Carroll County Public Schools Elementary Mathematics Instructional Guide (5 th Grade) AugustSeptember (12 days) Unit #1 : Geometry


 Oscar Alexander
 2 years ago
 Views:
Transcription
1 Carroll County Public Schools Elementary Mathematics Instructional Guide (5 th Grade) Common Core and Research from the CCSS Progression Documents Geometry Students learn to analyze and relate categories of twodimensional and threedimensional shapes explicitly based on their properties.5.g.4 Based on analysis of properties, they classify twodimensional figures in hierarchies. For example, they conclude that all rectangles are parallelograms, because they are all quadrilaterals with two pairs of opposite, parallel, equallength sides (MP3). In this way, they relate certain categories of shapes as subclasses of other categories.5.g.3 This leads to understanding propagation of properties; for example, students understand that squares possess all properties of rhombuses and of rectangles. Therefore, if they then show that rhombuses diagonals are perpendicular bisectors of one another, they infer that squares diagonals are perpendicular bisectors of one another as well. Note that in the U.S., that the term trapezoid has two different meanings: T(E)exclusive and T(I) inclusive T(E): a trapezoid is a quadrilateral with exactly one pair of parallel sides T(I): a trapezoid is a quadrilateral with at least one pair of parallel sides. These different meanings result in different classifications. According to T(E), a parallelogram is not a trapezoid; according to T(I), a parallelogram is a trapezoid. Both definitions are legitimate; however; when teaching trapezoids to 4 th and 5 th graders, we will use the inclusive definition since most college bound textbooks and PARCC use the inclusive definition. A note about research The ability to describe, use, and visualize the effects of composing and decomposing geometric regions is significant in that the concepts and actions of creating and then iterating units and higherorder units in the context of constructing patterns, measurin g, and computing are established bases for mathematical understanding and analysis. Additionally, there is suggestive evidence that this type of composition corresponds with, and may support, children s ability to compose and decompose numbers. Coordinate Planes Students extend their Grade 4 pattern work by working briefly with two numerical patterns that can be related and examining these relationships within sequences of ordered pairs and in the graphs in the first quadrant of the coordinate plane. 5.OA.3 This work prepares students for studying proportional relationships and functions in middle school. Fifth grade students extend their knowledge of the coordinate plane, understanding the continuous nature of twodimensional space and the role of fractions in specifying locations in that space. Thus, spatial structuring underlies coordinates for the plane as well, and students learn both to apply it and to distinguish the objects that are structured. For example, they learn to interpret the components of a rectangular grid structure as line segments or lines (rather than regions) and understand the precision of location that these lines require, rather than treating them as fuzzy boundaries or indicators of intervals. Students learn to reconstruct the levels of counting and quantification that they had already constructed in the domain of discrete objects to the coordination of (at first) two continuous linear measures. That is, they learn to apply their knowledge of number and length to the order and distance relationships of a coordinate grid and to coordinate this across two dimensions. 5.G.1 1
2 Carroll County Public Schools Elementary Mathematics Instructional Guide (5 th Grade) Although students can often locate a point, these understandings are beyond simple skills. For example, initially, students often fail to distinguish between two different ways of viewing the point (2, 3), say, as instructions: right 2, up 3 ; and as the point defined by being a distance 2 from the xaxis and a distance 3 from the yaxis. In these two descriptions the 2 is first associated with the xaxis, then with the yaxis. They connect ordered pairs of (whole number) coordinates to points on the grid, so that these coordinate pairs constitute numerical objects and ultimately can be operated upon as single mathematical entities. Students solve mathematical and realworld problems using coordinates. For example, they plan to draw a symmetric figure using computer software in which students input coordinates that are then connected by line segments. 5.G.2 Progressions for the Common Core State Standards in Mathematics (draft) Commoncoretools.wordpress.com 2
3 Carroll County Public Schools Elementary Mathematics Instructional Guide (5 th Grade) The chart below highlights the key understandings of this cluster along with important questions that teachers should pose to promote these understandings. The chart also includes key vocabulary that should be modeled by teachers and used by students to show precision of language when communicating mathematically. Enduring Understandings Essential Questions Key Vocabulary TwoDimensional figures are classified by their properties. TwoDimensional figures can fit into more than one category. Identify and describe properties of twodimensional figures more precisely. Graphical representations can be used to make predications and interpretations about real world situations. How can plane figures be categorized and classified? What is a quadrilateral? What are the properties of quadrilaterals? How can you classify different types of quadrilaterals? How are quadrilaterals alike and different? How can angle and side measures help us to create and classify triangles? Why