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


 Augustine Hardy
 11 months ago
 Views:
Transcription
1 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, and spheres. Use the formulas for volumes to solve realworld and mathematical problems. Essential Questions What are the similarities and differences between cube roots and square roots? What is the relationship between cubes and cube roots? Mathematical Practices to Be Integrated 4 Model with mathematics. Solve realworld problems involving volume of cones, cylinders, and spheres. 6 Attend to precision. Choose the appropriate volume formula for a given threedimensional shape. Calculate volume using the order of operations accurately. How is the volume of a cylinder related to the volume of a cone? How is the area of a circle related to finding the volume of a cylinder? Providence Public Schools D117
2 Version 4 Cylinders, and Spheres (6 8 days) Standards Common Core State Standards for Mathematical Content Expressions and Equations 8.EE Work with radicals and integer exponents. 8.EE.2 Use square root and cube root symbols to represent solutions to equations of the form x 2 = p and x 3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that 2 is irrational. Geometry 8.G Solve realworld and mathematical problems involving volume of cylinders, cones, and spheres. 8.G.9 Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve realworld and mathematical problems. Common Core State Standards for Mathematical Practice 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, twoway 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. 6 Attend to precision. Mathematically proficient students try to communicate precisely to others. They try to use clear definitions in discussion with others and in their own reasoning. They state the meaning of the symbols they choose, including using the equal sign consistently and appropriately. They are careful about specifying units of measure, and labeling axes to clarify the correspondence with quantities in a problem. They calculate accurately and efficiently, express numerical answers with a degree of precision appropriate for the problem context. In the elementary grades, students give carefully formulated explanations to each other. By the time they reach high school they have learned to examine claims and make explicit use of definitions. D118 Providence Public Schools
3 Grade 8 Mathematics, Quarter 4, Unit 4.3 Cylinders, and Spheres (6 8 days) Version 4 Clarifying the Standards Prior Learning In Grade 6, students solved realworld and mathematical problems involving area, surface area, and volume. In Grade 7, students continued their work with area, solving problems involving the area and circumference of a circle and surface area of threedimensional objects. In preparation for work on congruence and similarity in Grade 8, they reasoned about relationships among twodimensional figures using scale drawings and informal geometric constructions, and they gained familiarity with the relationships between angles formed by intersecting lines. In Grade 7, students worked with threedimensional figures, relating them to twodimensional figures by examining crosssections. They solved realworld and mathematical problems involving area, surface area, and volume of two and threedimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. Current Learning In this unit, students work with radicals and integer exponents, specifically cube roots and cubes. They also complete their work on volume by solving problems involving cones, cylinders, and spheres. Future Learning In Algebra 1, students will work with rational exponents. In Geometry and Precalculus, students will explain volume formulas and use them to solve problems. Additional Findings The measurement of volume presents some additional complexities for reasoning about the structure of space, primarily because the units of measure must be coordinated in three dimensions. Therefore, a wide range of experiences is necessary to clarify these complexities. (Adding it Up, p. 284) Assessment When constructing an endofunit assessment, be aware that the assessment should measure your students understanding of the big ideas indicated within the standards. The CCSS for Mathematical Content and the CCSS for Mathematical Practice should be considered when designing assessments. Standardsbased mathematics assessment items should vary in difficulty, content, and type. The assessment should comprise a mix of items, which could include multiple choice items, short and extended response items, and performancebased tasks. When creating your assessment, you should be mindful when an item could be differentiated to address the needs of students in your class. The mathematical concepts below are not a prioritized list of assessment items, and your assessment is not limited to these concepts. However, care should be given to assess the skills the students have developed within this unit. The assessment should provide you with credible evidence as to your students attainment of the mathematics within the unit. Use square root and cube root symbols to represent solutions to equations in the form of x 3 = p. Evaluate cube roots of small perfect cubes using volume formulas. Know and use formulas for volumes of cones, cylinders, and spheres to solve realworld problems. Providence Public Schools D119
