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

Size: px
Start display at page:

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

Transcription

1 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

2 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

3 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

4 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

6 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

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

8 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

9 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

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

11 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

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

13 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

14 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

15 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

16 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

17 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

18 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

19 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

20 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

21 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

22 Copyright 2007 by Noyce Foundation 95

23 A Question of Numbers This problem gives you the chance to: show you can compare and order numbers Holly s class is learning about big numbers. 1. Here is part of the class number line Put an X on the number line, on the place that is halfway between 650 and 660. What is the number that should be there? 2. Holly knows a pony weighs between 365 pounds and 425 pounds. Write a possible number for the weight of a pony. pounds 3. The activity center swimming pool holds between 1,875 gallons and 1,940 gallons of water. Write a possible number for the amount of water the swimming pool holds. gallons 4. A school computer could cost between \$2,950 and \$3,055. Give three possible prices for the computer. \$ \$ \$ Copyright 2007 by Mathematics Assessment 96 A Question of Numbers Test 3

24 5. The American Revolution started in 1775 and finished in In which year was it halfway through? Show how you know using this number line Holly s teacher says the school library has 1000 books. Holly thinks that the library may have 40 more books. What is the greatest number of books that the library could have? Show how you figured this out. Tom thinks that the library may have 40 fewer books than What is the smallest number of books that the library could have? Show how you figured this out. 8 Copyright 2007 by Mathematics Assessment 97 A Question of Numbers Test 3

25 Task 5: A Question of Numbers The core elements of performance required by this task are: show you can compare and order numbers Based on these, credit for specific aspects of performance should be assigned as follows Rubric points section points 1. Gives correct answer: Draws an X in the correct place on the number line Gives correct answer such as: 380 pounds Gives correct answer: such as 1,920 gallons. 1 Gives correct answers such as: \$2955 \$3000 \$ Gives correct answer: 1779 and Marks the correct year on the number line. 6. Gives correct answer: 1040 and Shows Gives correct answer: 960 and Shows Total Points Copyright 2007 by Mathematics Assessment 98 A Question of Numbers Test 3

27 Looking at Student Work on A Question of Numbers Student A is able to use the number line to find numbers within a given range or to divide a range halfway. The student understands the mathematical use of the word between and uses landmark or friendly numbers to name values between. Notice how Student A puts all the values on the number line, identifies the section being considered, then labels the midpoint. Student A Copyright 2007 by Noyce Foundation 100

28 Student A, part 2 Copyright 2007 by Noyce Foundation 101

29 Student B uses the number line as a tool. See the marking off of equal distances to locate the midpoint in part 1. The student sees the number line as a series of numbers between two end points, but has not quite mastered how to scale in all the values or measure in equal units. (See part 5. The student is trying to count backwards to the middle, but makes a stumble. The student has a very clear, clean explanation for finding the most and least books. Student B Copyright 2007 by Noyce Foundation 102

30 Student B, part 2 Copyright 2007 by Noyce Foundation 103

31 This idea of measuring off equal units or scaling the number line was difficult for students. Notice Student C attempted the idea and then simplified the number line to just the relevant numbers. Student D was able to think about the locations for starting and ending numbers and then put in the appropriate midpoint without counting every number. Student E combines measuring equal units, with marking off the starting, ending and midpoints. Student C Student D Student E Copyright 2007 by Noyce Foundation 104

32 Student F may or may not have had experience with a number line, but is able to use other strategies to find the midpoint. Then Student F is able to estimate the location of that value on the number line. Notice the full explanation for finding the values in part 6. Student F Copyright 2007 by Noyce Foundation 105

33 Student G tries to use subtraction to find the midpoint. But does not use that information to find the midpoint. How could the 8 be used to find the midpoint? What would be the next step(s)? Notice how the student uses place value units to find the total number of books in the library. Student G Copyright 2007 by Noyce Foundation 106

34 Student H is able to measure the scale and locate the endpoints for the war, but doesn t count off the spaces to locate an exact midpoint. Notice that student H seems to understand the concept of ± 40, but has further work of finding values within the range of possibility. Student H Copyright 2007 by Noyce Foundation 107

35 Some students are having difficulty applying ideas about place value to computation. Student I has 4 points on page 1 of the task, but lines up thousands and tens when adding and subtracting. Student J puts the 4 tens in the hundreds column. Student K and L have trouble with place value which leads to procedural errors in using the standard algorithm. Notice Student K also has trouble thinking about what comes after Student I Student J Copyright 2007 by Noyce Foundation 108 Student K

36 Student L Copyright 2007 by Noyce Foundation 109

37 Understanding mathematical terminology or academic language is often different from common word usage. Student M relies too heavily on finding and circling key words, rather than teasing out what is being asked in the question. In this particular problem, and does not mean the combining of two values, but is identifying two points that are similar because that represent endpoints. Student M Copyright 2007 by Noyce Foundation 110