are some quadrilaterals classified as parallelograms? Why is a square always a rectangle? What are ways to classify triangles? Where is geometry found in your everyday world? How does the coordinate system work? How do coordinate grids help you organize information? The terms below are for teacher reference only and are not to be memorized by the students. Teachers should present these concepts to students with models and real life examples. Students should understand the concepts involved and be able to recognize and/or demonstrate them with words, models, pictures, or numbers. Geometry acute angle acute triangle circle congruence/congruent equilateral triangle half circle/semicircle hexagon irregular polygon isosceles triangle kite obtuse angle parallel lines parallelogram pentagon perpendicular lines plane figure polygon quadrilateral rectangle regular polygon right angle right triangle rhombus/rhombi scalene triangle square triangle trapezoid twodimensional vertex Coordinate Planes Coordinate system Coordinate plane First quadrant Points Lines Axis/Axes xaxis yaxis Horizontal Vertical Intersection of lines Origin Ordered Pairs Coordinates xcoordinate ycoordinate 3
4 Carroll County Public Schools Elementary Mathematics Instructional Guide (5 th Grade) Throughout this cluster, students will develop their use of the 8 Mathematical Practices while learning the instructional standards. Specific connections to this cluster and instructional strategies are provided in the following chart. Standards for Mathematical Practice 1. Make sense of problems and persevere in solving them Cluster Connections and Instructional Strategies Students make sense of problems involving twodimensional figures based on their geometric properties. Students make sense of solving real world problems involving points on the coordinate plane. 2. Reason abstractly and quantitatively Students demonstrate abstract reasoning about rational relationships among geometric properties. Students go beyond simple recognition to an analysis of the properties and how they interrelate. Students demonstrate abstract reasoning about ordered pairs with their visual representations. 3. Construct viable arguments and critique the reasoning of others Students construct and critiques arguments regarding their knowledge of triangles and the ability to belong to one or more of the categories and subcategories. Students construct and critique arguments regarding patterns and relationship of ordered pairs as they are plotted on a coordinate plane to represent realworld contexts. 4. Model with mathematics Students use tables to identify and draw all three types of triangles comparing their attributes in mathematical and realworld contexts. Students use the coordinate plane to compare two numbers in mathematical and realworld contexts. 5. Use appropriate tools strategically Students select and use tools such as tables and the quadrilateral hierarchy to represent situations involving the categories and subcategories of twodimensional figures. Students select and use tools such as number line models and the coordinate plane to represent situations involving positive numbers. 6. Attend to precision Students attend to the geometric precision when classifying twodimensional figures in the hierarchy. Students attend to the language of realworld situations to determine how far to travel from the origin and the given direction of the coordinates being represented. 7. Look for and make use of structure Students relate the attributes belonging to a category of twodimensional figures also belong to all subcategories of that category. Students relate the structure of number lines to values of positive integers as they use the coordinate plane. 8. Look for and express regularity in repeated reasoning Students relate new experiences to experiences with similar contexts when studying the hierarchy of polygons based on properties. Students relate new experiences to experiences with similar contexts when studying positive representations of distance and quantity. 4
5 Classify twodimensional figures into categories based on their properties. Carroll County Public Schools Elementary Mathematics Instructional Guide (5 th Grade) Maryland College and Career Ready Standards 5.G.3 Understand that attributes belonging to a category of twodimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. SMP.3 Construct viable arguments and critique the reasoning of others SMP.7 Look for and make use of structure SMP.5 Use appropriate tools strategically Instructional Strategies and Resource Support This standard calls for students to reason about the attributes (properties) of shapes. Student should have experiences discussing the property of shapes and reasoning. Example: Examine whether all quadrilaterals have right angles. Give examples and nonexamples. Example: If the opposite sides on a parallelogram are parallel and congruent, then rectangles are parallelograms A sample of questions that might be posed to students include: A parallelogram has 4 sides with both sets of opposite sides parallel. What types of quadrilaterals are parallelograms? Regular polygons have all of their sides and angles congruent. Name or draw some regular polygons. All rectangles have 4 right angles. Squares have 4 right angles so they are also rectangles. True or False? A trapezoid has 2 sides parallel so it must be a parallelogram. True or False? Use tangrams to have students make shapes using a designated number of tangram pieces. For example: make a square, rectangle, trapezoid and a parallelogram by using 3 tangram pieces for each. Which of the figures can you make using only 2 tangram pieces? Make quadrilaterals using Geoboards. Record several on dot paper. Have students bring the dot paper quadrilaterals to small group instruction