# Using Nets to Find Surface Area Grade Eight

Save this PDF as:

Size: px
Start display at page:

## Transcription

1 Ohio Standards Connection: Geometry and Spatial Sense Benchmark E Draw and construct representations of two- and three-dimensional geometric objects using a variety of tools, such as straightedge, compass, and technology. Indicator 6 Draw nets for a variety of prisms, pyramids, cylinders and cones. Measurement Benchmark B Use formulas to find surface area and volume for specified threedimensional objects accurate to a specified level of precision. Indicator 4 Derive formulas for surface area and volume and justify them using geometric models and common materials. For example, find: a. the surface area of a cylinder as a function of its height and radius; b. that the volume of a pyramid (or cone) is one-third of the volume of a prism (or cylinder) with the same base area and height. Lesson Summary: In this four-part lesson, students explore three-dimensional objects (prisms, pyramids, cylinders and cones) to draw nets. Students use the understanding of drawing nets to find the surface area of pyramids and cylinders. Students discuss surface area by using visual representations of nets to derive formulas for the surface area of each object. Journal writing and quick-write prompts allow students to reflect on their understanding. Multiple entry points into the lesson serve students of different abilities. Part One acts as remediation or an introduction for students who have no prior experience with nets. Students who understand nets may begin with Part Two, Making Conjectures about Nets; or Parts Three and Four, Surface Area. Estimated Duration: Two to three hours Commentary: Mathematics Academic Content Standards for grades five to seven initially develop the concept of surface area of threedimensional objects. In grade eight, students derive formulas for finding surface area. As students draw upon multiple senses in a learning episode, they more easily remember, recall and connect learning experiences. Using Nets to Find Surface Area captures students senses through building models and visual representations, discussing and supporting conjectures in collaboration with other students, reflecting upon learning and communicating in writing. Pre-Assessment: Distribute page one of the Hexomino Patterns, Attachment A. Ask students which of the hexominoes, when folded on the lines, makes a three-dimensional object. Allow students to analyze the four hexominoes. As students work, question individuals about how they came to their conclusions. Observe their strategies and evaluate understanding based on the following questions: a. Does the student recognize nets and non-nets without folding? b. Does the student need to fold the pattern to determine if it is a net? 1

2 Benchmark C Apply indirect measurement techniques, tools and formulas, as appropriate, to find perimeter, circumference and area of circles, triangles, quadrilaterals and composite shapes, and to find volume of prisms, cylinders, andpyramids. Indicator 5 Determine the surface area for pyramids by analyzing their parts. Mathematical Processes Benchmarks A. Formulate a problem or mathematical model in response to a specific need or situation, determine information required to solve the problem, choose method for obtaining this information, and set limits for acceptable solution. D. Apply reasoning skills to construct logical verifications or counter-examples to test conjectures and to justify and defend algorithms and solutions. G. Write clearly and coherently about mathematical thinking and ideas. c. Does the student understand folding on the lines to create a three dimensional object? For each hexomino, ask all students in the class to give you simultaneous visual cues (thumbs-up/thumbs-down) as to whether it can be folded into a three-dimensional object. Ask students to name or define two-dimensional patterns that can be folded into three-dimensional shapes (nets). Instructional Tip: If students struggle to meet the expectations of this task or demonstrate little understanding of nets, go to Instructional Procedures Part One, which provides students experience with nets. If students succeed or appear to have some background knowledge of nets, continue with the rest of the pre-assessment exercises and begin with Part Two of the lesson. Provide small groups of students a variety of threedimensional models including triangular and rectangular prisms, triangular and rectangular pyramids, cones and cylinders. Direct students to sketch a net for the objects. Observe students and determine which students: a. Draw nets without assistance; b. Experience difficulty drawing one to two specified nets, or c. Experience difficulty drawing any net. Use a checklist or take anecdotal notes describing student strategies/understanding. Collect the drawings of student work to determine how to proceed with instruction. Scoring Guidelines: Observe students to determine their understanding of identifying and defining nets. Record data and categorize students by level of understanding. 2