4 Version 4 Cylinders, and Spheres (6 8 days) Instruction Learning Objectives Students will be able to: Review how to determine area and perimeter of rectangles and triangles. Determine surface area and volume of rectangular prisms and triangular prisms. Determine surface area and volume of cylinders. Determine volume of cones and spheres. Apply formulas for volume of cylinders, cones, spheres, and prisms. Demonstrate understanding of volume in realworld problems. Resources Supplemental Geometry and Measurement Unit found in the Supplemental Unit Materials section of this binder. Note: The district resources may contain content that goes beyond the standards addressed in this unit. See the Planning for Effective Instructional Design and Delivery and Assessment sections for specific recommendations. Materials Centimeter or inch cubes, grid paper, sand or rice, transparent cylinders, scissors and tape, stiff blank paper, clear plastic models of a prism and pyramid with same height and base (optional), clear plastic models of a cone and cylinder with same height and radius (optional), rulers, student notebooks. Instructional Considerations Key Vocabulary Cube root Planning for Effective Instructional Design and Delivery Teachers should review the Mathematics of the Unit found on page 3 of all CMP2 teacher editions prior to planning. Reinforced vocabulary taught in previous grades or units: cone, cylinder, sphere, pyramid, rectangular prism, surface area, triangular prism, and volume. Living word walls will assist all students in developing content language. Word walls should be visible to all students, focus on the current unit s vocabulary, and have pictures, examples, and/or diagrams to accompany the definitions. Be sure to read the Mathematics Background included in the resources for the unit of study. This is an indepth discussion about the big ideas in the Filling and Wrapping unit an excellent overview of developmentally appropriate sequencing of 3D geometry concepts. D120 Providence Public Schools
5 Grade 8 Mathematics, Quarter 4, Unit 4.3 Cylinders, and Spheres (6 8 days) Version 4 As students are working on the first two lessons of this unit, monitor progress and informally assess students prior knowledge of the 7thgrade CCSS. If students are struggling, ask questions to elicit discussions around the objectives of the lesson. With regard to volume, it is important to reinforce the idea that Area of the Base Height = Volume. Students intuitively understand this as a layering idea, as developed in their 7thgrade experiences. Continue to reinforce this notion when discussing the volume of prisms and cylinders. Lesson 3 uses nonlinguistic representations to represent knowledge. Students will build a physical model of a cylinder in order to better understand its attributes and the formulas for finding the volume. Lesson 4.2 extends the study of volume to pyramids and cones. You can conduct the experiments as a demonstration, but students will develop a greater understanding if they are able to build the models and determine the relationships for themselves. Upon completion of lesson 4.2, use an identifying similarities and differences strategy to deepen conceptual knowledge of prisms, pyramids, cylinders, cones, and spheres. Students will create a comparison matrix comparing attributes of various 3D shapes. A sample chart is provided below. Rectangular prism Triangular prism Rectangular pyramid Triangular pyramid Cylinder Cone Sphere Picture Attributes Formulas Examples CMP2 has online resources that may be helpful in planning for all units of study. Visit and sign on to SuccessNet. Incorporate the Essential Questions as part of the daily lesson. Options include using them as a do now to activate prior knowledge of the previous day s lesson, using them as an exit ticket by having students respond to it and post it, or hand it in as they exit the classroom, or using them as other formative assessments. Essential questions should be included in the unit assessment. For planning considerations read through the teacher edition for suggestions about scaffolding techniques, using additional examples, and differentiated instructional guidelines as suggested by the CMP resource. Providence Public Schools D121
6 Version 4 Cylinders, and Spheres (6 8 days) Notes D122 Providence Public Schools
Overview. Essential Questions. Grade 7 Mathematics, Quarter 3, Unit 3.3 Area and Circumference of Circles. Number of instruction days: 3 5
Area and Circumference of Circles Number of instruction days: 3 5 Overview Content to Be Learned Develop an understanding of the formulas for the area and circumference of a circle. Explore the relationship
More informationOverview. Essential Questions. Grade 4 Mathematics, Quarter 3, Unit 3.3 Multiplying Fractions by a Whole Number
Multiplying Fractions by a Whole Number Overview Number of instruction days: 8 10 (1 day = 90 minutes) Content to Be Learned Understand that a fraction can be written as a multiple of unit fractions with
