics Geometry: Lesson 2 Read aloud to the students the material that is printed in boldface type inside the boxes. Information in regular type inside the boxes and all information outside

Dear Grade 4 Families, During the next few weeks, our class will be exploring geometry. Through daily activities, we will explore the relationship between flat, two-dimensional figures and solid, three-dimensional

Ohio Standards Connection Geometry and Spatial Sense Benchmark A Provide rationale for groupings and comparisons of two-dimensional figures and three-dimensional objects. Indicator 3 Identify similarities

### 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.

### Overview. Essential Questions. Grade 2 Mathematics, Quarter 4, Unit 4.4 Representing and Interpreting Data Using Picture and Bar Graphs

Grade 2 Mathematics, Quarter 4, Unit 4.4 Representing and Interpreting Data Using Picture and Bar Graphs Overview Number of instruction days: 7 9 (1 day = 90 minutes) Content to Be Learned Draw a picture

### 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

### 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 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

### Georgia Standards of Excellence 2015-2016 Mathematics

Georgia Standards of Excellence 2015-2016 Mathematics Standards GSE Coordinate Algebra K-12 Mathematics Introduction Georgia Mathematics focuses on actively engaging the student in the development of mathematical

### Activities Grades K 2 THE FOUR-SQUARE QUILT. Put triangles together to make patterns.

Activities Grades K 2 www.exploratorium.edu/geometryplayground/activities THE FOUR-SQUARE QUILT Put triangles together to make patterns. [45 minutes] Materials: Four-Square Quilt Template (attached) Triangle

### 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:

### 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,

### 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,

### HIGH SCHOOL GEOMETRY: COMPANY LOGO

HIGH SCHOOL GEOMETRY: COMPANY LOGO UNIT OVERVIEW This 3-4 week unit uses an investigation of rigid motions and geometric theorems to teach students how to verify congruence of plane figures and use the

### Which Shape? Student Task Core Idea 4 Geometry and Measurement

Which Shape? Student Task Core Idea 4 Geometry and Measurement Identify circles, triangles, and squares among a collection of shapes. Identify two attributes of all triangles. Recognize and use characteristics,

### Grade 3 Core Standard III Assessment

Grade 3 Core Standard III Assessment Geometry and Measurement Name: Date: 3.3.1 Identify right angles in two-dimensional shapes and determine if angles are greater than or less than a right angle (obtuse

### 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

### 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:

### 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

### Preparation Prepare a set of standard triangle shapes for each student. The shapes are found in the Guess My Rule Cards handout.

Classifying Triangles Student Probe How are triangles A, B, and C alike? How are triangles A, B, and C different? A B C Answer: They are alike because they each have 3 sides and 3 angles. They are different

### 1st Grade Math Standard I Rubric. Number Sense. Score 4 Students show proficiency with numbers beyond 100.

1st Grade Math Standard I Rubric Number Sense Students show proficiency with numbers beyond 100. Students will demonstrate an understanding of number sense by: --counting, reading, and writing whole numbers

### Scope and Sequence KA KB 1A 1B 2A 2B 3A 3B 4A 4B 5A 5B 6A 6B

Scope and Sequence Earlybird Kindergarten, Standards Edition Primary Mathematics, Standards Edition Copyright 2008 [SingaporeMath.com Inc.] The check mark indicates where the topic is first introduced

### ISAT Mathematics Performance Definitions Grade 4

ISAT Mathematics Performance Definitions Grade 4 EXCEEDS STANDARDS Fourth-grade students whose measured performance exceeds standards are able to identify, read, write, represent, and model whole numbers

### Kindergarten to Grade 3. Geometry and Spatial Sense

Kindergarten to Grade 3 Geometry and Spatial Sense Every effort has been made in this publication to identify mathematics resources and tools (e.g., manipulatives) in generic terms. In cases where a particular

### 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

### CCSS Mathematics Implementation Guide Grade 5 2012 2013. First Nine Weeks

First Nine Weeks s The value of a digit is based on its place value. What changes the value of a digit? 5.NBT.1 RECOGNIZE that in a multi-digit number, a digit in one place represents 10 times as much

### GRADE 8 MATH: TALK AND TEXT PLANS

GRADE 8 MATH: TALK AND TEXT PLANS UNIT OVERVIEW This packet contains a curriculum-embedded Common Core standards aligned task and instructional supports. The task is embedded in a three week unit on systems

### Estimating Angle Measures

1 Estimating Angle Measures Compare and estimate angle measures. You will need a protractor. 1. Estimate the size of each angle. a) c) You can estimate the size of an angle by comparing it to an angle