3 Post-Assessment: Option 1 Provide three-dimensional objects to small groups. When possible, use real-world objects such as cans, rectangular boxes, glass prisms and orange cones. Students draw nets of prisms (triangular and rectangular), pyramids (triangular and rectangular), cylinder and cone, and determine surface area of pyramids and cylinders. Scoring Guidelines: Use the rubric to score student work. 4 points Draws nets for the four three-dimensional objects (prisms, pyramids, cones and cylinders). 3 points Draws nets for three of the four three-dimensional objects (prisms, pyramids, cones and cylinders). 2 points Draws nets for two of the four three-dimensional objects (prisms, pyramids, cones and cylinders). 1 point Draws nets for one of the four three-dimensional objects (prisms, pyramids, cones and cylinders). 0 points Draws all nets incorrectly or makes no attempt. Drawings do not show correct faces of the three-dimensional object. Option Two Use nets created by the students in previous lessons to create an assessment for recognizing nets and non-nets. Copy the drawings on paper for each student or copy onto a transparency and show the drawings on an overhead projector. Present 10 examples of nets and non-nets. Have students write responses on separate answer/notebook sheets, identifying three-dimensional object, and indicating if the drawing is or is not a net. Instructional Tip: For students who cannot identify nets, reduce the complexity and number of the threedimensional figures used to assess drawing nets. Scoring Guidelines: Use the rubric to score student work. 4 points Identifies 10 pattern shapes correctly, naming the three-dimensional object formed by the net and identifying non-nets. 3 points Identifies eight to nine of the pattern shapes correctly, naming the threedimensional object and identifying non-nets. 2 points Identifies six to seven pattern shapes correctly, naming the three-dimensional object and identifying non-nets. 1 points Identifies one to five pattern shapes correctly, naming the three-dimensional object and identifying non-nets. 3

4 Option Three Provide students with models or common objects in the shape of cylinders and pyramids. Instruct them to find the surface area of each object. Explain the method for solving and provide reasoning for formulas used. Scoring Guidelines: Use the rubric to score student work. Score Characteristics 2 points Accurately finds surface area for cylinders and pyramids, and clearly explains reasoning for strategies and formulas used. 1 point Accurately finds surface area and clearly explains reasoning for one of the two objects (pyramid or cylinder). OR Accurately finds surface area for both objects, but explanation is unclear, irrelevant or not provided. OR Finds surface area incorrectly, but explains reasoning for appropriate methods to find surface area. 0 points Incorrectly calculates surface area. Explanation provides little evidence of reasoning associated with the problem. Instructional Procedures: Part One What are Nets? 1. Complete the pre-assessment activity. If students provide evidence that they are familiar with nets, proceed to Part Two of the lesson. 2. Provide intervention activities to familiarize students with nets. a. Distribute a set of hexomino patterns, Attachment A, Hexomino Patterns, pages one through seven to groups of four students. Discuss the attributes of a cube. Have groups make lists of attributes of a cube (number of sides, all sides are congruent, angle measures, lines of symmetry). Give a sheet of paper to one student in the group. The student writes an attribute that he/she knows and initials the attribute. The student passes the paper to the next person who writes another attribute of a cube and initials. Give two to three minutes to develop the lists. Have a reporter share the groups knowledge of cubes. Students should recognize that a cube is made of six identical squares. b. Refer students to the hexominoes. Each shape contains six sides that are square. Ask students, Which shapes could be folded on the lines to create a cube? Have students classify the hexominoes into nets that make cubes and those that do not. For students needing assistance, allow them to cut a few of the hexominoes and fold them to see if they make cubes. Divide the eight pages of hexominoes among the group members. c. Groups share results about which hexominoes are nets and which are not. d. Ask students if there are common characteristics of the nets for a cube. Give time for the groups to discuss and share conjectures or counter-examples for nets of cubes. For example, shapes with four blocks making a square and having a common vertex will not be nets. 4