More informationOverview. 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
More informationOverview. Essential Questions. Grade 7 Mathematics, Quarter 4, Unit 4.2 Probability of Compound Events. Number of instruction days: 8 10
Probability of Compound Events Number of instruction days: 8 10 Overview Content to Be Learned Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. Understand
More informationOverview. 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
More informationQuadratic Functions: Complex Numbers
Algebra II, Quarter 1, Unit 1.3 Quadratic Functions: Complex Numbers Overview Number of instruction days: 1214 (1 day = 53 minutes) Content to Be Learned Mathematical Practices to Be Integrated Develop
More informationModeling in Geometry
Modeling in Geometry Overview Number of instruction days: 810 (1 day = 53 minutes) Content to Be Learned Mathematical Practices to Be Integrated Use geometric shapes and their components to represent
More informationDescribing 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: 810 (1 day = 90 minutes) Content to Be Learned Distinguish between linear and
More informationOverview. Essential Questions. Precalculus, Quarter 2, Unit 2.4 Interpret, Solve, and Graph Inverse Trigonometric Functions
Trigonometric Functions Overview Number of instruction days: 3 5 (1 day = 53 minutes) Content to Be Learned Use restricted domains in order to construct inverse Use inverse trigonometric functions to solve
More informationPrecalculus, Quarter 2, Unit 2.2 Use the Unit Circle and Right Triangle Trigonometry to Find Special Angle Ratios. Overview
Use the Unit Circle and Right Triangle Trigonometry to Find Special Angle Ratios Overview Number of instruction days: 4 6 (1 day = 53 minutes) Content to Be Learned Use arc length of the unit circle to
More informationGary School Community Corporation Mathematics Department Unit Document. Unit Number: 8 Grade: 2
Gary School Community Corporation Mathematics Department Unit Document Unit Number: 8 Grade: 2 Unit Name: YOU SEE IT!!! (2D & 3D Shapes) Duration of Unit: 18 days UNIT FOCUS Students describe and analyze
More informationPythagorean Theorem. Overview. Grade 8 Mathematics, Quarter 3, Unit 3.1. Number of instructional days: 15 (1 day = minutes) Essential questions
Grade 8 Mathematics, Quarter 3, Unit 3.1 Pythagorean Theorem Overview Number of instructional days: 15 (1 day = 45 60 minutes) Content to be learned Prove the Pythagorean Theorem. Given three side lengths,
More informationInteger 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.
More informationOverview. 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,
More informationGrade 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 multidigit whole numbers using understanding of place value. Recognize that the
More informationSolving Equations with One Variable
Grade 8 Mathematics, Quarter 1, Unit 1.1 Solving Equations with One Variable Overview Number of Instructional Days: 15 (1 day = 45 minutes) Content to Be Learned Solve linear equations in one variable
More informationQuadratic and Linear Systems
Mathematical Models with Applications, Quarter 3, Unit 3.1 Quadratic and Linear Systems Overview Number of instruction days: 57 (1 day = 53 minutes) Content to Be Learned Mathematical Practices to Be
More informationGrade 8 Unit 2 Pythagorean Theorem Applications. Assessment Plan
Grade 8 Unit 2 Pythagorean Theorem Applications Work with radicals and integer exponents Assessment Plan 8. EE.2 Use square root and cube root symbols to represent solutions to equations. Evaluate square
More informationCommon 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
More informationFor 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
More informationPA 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
More informationOverview. Essential Questions. Precalculus, Quarter 1, Unit 1.4 Analyzing Exponential and Logarithmic Functions
Analyzing Exponential and Logarithmic Functions Overview Number of instruction days: 5 7 (1 day = 53 minutes) Content to Be Learned Rewrite radical expressions using the properties of exponents. Rewrite
More informationOverview. 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 >,
More informationLinear Systems of Inequalities
Mathematical Models with Applications, Quarter 2, Unit 2.2 Linear Systems of Inequalities Overview Number of instruction days: 57 (1 day = 53 minutes) Content to Be Learned Mathematical Practices to Be
More informationMultiplying Fractions by a Whole Number
Grade 4 Mathematics, Quarter 3, Unit 3.1 Multiplying Fractions by a Whole Number Overview Number of Instructional Days: 15 (1 day = 45 60 minutes) Content to be Learned Apply understanding of operations
More informationDerive and Apply Geometric Formulas
Derive and Apply Geometric Formulas Overview Number of instruction days: 8 10 (1 day = 53 minutes) Content to Be Learned Mathematical Practices to Be Integrated Write an explanation of the formula for
More informationPolynomial 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.