8 th Grade Task 2 Rugs Student Task Core Idea 4 Geometry and Measurement Find perimeters of shapes. Use Pythagorean theorem to find side lengths. Apply appropriate techniques, tools and formulas to determine

### 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

### Pocantico Hills School District Grade 1 Math Curriculum Draft

Pocantico Hills School District Grade 1 Math Curriculum Draft Patterns /Number Sense/Statistics Content Strands: Performance Indicators 1.A.1 Determine and discuss patterns in arithmetic (what comes next

### angle attribute Figure 1 4 right angles opposite sides parallel Lesson 14 5 Lesson 14 4 Vocab

Vocab angle attribute 006_055_G4_VisV_101741.indd Page F46 2/13/10 11:27:36 PM u-s014 /Volumes/114/GO00403/GO00403_Natl_Visual_Voca_Cards_G4%0 Figure 1 4 right angles opposite sides parallel endpoint hexagon

### Classifying Lesson 1 Triangles

Classifying Lesson 1 acute angle congruent scalene Classifying VOCABULARY right angle isosceles Venn diagram obtuse angle equilateral You classify many things around you. For example, you might choose

### Building a Bridge to Academic Vocabulary in Mathematics

Building a Bridge to Academic Vocabulary in Mathematics AISD Elementary Mathematics Department How Students Develop a Repertoire of Academic English in Mathematics Developed and researched by the AISD

### 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.

A Correlation of to the Minnesota Academic Standards Grades K-6 G/M-204 Introduction This document demonstrates the high degree of success students will achieve when using Scott Foresman Addison Wesley

### Drawing 3-D Objects in Perspective

Mathematics Instructional Materials SAS#.1 (one per pair of students) SAS#.2 (one per pair of students) TIS#.1 (transparency) TIS#.2 (transparency) TIS#.3 (Journal prompt) Isometric Dot Paper Isometric

### Explorations with Shapes Kindergarten

Ohio Standards Connections Geometry and Spatial Sense Benchmark C Sort and compare twodimensional figures and threedimensional objects according to their characteristics and properties. Indicator 1 Identify

experiences understanding what the mean reflects about the data and how changes in data will affect the average. The purpose of statistics is to give a picture about the data. Students need to be able

### 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

### Nancy Rubino, PhD Senior Director, Office of Academic Initiatives The College Board

Nancy Rubino, PhD Senior Director, Office of Academic Initiatives The College Board Amy Charleroy Director of Arts, Office of Academic Initiatives The College Board Two approaches to alignment: Identifying

### STRAND: Number and Operations Algebra Geometry Measurement Data Analysis and Probability STANDARD:

how August/September Demonstrate an understanding of the place-value structure of the base-ten number system by; (a) counting with understanding and recognizing how many in sets of objects up to 50, (b)

### Area Formulas TEACHER NOTES MATH NSPIRED. Math Objectives. Vocabulary. About the Lesson. TI-Nspire Navigator System

Math Objectives Students will be able to describe how the area of a parallelogram relates to the area of a rectangle with the same base and height. Students will be able to describe how the area of a triangle

### Using Algebra Tiles from Polynomials to Factoring

Using Algebra Tiles from Polynomials to Factoring For more information about the materials you find in this packet, contact: Chris Mikles (888) 808-4276 mikles@cpm.org CPM Educational Program 203, all

### Geometry of 2D Shapes

Name: Geometry of 2D Shapes Answer these questions in your class workbook: 1. Give the definitions of each of the following shapes and draw an example of each one: a) equilateral triangle b) isosceles

### Big Ideas in Mathematics

Big Ideas in Mathematics which are important to all mathematics learning. (Adapted from the NCTM Curriculum Focal Points, 2006) The Mathematics Big Ideas are organized using the PA Mathematics Standards

### 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

### Volume of Right Prisms Objective To provide experiences with using a formula for the volume of right prisms.

Volume of Right Prisms Objective To provide experiences with using a formula for the volume of right prisms. www.everydaymathonline.com epresentations etoolkit Algorithms Practice EM Facts Workshop Game

### Current Standard: Mathematical Concepts and Applications Shape, Space, and Measurement- Primary

Shape, Space, and Measurement- Primary A student shall apply concepts of shape, space, and measurement to solve problems involving two- and three-dimensional shapes by demonstrating an understanding of:

### DELAWARE MATHEMATICS CONTENT STANDARDS GRADES 9-10. PAGE(S) WHERE TAUGHT (If submission is not a book, cite appropriate location(s))

Prentice Hall University of Chicago School Mathematics Project: Advanced Algebra 2002 Delaware Mathematics Content Standards (Grades 9-10) STANDARD #1 Students will develop their ability to SOLVE PROBLEMS