5 Another example, shapes with the squares extended on the same side will not be nets. e. Have the reporters share comparisons developed by the groups. Compose a list of conjectures for nets on chart paper. f. Introduce the term net. Explain that any hexomino which creates a cube when folded is called a net. Provide students time to write a definition of net in their own words in journals or notebooks. Direct the students to complete a quick-chat with partners using the following questions: What conjectures can we make about nets and non-nets? How can we use the conjectures to develop nets for other solids? Part Two Conjectures for Nets 3. Tell students to make additional examples of nets and non-nets for geometric objects. Provide each pair of students with a model of a geometric solid (rectangular prism, triangular prism, pyramid with a triangular base, pyramid with a rectangular base, cone and cylinder). Students create two nets and two non-nets (includes all faces of the objects) for the solid. 4. After drawing examples of the nets and non-nets, direct pairs of students to meet with other pairs of students. Students share the example they have created to determine which drawings are nets and which are not. Give two minutes for the partners to share before changing partners. 5. Develop a list of conjectures for the net of each three-dimensional object. See examples in Part One of conjectures for nets of cubes. Examples of conjectures may include: The edges of a base of a pyramid have to be adjacent to the edges of the lateral faces; Prisms have at least two sets of congruent sides; Opposite sides of a pyramid with a rectangular base are congruent (incorrect). 6. Ask students to share their conjectures and record them on the board or chart paper. 7. Tell students to test two conjectures from the list and answer the following questions: What evidence do you have to support your conjecture? Are there any counter-examples that support or do not support the conjecture? They record notes and sketches in a journal or notebook. 5

9 hexagonal prism, an icosahedron, octahedron, dodecahedron, truncated cube, truncated octahedron, truncated tetrahedron, truncated icosahedron, the child s initial in threedimensional form, etc.) Ask students what a net for a sphere might look like. Allow students to work in groups to create a net for a sphere and then present their ideas to the class. Allow students to evaluate the ideas of each group constructively, focusing on the attributes of the sphere and proposed net. Show students two-dimensional maps of Earth as an example. Homework Options and Home Connections: Make a net for a cereal box, tissue box, etc, on grid paper. Determine the surface area and create a net similar to the box. Students working beyond the standard may create nets for irregular objects Interdisciplinary Connections: Art Make mobiles or sculptures with the three-dimensional objects cut and assembled from the nets. Materials and Resources: The inclusion of a specific resource in any lesson formulated by the Ohio Department of Education should not be interpreted as an endorsement of that particular resource, or any of its contents, by the Ohio Department of Education. The Ohio Department of Education does not endorse any particular resource. The Web addresses listed are for a given site s main page, therefore, it may be necessary to search within that site to find the specific information required for a given lesson. Please note that information published on the Internet changes over time, therefore the links provided may no longer contain the specific information related to a given lesson. Teachers are advised to preview all sites before using them with students. For the teacher: Hexomino patterns, models of geometric solids, pattern blocks For the student: Hexomino patterns, models of geometric solids, grid paper, transparent tape, scissors Vocabulary: attributes cone conjecture cube cylinder edge face hexagonal prism net octagonal prism triangular prism triangular pyramid 9

10 Technology Connection: Use computer software or graphing calculators for drawing nets. Research Connections: "BSCS Science: An Inquiry Approach." BSCS Biological Sciences Curriculum Study. 23 Dec Marzano, Robert J., Jane E. Pollock and Debra Pickering. Classroom Instruction that Works: Research-Based Strategies for Increasing Student Achievement, Alexandria, Va: Association for Supervision and Curriculum Development, Sousa, David A. How the Brain Learns: A Classroom Teacher s Guide. Reston, Va: NASSP, General Tips: Copy hexomino patterns on card stock and laminate to preserve for several years. For further development of formulas for volume and surface area, have students make additional nets on cm grid paper and wrap solids made from centimeter cubes. Attachments: Attachment A, Hexomino Patterns Attachment B, Mathematics Exit Note Attachment C, Nets Quick Write Attachment D, Pyramid Net Attachment E, Creating Similar Nets 10