More informationMathematics Interim Assessment Blocks Blueprint V
67 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
More informationWORK SCHEDULE: MATHEMATICS 2007
, K WORK SCHEDULE: MATHEMATICS 00 GRADE MODULE TERM... LO NUMBERS, OPERATIONS AND RELATIONSHIPS able to recognise, represent numbers and their relationships, and to count, estimate, calculate and check
More information8 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
More informationPerimeter, Area and Volume What Do Units Tell You About What Is Being Measured? Overview
Perimeter, Area and Volume What Do Units Tell You About What Is Being Measured? Overview Summary of Lessons: This set of lessons was designed to develop conceptual understanding of the unique attributes
More informationUsing Nets to Find Surface Area Grade Eight
Ohio Standards Connection: Geometry and Spatial Sense Benchmark E Draw and construct representations of two and threedimensional geometric objects using a variety of tools, such as straightedge, compass,
More informationOverview. Essential Questions. Grade 4 Mathematics, Quarter 2, Unit 2.1 Multiplying MultiDigit Whole Numbers
Multiplying MultiDigit Whole Numbers Overview Number of instruction days: 5 7 (1 day = 90 minutes) Content to Be Learned Use strategies based on place value and properties of operations to multiply a
More informationCommon Core State Standards for Mathematics Accelerated 7th Grade
A Correlation of 2013 To the to the Introduction This document demonstrates how Mathematics Accelerated Grade 7, 2013, meets the. Correlation references are to the pages within the Student Edition. Meeting
More informationOverview. Essential Questions. Grade 5 Mathematics, Quarter 3, Unit 3.2 Multiplying and Dividing With Decimals
Multiplying and Dividing With Decimals Overview Number of instruction days: 9 11 (1 day = 90 minutes) Content to Be Learned Multiply decimals to hundredths. Divide decimals to hundredths. Use models, drawings,
More informationPreAlgebra 2008. Academic Content Standards Grade Eight Ohio. Number, Number Sense and Operations Standard. Number and Number Systems
Academic Content Standards Grade Eight Ohio PreAlgebra 2008 STANDARDS Number, Number Sense and Operations Standard Number and Number Systems 1. Use scientific notation to express large numbers and small
More informationNumber and Numeracy SE/TE: 43, 49, 140145, 367369, 457, 459, 479
Ohio Proficiency Test for Mathematics, New Graduation Test, (Grade 10) Mathematics Competencies Competency in mathematics includes understanding of mathematical concepts, facility with mathematical skills,
More informationCreating, 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
More informationNumber Sense and Operations
Number Sense and Operations representing as they: 6.N.1 6.N.2 6.N.3 6.N.4 6.N.5 6.N.6 6.N.7 6.N.8 6.N.9 6.N.10 6.N.11 6.N.12 6.N.13. 6.N.14 6.N.15 Demonstrate an understanding of positive integer exponents
More informationGary School Community Corporation Mathematics Department Unit Document. Unit Number: 3 Grade: 4
Gary School Community Corporation Mathematics Department Unit Document Unit Number: 3 Grade: 4 Unit Name: Measurement with Angles and Rectangles Duration of Unit: 20 Days UNIT FOCUS In this unit, students
More informationStandards 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:
More informationMath Foundations IIB Grade Levels 912
Math Foundations IIB Grade Levels 912 Math Foundations IIB introduces students to the following concepts: integers coordinate graphing ratio and proportion multistep equations and inequalities points,
More informationMiddle Grades Mathematics 5 9
Middle Grades Mathematics 5 9 Section 25 1 Knowledge of mathematics through problem solving 1. Identify appropriate mathematical problems from realworld situations. 2. Apply problemsolving strategies
More informationScope & Sequence MIDDLE SCHOOL