and use them to sort the quadrilaterals by different attributes or properties. Teaching StudentCentered Mathematics (Grades 35) pg. 212 Shape Sorts  Activity 8.1 (BLMs 2026) pg. 213 What's My Shape  Activity 8.2 pg. 214 Constructing & Dissecting Shapes (BLM 27) pg. 217 *Can You Make It  Activity 8.5 pg. 221 Categories of TwoDimensional Shapes  Table 8.1 Students make use of structure to build a logical progression of statements and explore hierarchical relationships among 2dimensional shapes (SMP.3, SMP.7) Sample Formatives What property do they have in common? Name each shape. Explain how the two shapes are alike and how they are different. Use the Geoboards to draw two different quadrilaterals. Name each of the quadrilaterals. Compare the properties of the quadrilaterals you drew. Complete the table by placing Xs in each column to indicate properties of each figure. 5
6 Classify twodimensional figures into categories based on their properties. Carroll County Public Schools Elementary Mathematics Instructional Guide (5 th Grade) Maryland College and Career Ready Standards 5.G.4. Classify twodimensional figures in a hierarchy based on properties. SMP.3 Construct viable arguments and critique the reasoning of others Instructional Strategies and Resource Support Figures from previous grades: polygon, rhombus/rhombi, rectangle, square, triangle, quadrilateral, pentagon, hexagon, cube, trapezoid, half/quarter circle, circle Example: Create a Hierarchy Diagram using the following terms: polygons a closed plane figure formed from line segments that meet only at their endpoints. quadrilaterals  a foursided polygon. parallelogram a quadrilateral with two pairs of parallel and congruent sides. rectangle a quadrilateral with two pairs of congruent, parallel sides and four right angles. rhombus a parallelogram with all four sides equal in length. square a parallelogram with four congruent sides and four right angles. trapezoida quadrilateral with at least one pair of parallel sides. Sample Formatives Put the labels from the word box in the appropriate box to make the diagram true. SMP.7 Look for and make use of structure SMP.5 Use appropriate tools strategically Student should be able to reason about the attribute/properties of shapes by examining: What are ways to classify triangles? Which quadrilaterals have opposite angles congruent and why is this true of certain quadrilaterals? How many lines of symmetry does a regular polygon have? Why can t all rectangles be classified as squares? Teaching StudentCentered Mathematics (Grades 35) pg. 222 Figure 8.11 (Bottom figure) pg. 225 Triangle Sort  Activity 8.7 (BLM 29) pg. 226 Property Lists for Quadrilaterals Activity 8.8 (BLM 3033) pg. 227 Diagonal Strips  Activity 8.9, *Figure 8.16 pg. 230 Minimal Defining Lists  Activity 8.11 pg. 231 True or False  Activity 8.12 Students make use of structure to build a logical progression of statements and explore hierarchical relationships among 2dimensional shapes (MP.3, MP.7) 6
7 Graph points on the coordinate plane to solve realworld and mathematical problems. Carroll County Public Schools Elementary Mathematics Instructional Guide (5 th Grade) Maryland College and CareerReady Standards Instructional Strategies and Resource Support Sample Formatives 5.G.1. Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x axis and xcoordinate, yaxis and y coordinate). TSCMpage G.1 and 5.G.2 These standards deal with only the first quadrant (positive numbers) in the coordinate plane. Although students can often locate a point, these understandings are beyond simple skills. For example, initially, students often fail to distinguish between two different ways of viewing the point (2, 3), say, as instructions: right 2, up 3 ; and as the point defined by being a distance 2 from the yaxis and a distance 3 from the xaxis. In these two descriptions the 2 is first associated with the xaxis, then with the yaxis. Plot the ordered pairs on the coordinate plane. Label the points as indicated. 5.G.2. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. SMP.6 Attend to precision SMP.4 Model with mathematics SMP.2 Reason abstractly and quantitatively SMP.5 Use appropriate tools strategically Students precisely describe the coordinate of points and the relationship of the coordinate plane to the number line (SMP.6). Students both generate and identify relationship in numerical patterns, using the coordinate plane as a way of representing these relationship and patterns (SMP.4) 7
8 Graph points on the coordinate plane to solve realworld and mathematical problems. Carroll County Public Schools Elementary Mathematics Instructional Guide (5 th Grade) Maryland College and CareerReady Standards 5.G.2. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. SMP.6 Attend to precision SMP.4 Model with mathematics SMP.5 Use appropriate tools strategically SMP.1 Make sense of problems and persevere in solving them Instructional Strategies and Resource Support This standard references realworld and mathematical problems, including the traveling from one point to another and identifying the coordinates of missing points in geometric figures, such as squares, rectangles, and parallelograms. Example 1: Students precisely describe the coordinate of points and the relationship of the coordinate plane to the number line (SMP.6). Students both generate and identify relationship in numerical patterns, using the coordinate plane as a way of representing these relationship and patterns (SMP.4) Sample Formatives Plot the following points on the coordinate grid. Plot a fourth point on the grid to form a rectangle with all 4 point are connected. Write the coordinates for the point you plotted. 8
Featured Mathematical Practice: MP.5. Use appropriate tools strategically. MP.6. Attend to precision.
