3 rd Grade Mathematics


 Abner Jefferson
 2 years ago
 Views:
Transcription
1 3 rd Grade Mathematics Unit #3 : Relating Area to Multiplication and Division Pacing: 29 Days Unit Overview In this unit, students extend their understanding of multiplication and division (Unit 2) by applying it to realworld problems involving area. This unit is designed to be a short, yet thorough, dive into many of the measurement concepts of the grade. Students will reason abstractly and quantitatively by connecting concepts of area with multiplication and arrays (MP.2). The unit emphasizes modeling, as students are required to create area models and various polygons to solve area and perimeter problems (MP.4). Students also compare rectangles with the same area but different dimensions and look for patterns in the shapes of the rectangles (MP.7). Prerequisite Skills Vocabulary Mathematical Practices Find the sum of an equation with 3 or more addends. Multiplication facts 112 Partition (decompose) a rectangle into rows and columns of samesize squares. Apply the distributive property to find the product of two factors. Construct rectangular arrays. Write a multiplication equation that represents a given array. Perimeter Area Unit Square Square Unit Formula Dimensions Length Width Rectangular Composite Figure Decompose Partition Distributive property Rectilinear Shape Array Column Row Precision Gaps Overlaps Tiling Polygon Quadrilateral MP.1: Make sense of problems and persevere in solving them MP.2: Reason abstractly and quantitatively MP.3: Construct viable arguments and critique the reasoning of others MP.4: Model with mathematics MP.5: Use appropriate tools strategically MP.6: Attend to precision MP.7: Look for and make use of structure MP.8: Look for and express regularity in repeated reasoning 1 Page
2 Additional Standards (10%) Major Standards (70%) Common Core State Standards 3.MD.8: Solve Problems Involving Perimeters of Polygons 3.MD.5: Understand Concepts of Area Measurement and Square Units 3.MD.6: Measure Area by Counting Unit Squares 3.MD.7: Relate Area to Multiplication and Division 3.MD.7a: Find the Area of Rectangles by Tiling 3.MD.7b: Find the Area of Rectangles by Multiplying 3.MD.7c: Area and Distributive Property 3.MD.7d: Area Addition and Decomposition 3.OA.4: Unknowns in Multiplication and Division Equations According to the PARCC Model Content Framework, Standard 3.MD.7 should serve as opportunity for indepth focus based on the content of this unit: Area is a major concept within measurement, and area models must function as a support for multiplicative reasoning in grade 3 and beyond. Measurement contexts for multiplication and division should serves as an example of opportunities for connecting mathematical content and mathematical practices: Students will analyze a number of situation types for multiplication and division, including arrays and measurement contexts. Extending their understanding of multiplication and division to these situations requires that they make sense of problems and persevere in solving them (MP.1), look for and make use of structure (MP.7), as they model these situations with mathematical forms (MP.4), and attend to precision (MP.6) as they distinguish different kinds of situations over time (MP.8). N/A N/A Progression of Skills 2 nd Grade 3 rd Grade 4 th Grade 2.G.2: Partition a rectangle into rows and columns of samesize squares and count to find the total number of them. 2.MD.1: Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes. 3.OA.3: Determine whether a group of objects (up to 20) has an odd or even number of members, e.g., by pairing objects or counting them by 2s; write an equation to express an even number as a sum of two equal addends. 3.MD.5: Recognize area as an attribute of plane figures and understand concepts of area measurement. 3.MD.6: Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units). 3.MD.7: Relate area to the operations of multiplication and addition. 3.MD.8: Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters. 3.OA.4: Determine the unknown whole number in a multiplication or division equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8? = 48, 5 = _ 3, 6 6 =? N/A 4.MD.3: Apply the area and perimeter formulas for rectangles in real world and mathematical problems. For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor. N/A 4.MD.3: Apply the area and perimeter formulas for rectangles in real world and mathematical problems. For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor. 4.OA.2: Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison. 2 Page
3 Big Ideas Perimeter is a measurement of the distance around a figure. Area is a measurement of the amount of flat space a figure takes up. What is a square unit? Why do we use square units to find and report the area of twodimensional shapes? Rectangles are composed of arrays (rows and columns). Therefore, we can use tiling and multiplication to find the area of a rectangle by multiplying the number of columns that compose its length by the number of rows that compose its height Given a perimeter, you can create shapes with various dimensions and therefore different areas. Given an area, you can create a rectangle with various dimensions and therefore various perimeter. Know/Understand Perimeter is additive: the sum of all side lengths equals the perimeter. Area is measured in square units. A square unit is a rectangle with equal side lengths. The size of the square unit affects the area. A figure that can be covered by n unit squares with no gaps or overlaps has an area of n square units. The dimensions of a rectangle are called its length and width. A composite figure is made up of two or more figures. Rectangles may have the same area, but different perimeters and vice versa. Students Will Be Able To Add side lengths to determine the perimeter of a figure. Solve for missing side lengths given the perimeter of a figure. Tile a rectangle and count square units to determine the area. Find the area and perimeter of a rectangle on a grid. Multiply side lengths of a figure to determine the area. Use the Distributive Property to find the area of rectangles with side lengths greater than 12. Find the area of a composite figure by decomposing into or composing rectangles The Distributive Property can be used as a tool to find the area of rectangles with greater side lengths. You can find the area of complex or composite shapes by decomposing them into familiar (rectangular) shapes 3 Page