### 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

### Line Segments, Rays, and Lines

HOME LINK Line Segments, Rays, and Lines Family Note Help your child match each name below with the correct drawing of a line, ray, or line segment. Then observe as your child uses a straightedge to draw

### NEW MEXICO Grade 6 MATHEMATICS STANDARDS

PROCESS STANDARDS To help New Mexico students achieve the Content Standards enumerated below, teachers are encouraged to base instruction on the following Process Standards: Problem Solving Build new mathematical

### 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

### Assessment Anchors and Eligible Content

M07.A-N The Number System M07.A-N.1 M07.A-N.1.1 DESCRIPTOR Assessment Anchors and Eligible Content Aligned to the Grade 7 Pennsylvania Core Standards Reporting Category Apply and extend previous understandings

### 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,

### Lesson #13 Congruence, Symmetry and Transformations: Translations, Reflections, and Rotations

Math Buddies -Grade 4 13-1 Lesson #13 Congruence, Symmetry and Transformations: Translations, Reflections, and Rotations Goal: Identify congruent and noncongruent figures Recognize the congruence of plane

### 37 Basic Geometric Shapes and Figures

37 Basic Geometric Shapes and Figures In this section we discuss basic geometric shapes and figures such as points, lines, line segments, planes, angles, triangles, and quadrilaterals. The three pillars

### 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

### Elementary Mathematics Learning Segment Overview

edtpa Elementary Education Assessment Hbook Elementary Mathematics Learning Segment Overview Central Focus: Students should be able to name, draw identify of 2- Dimensional Shapes. State-adopted Content

### Mathematics Content Courses for Elementary Teachers

Mathematics Content Courses for Elementary Teachers Sybilla Beckmann Department of Mathematics University of Georgia Massachusetts, March 2008 Sybilla Beckmann (University of Georgia) Mathematics for Elementary

### Support Materials for Core Content for Assessment. Mathematics

Support Materials for Core Content for Assessment Version 4.1 Mathematics August 2007 Kentucky Department of Education Introduction to Depth of Knowledge (DOK) - Based on Norman Webb s Model (Karin Hess,

### COMMON CORE STATE STANDARDS FOR MATHEMATICS 3-5 DOMAIN PROGRESSIONS

COMMON CORE STATE STANDARDS FOR MATHEMATICS 3-5 DOMAIN PROGRESSIONS Compiled by Dewey Gottlieb, Hawaii Department of Education June 2010 Operations and Algebraic Thinking Represent and solve problems involving

### Natural Disaster Recovery and Quadrilaterals

Natural Disaster Recovery and Quadrilaterals I. UNIT OVERVIEW & PURPOSE: In this unit, students will apply their knowledge of quadrilaterals to solve mathematics problems concerning a tornado that struck

### 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

### Numbers Plus Preschool Mathematics Curriculum: Teacher s Manual

Number and operations involves understanding whole numbers and realizing that numbers represent quantity. It includes learning number words and symbols, counting, comparing and ordering quantities, composing

### Grade 5 Math Content 1

Grade 5 Math Content 1 Number and Operations: Whole Numbers Multiplication and Division In Grade 5, students consolidate their understanding of the computational strategies they use for multiplication.

### Curriculum Overview Standards & Skills

Curriculum Overview Standards & Skills You CAN Do The Rubik's Cube Instructional Curriculum Curriculum Overview / Skills & Standards How to Solve The Rubik's Cube Part 1 - Curriculum Overview Part 2 -

### 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,

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

### Curriculum Map by Block Geometry Mapping for Math Block Testing 2007-2008. August 20 to August 24 Review concepts from previous grades.

Curriculum Map by Geometry Mapping for Math Testing 2007-2008 Pre- s 1 August 20 to August 24 Review concepts from previous grades. August 27 to September 28 (Assessment to be completed by September 28)

### Grade 1 Geometric Shapes Conceptual Lessons Unit Outline Type of Knowledge & SBAC Claim Prerequisite Knowledge:

Grade 1 Geometric Shapes Conceptual Lessons Unit Outline Type of Knowledge & SBAC Claim Prerequisite Knowledge: Standards: Lesson Title and Objective/Description Shape names: square, rectangle, triangle,

### Common Core Unit Summary Grades 6 to 8

Common Core Unit Summary Grades 6 to 8 Grade 8: Unit 1: Congruence and Similarity- 8G1-8G5 rotations reflections and translations,( RRT=congruence) understand congruence of 2 d figures after RRT Dilations

### 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: Family Letter

Name Date Time HOME LINK Unit 1: Family Letter Introduction to Third Grade Everyday Mathematics Welcome to Third Grade Everyday Mathematics. It is part of an elementary school mathematics curriculum developed