Domain: Geometry 4.G Mathematical Content Standard: 1. Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in twodimensional figures.
More informationacute angle acute triangle Cartesian coordinate system concave polygon congruent figures
acute angle acute triangle Cartesian coordinate system concave polygon congruent figures convex polygon coordinate grid coordinates dilatation equilateral triangle horizontal axis intersecting lines isosceles
More informationLine. A straight path that continues forever in both directions.
Geometry Vocabulary Line A straight path that continues forever in both directions. Endpoint A point that STOPS a line from continuing forever, it is a point at the end of a line segment or ray. Ray A
More information1 st Grade Mathematics
1 st Grade Mathematics Unit # 5: Composing and Partitioning Shapes/Time Pacing: 15 days Unit Overview 1 In lessons 13, students identify the defining parts, or attributes, of two and threedimensional
More informationGeometry 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
More informationRectangular Prisms Dimensions
Rectangular Prisms Dimensions 5 Rectangular prisms are (3D) threedimensional figures, which means they have three dimensions: a length, a width, and a height. The length of this rectangular prism is
More informationCalifornia Common Core State Standards Comparison FOURTH GRADE
1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others 4. Model with mathematics. Standards
More informationGrade 5 Math Curriculum Guide
Grade 5 Math Curriculum Guide Lesson 1 1 st Nine Weeks Unit 1: Number and Operations in Base Ten Understand Place Value 5.NBT.1. Recognize that in a multidigit number, a digit in one place represents
More informationCONSTRUCTING TASK: SHAPE SORTER Adapted from Activity 8.1 in Teaching Student Centered Mathematics 35, by John Van de Walle and LouAnn Lovin
CONSTRUCTING TASK: SHAPE SORTER Adapted from Activity 8.1 in Teaching Student Centered Mathematics 35, by John Van de Walle and LouAnn Lovin STANDARDS FOR MATHEMATICAL CONTENT MCC3.G.1 Understand that
More information*1. Derive formulas for the area of right triangles and parallelograms by comparing with the area of rectangles.