4 SWBAT 1 Measure the perimeter of a figure in centimeters and inches using string and rulers 2 Use grid paper, rulers, and the perimeter formula to find the perimeter of a figure. Key Points/ Teaching Tips This should be a handson, kinesthetic, conceptual lesson about perimeter. In addition to using string and rulers/meter sticks, students may explore perimeter through geoboards and rubber bands, by walking around the perimeter of the room, by tracing the boundaries of shapes, or by searching the school for examples of perimeter (i.e. bulletin board boarders, door frames, etc.). Students will understand perimeter as the distance around the outside of a figure Students do not need to be adding side lengths until the next lesson. Students should measure the perimeter of objects to the nearest whole inch and centimeter in order to support standard 3.MD.2 and their understanding of the relationship between the size of a unit and the number of units needed. According to the unpacked standards guide, students should work through determining perimeter in the following progression: 1. Side lengths are marked off so that students can count unit lengths. 2. Side lengths are labeled with numerals. 3. Students mark off unit lengths with a ruler and label the length of each side. This lesson should give students an opportunity to practice all three. Unit Sequence Exit Ticket 1. Trace the perimeter of the shape below with a crayon: a. Explain in writing how you know you outlined the perimeter of the shape. 2. Use string and your rulers to find the perimeter of the shape above to the nearest inch and the nearest centimeter. Be sure to label your answers with the correct units. 3. Compare the perimeters of the objects in centimeters to the perimeters in inches. What do you notice? 1. Find the perimeter of the shape below: 2. Find the perimeter of Shape B below. Write an equation to support your answer. Instructional Resources 1 Chapter 13, Lesson 1 Module 7, Lesson 10 Homework Chapter 13, Lesson 2 Module 7 Lessons 12 & 13 1 Teachers should be aware that the curriculum covers geometry before perimeter; therefore, resources must be adapted accordingly. 4 Page
5 When using grid paper, students must attend to precision when counting around the corners (i.e. a common misconception is that students count square units instead of unit lengths). Students may benefit from being required to trace each square unit as they count. 3. Measure and label the side lengths of the shape below in centimeters. Then find the perimeter. 3 Given the perimeter of a figure, students will find a missing side length. Students should be able to name squares and rectangles and pay special attention to patterns in the side lengths of each. They should be able to use these patterns and what they know about the nature of squares and rectangles to reason about missing side lengths for these shapes. For other polygons, students should practice writing equations with letters or symbols standing for the unknown (missing side length). Sample PARCC EOY assessment question: 1. The perimeter of the triangle shown below is 48 inches. Find the unknown side length. 16 in. 2. The perimeter of the figure below is 26 feet. 10 ft.?? 10 ft. 20 in. 3 Chapter 13, Lesson 2 Module 7, Lesson 14 5 Page
6 a. Write an equation to represent the perimeter of the figure. Find the unknown. b. Use your knowledge about this figure to explain another way to find the unknown. 3. A garden has eight equal sides and has a perimeter of 56 meters. Circle the equation that gives the length, in meters, of each side. Use pictures, words, and your knowledge of mathematical operations to defend your answer. a = 65 b = 48 c = 7 4 Given side lengths in a realworld context, students will solve word problems to determine perimeter. When solving realworld problems about perimeter, a common misconception is for students to only add the side lengths given instead of finding the distance all the way around the shape (i.e for a rectangle with dimensions 7 by 6, instead of ). This should be an explicit teaching point. Sample PARCC EOY assessment question: Lavina wants to place a fence around a rectangular play area for her rabbits. The play area will be 7feet long and 4feet wide. What is the total length of the fence, in feet, Lavina needs to place around the play area? 1. Marvin draws a border around a letter that is 9 inches wide and 8 inches long. How many inches of border does Marvin draw? Draw a picture to support your answer. 2. Marlene ropes off a square section of her yard where she plants grass. One side of the square measures 9 yards. What is the total length of rope Marlene uses? 3. Write your own word problem for a classmate that would require him or her to find the perimeter of a figure. Create an answer key and use words and pictures to explain why your classmate would need to find the perimeter. Module 7, Lesson 15 5 Flex Day (Instruction Based on Data) Recommended Resources: Engage NY Module 7 Lesson 23 Finding and Measuring Perimeter Perimeter with Color Tiles 6 Page
7 6 Explore the area of rectangles by using tiles; attend to precision when tiling by ensuring there are no gaps or overlaps. According to the unpacked standards guide, students should have ample experiences filling a region with square tiles before transitioning to pictorial representations on graph paper. Students should understand area as the amount of flat space a shape takes up Students should be able to articulate why we use square units to measure area. Tiling a Tabletop provides a good foundation for an inquiry lesson on this topic. In addition to using notebook paper and index cards, students might also try describing the amount of flat space a shape takes up using circle counters so that they discover the importance of square units in being able to cover a figure. 1. Use square unit tiles to find the area of the shape below. Make sure to label your answer correctly. (Include picture of a rectangle that can be measured exactly using square unit tiles.) 2. Does the picture below accurately show the area of Rectangle A? Why or why not? 3. Why do we measure area in square units? Chapter 13 Foldable: 1 square unit LearnZillion: Find the Area of a Shape Tiling a Tabletop Error analysis: 7 Page