11 Attachment A Hexomino Patterns 11

12 Attachment A (Continued) 12

13 Attachment A (Continued) 13

14 Attachment A (Continued) 14

15 Attachment A (Continued) 15

16 Attachment A (Continued) 16

17 Attachment A (Continued) 17

18 Attachment B Mathematics Exit Note Name Date Notes/Explanations: 18

19 What I know about nets Using Nets to Find Surface Area Grade Eight Attachment C Nets Quick Write Evidence of my understanding Draw examples of four different nets. 19

20 Attachment D Pyramid Net 20

21 Attachment E Creating Similar Nets Directions: Draw two nets that are similar to the net below. One should be smaller and one larger. Compare the surface area and volume of the three nets. Analyze the measurements for patterns. Describe the pattern and make a conjecture about similar figures. 21

### Number System Properties Grade Nine

Ohio Standards Connection: Number, Number Sense and Operations Benchmark C Apply properties of operations and the real number system, and justify when they hold for a set of numbers. Indicator 1 Identify

### Classifying Shapes and Figures Grade Four

Ohio Standards Connection Geometry and Spatial Sense Benchmark E Use attributes to describe, classify and sketch plane figures and build solid objects Indicator 2 Describe, classify, compare and model

### Name Date Period. 3D Geometry Project

Name 3D Geometry Project Part I: Exploring Three-Dimensional Shapes In the first part of this WebQuest, you will be exploring what three-dimensional (3D) objects are, how to classify them, and several

### 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

Ohio Standards Connection Geometry and Spatial Sense Benchmark E Use proportions to express relationships among corresponding parts of similar figures. Indicator 1 Use proportional reasoning to describe

### Grade 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

### Solving Problems Involving Chords, Radii, Tangents, Secants and Arcs within the Same Circle Grade Ten

Ohio Standards Connection: Geometry and Spatial Sense Benchmark C Recognize and apply angle relationships in situations involving intersecting lines, perpendicular lines and parallel lines. Indicator 10

### Module: Mathematical Reasoning

Module: Mathematical Reasoning Lesson Title: Using Nets for Finding Surface Area Objectives and Standards Students will: Draw and construct nets for 3-D objects. Determine the surface area of rectangular

### 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,

### Objectives/Outcomes. Materials and Resources. Grade Level: Title/Description of Lesson. Making a 3-dimensional sculpture using a 2dimensional patterns

V Viissuuaall & &P Peerrffoorrm miinngg A Arrttss P Prrooggrraam m,, S SJJU US SD D A Arrttss & &M Maatthh C Coonnnneeccttiioonnss Title/Description of Lesson Making a 3-dimensional sculpture using a 2dimensional

### Constructing Geometric Solids

Constructing Geometric Solids www.everydaymathonline.com Objectives To provide practice identifying geometric solids given their properties; and to guide the construction of polyhedrons. epresentations

### Simplifying Numerical Expressions Grade Five

Ohio Standards Connection Number, Number Sense and Operations Benchmark E Use order of operations, including use of parenthesis and exponents to solve multi-step problems, and verify and interpret the

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

### Indirect Measurement Technique: Using Trigonometric Ratios Grade Nine

Ohio Standards Connections Measurement Benchmark D Use proportional reasoning and apply indirect measurement techniques, including right triangle trigonometry and properties of similar triangles, to solve

### Geometry Vocabulary Booklet

Geometry Vocabulary Booklet Geometry Vocabulary Word Everyday Expression Example Acute An angle less than 90 degrees. Adjacent Lying next to each other. Array Numbers, letter or shapes arranged in a rectangular

### UNIT PLAN. Big Idea/Theme: Shapes can be analyzed, described, and related to our physical world.

UNIT PLAN Grade Level: 2 Unit #: 5 Unit Name: Geometry Big Idea/Theme: Shapes can be analyzed, described, and related to our physical world. Culminating Assessment: Use real world objects from home, create