38 Student N has trouble distinguishing between the number with the greatest absolute value and adding more books to obtain the greatest possible value. This example shows the subtleties required for reading academic material. Student N Copyright 2007 by Noyce Foundation 111

39 3 rd Grade Task 5 A Question of Numbers Student Task Core Idea 1 Number Properties Compare and order numbers using values and number lines. Make a reasonable argument to find the midpoint of a range of numbers. Understand numbers, ways of representing numbers, relationships among numbers and number systems. Develop understanding of the relative magnitude of whole numbers and the concepts of sequence, quantity, and the relative positions of numbers. Mathematics in this task: Ability to measure in equal size units on a number line Ability to count around tens, hundreds, and thousands Ability to find a numerical midpoint and to find and compare numbers within a range Understand most and least in the mathematical sense of ± 40. Based on teacher observations, this is what third graders knew and were able to do: Find and name the middle number on a number line (part 1) when the scale marks are drawn in Find the most books that could be in a library Find points between two numbers Areas of difficulty for students: Subtracting from 1000 Finding a midpoint between two numbers on a number line, when the intervals are not marked and the endpoints for the task are different from the endpoints on a number line Marking off equal intervals, dividing something into ten parts Understanding that between does not include the endpoints Copyright 2007 by Noyce Foundation 112

40 The maximum score available for this task is 8 points. The minimum score needed for a level 3 response, meeting standard, is 4 points. Most students, about 87%, could find and name the midpoint on a scaled number line. Many students, about 71%, could locate the midpoint on a number line, and find values between two endpoints (parts 2 and 3). More than half, 58%, could also find three values between two endpoints. 26% could also find solutions for thinking about the most and least books in the library. 8% could meet all the demands of the task including scaling their own number line to find a midpoint where the endpoints were not the ends of the number line. 7% of the students scored no points on this task. Only 38% of those students attempted the task. Copyright 2007 by Noyce Foundation 113

43 Copyright 2007 by Noyce Foundation 116

44 Activities from website for San Diego School District: Mathematics Dept. Third grade Copyright 2007 by Noyce Foundation 117

### 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

### 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

### 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

### 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

### 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.

### 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

### 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

### 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.

### 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

### 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

### 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

### 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)

### 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

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

### 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,

### 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

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

### 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

### 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

### 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

### 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

E XPLORING QUADRILATERALS E 1 Geometry State Goal 9: Use geometric methods to analyze, categorize and draw conclusions about points, lines, planes and space. Statement of Purpose: The activities in this

### Third Grade Shapes Up! Grade Level: Third Grade Written by: Jill Pisman, St. Mary s School East Moline, Illinois Length of Unit: Eight Lessons

Third Grade Shapes Up! Grade Level: Third Grade Written by: Jill Pisman, St. Mary s School East Moline, Illinois Length of Unit: Eight Lessons I. ABSTRACT This unit contains lessons that focus on geometric

### 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

### 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

### 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

### 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:

### 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

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

### Unit 8 Angles, 2D and 3D shapes, perimeter and area

Unit 8 Angles, 2D and 3D shapes, perimeter and area Five daily lessons Year 6 Spring term Recognise and estimate angles. Use a protractor to measure and draw acute and obtuse angles to Page 111 the nearest

### 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

### Prentice Hall Mathematics: Course 1 2008 Correlated to: Arizona Academic Standards for Mathematics (Grades 6)

PO 1. Express fractions as ratios, comparing two whole numbers (e.g., ¾ is equivalent to 3:4 and 3 to 4). Strand 1: Number Sense and Operations Every student should understand and use all concepts and

### 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,

### CCSS-M Critical Areas: Kindergarten

CCSS-M Critical Areas: Kindergarten Critical Area 1: Represent and compare whole numbers Students use numbers, including written numerals, to represent quantities and to solve quantitative problems, such

### 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

### NUMBER CORNER YEARLONG CONTENT OVERVIEW

August & September Workouts Calendar Grid Quilt Block Symmetries Identifying shapes and symmetries Calendar Collector Two Penny Toss Probability and data analysis Computational Fluency Mental Math Fluently

### Drawing Lines of Symmetry Grade Three

Ohio Standards Connection Geometry and Spatial Sense Benchmark H Identify and describe line and rotational symmetry in two-dimensional shapes and designs. Indicator 4 Draw lines of symmetry to verify symmetrical

### 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

### Objective To guide exploration of the connection between reflections and line symmetry. Assessment Management

Line Symmetry Objective To guide exploration of the connection between reflections and line symmetry. www.everydaymathonline.com epresentations etoolkit Algorithms Practice EM Facts Workshop Game Family