Math in Focus is a registered trademark of Times Publishing Limited. Houghton Mifflin Harcourt Publishing Company. All rights reserved. Printed in the U.S.A. 06/13 MS77941n Scope & Sequence MIDDLE SCHOOL
More informationUnderstanding the Progression of Math Courses in NEISD
Understanding the Progression of Math Courses in NEISD According to House Bill 1 (HB1), students in Texas are required to obtain credits for four courses in each subject area of the foundation curriculum
More informationIn this lesson, students practice the essential skill
LEVEL NATIONAL MATH + SCIENCE INITIATIVE a b c a b b c b a c b a c b a c b Since a 0, a c b Algebra 1 or Math 1 in a unit on solving multistep equations Mathematics Literal Equations Geometric Formulas
More informationNEW 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
More informationPolynomials and Polynomial Functions
Algebra II, Quarter 1, Unit 1.4 Polynomials and Polynomial Functions Overview Number of instruction days: 1315 (1 day = 53 minutes) Content to Be Learned Mathematical Practices to Be Integrated Prove
More informationOverview. 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 wholenumber quotients with remainders of up to fourdigit dividends
More informationGrades K6. Correlated to the Common Core State Standards
Grades K6 Correlated to the Common Core State Standards Kindergarten Standards for Mathematical Practice Common Core State Standards Standards for Mathematical Practice Kindergarten The Standards for
More information3 rd 5 th Grade Math Core Curriculum Anna McDonald School
3 rd 5 th Grade Math Core Curriculum Anna McDonald School Our core math curriculum is only as strong and reliable as its implementation. Ensuring the goals of our curriculum are met in each classroom,
More informationTargetStrategies Aligned Mathematics Strategies Arkansas Student Learning Expectations Geometry
TargetStrategies Aligned Mathematics Strategies Arkansas Student Learning Expectations Geometry ASLE Expectation: Focus Objective: Level: Strand: AR04MGE040408 R.4.G.8 Analyze characteristics and properties
More informationFunctional Math II. Information CourseTitle. Types of Instruction
Functional Math II Course Outcome Summary Riverdale School District Information CourseTitle Functional Math II Credits 0 Contact Hours 135 Instructional Area Middle School Instructional Level 8th Grade
More informationMathematics Common Core Cluster. Mathematics Common Core Standard. Domain
Mathematics Common Core Domain Mathematics Common Core Cluster Mathematics Common Core Standard Number System Know that there are numbers that are not rational, and approximate them by rational numbers.
More informationUnderstanding 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
More informationPrentice Hall Connected Mathematics 2, 7th Grade Units 2009
Prentice Hall Connected Mathematics 2, 7th Grade Units 2009 Grade 7 C O R R E L A T E D T O from March 2009 Grade 7 Problem Solving Build new mathematical knowledge through problem solving. Solve problems
More informationPerfume Packaging. Ch 5 1. Chapter 5: Solids and Nets. Chapter 5: Solids and Nets 279. The Charles A. Dana Center. Geometry Assessments Through
Perfume Packaging Gina would like to package her newest fragrance, Persuasive, in an eyecatching yet costefficient box. The Persuasive perfume bottle is in the shape of a regular hexagonal prism 10 centimeters
More informationGeometry 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
More informationArea, Perimeter, Surface Area and Change Overview
Area, Perimeter, Surface Area and Change Overview Enduring Understanding: (5)ME01: Demonstrate understanding of the concept of area (5)ME02: Demonstrate understanding of the differences between length
More informationGlencoe. correlated to SOUTH CAROLINA MATH CURRICULUM STANDARDS GRADE 6 33, 58 84, 87 16, 49