### Warning! Construction Zone: Building Solids from Nets

Brief Overview: Warning! Construction Zone: Building Solids from Nets In this unit the students will be examining and defining attributes of solids and their nets. The students will be expected to have

### Linear, Square and Cubic Units Grade Five

Ohio Standards Connection Measurement Benchmark F Analyze and explain what happens to area and perimeter or surface area and volume when the dimensions of an object are changed. Indicator 4 Demonstrate

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

### TargetStrategies 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

### CK-12 Geometry: Exploring Solids

CK-12 Geometry: Exploring Solids Learning Objectives Identify different types of solids and their parts. Use Euler s formula to solve problems. Draw and identify different views of solids. Draw and identify

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

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

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

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

Ohio Standards Connection: Number, Number Sense, and Operations Benchmark G Estimate, compute and solve problems involving real numbers, including ratio, proportion and percent, and explain solutions.

### Implementing the 6 th Grade GPS via Folding Geometric Shapes. Presented by Judy O Neal

Implementing the 6 th Grade GPS via Folding Geometric Shapes Presented by Judy O Neal (joneal@ngcsu.edu) Topics Addressed Nets Prisms Pyramids Cylinders Cones Surface Area of Cylinders Nets A net is a

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

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

### SA B 1 p where is the slant height of the pyramid. V 1 3 Bh. 3D Solids Pyramids and Cones. Surface Area and Volume of a Pyramid

Accelerated AAG 3D Solids Pyramids and Cones Name & Date Surface Area and Volume of a Pyramid The surface area of a regular pyramid is given by the formula SA B 1 p where is the slant height of the pyramid.

### Junior Math Circles March 10, D Geometry II

1 University of Waterloo Faculty of Mathematics Junior Math Circles March 10, 2010 3D Geometry II Centre for Education in Mathematics and Computing Opening Problem Three tennis ball are packed in a cylinder.

### Shape Dictionary YR to Y6

Shape Dictionary YR to Y6 Guidance Notes The terms in this dictionary are taken from the booklet Mathematical Vocabulary produced by the National Numeracy Strategy. Children need to understand and use

### 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

### Grade 7 Mathematics, Quarter 4, Unit 4.1. Probability. Overview

Grade 7 Mathematics, Quarter 4, Unit 4.1 Probability Overview Number of instructional days: 8 (1 day = 45 minutes) Content to be learned Understand how to use counting techniques to solve problems involving

### NCLB Math Institute Summer 2011

NCLB Math Institute Summer 2011 Faculty Name: Glenda Lollis-Hawkins School: Cypress Park Elementary Grade Level: 4 1. Teaching Objective(s): Analyze and describe the similarities and differences between

### Finding Volume of Rectangular Prisms

MA.FL.7.G.2.1 Justify and apply formulas for surface area and volume of pyramids, prisms, cylinders, and cones. MA.7.G.2.2 Use formulas to find surface areas and volume of three-dimensional composite shapes.

### 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

### 5.2. Nets and Solids LESSON. Vocabulary. Explore. Materials

LESSON 5.2 Nets and Solids A net is a flat figure that can be folded to form a closed, three- dimensional object. This type of object is called a geometric solid. Inv 1 Use a Net 229 Inv 2 Use Nets to

### Area of Parallelograms (pages 546 549)

A Area of Parallelograms (pages 546 549) A parallelogram is a quadrilateral with two pairs of parallel sides. The base is any one of the sides and the height is the shortest distance (the length of a perpendicular

### CHAPTER 6 - PRISMS AND ANTIPRISMS

CHAPTER 6 - PRISMS AND ANTIPRISMS Prisms and antiprisms are simple yet attractive constructions, and form an interesting addition to the collection of geometric solids. They can adapt readily to unique

Ohio Standards Connection: Government Benchmark A Identify the responsibilities of the branches of the U.S. government and explain why they are necessary. Indicator 2 Explain the structure of local governments