8 7 Use grid paper to find the area of a figure and to create figures with a given area. Students may benefit from exploring this objective with geoboards before working with grid paper. Students should understand that the size of the square unit affects the area of the figure. 1. Each is 1 square unit. What is the area of each of the following rectangles? Chapter 13 Lessons 3 & 4 Module 4, Lesson 3 Students may notice that multiple different shapes can have the same area. This will be revisited later in the unit. 2. Find the area of the figure below. Label your answer in square units. 3. Use the appropriate resources to draw a rectangle with an area of 8 square centimeters and a rectangle with an area of 8 square inches. What do you notice about these two rectangles? Explain. 1. Use a ruler to measure the side lengths of the rectangle in centimeters. Use your measurements to tile the rectangle with square centimeters. Find the area. 8 Use rulers or labeled side lengths to separate rectangles into square units. A common misconception is for students to fill a rectangle with square units without attending to the given side lengths. (For example, a student may make 4 columns even though the side length is labeled as 3 units.) This should be an explicit teaching point, and students should be required to attend to precision by checking their drawings to ensure that it matches the labeled side length. Chapter 13, Lesson 5 Module 4, Lesson 4 8 Page
9 Students should learn the word dimensions and recognize that this refers to the side lengths of a shape. Area = square centimeters 2. Use the given side lengths to tile the rectangle with square units. Find the area. 3 units 6 units 3. Why is perimeter measured in units and area measured in square units? 9 Relate area to arrays in order to apply skipcounting and multiplication strategies to determine the area of a rectangle. Students should draw on their foundation with arrays from Unit 2. They should be able to describe area as repeated groups of equal size of square units. 1. Darren has a total of 28 squarecentimeter tiles. He arranges them into 7 equal rows. Draw Darren s rectangle and label the side lengths. a. Write an addition equation to find the total area. b. Write a multiplication equation to find the total area. 2. How is the area of a rectangle related to multiplication? Chapter 13, Lesson 5 Module 4, Lesson 5 9 Page
10 10 Complete rows or columns to complete arrays and form rectangles According to the unpacked standards guide, many activities that involve seeing and making arrays of squares to form a rectangle might be needed to build robust conceptions of a rectangular area structured into squares. This lesson is included to provide students with additional exposure to arrays. 1. Each represents a 1cm square. Draw to find the number of rows and columns in each array. Then, fill in the blanks to make a true equation to represent the array s area Module 4 Lessons 6 & 7 x = square centimeters 2. Label the side lengths of Rectangle A on the grid below. Use a straight edge to draw a grid of equal size squares within Rectangle A. Find the total area of Rectangle A. 3. Mary skipcounts by 6s and Julio skipcounts by 7s to find the total number of square units in the array. Who is correct? Use pictures, numbers, and words to explain your answer. 11 Flex Day (Instruction Based on Data) Recommended Resources: Doubling, Halving, Tripling Find the Area Area Compare Module 7, Lesson 10 How Big is a Desk? 10 Page
11 12 Use equations and fact families to find the missing side length of a rectangle. Module 4, Lesson 8 Exit Ticket 1. Write a multiplication sentence to find the area of the rectangle below: Module 4, Lesson 8 Chapter 13, Lesson 6 2. Write a multiplication sentence and a division sentence to find the unknown side length for the rectangle below: 3. Ria draws a rectangle that has a side length of 4 inches and an area of 28 square inches. What is the other side length? Use words, pictures, and equations to support your answer. 11 Page
12 13 Apply the distributive property to find the area of rectangles. Pacing: 2 days Students should practice first with rectangles with grids, then with rectangles where only the side lengths are labeled. Inquirybased question from Smarter Balanced: In the picture below, Rectangle A has a width of 3 ft., Rectangle B has a width of 2 ft., and both of them have a length of 4 ft. Rectangle C was formed by sticking Rectangle A and Rectangle B together along one of their lengths. This is shown with the dotted line. 1. Label the side lengths of the shaded and unshaded rectangles. Then find the total area of the large rectangle by adding the areas of the 2 smaller rectangles. Chapter 13, Lesson 7 Module 4 Lessons 9 & 10 Breaking Apart Arrays Find the area of the rectangle below by using the Distributive Property to decompose the longer side into a sum. 15 ft. 4 ft. a. What is the area of Rectangle A? b. What is the area of Rectangle B? c. What is the sum of the areas of Rectangles A and B? d. What is the width of Rectangle C? How do you know? e. What is the area of Rectangle C? f. Compare your answers in (c) and (e). Are they the same? Why or why not? 3. How are the operations of addition and multiplication used when finding area using the Distributive Property? 12 Page
13 15 Apply the distributive property to solve word problems about the area of rectangles. Students should have practice matching expressions with real world situations. See the example below from the NY State Assessment: The garden below was divided into regions one for carrots and one for peas. Sample PARCC assessment question: 1. There is a large mural made of colored tiles at the entrance to Rena s school. A part of the mural was damaged in a heavy storm. The part of the mural that was NOT damaged is 5 tiles long and 4 tiles high. Chapter 13, Lesson 7 Module 4 Lesson 12 Which expression represents the area, in square units, of the whole garden? a. (5 + 10) + (5 + 6) b. (5 x 10) + (5 x 6) c. (5 x 10) + (5 x 6) d. (5 + 10) x (5 + 6) Rena wants to know how many tiles need to be replaced. a. Choose an expression from the options box to write in each of the two blanks to make a true statement. Designing a Flower Bed Sample question from Arizona Common Core: Joe and John made a poster that was 4 by 5. Mary and Amir made a poster that was 4 by 3. They placed their posters on a wall sidebyside so that there was no space between them. How much area will the two posters cover? Draw a picture to help explain your answer. b. How many tiles need to be replaced in the mural? Explain how you found your answer. Sample Smarter Balanced: 2. Jasper used the expression 5 x (10 + 3) to find the area of a rectangular closet floor, in square feet. a. On a grid, draw a rectangle that could be the one Jasper measured. b. What is the area of the closet floor in square feet? 3. Jasper has 200 square feet of tile. He will use some of the tile to cover the closet floor. He will only use whole tiles. a. How many square feet of tile will Jasper have left after covering the closet floor with 13 Page