Students: 1. Students understand and compute volumes and areas of simple objects. *1. Derive formulas for the area of right triangles and parallelograms by comparing with the area of rectangles. Review
More informationUnit 6 Grade 7 Geometry
Unit 6 Grade 7 Geometry Lesson Outline BIG PICTURE Students will: investigate geometric properties of triangles, quadrilaterals, and prisms; develop an understanding of similarity and congruence. Day Lesson
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 informationProblem of the Month The Shape of Things
Problem of the Month The Problems of the Month (POM) are used in a variety of ways to promote problem solving and to foster the first standard of mathematical practice from the Common Core State Standards:
More informationGrade 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
More information7. 6 Justifying Constructions
31 7. 6 Justifying Constructions A Solidify Understanding Task CC BY THOR https://flic.kr/p/9qkxv Compass and straightedge constructions can be justified using such tools as: the definitions and properties
More informationGeometry of 2D Shapes
Name: Geometry of 2D Shapes Answer these questions in your class workbook: 1. Give the definitions of each of the following shapes and draw an example of each one: a) equilateral triangle b) isosceles
More informationConstructing Symmetrical Shapes
07NEM5WBAnsCH07 7/20/04 4:36 PM Page 62 1 Constructing Symmetrical Shapes 1 Construct 2D shapes with one line of symmetry A line of symmetry may be horizontal or vertical 2 a) Use symmetry to complete
More informationConsolidation of Grade 6 EQAO Questions Geometry and Spatial Sense
Consolidation of Grade 6 EQAO Questions Geometry and Spatial Sense Compiled by Devika WilliamYu (SE2 Math Coach) Overall Expectations GV1 Classify and construct polygons and angles GV2 GV3 Sketch threedimensional
More informationInvestigating Quadrilaterals Grade Four
Ohio Standards Connection Geometry and Spatial Sense Benchmark A Provide rationale for groupings and comparisons of twodimensional figures and threedimensional objects. Indicator 3 Identify similarities
More informationMATHEMATICS 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
More informationGrade 3 Core Standard III Assessment
Grade 3 Core Standard III Assessment Geometry and Measurement Name: Date: 3.3.1 Identify right angles in twodimensional shapes and determine if angles are greater than or less than a right angle (obtuse
More informationMathematics Grade 5 Year in Detail (SAMPLE)
Unit 1 Unit 2 Unit 3 Unit 4 Unit 5 Unit 6 Unit 7 Unit 8 Unit 9 Unit 10 Whole number operations Place value with decimals Add and Subtract Decimals Add and Subtract Fractions Multiply and Divide Decimals
More informationClassifying 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
More information39 Symmetry of Plane Figures
39 Symmetry of Plane Figures In this section, we are interested in the symmetric properties of plane figures. By a symmetry of a plane figure we mean a motion of the plane that moves the figure so that
More informationProgressions for the Common Core State Standards in Mathematics (draft)
Progressions for the Common Core State Standards in Mathematics (draft) cthe Common Core Standards Writing Team 23 June 2012 1 K 6, Geometry Overview Like core knowledge of number, core geometrical knowledge
More information11.3 Curves, Polygons and Symmetry
11.3 Curves, Polygons and Symmetry Polygons Simple Definition A shape is simple if it doesn t cross itself, except maybe at the endpoints. Closed Definition A shape is closed if the endpoints meet. Polygon
More informationGeometry Is A Verb: Making Elementary School Geometry Come Alive
Geometry Is A Verb: Making Elementary School Geometry Come Alive Tad Watanabe Kennesaw State University twatanab@kennesaw.edu http://science.kennesaw.edu/~twatanab/geometry.pdf Geometry: NCTM Focal Points
More informationPerformance 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
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 informationShape and Space. General Curriculum Outcome E: Students will demonstrate spatial sense and apply geometric concepts, properties and relationships.
Shape and Space General Curriculum Outcome E: Students will demonstrate spatial sense and apply geometric concepts, properties and relationships. Elaboration Instructional Strategies/Suggestions KSCO:
More informationEstimating Angle Measures
1 Estimating Angle Measures Compare and estimate angle measures. You will need a protractor. 1. Estimate the size of each angle. a) c) You can estimate the size of an angle by comparing it to an angle
More informationGrade 3 Unit 7 Geometry and Measurement Mathematics
Number of Days: 18 Unit Goals Stage 1 Traditional: April 27 May 20; Track B: June 8 July 1 (17 days) Unit Description: In Unit 7 the students reason with shapes and their attributes, including perimeter
More informationMath 6: Unit 7: Geometry Notes 2Dimensional Figures
Math 6: Unit 7: Geometry Notes Dimensional Figures Prep for 6.G.A.1 Classifying Polygons A polygon is defined as a closed geometric figure formed by connecting line segments endpoint to endpoint. Polygons
More information37 Basic Geometric Shapes and Figures
37 Basic Geometric Shapes and Figures In this section we discuss basic geometric shapes and figures such as points, lines, line segments, planes, angles, triangles, and quadrilaterals. The three pillars
More informationFinding Parallelogram Vertices
About Illustrations: Illustrations of the Standards for Mathematical Practice (SMP) consist of several pieces, including a mathematics task, student dialogue, mathematical overview, teacher reflection
More informationBegin 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
More informationThird Grade Common Core Standards & Learning Targets
Third Grade Common Core Standards & Learning Targets CCS Standards: Operations and Algebraic Thinking 3.OA.1. Interpret products of whole numbers, e.g., interpret 5 7 as the total number of objects in
More informationE XPLORING QUADRILATERALS
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
More informationGrade 4  Module 4: Angle Measure and Plane Figures
Grade 4  Module 4: Angle Measure and Plane Figures Acute angle (angle with a measure of less than 90 degrees) Angle (union of two different rays sharing a common vertex) Complementary angles (two angles
More information100 Math Facts 6 th Grade
100 Math Facts 6 th Grade Name 1. SUM: What is the answer to an addition problem called? (N. 2.1) 2. DIFFERENCE: What is the answer to a subtraction problem called? (N. 2.1) 3. PRODUCT: What is the answer
More informationA 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
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 informationState whether the figure appears to have line symmetry. Write yes or no. If so, copy the figure, draw all lines of symmetry, and state their number.