### 3 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,

### In Problems #1 - #4, find the surface area and volume of each prism.

Geometry Unit Seven: Surface Area & Volume, Practice In Problems #1 - #4, find the surface area and volume of each prism. 1. CUBE. RECTANGULAR PRISM 9 cm 5 mm 11 mm mm 9 cm 9 cm. TRIANGULAR PRISM 4. TRIANGULAR

### Points of Concurrency Related to Archaeology Grade Ten

Ohio Standards Connection: Geometry and Spatial Sense Benchmark A Formally define geometric figures. Indicator 1 Formally define and explain key aspects of geometric figures, including: a. interior and

Ohio Standards Connection Data Analysis and Probability Benchmark F Determine and use the range, mean, median and mode to analyze and compare data, and explain what each indicates about the data. Indicator

### Session 9 Solids. congruent regular polygon vertex. cross section edge face net Platonic solid polyhedron

Key Terms for This Session Session 9 Solids Previously Introduced congruent regular polygon vertex New in This Session cross section edge face net Platonic solid polyhedron Introduction In this session,

### 17.1 Cross Sections and Solids of Rotation

Name Class Date 17.1 Cross Sections and Solids of Rotation Essential Question: What tools can you use to visualize solid figures accurately? Explore G.10.A Identify the shapes of two-dimensional cross-sections

### Polygons and Area. Overview. Grade 6 Mathematics, Quarter 4, Unit 4.1. Number of instructional days: 12 (1 day = minutes)

Grade 6 Mathematics, Quarter 4, Unit 4.1 Polygons and Area Overview Number of instructional days: 12 (1 day = 45 60 minutes) Content to be learned Calculate the area of polygons by composing into rectangles

### Area of Parallelograms, Triangles, and Trapezoids (pages 314 318)

Area of Parallelograms, Triangles, and Trapezoids (pages 34 38) Any side of a parallelogram or triangle can be used as a base. The altitude of a parallelogram is a line segment perpendicular to the base

### Area of a triangle: The area of a triangle can be found with the following formula: 1. 2. 3. 12in

Area Review Area of a triangle: The area of a triangle can be found with the following formula: 1 A 2 bh or A bh 2 Solve: Find the area of each triangle. 1. 2. 3. 5in4in 11in 12in 9in 21in 14in 19in 13in

### Mathematics 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

### 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

### Marie has a winter hat made from a circle, a rectangular strip and eight trapezoid shaped pieces. y inches. 3 inches. 24 inches

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

### Angle - a figure formed by two rays or two line segments with a common endpoint called the vertex of the angle; angles are measured in degrees

Angle - a figure formed by two rays or two line segments with a common endpoint called the vertex of the angle; angles are measured in degrees Apex in a pyramid or cone, the vertex opposite the base; in

### 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

### Activity Set 4. Trainer Guide

Geometry and Measurement of Solid Figures Activity Set 4 Trainer Guide Mid_SGe_04_TG Copyright by the McGraw-Hill Companies McGraw-Hill Professional Development GEOMETRY AND MEASUREMENT OF SOLID FIGURES

### Teaching Guidelines. Knowledge and Skills: Can specify defining characteristics of common polygons

CIRCLE FOLDING Teaching Guidelines Subject: Mathematics Topics: Geometry (Circles, Polygons) Grades: 4-6 Concepts: Property Diameter Radius Chord Perimeter Area Knowledge and Skills: Can specify defining

### Surface Area and Volume

1 Area Surface Area and Volume 8 th Grade 10 days by Jackie Gerwitz-Dunn and Linda Kelly 2 What do you want the students to understand at the end of this lesson? The students should be able to distinguish

### Most classrooms are built in the shape of a rectangular prism. You will probably find yourself inside a polyhedron at school!

3 D OBJECTS Properties of 3 D Objects A 3 Dimensional object (3 D) is a solid object that has 3 dimensions, i.e. length, width and height. They take up space. For example, a box has three dimensions, i.e.