14 tile? b. Jasper wants to use some of the remaining tile to cover the floor of a kitchen. The kitchen is 12 feet long and 12 feet wide. Does Jasper have enough tiles to cover the kitchen floor? Show how you got your answer using drawings, mathematical expressions or equations, and words. 16 Use grid paper to find the area of composite figures. Provide an opportunity for students to do the heavy lifting by presenting them with a complex shape with given side lengths first ask them to calculate the perimeter, then give them think time to brainstorm how they could find the area (allow them to discuss in small groups). You may provide tiles for them to recreate the shape and test their theories. Students should begin their work with composite figures by using grid paper to: Decompose rectilinear figures into rectangles (2 or more) Compose rectangles in order to subtract a known area Module 4, Lesson 13 Concept Development Problems 1 & 2 (with grid paper), Problem Set #1, Homework #12 Students may benefit from coloring the rectangles they have created with different colors. They should be required to label the dimensions of these new shapes. 1. Find the total area of the figure below by decomposing it into 2 rectangles. 2. Find the total area of the figure above by composing a rectangle in order to subtract a known area. 3. For either #1 or #2, explain how you found the area. Include the following words in your answer: compose/decompose, add/subtract, area, and composite figure. Module 4, Lesson 13 Finding the Area of Complex Figures: Lessons 13 & Page
15 17 Find the area of composite figures in which all side lengths are labeled. Students should continue their work with composite figures by working without grid paper, but solving problems in which necessary side lengths are labeled. They must attend to precision when choosing which dimensions to use to find the area of the decomposed rectangles. 1. Find the area of the figure below three ways. Show two ways to decompose the figure and one way to compose a rectangle around it Module 4 Lessons 13 & 14 Chapter 13, Lesson 8 Module 4, Lesson 13 Problem Set #2 Module 4, Lesson 14 Problem Set #34 Chapter 13, Lesson 8 Example 2, Independent Practice #23, 5 Finding the Area of Complex Figures: Lesson Max found the area of the composite figure below: (10 x 4) + (8 x 3) = = 64 square inches Is Max correct? Use pictures, words, and numbers to explain your reasoning. If you believe he is incorrect, find the correct answer. 15 Page
GRADE 3 MATH: CITY FARMERS
GRADE 3 MATH: CITY FARMERS UNIT OVERVIEW This instructional bundle contains a task aligned to the Content Core standards and additional supports for diverse learners. The task is embedded in a 45 week
More informationArizona s College and Career Ready Standards Mathematics
Arizona s College and Career Ready Mathematics Mathematical Practices Explanations and Examples Third Grade ARIZONA DEPARTMENT OF EDUCATION HIGH ACADEMIC STANDARDS FOR STUDENTS State Board Approved June
More informationfor the Common Core State Standards 2012
A Correlation of for the Common Core State s 2012 to the Common Core Georgia Performance s Grade 2 FORMAT FOR CORRELATION TO THE COMMON CORE GEORGIA PERFORMANCE STANDARDS (CCGPS) Subject Area: K12 Mathematics
More information2 nd Grade Mathematics Unpacked Content For the new Common Core State Standards that will be effective in all North Carolina schools in the 201213.
2 nd Grade Mathematics Unpacked Content For the new Common Core State Standards that will be effective in all North Carolina schools in the 201213. This document is designed to help North Carolina educators
More informationGrade 1. M3: Ordering and Expressing Length Measurements as Numbers
Grade 1 Key Areas of Focus for Grades K2: Addition and subtractionconcepts, skills and problem solving Expected Fluency: Add and Subtract within 10 Module M1: Addition and Subtraction of Numbers to 10
More informationVoyager Sopris Learning Vmath, Levels CI, correlated to the South Carolina College and CareerReady Standards for Mathematics, Grades 28
Page 1 of 35 VMath, Level C Grade 2 Mathematical Process Standards 1. Make sense of problems and persevere in solving them. Module 3: Lesson 4: 156159 Module 4: Lesson 7: 220223 2. Reason both contextually
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 informationMath Journal HMH Mega Math. itools Number
Lesson 1.1 Algebra Number Patterns CC.3.OA.9 Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. Identify and
More informationGrade 4  Module 5: Fraction Equivalence, Ordering, and Operations
Grade 4  Module 5: Fraction Equivalence, Ordering, and Operations Benchmark (standard or reference point by which something is measured) Common denominator (when two or more fractions have the same denominator)
More informationTask: Representing the National Debt 7 th grade
Tennessee Department of Education Task: Representing the National Debt 7 th grade Rachel s economics class has been studying the national debt. The day her class discussed it, the national debt was $16,743,576,637,802.93.
More informationProblem Solving Students will demonstrate their ability to solve problems in mathematics including problems with openended answers.
Title: Designing Our School Garden Brief Overview: This performancebased assessment integrates geometric problem solving with realworld application. Students will design a garden with a variety of flowers
More informationMathematics as Reasoning Students will use reasoning skills to determine the best method for maximizing area.
Title: A Pen for Penny Brief Overview: This unit is a reinforcement of the concepts of area and perimeter of rectangles. Methods for maximizing area while perimeter remains the same are also included.