State whether the figure appears to have line symmetry. Write yes or no. If so, copy the figure, draw all lines of symmetry, and state their number. esolutions Manual  Powered by Cognero Page 1 1. A figure
More informationGeometry Module 4 Unit 2 Practice Exam
Name: Class: Date: ID: A Geometry Module 4 Unit 2 Practice Exam Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Which diagram shows the most useful positioning
More informationUnit 3: Triangle Bisectors and Quadrilaterals
Unit 3: Triangle Bisectors and Quadrilaterals Unit Objectives Identify triangle bisectors Compare measurements of a triangle Utilize the triangle inequality theorem Classify Polygons Apply the properties
More informationMathematics Task Arcs
Overview of Mathematics Task Arcs: Mathematics Task Arcs A task arc is a set of related lessons which consists of eight tasks and their associated lesson guides. The lessons are focused on a small number
More informationArchdiocese of Washington Catholic Schools Academic Standards Mathematics
5 th GRADE Archdiocese of Washington Catholic Schools Standard 1  Number Sense Students compute with whole numbers*, decimals, and fractions and understand the relationship among decimals, fractions,
More informationSHAPE, SPACE AND MEASURES
SHPE, SPCE ND MESURES Pupils should be taught to: Understand and use the language and notation associated with reflections, translations and rotations s outcomes, Year 7 pupils should, for example: Use,
More informationparallel lines perpendicular lines intersecting lines vertices lines that stay same distance from each other forever and never intersect
parallel lines lines that stay same distance from each other forever and never intersect perpendicular lines lines that cross at a point and form 90 angles intersecting lines vertices lines that cross
More informationCollegium Charter School Grade 5 Math Scope & Sequence. Global Vision. We Use Math in Our Everyday Lives
Collegium Charter School Grade 5 Math Scope & Sequence Global Vision We Use Math in Our Everyday Lives Updated August 2015 Standards of Mathematical Practice (Habits of Mind) in 5th grade: 1. Make sense
More informationCOORDINATE GEOMETRY AND TRANSFORMATIONS
COORDINATE GEOMETRY AND TRANSFORMATIONS i 2 t 2 Final Project 5Day Unit Plan 8 th Grade Math Lab Helen Roseler December 1, 2003 1 Preface Math Lab is an additional math class designed to deliver Academic
More informationOverview Mathematical Practices Congruence
Overview Mathematical Practices Congruence 1. Make sense of problems and persevere in Experiment with transformations in the plane. solving them. Understand congruence in terms of rigid motions. 2. Reason
More informationGeometry Progress Ladder
Geometry Progress Ladder Maths Makes Sense Foundation Endofyear objectives page 2 Maths Makes Sense 1 2 Endofblock objectives page 3 Maths Makes Sense 3 4 Endofblock objectives page 4 Maths Makes
More informationAnalysis in Geometry. By Danielle Long. Grade Level: 8 th. Time: 550 minute periods. Technology used: Geometer s sketchpad Geoboards NLVM website
Analysis in Geometry By Danielle Long Grade Level: 8 th Time: 550 minute periods Technology used: Geometer s sketchpad Geoboards NLVM website 1 NCTM Standards Addressed Problem Solving Geometry Algebra
More information4 Mathematics Curriculum
Common Core 4 Mathematics Curriculum G R A D E GRADE 4 MODULE 4 Table of Contents GRADE 4 MODULE 4 Angle Measure and Plane Figures Module Overview... i Topic A: Lines and Angles... 4.A.1 Topic B: Angle
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 informationDate: Period: Symmetry
Name: Date: Period: Symmetry 1) Line Symmetry: A line of symmetry not only cuts a figure in, it creates a mirror image. In order to determine if a figure has line symmetry, a figure can be divided into
More informationLesson 1: Exploring Polygons
Lesson 1: Exploring Polygons Objectives: Students will be able to identify whether a given shape is a polygon using the properties of polygons. Students will be able to identify and name polygons that
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 informationSession 7 Symmetry. coordinates reflection rotation translation
Key Terms for This Session Session 7 Symmetry Previously Introduced coordinates reflection rotation translation New in This Session: frieze pattern glide reflection reflection or line symmetry rotation
More informationascending order decimal denominator descending order Numbers listed from largest to smallest equivalent fraction greater than or equal to SOL 7.