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

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

### Name: Date: Geometry Solid Geometry. Name: Teacher: Pd:

Name: Date: Geometry 2012-2013 Solid Geometry Name: Teacher: Pd: Table of Contents DAY 1: SWBAT: Calculate the Volume of Prisms and Cylinders Pgs: 1-7 HW: Pgs: 8-10 DAY 2: SWBAT: Calculate the Volume of

### Surface Area and Volume Learn it, Live it, and Apply it! Elizabeth Denenberg

Surface Area and Volume Learn it, Live it, and Apply it! Elizabeth Denenberg Objectives My unit for the Delaware Teacher s Institute is a 10 th grade mathematics unit that focuses on teaching students

### Wednesday, February 22 / Thursday, February 23. Student Objective (Obj. 3b) TSW identify three dimensional figures from nets.

Course: 7 th Grade Math DETAIL LESSON PLAN Wednesday, February 22 / Thursday, February 23 Student Objective (Obj. 3b) TSW identify three dimensional figures from nets. Lesson 8-9 Three-Dimensional Figures

### 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

### 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:

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

### 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

### How does one make and support a reasonable conclusion regarding a problem? How does what I measure influence how I measure?

Middletown Public Schools Mathematics Unit Planning Organizer Subject Mathematics Grade/Course Grade 7 Unit 3 Two and Three Dimensional Geometry Duration 23 instructional days (+4 days reteaching/enrichment)

### Perimeter, 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

### Begin recognition in EYFS Age related expectation at Y1 (secure use of language)

For more information - http://www.mathsisfun.com/geometry Begin recognition in EYFS Age related expectation at Y1 (secure use of language) shape, flat, curved, straight, round, hollow, solid, vertexvertices

### Stage 3 Outcome Language Teaching and Learning Activities Notes/ Future Directions/Evaluation Date Ignition Activities Barrier Game.

Stage 3 Outcome A student: describes and represents mathematical situations in a variety of ways using mathematical terminology and some conventions MA3-1WM identifies three-dimensional objects, including

### To Be or Not to Be Democratic Grade Seven

Ohio Standards Connection: Government Benchmark C Compare the defining characteristics of democracies, monarchies and dictatorships. Indicator 1 Compare direct and representative democracy using examples

### 12 Surface Area and Volume

12 Surface Area and Volume 12.1 Three-Dimensional Figures 12.2 Surface Areas of Prisms and Cylinders 12.3 Surface Areas of Pyramids and Cones 12.4 Volumes of Prisms and Cylinders 12.5 Volumes of Pyramids

### IWITNESS NEWS: BREAKING IN TO GEOMETRY ASHLEY BAILEY, BEAR CREEK MIDDLE SCHOOL

IWITNESS NEWS: BREAKING IN TO GEOMETRY ASHLEY BAILEY, BEAR CREEK MIDDLE SCHOOL Unit Overview In this interactive geometry unit, students work in differentiated groups to master finding the area and volume

### Packaging Engineering

Project Packaging Engineering Objectives To use nets to represent and calculate the surface area of 3-dimensional shapes; and to apply concepts of area, surface area, and volume to design a package for

### Performance Based Learning and Assessment Task A Day at the Beach! I. ASSESSSMENT TASK OVERVIEW & PURPOSE: The goal of this activity is to calculate

Performance Based Learning and Assessment Task A Day at the Beach! I. ASSESSSMENT TASK OVERVIEW & PURPOSE: The goal of this activity is to calculate volume and complete problems involving volume and rate.

### Perfume 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 cost-efficient box. The Persuasive perfume bottle is in the shape of a regular hexagonal prism 10 centimeters

### Super Sort - Kindergarten

Ohio Standards Connection Patterns, Functions and Algebra Benchmark A Sort, classify and order objects by size number and other properties, and describe the attributes used. Indicator 1 Sort, classify

### 6 th Grade New Mexico Math Standards

Strand 1: NUMBER AND OPERATIONS Standard: Students will understand numerical concepts and mathematical operations. 5-8 Benchmark 1: Understand numbers, ways of representing numbers, relationships among

### MATHEMATICS Grade 6 Standard: Number, Number Sense and Operations

Standard: Number, Number Sense and Operations Number and Number C. Develop meaning for percents including percents greater than 1. Describe what it means to find a specific percent of a number, Systems