More informationtips Grade TARGETED INVERVENTION: PRACTICE and STRATEGIES MATHEMATICS TUTORING
UTAH STATE OFFICE OF EDUCATION TARGETED INVERVENTION: PRACTICE and STRATEGIES tips MATHEMATICS TUTORING Grade Utah State Office of Education 250 East 500 South P.O. Box 144200 Salt Lake City, UT 841144200
More informationMathematical Practices
The New Illinois Learning Standards for Mathematics Incorporating the Common Core Mathematical Practices Grade Strand Standard # Standard K12 MP 1 CC.K12.MP.1 Make sense of problems and persevere in
More informationSTRAND: Number and Operations Algebra Geometry Measurement Data Analysis and Probability STANDARD:
how August/September Demonstrate an understanding of the placevalue structure of the baseten number system by; (a) counting with understanding and recognizing how many in sets of objects up to 50, (b)
More informationInvestigating Area Under a Curve
Mathematics Investigating Area Under a Curve About this Lesson This lesson is an introduction to areas bounded by functions and the xaxis on a given interval. Since the functions in the beginning of the
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 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 informationK12 Louisiana Student Standards for Mathematics: Table of Contents
K12 Louisiana Student Standards for Mathematics: Table of Contents Introduction Development of K12 Louisiana Student Standards for Mathematics... 2 The Role of Standards in Establishing Key Student Skills
More informationMAFS: Mathematics Standards GRADE: K
MAFS: Mathematics Standards GRADE: K Domain: COUNTING AND CARDINALITY Cluster 1: Know number names and the count sequence. CODE MAFS.K.CC.1.1 Count to 100 by ones and by tens. MAFS.K.CC.1.2 MAFS.K.CC.1.3
More information2 nd Grade Texas Mathematics: Unpacked Content
2 nd Grade Texas Mathematics: Unpacked Content What is the purpose of this document? To increase student achievement by ensuring educators understand specifically what the new standards mean a student
More informationWarning! 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
More informationExplore architectural design and act as architects to create a floor plan of a redesigned classroom.
ARCHITECTURAL DESIGN AT A GLANCE Explore architectural design and act as architects to create a floor plan of a redesigned classroom. OBJECTIVES: Students will: Use prior knowledge to discuss functions
More informationGeometry Notes PERIMETER AND AREA
Perimeter and Area Page 1 of 57 PERIMETER AND AREA Objectives: After completing this section, you should be able to do the following: Calculate the area of given geometric figures. Calculate the perimeter
More informationCommon Core State Standards for. Mathematics
Common Core State Standards for Mathematics Table of Contents Introduction 3 Standards for Mathematical Practice 6 Standards for Mathematical Content Kindergarten 9 Grade 1 13 Grade 2 17 Grade 3 21 Grade
More informationChapter 4: The Concept of Area
Chapter 4: The Concept of Area Defining Area The area of a shape or object can be defined in everyday words as the amount of stuff needed to cover the shape. Common uses of the concept of area are finding
More informationSouth Carolina College and CareerReady Standards for Mathematics
South Carolina College and CareerReady Standards for Mathematics South Carolina Department of Education Columbia, South Carolina 2015 State Board of Education Approved First Reading on February 11, 2015
More informationBig Ideas in Mathematics
Big Ideas in Mathematics which are important to all mathematics learning. (Adapted from the NCTM Curriculum Focal Points, 2006) The Mathematics Big Ideas are organized using the PA Mathematics Standards
More informationSouth Carolina College and CareerReady Standards for Mathematics
South Carolina College and CareerReady Standards for Mathematics South Carolina Department of Education Columbia, South Carolina 2015 State Board of Education Approved First Reading on February 11, 2015
More informationIllinois State Standards Alignments Grades Three through Eleven
Illinois State Standards Alignments Grades Three through Eleven Trademark of Renaissance Learning, Inc., and its subsidiaries, registered, common law, or pending registration in the United States and other
More informationJust want the standards alone? You can find the standards alone at http://corestandards.org/thestandards
4 th Grade Mathematics Unpacked Content For the new Common Core State Standards that will be effective in all North Carolina schools in the 201213 school year. This document is designed to help North
More informationr the COR Common Core State Standards Learning Pathways
BUI LT fo COM r the MON COR E 2015 2016 Common Core State Standards Learning Pathways Table of Contents Grade 3...3 Grade 4...8 Grade 5... 13 Grade 6... 18 Grade 7...26 Grade 8...32 Algebra Readiness...36
More informationManitoba Curriculum. Alignment with Mathletics. Supported by independent evidencebased research and practice. Powerful reporting.
Supported by independent evidencebased research practice. Follows provincial curricula Powerful reporting Student centred Content Kindergarten Grade 1 Grade 2 02 04 08 Grade 10 Applied & PreCalculus
More informationMathematics Curriculum
New York State Common Core 3 G R A D E Mathematics Curriculum GRADE 3 MODULE 1 Topic B Division as an Unknown Factor Problem 3.OA.2, 3.OA.6, 3.OA.3, 3.OA.4 Focus Standard: 3.OA.2 Interpret wholenumber
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 informationA Concrete Introduction. to the Abstract Concepts. of Integers and Algebra using Algebra Tiles
A Concrete Introduction to the Abstract Concepts of Integers and Algebra using Algebra Tiles Table of Contents Introduction... 1 page Integers 1: Introduction to Integers... 3 2: Working with Algebra Tiles...