SOL 7.1 ascending order Numbers listed in order from smallest to largest decimal The numbers in the base 10 number system, having one or more places to the right of a decimal point denominator The bottom
More informationClassifying 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
More informationCoordinate Coplanar Distance Formula Midpoint Formula
G.(2) Coordinate and transformational geometry. The student uses the process skills to understand the connections between algebra and geometry and uses the oneand twodimensional coordinate systems to
More informationCentroid: The point of intersection of the three medians of a triangle. Centroid
Vocabulary Words Acute Triangles: A triangle with all acute angles. Examples 80 50 50 Angle: A figure formed by two noncollinear rays that have a common endpoint and are not opposite rays. Angle Bisector:
More informationUnit 6 Grade 7 Geometry
Unit 6 Grade 7 Geometry Lesson Outline BIG PICTURE Students will: investigate geometric properties of triangles, quadrilaterals, and prisms; develop an understanding of similarity and congruence. Day Lesson
More informationShape 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
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 information4TH GRADE FIRST QUARTER MATHEMATICS STANDARDS. Vocabulary. answers using mental computation and estimation strategies including rounding.
4TH GRADE FIRST QUARTER MATHEMATICS STANDARDS Critical Area: Developing understanding and fluency with multidigit multiplication, and developing understanding of dividing to find quotients involving multidigit
More information35 Mathematics Common Core State Standards Grouped by Domains
Domain: Operations and Algebraic Thinking Third: Understand properties of multiplication and the relationship between multiplication and division. operation, multiply, divide, factor, product, quotient,
More informationMA.7.G.4.2 Predict the results of transformations and draw transformed figures with and without the coordinate plane.
MA.7.G.4.2 Predict the results of transformations and draw transformed figures with and without the coordinate plane. Symmetry When you can fold a figure in half, with both sides congruent, the fold line
More informationMath Common Core Standards Fourth Grade
Operations and Algebraic Thinking (OA) Use the four operations with whole numbers to solve problems. OA.4.1 Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 7 as a statement
More informationUnit Background. Stage 1: Big Goals
Course: 7 th Grade Mathematics Unit Background Unit Title Angle Relationships, Transversals & 3Dimensional Geometry Does the unit title reflect the standards? PCCMS Unit Reviewer (s): Unit Designer: Resources
More informationCOMMON CORE STATE STANDARDS FOR MATHEMATICS 35 DOMAIN PROGRESSIONS
COMMON CORE STATE STANDARDS FOR MATHEMATICS 35 DOMAIN PROGRESSIONS Compiled by Dewey Gottlieb, Hawaii Department of Education June 2010 Operations and Algebraic Thinking Represent and solve problems involving
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 informationGeometry and Measurement
The student will be able to: Geometry and Measurement 1. Demonstrate an understanding of the principles of geometry and measurement and operations using measurements Use the US system of measurement for
More informationTarget To know the properties of a rectangle
Target To know the properties of a rectangle (1) A rectangle is a 3D shape. (2) A rectangle is the same as an oblong. (3) A rectangle is a quadrilateral. (4) Rectangles have four equal sides. (5) Rectangles
More informationInteractive Math Glossary Terms and Definitions
Terms and Definitions Absolute Value the magnitude of a number, or the distance from 0 on a real number line Additive Property of Area the process of finding an the area of a shape by totaling the areas
More informationGeometry. Unit 6. Quadrilaterals. Unit 6
Geometry Quadrilaterals Properties of Polygons Formed by three or more consecutive segments. The segments form the sides of the polygon. Each side intersects two other sides at its endpoints. The intersections
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 informationYear 1 Maths Expectations
Times Tables I can count in 2 s, 5 s and 10 s from zero. Year 1 Maths Expectations Addition I know my number facts to 20. I can add in tens and ones using a structured number line. Subtraction I know all