### Grade 4 Unit 3: Multiplication and Division; Number Sentences and Algebra

Grade 4 Unit 3: Multiplication and Division; Number Sentences and Algebra Activity Lesson 3-1 What s My Rule? page 159) Everyday Mathematics Goal for Mathematical Practice GMP 2.2 Explain the meanings

### 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.

### 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

### 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,

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

### Charlesworth School Year Group Maths Targets

Charlesworth School Year Group Maths Targets Year One Maths Target Sheet Key Statement KS1 Maths Targets (Expected) These skills must be secure to move beyond expected. I can compare, describe and solve

### BPS Math Year at a Glance (Adapted from A Story Of Units Curriculum Maps in Mathematics K-5) 1

Grade 4 Key Areas of Focus for Grades 3-5: Multiplication and division of whole numbers and fractions-concepts, skills and problem solving Expected Fluency: Add and subtract within 1,000,000 Module M1:

### Fourth Grade Math Standards and "I Can Statements"

Fourth Grade Math Standards and "I Can Statements" Standard - CC.4.OA.1 Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 x 7 as a statement that 35 is 5 times as many as 7 and

### 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

Ohio Standards Connection Geometry and Spatial Sense Benchmark I Describe, identify and model reflections, rotations and translations, using physical materials. Indicator 7 Identify, describe and use reflections

### 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

### 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,

### 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:

### 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.

### Fractions as Numbers INTENSIVE INTERVENTION. National Center on. at American Institutes for Research

National Center on INTENSIVE INTERVENTION at American Institutes for Research Fractions as Numbers 000 Thomas Jefferson Street, NW Washington, DC 0007 E-mail: NCII@air.org While permission to reprint this

### Fun with Fractions: A Unit on Developing the Set Model: Unit Overview www.illuminations.nctm.org

Fun with Fractions: A Unit on Developing the Set Model: Unit Overview www.illuminations.nctm.org Number of Lessons: 7 Grades: 3-5 Number & Operations In this unit plan, students explore relationships among

### 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

### 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

### 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

### This puzzle is based on the following anecdote concerning a Hungarian sociologist and his observations of circles of friends among children.

0.1 Friend Trends This puzzle is based on the following anecdote concerning a Hungarian sociologist and his observations of circles of friends among children. In the 1950s, a Hungarian sociologist S. Szalai

### 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

### Unit 6 Number and Operations in Base Ten: Decimals

Unit 6 Number and Operations in Base Ten: Decimals Introduction Students will extend the place value system to decimals. They will apply their understanding of models for decimals and decimal notation,

### 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

### Kindergarten Math Content 1

Kindergarten Math Content 1 Number and Operations: Whole Numbers Counting and the Number System A main focus in Kindergarten is counting, which is the basis for understanding the number system and for

### The GED math test gives you a page of math formulas that

Math Smart 643 The GED Math Formulas The GED math test gives you a page of math formulas that you can use on the test, but just seeing the formulas doesn t do you any good. The important thing is understanding

### Math Games For Skills and Concepts

Math Games p.1 Math Games For Skills and Concepts Original material 2001-2006, John Golden, GVSU permission granted for educational use Other material copyright: Investigations in Number, Data and Space,

### 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

### Kindergarten Math Curriculum Course Description and Philosophy Text Reference:

Kindergarten Math Curriculum Course Description and Philosophy How do numbers and math affect our daily lives? What types of problems can be solved by understanding numbers and math concepts? Through inquiry,

### I. ASSESSSMENT TASK OVERVIEW & PURPOSE:

Performance Based Learning and Assessment Task Surface Area of Boxes I. ASSESSSMENT TASK OVERVIEW & PURPOSE: In the Surface Area of Boxes activity, students will first discuss what surface area is and

### 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

### In mathematics, there are four attainment targets: using and applying mathematics; number and algebra; shape, space and measures, and handling data.

MATHEMATICS: THE LEVEL DESCRIPTIONS In mathematics, there are four attainment targets: using and applying mathematics; number and algebra; shape, space and measures, and handling data. Attainment target

### 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

### a. Look under the menu item Introduction to see how the standards are organized by Standards, Clusters and Domains.

Chapter One Section 1.1 1. Go to the Common Core State Standards website (http://www.corestandards.org/math). This is the main site for further questions about the Common Core Standards for Mathematics.

### -- Martensdale-St. Marys Community School Math Curriculum

-- Martensdale-St. Marys Community School Standard 1: Students can understand and apply a variety of math concepts. Benchmark; The student will: A. Understand and apply number properties and operations.

Grade FCAT 2.0 Mathematics Sample Answers This booklet contains the answers to the FCAT 2.0 Mathematics sample questions, as well as explanations for the answers. It also gives the Next Generation Sunshine

### Unit 1 Number Sense. In this unit, students will study repeating decimals, percents, fractions, decimals, and proportions.