More informationInterpreting Graphs. Interpreting a Bar Graph
1.1 Interpreting Graphs Before You compared quantities. Now You ll use graphs to analyze data. Why? So you can make conclusions about data, as in Example 1. KEY VOCABULARY bar graph, p. 3 data, p. 3 frequency
More informationVISUAL ALGEBRA FOR COLLEGE STUDENTS. Laurie J. Burton Western Oregon University
VISUAL ALGEBRA FOR COLLEGE STUDENTS Laurie J. Burton Western Oregon University VISUAL ALGEBRA FOR COLLEGE STUDENTS TABLE OF CONTENTS Welcome and Introduction 1 Chapter 1: INTEGERS AND INTEGER OPERATIONS
More informationGeorgia Standards Alignment Grades One through Six
Georgia Standards Alignment Grades One through Six Trademark of Renaissance Learning, Inc., and its subsidiaries, registered, common law, or pending registration in the United States and other countries.
More informationTeaching & Learning Plans. Arithmetic Sequences. Leaving Certificate Syllabus
Teaching & Learning Plans Arithmetic Sequences Leaving Certificate Syllabus The Teaching & Learning Plans are structured as follows: Aims outline what the lesson, or series of lessons, hopes to achieve.
More informationNew York State. P12 Common Core. Learning Standards for. Mathematics
New York State P12 Common Core Learning Standards for Mathematics This document includes all of the Common Core State Standards in Mathematics plus the New York recommended additions. All of the New York
More informationPerformance Level Descriptors Grade 6 Mathematics
Performance Level Descriptors Grade 6 Mathematics Multiplying and Dividing with Fractions 6.NS.12 Grade 6 Math : SubClaim A The student solves problems involving the Major Content for grade/course with
More information3 Mathematics Curriculum
New York State Common Core 3 Mathematics Curriculum GRADE GRADE 3 MODULE 5 Table of Contents GRADE 3 MODULE 5 Fractions as Numbers on the Number Line Module Overview... i Topic A: Partition a Whole into
More informationExploring Geometric Probabilities with Buffon s Coin Problem
Exploring Geometric Probabilities with Buffon s Coin Problem Kady Schneiter Utah State University kady.schneiter@usu.edu Published: October 2012 Overview of Lesson Investigate Buffon s coin problem using
More informationMathematics Curriculum Guide Precalculus 201516. Page 1 of 12
Mathematics Curriculum Guide Precalculus 201516 Page 1 of 12 Paramount Unified School District High School Math Curriculum Guides 2015 16 In 2015 16, PUSD will continue to implement the Standards by providing
More informationNumber Relationships. Suggested Time: 4
Number Relationships Suggested Time: 4 1 2 Weeks 55 NUMBER RELATIONSHIPS Unit Overview Focus and Context This unit focuses on finding factors and multiples of whole numbers to 100, classifying numbers
More informationGeorgia Standards of Excellence Frameworks. Mathematics. GSE Grade 7 Unit 2: Expressions and Equations
Georgia Standards of Excellence Frameworks Mathematics GSE Grade 7 Unit 2: Expressions and Equations These materials are for nonprofit educational purposes only. Any other use may constitute copyright
More informationFirst Grade Exploring TwoDigit Numbers
First Grade Exploring TwoDigit Numbers http://focusonmath.files.wordpress.com/2011/02/screenshot20110217at31019pm.png North Carolina Department of Public Instruction www.ncdpi.wikispaces.net
More informationFree PreAlgebra Lesson 55! page 1
Free PreAlgebra Lesson 55! page 1 Lesson 55 Perimeter Problems with Related Variables Take your skill at word problems to a new level in this section. All the problems are the same type, so that you can
More informationUnit 7 Quadratic Relations of the Form y = ax 2 + bx + c
Unit 7 Quadratic Relations of the Form y = ax 2 + bx + c Lesson Outline BIG PICTURE Students will: manipulate algebraic expressions, as needed to understand quadratic relations; identify characteristics
More informationFourth Grade Fractions
Fourth Grade Fractions http://upload.wikimedia.org/wikibooks/en/9/92/fractions_of_a_square.jpg North Carolina Department of Public Instruction www.ncdpi.wikispaces.net Overview The implementation of the
More informationThis lesson introduces students to decimals.
NATIONAL MATH + SCIENCE INITIATIVE Elementary Math Introduction to Decimals LEVEL Grade Five OBJECTIVES Students will compare fractions to decimals. explore and build decimal models. MATERIALS AND RESOURCES
More informationUnit 5 Area. What Is Area?
Trainer/Instructor Notes: Area What Is Area? Unit 5 Area What Is Area? Overview: Objective: Participants determine the area of a rectangle by counting the number of square units needed to cover the region.