More informationof surface, 569571, 576577, 578581 of triangle, 548 Associative Property of addition, 12, 331 of multiplication, 18, 433
Absolute Value and arithmetic, 730733 defined, 730 Acute angle, 477 Acute triangle, 497 Addend, 12 Addition associative property of, (see Commutative Property) carrying in, 11, 92 commutative property
More informationGeometry. Higher Mathematics Courses 69. Geometry
The fundamental purpose of the course is to formalize and extend students geometric experiences from the middle grades. This course includes standards from the conceptual categories of and Statistics and
More informationGeorgia Standards of Excellence Curriculum Frameworks. Mathematics. GSE Fifth Grade Unit 5: 2D Figures
Georgia Standards of Excellence Curriculum Frameworks GSE Fifth Grade Unit 5: 2D Figures Mathematics These materials are for nonprofit educational purposes only. Any other use may constitute copyright
More informationAlgebra Geometry Glossary. 90 angle
lgebra Geometry Glossary 1) acute angle an angle less than 90 acute angle 90 angle 2) acute triangle a triangle where all angles are less than 90 3) adjacent angles angles that share a common leg Example:
More informationVocabulary List Geometry Altitude the perpendicular distance from the vertex to the opposite side of the figure (base)
GEOMETRY Vocabulary List Geometry Altitude the perpendicular distance from the vertex to the opposite side of the figure (base) Face one of the polygons of a solid figure Diagonal a line segment that
More informationPrairieHills Elementary School District 144 Kindergarten ~ MATH Curriculum Map
Quarter 1 PrairieHills Elementary School District 144 Kindergarten ~ MATH Curriculum Map Domain(s): Counting and Cardinality Geometry Cluster(s): Identify and describe shapes (squares, circles, triangles,
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 informationProperties of Polygons Objective To explore the geometric properties of polygons.
Properties of Polygons Objective To explore the geometric properties of polygons. www.everydaymathonline.com epresentations etoolkit Algorithms Practice EM Facts Workshop Game Family Letters Assessment
More informationChapter 1: Essentials of Geometry
Section Section Title 1.1 Identify Points, Lines, and Planes 1.2 Use Segments and Congruence 1.3 Use Midpoint and Distance Formulas Chapter 1: Essentials of Geometry Learning Targets I Can 1. Identify,
More informationGeometry Enduring Understandings Students will understand 1. that all circles are similar.
High School  Circles Essential Questions: 1. Why are geometry and geometric figures relevant and important? 2. How can geometric ideas be communicated using a variety of representations? ******(i.e maps,
More informationDistance, Midpoint, and Pythagorean Theorem
Geometry, Quarter 1, Unit 1.1 Distance, Midpoint, and Pythagorean Theorem Overview Number of instructional days: 8 (1 day = 45 minutes) Content to be learned Find distance and midpoint. (2 days) Identify
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 informationMathematics. Mathematical Practices
Mathematical Practices 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with
More informationGeometry Vocabulary. Created by Dani Krejci referencing:
Geometry Vocabulary Created by Dani Krejci referencing: http://mrsdell.org/geometry/vocabulary.html point An exact location in space, usually represented by a dot. A This is point A. line A straight path
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 informationChapter 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 twodimensional
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 informationCAMI Education linked to CAPS: Mathematics
 1  TOPIC 1.1 Whole numbers _CAPS curriculum TERM 1 CONTENT Mental calculations Revise: Multiplication of whole numbers to at least 12 12 Ordering and comparing whole numbers Revise prime numbers to
More informationExcel Math Fourth Grade Standards for Mathematical Practice
Excel Math Fourth Grade Standards for Mathematical Practice The Common Core State Standards for Mathematical Practice are integrated into Excel Math lessons. Below are some examples of how we include these
More informationCARMEL CLAY SCHOOLS MATHEMATICS CURRICULUM
GRADE 4 Standard 1 Number Sense Students understand the place value of whole numbers and decimals to two decimal places and how whole numbers 1 and decimals relate to simple fractions. 4.1.1 Read and write
More information