Glencoe correlated to SOUTH CAROLINA MATH CURRICULUM STANDARDS GRADE 6 STANDARDS 68 Number and Operations (NO) Standard I. Understand numbers, ways of representing numbers, relationships among numbers,
More informationModule: Mathematical Reasoning
Module: Mathematical Reasoning Lesson Title: Using Nets for Finding Surface Area Objectives and Standards Students will: Draw and construct nets for 3D objects. Determine the surface area of rectangular
More informationPerformance Assessment Task Symmetrical Patterns Grade 4. Common Core State Standards Math  Content Standards
Performance Assessment Task Symmetrical Patterns Grade 4 The task challenges a student to demonstrate understanding of the concept of symmetry. A student must be able to name a variety of twodimensional
More informationMathematics Lesson Plan for Seventh Grade
Mathematics Lesson Plan for Seventh Grade For the Lesson on Friday, January 24, 2003 At the Harriet Tubman Middle School, Portland, Oregon Instructor: Akihiko Takahashi 1. Title of the Lesson: Which container
More informationProblem 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:
More informationCCSS: 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
More informationGrade 9 Mathematics Unit 3: Shape and Space Sub Unit #1: Surface Area. Determine the area of various shapes Circumference
1 P a g e Grade 9 Mathematics Unit 3: Shape and Space Sub Unit #1: Surface Area Lesson Topic I Can 1 Area, Perimeter, and Determine the area of various shapes Circumference Determine the perimeter of various
More informationAlgebra 1 2008. Academic Content Standards Grade Eight and Grade Nine Ohio. Grade Eight. Number, Number Sense and Operations Standard
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
More informationEVERY DAY COUNTS CALENDAR MATH 2005 correlated to
EVERY DAY COUNTS CALENDAR MATH 2005 correlated to Illinois Mathematics Assessment Framework Grades 35 E D U C A T I O N G R O U P A Houghton Mifflin Company YOUR ILLINOIS GREAT SOURCE REPRESENTATIVES:
More informationCampbellsport 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:
More informationDOUBLE, DOUBLE: LOOKING AT THE EFFECT OF CHANGE
DOUBLE, DOUBLE: LOOKING AT THE EFFECT OF CHANGE ON PERIMETER, AREA AND VOLUME Outcome (lesson objective) Students will demonstrate how changes in the dimensions of squares, rectangles, and circles affect
More informationCOMMON CORE STATE STANDARDS FOR MATHEMATICS K5 Overview
COMMON CORE STATE STANDARDS FOR MATHEMATICS K5 Overview Compiled by Dewey Gottlieb, Hawaii Department of Education June 2010 Kindergarten Counting and Cardinality Operations and Algebraic Thinking Number
More informationOverview. Essential Questions. Grade 5 Mathematics, Quarter 3, Unit 3.1 Adding and Subtracting Decimals
Adding and Subtracting Decimals Overview Number of instruction days: 12 14 (1 day = 90 minutes) Content to Be Learned Add and subtract decimals to the hundredths. Use concrete models, drawings, and strategies
More informationSuch 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
More informationDomain: Geometry (G) Cluster: Understand and apply the Pythagorean Theorem.
Domain: Geometry (G) Cluster: Understand and apply the Pythagorean Theorem. Standard: 8.G.6. Explain a proof of the Pythagorean Theorem and its converse. MP.3. Construct viable arguments and critique the
More informationGrade Level Expectations for the Sunshine State Standards
for the Sunshine State Standards Mathematics Grades 68 FLORIDA DEPARTMENT OF EDUCATION http://www.myfloridaeducation.com/ Strand A: Number Sense, Concepts, and Operations Standard 1: The student understands
More informationEXPLAINING AREA AND CIRCUMFERENCE OF A CIRCLE
EXPLAINING AREA AND CIRCUMFERENCE OF A CIRCLE 7.G.4 CONTENTS The types of documents contained in the unit are listed below. Throughout the unit, the documents are arranged by lesson. LEARNING MAP INFORMATION
More informationwith functions, expressions and equations which follow in units 3 and 4.