More informationConsultant: Lynn T. Havens. Director of Project CRISS Kalispell, Montana
Teacher Annotated Edition Study Notebook Consultant: Lynn T. Havens SM Director of Project CRISS Kalispell, Montana i_sn_c1fmtwe_893629.indd i 3/16/09 9:17:03 PM Copyright by The McGrawHill Companies,
More information7.2 Quadratic Equations
476 CHAPTER 7 Graphs, Equations, and Inequalities 7. Quadratic Equations Now Work the Are You Prepared? problems on page 48. OBJECTIVES 1 Solve Quadratic Equations by Factoring (p. 476) Solve Quadratic
More informationGrade 6 Mathematics Common Core State Standards
Grade 6 Mathematics Common Core State Standards Standards for Mathematical Practice HOW make sense of problems, persevere in solving them, and check the reasonableness of answers. reason with and flexibly
More informationMajor Work of the Grade
Counting and Cardinality Know number names and the count sequence. Count to tell the number of objects. Compare numbers. Kindergarten Describe and compare measurable attributes. Classify objects and count
More informationWilliam Floyd Union Free School District. A Parent s Math Resource Guide to 2nd Grade Mathematics
William Floyd Union Free School District A Parent s Math Resource Guide to 2nd Grade Mathematics Dear Parents, The Parent s Math Resource Guide is a resource to assist you in becoming familiar with Common
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 informationCommon Core State Standards for Mathematics for California Public Schools Kindergarten Through Grade Twelve
Common Core State Standards for Mathematics for California Public Schools Kindergarten Through Grade Twelve Adopted by the California State Board of Education August 2010 Updated January 2013 Prepublication
More informationThe Distributive Property
The Distributive Property Objectives To recognize the general patterns used to write the distributive property; and to mentally compute products using distributive strategies. www.everydaymathonline.com
More informationA Second Course in Mathematics Concepts for Elementary Teachers: Theory, Problems, and Solutions
A Second Course in Mathematics Concepts for Elementary Teachers: Theory, Problems, and Solutions Marcel B. Finan Arkansas Tech University c All Rights Reserved First Draft February 8, 2006 1 Contents 25
More informationLESSONS FOR LEARNING FOR THE COMMON CORE STATE STANDARDS IN MATHEMATICS
GRADE 1 LESSONS FOR LEARNING FOR THE COMMON CORE STATE STANDARDS IN MATHEMATICS PUBLIC SCHOOLS OF NORTH CAROLINA State Board of Education Department of Public Instruction K12 MATHEMATICS http://www.ncpublicschools.org/curriculum/mathematics/
More informationProblem of the Month: Digging Dinosaurs
: The Problems of the Month (POM) are used in a variety of ways to promote problem solving and to foster the first standard of mathematical practice from the Common Core State Standards: Make sense of
More informationPreCalculus Unit Plan: Vectors and their Applications. Dr. MohrSchroeder. Fall 2012. University of Kentucky. Jessica Doering.
PreCalculus Unit Plan: Vectors and their Applications Dr. MohrSchroeder Fall 2012 University of Kentucky Jessica Doering Andrea Meadors Stephen Powers Table of Contents Narrative and Overview of Unit
More informationWarmUp 1. 1. What is the least common multiple of 6, 8 and 10?
WarmUp 1 1. What is the least common multiple of 6, 8 and 10? 2. A 16page booklet is made from a stack of four sheets of paper that is folded in half and then joined along the common fold. The 16 pages
More informationUsing the Area Model to Teach Multiplying, Factoring and Division of Polynomials
visit us at www.cpm.org Using the Area Model to Teach Multiplying, Factoring and Division of Polynomials For more information about the materials presented, contact Chris Mikles mikles@cpm.org From CCA
More informationcalled and explain why it cannot be factored with algebra tiles? and explain why it cannot be factored with algebra tiles?
Factoring Reporting Category Topic Expressions and Operations Factoring polynomials Primary SOL A.2c The student will perform operations on polynomials, including factoring completely first and seconddegree
More informationMath at a Glance for April
Audience: School Leaders, Regional Teams Math at a Glance for April The Math at a Glance tool has been developed to support school leaders and region teams as they look for evidence of alignment to Common
More informationPractice Task: The Factor Game
Practice Task: The Factor Game This task requires students to demonstrate understanding of factors and multiples of whole numbers. STANDARDS FOR MATHEMATICAL CONTENT MCC4.OA.4 Find all factor pairs for
More information2 Mathematics Curriculum
New York State Common Core 2 Mathematics Curriculum GRADE GRADE 2 MODULE 3 Topic E: Model Numbers Within 1000 with Place Value Disks 2.NBT.A Focus Standard: 2.NBT.A Understand place value. Instructional
More informationArea and Volume Equations
Area and Volume Equations MODULE 16? ESSENTIAL QUESTION How can you use area and volume equations to solve realworld problems? LESSON 16.1 Area of Quadrilaterals 6.8.B, 6.8.D LESSON 16. Area of Triangles
More informationDifferentiated Instruction Strategies
Miss Taylor Brooke Stancil s Differentiated Instruction Strategies Choral Response: Choral response is a very simple technique in which the teacher asks questions to the class as a whole and the students
More informationLine Segments, Rays, and Lines
HOME LINK Line Segments, Rays, and Lines Family Note Help your child match each name below with the correct drawing of a line, ray, or line segment. Then observe as your child uses a straightedge to draw
More informationTennessee Mathematics Standards 20092010 Implementation. Grade Six Mathematics. Standard 1 Mathematical Processes
Tennessee Mathematics Standards 20092010 Implementation Grade Six Mathematics Standard 1 Mathematical Processes GLE 0606.1.1 Use mathematical language, symbols, and definitions while developing mathematical
More informationSQUARESQUARE ROOT AND CUBECUBE ROOT
UNIT 3 SQUAREQUARE AND CUBEUBE (A) Main Concepts and Results A natural number is called a perfect square if it is the square of some natural number. i.e., if m = n 2, then m is a perfect square where m
More informationCommon Core Unit Summary Grades 6 to 8