Ohio Standards Connection Geometry and Spatial Sense Benchmark C Specify locations and plot ordered pairs on a coordinate plane. Indicator 6 Extend understanding of coordinate system to include points

### Natural Beauty. 6 th Grade. Module Overview. Module Purpose. Module Outline. Module Prerequisite Skills & Concepts

Natural Beauty 6 th Grade Duration 2 4 classes (depending on length of class) and a Museum visit Location Gem & Mineral Hall Supplies See individual lessons Standards CCS Math 6.G.1.2.4.5. Visual Art 6.2.1.2.3.4

### 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

### A Teacher Resource Package for the Primary Grades

A Teacher Resource Package for the Primary Grades Notes for Teachers: These are intended to be a starting point to help your class apply what they have learned in the Geometry and Spatial Sense strand

### 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

### Main Idea in Informational Text Grade Three

Ohio Standards Connection Informational, Technical and Persuasive Text Benchmark C Identify the central ideas and supporting details of informational text. Indicator 3 Identify and list the important central

### 3D shapes. Level A. 1. Which of the following is a 3-D shape? A) Cylinder B) Octagon C) Kite. 2. What is another name for 3-D shapes?

Level A 1. Which of the following is a 3-D shape? A) Cylinder B) Octagon C) Kite 2. What is another name for 3-D shapes? A) Polygon B) Polyhedron C) Point 3. A 3-D shape has four sides and a triangular

### SOLID SHAPES M.K. HOME TUITION. Mathematics Revision Guides Level: GCSE Higher Tier

Mathematics Revision Guides Solid Shapes Page 1 of 19 M.K. HOME TUITION Mathematics Revision Guides Level: GCSE Higher Tier SOLID SHAPES Version: 2.1 Date: 10-11-2015 Mathematics Revision Guides Solid

### CC Investigation 4: Measurement

Content Standards 6.G., 6.G. CC Investigation : Measurement Mathematical Goals At a Glance PACING 3 days DOMAIN: Geometry Find the volume of a right rectangular prism with fractional edge lengths by packing

### Area, 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

### Geometry Project. A 5 th Grade Unit. Cadie Fairchild Dan Fairchild Red Lake Elementary

Geometry Project A 5 th Grade Unit Cadie Fairchild Fairchild@redlake.k12.mn.us Dan Fairchild dfairch@redlak.k12.mn.u s Red Lake Elementary Executive Summary In our unit, we will be spending our time on

Ohio Standards Connection: Economics Benchmark A Explain the opportunity costs involved in the allocation of scarce productive resources. Indicator 1 Define opportunity cost and give an example of the

### 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

### Every 3-dimensional shape has three measurements to describe it: height, length and width.

Every 3-dimensional shape has three measurements to describe it: height, length and width. Height Width Length Faces A face is one of the flat sides of a three-dimensional shape. Faces A cuboid has 6 flat

### Geometry and Measurement

Geometry and Measurement (Developmentally Appropriate Lessons for K-5 Students) Amanda Anderson Title I Teacher Lincoln Elementary aanderson@bemidji.k12.mn.us Executive Summary This 10-day unit plan is

### 12-8 Congruent and Similar Solids

Determine whether each pair of solids is similar, congruent, or neither. If the solids are similar, state the scale factor. Ratio of radii: Ratio of heights: The ratios of the corresponding measures are

### Teaching Mathematics Vocabulary Using Hands-On Activities From an MSP Grant Summer Institute

Teaching Mathematics Vocabulary Using Hands-On Activities From an MSP Grant Summer Institute Dr. Carroll G. Wells (Co-authors: Dr. Randy Bouldin, Dr. Ben Hutchinson, Dr. Candice McQueen) Department of

### 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

### 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)

Ohio Standards Connection Reading Applications: Literary Text Benchmark C Identify the elements of plot and establish a connection between an element and a future event. Indicator 3 Identify the main incidents