Grade 8 Overview View unit yearlong overview here The unit design was created in line with the areas of focus for grade 8 Mathematics as identified by the Common Core State Standards and the PARCC Model
More informationMeasurement 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 realworld and mathematical
More informationMathematics Connecticut Preschool Standards to Common Core State Standards Continuum. Preschool  Kindergarten
Mathematics Connecticut Preschool Standards to Common Core State Standards Continuum Preschool  Kindergarten Connecticut PreschoolKindergarten Standards Continuum for Mathematics On July 7, 2010, with
More informationG 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.
More informationProblem 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
More informationPrentice Hall Mathematics: Course Correlated to: Alaska State Content Standards: Math (Grade 7)
Alaska State Content Standards: Math (Grade 7) A. A student should understand mathematical facts, concepts, principles, and theories. 1. understand and use numeration, including numbers, number systems,
More informationGreater 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
More informationPerformance Based Learning and Assessment Task Confetti Task
Performance Based Learning and Assessment Task Confetti Task I. ASSESSMENT TASK OVERVIEW & PURPOSE: In this task, Geometry students will investigate how surface area and volume is used to estimate the
More informationUnit 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
More informationMathematics Curricular Guide SIXTH GRADE SCHOOL YEAR. Updated: Thursday, December 02, 2010
Mathematics Curricular Guide SIXTH GRADE 20102011 SCHOOL YEAR 1 MATHEMATICS SCOPE & SEQUENCE Unit Title Dates Page 1. CMP 2 Bits and Pieces I... 3 2. How Likely Is It? (Probability)... 6 3. CMP 2 Bits
More informationStudents will understand 1. use numerical bases and the laws of exponents
Grade 8 Expressions and Equations Essential Questions: 1. How do you use patterns to understand mathematics and model situations? 2. What is algebra? 3. How are the horizontal and vertical axes related?
More information1. Mathematics Content/Alignment with the Standards Correlation to California Algebra Readiness Standards
PROGRAM DESCRIPTION The goal of Prentice Hall Connecting to Algebra is to fully prepare students for success in Algebra 1 by thoroughly covering the Algebra Readiness standards outlined by the California
More informationSURFACE AREA AND VOLUME
SURFACE AREA AND VOLUME In this unit, we will learn to find the surface area and volume of the following threedimensional solids:. Prisms. Pyramids 3. Cylinders 4. Cones It is assumed that the reader has
More informationCommon 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
More informationIn 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
More informationImplementing the K8 th grade Common Core Math Standards
In consultation with the Archdiocese of San Francisco presents Implementing the K8 th grade Common Core Math Standards Catapult Contact Information: Heather Hutchinson Regional Director (310) 8970553
More informationDivision 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
More informationUnderstand the Concepts of Ratios and Unit Rates to Solve RealWorld Problems
Grade 6 Mathematics, Quarter 2, Unit 2.1 Understand the Concepts of Ratios and Unit Rates to Solve RealWorld Problems Overview Number of instructional days: 10 (1 day = 45 60 minutes) Content to be learned
More informationNew York State Mathematics Content Strands, Grade 6, Correlated to Glencoe MathScape, Course 1 and Quick Review Math Handbook Book 1
New York State Mathematics Content Strands, Grade 6, Correlated to Glencoe MathScape, Course 1 and The lessons that address each Performance Indicator are listed, and those in which the Performance Indicator
More informationGrade 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.
More informationNCLB Math Institute Summer 2011
NCLB Math Institute Summer 2011 Faculty Name: Glenda LollisHawkins School: Cypress Park Elementary Grade Level: 4 1. Teaching Objective(s): Analyze and describe the similarities and differences between
More informationMath Content
20122013 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
More informationIntroduction. The Aims & Objectives of the Mathematical Portion of the IBA Entry Test
Introduction The career world is competitive. The competition and the opportunities in the career world become a serious problem for students if they do not do well in Mathematics, because then they are
More informationVolumes of Revolution
Mathematics Volumes of Revolution About this Lesson This lesson provides students with a physical method to visualize dimensional solids and a specific procedure to sketch a solid of revolution. Students
More information