Common Core Unit Summary Grades 6 to 8 Grade 8: Unit 1: Congruence and Similarity 8G18G5 rotations reflections and translations,( RRT=congruence) understand congruence of 2 d figures after RRT Dilations
More informationFree PreAlgebra Lesson 8 page 1
Free PreAlgebra Lesson 8 page 1 Lesson 8 Factor Pairs Measuring more accurately requires breaking our inches into fractions of an inch, little parts smaller than a whole inch. You can think ahead and
More informationBasic Math for the Small Public Water Systems Operator
Basic Math for the Small Public Water Systems Operator Small Public Water Systems Technology Assistance Center Penn State Harrisburg Introduction Area In this module we will learn how to calculate the
More informationUsing Algebra Tiles from Polynomials to Factoring
Using Algebra Tiles from Polynomials to Factoring For more information about the materials you find in this packet, contact: Chris Mikles (888) 8084276 mikles@cpm.org CPM Educational Program 203, all
More informationFactoring Polynomials
UNIT 11 Factoring Polynomials You can use polynomials to describe framing for art. 396 Unit 11 factoring polynomials A polynomial is an expression that has variables that represent numbers. A number can
More informationPossible Stage Two Mathematics Test Topics
Possible Stage Two Mathematics Test Topics The Stage Two Mathematics Test questions are designed to be answerable by a good problemsolver with a strong mathematics background. It is based mainly on material
More informationAcademic Standards for Mathematics
Academic Standards for Grades Pre K High School Pennsylvania Department of Education INTRODUCTION The Pennsylvania Core Standards in in grades PreK 5 lay a solid foundation in whole numbers, addition,
More informationAPPLICATIONS AND MODELING WITH QUADRATIC EQUATIONS
APPLICATIONS AND MODELING WITH QUADRATIC EQUATIONS Now that we are starting to feel comfortable with the factoring process, the question becomes what do we use factoring to do? There are a variety of classic
More informationCurriculum Overview Standards & Skills
Curriculum Overview Standards & Skills You CAN Do The Rubik's Cube Instructional Curriculum Curriculum Overview / Skills & Standards How to Solve The Rubik's Cube Part 1  Curriculum Overview Part 2 
More informationUsing Excel to find Perimeter, Area & Volume
Using Excel to find Perimeter, Area & Volume Level: LBS 4 V = lwh Goal: To become familiar with Microsoft Excel by entering formulas into a spreadsheet in order to calculate the perimeter, area and volume
More informationLesson 4: Surface Area
Lesson 4: Surface Area Selected Content Standards Benchmark Assessed M.3 Estimating, computing, and applying physical measurement using suitable units (e.g., calculate perimeter and area of plane figures,
More informationTeaching Algebra with Manipulatives. For use with Glencoe Algebra 1 Glencoe Algebra 2
Teaching Algebra with Manipulatives For use with Glencoe Algebra 1 Glencoe Algebra 2 Manipulatives Glencoe offers three types of kits to enhance the use of manipulatives in your PreAlgebra classroom.
More informationProblem of the Month Through the Grapevine
The Problems of the Month (POM) are used in a variety of ways to promote problem solving and to foster the first standard of mathematical practice from the Common Core State Standards: Make sense of problems
More informationGRADE 6 MATH: GROCERY SHOPPING AND THE QUILT OF A MATH TEACHER
GRADE 6 MATH: GROCERY SHOPPING AND THE QUILT OF A MATH TEACHER UNIT OVERVIEW This unit contains a curriculum embedded Common Core aligned task and instructional supports. The task is embedded in a 2 3
More informationGrade 6 Mathematics Assessment. Eligible Texas Essential Knowledge and Skills
Grade 6 Mathematics Assessment Eligible Texas Essential Knowledge and Skills STAAR Grade 6 Mathematics Assessment Mathematical Process Standards These student expectations will not be listed under a separate
More informationMultiplication Fact Strategies
Multiplication Fact Strategies Wichita Public Schools Curriculum and Instructional Design Mathematics Revised 201 KCCRS version Table of Contents Introduction Research Connections (Strategies) Making Meaning
More informationXV. Mathematics, Grade 10
XV. Mathematics, Grade 10 Grade 10 Mathematics Test The spring 2011 grade 10 MCAS Mathematics test was based on learning standards in the Massachusetts Mathematics Curriculum Framework (2000). The Framework
More informationProblem of the Month The Wheel Shop
Problem of the Month The Wheel Shop The Problems of the Month (POM) are used in a variety of ways to promote problem solving and to foster the first standard of mathematical practice from the Common Core
More informationNumber Sense and Numeration, Grades 4 to 6
Number Sense and Numeration, Grades 4 to 6 Volume 3 Multiplication A Guide to Effective Instruction in Mathematics, Kindergarten to Grade 6 2006 Every effort has been made in this publication to identify
More informationChapter 12 Making Meaning in Algebra Examining Students Understandings and Misconceptions
Assessing Mathematical Proficiency MSRI Publications Volume 53, 2007 Chapter 12 Making Meaning in Algebra Examining Students Understandings and Misconceptions DAVID FOSTER Students often get confused and
More informationCPM Educational Program
CPM Educational Program A California, NonProfit Corporation Chris Mikles, National Director (888) 8084276 email: mikles @cpm.org CPM Courses and Their Core Threads Each course is built around a few
More informationRatios and Proportional Relationships Set 1: Ratio, Proportion, and Scale... 1 Set 2: Proportional Relationships... 8
Table of Contents Introduction...v Standards Correlations... viii Materials List... x... 1 Set 2: Proportional Relationships... 8 The Number System Set 1: Integers and Absolute Value... 15 Set 2: Comparing
More informationMinistry of Education. The Ontario Curriculum. Mathematics. Mathematics Transfer Course, Grade 9, Applied to Academic
Ministry of Education The Ontario Curriculum Mathematics Mathematics Transfer Course, Grade 9, Applied to Academic 2 0 0 6 Contents Introduction....................................................... 2
More informationNUMBER CORNER YEARLONG CONTENT OVERVIEW
August & September Workouts Calendar Grid Quilt Block Symmetries Identifying shapes and symmetries Calendar Collector Two Penny Toss Probability and data analysis Computational Fluency Mental Math Fluently
More information