Unit 1 Number Sense In this unit, students will study repeating decimals, percents, fractions, decimals, and proportions. BLM Three Types of Percent Problems (p L-34) is a summary BLM for the material

### 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

### Linking Mathematics and Culture to Teach Geometry Concepts Vincent Snipes and Pamela Moses

Linking Mathematics and Culture to Teach Geometry Concepts Vincent Snipes and Pamela Moses Introduction Throughout history, mathematics has been used by different peoples in various ways. Arithmetic and

### Chapter 18 Symmetry. Symmetry of Shapes in a Plane 18.1. then unfold

Chapter 18 Symmetry Symmetry is of interest in many areas, for example, art, design in general, and even the study of molecules. This chapter begins with a look at two types of symmetry of two-dimensional

### MATHEMATICS: REPEATING AND GROWING PATTERNS First Grade. Kelsey McMahan. Winter 2012 Creative Learning Experiences

MATHEMATICS: REPEATING AND GROWING PATTERNS Kelsey McMahan Winter 2012 Creative Learning Experiences Without the arts, education is ineffective. Students learn more and remember it longer when they are

### Place Value (What is is the Value of of the the Place?)

Place Value (What is is the Value of of the the Place?) Second Grade Formative Assessment Lesson Lesson Designed and revised by Kentucky Department of Education Mathematics Specialists Field-tested by

### NCTM Curriculum Focal Points for Grade 5. Everyday Mathematics, Grade 5

NCTM Curriculum Focal Points and, Grade 5 NCTM Curriculum Focal Points for Grade 5 Number and Operations and Algebra: Developing an understanding of and fluency with division of whole numbers Students

### 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:

### 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:

### SHAPES, SHAPES EVERYWHERE!

SHAPES, SHAPES EVERYWHERE! A Second-Grade Geometry Unit Aligned with Mathematics Standards from Content Knowledge: A Compendium of Standards and Benchmarks for K 12 Education, 3rd Edition Regional Educational

### Performance Based Learning and Assessment Task Triangles in Parallelograms I. ASSESSSMENT TASK OVERVIEW & PURPOSE: In this task, students will

Performance Based Learning and Assessment Task Triangles in Parallelograms I. ASSESSSMENT TASK OVERVIEW & PURPOSE: In this task, students will discover and prove the relationship between the triangles

### 1A: Understand numbers, ways of representing numbers, relationships among numbers, and number systems.

NCTM STANDARD 1: Numbers and Operations Kindergarten Grade 2 1A: Understand numbers, ways of representing numbers, relationships among numbers, and number systems. Kindergarten Grade One Grade Two 1. Count

### 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,

### Discovering Math: Exploring Geometry Teacher s Guide

Teacher s Guide Grade Level: 6 8 Curriculum Focus: Mathematics Lesson Duration: Three class periods Program Description Discovering Math: Exploring Geometry From methods of geometric construction and threedimensional

### 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

Academic Content Standards Grade Eight and Grade Nine Ohio Algebra 1 2008 Grade Eight STANDARDS Number, Number Sense and Operations Standard Number and Number Systems 1. Use scientific notation to express

### Middle Value (Median) of a Set of Data

Middle Value (Median) of a Set of Data Objectives To guide children as they sort numerical data and arrange data in ascending or descending order, and as they find the middle value (median) for a set of

### 1 ENGAGE. 2 TEACH and TALK GO. Round to the Nearest Ten or Hundred

Lesson 1.2 c Round to the Nearest Ten or Hundred Common Core Standard CC.3.NBT.1 Use place value understanding to round whole numbers to the nearest 10 or 100. Lesson Objective Round 2- and 3-digit numbers

### 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,

### New York State Testing Program Grade 3 Common Core Mathematics Test. Released Questions with Annotations

New York State Testing Program Grade 3 Common Core Mathematics Test Released Questions with Annotations August 2013 THE STATE EDUCATION DEPARTMENT / THE UNIVERSITY OF THE STATE OF NEW YORK / ALBANY, NY

### CBA Fractions Student Sheet 1

Student Sheet 1 1. If 3 people share 12 cookies equally, how many cookies does each person get? 2. Four people want to share 5 cakes equally. Show how much each person gets. Student Sheet 2 1. The candy

### Kristen Kachurek. Circumference, Perimeter, and Area Grades 7-10 5 Day lesson plan. Technology and Manipulatives used:

Kristen Kachurek Circumference, Perimeter, and Area Grades 7-10 5 Day lesson plan Technology and Manipulatives used: TI-83 Plus calculator Area Form application (for TI-83 Plus calculator) Login application

### Mathematics Instructional Cycle Guide

Mathematics Instructional Cycle Guide Fractions on the number line 3NF2a Created by Kelly Palaia, 2014 Connecticut Dream Team teacher 1 CT CORE STANDARDS This Instructional Cycle Guide relates to the following