Document Sample

Lake County Schools Fourth Grade Math Curriculum Map Preface Teams of Lake County teachers created the curriculum maps in order to ensure that all students throughout the district receive a common curriculum. The maps help ensure that all state requirements are taught and that the content is divided into teachable segments with appropriate pacing. The curriculum maps will guide your instruction but provide flexibility based on the individual needs of students. The maps are living documents and feedback is requested of teachers to ensure continuous improvement. All teachers are expected to use the curriculum maps, in conjunction with data, to drive instruction. The maps were designed for the instruction to take place by quarter. There is some flexibility within the quarters for mastery and re-teaching. The expectation is that teachers will finish the content within each quarter in its entirety. The maps have been structured in such a way as to scaffold student learning. Listed below are a few of the new or updated features common to all curriculum maps: Essential Question(s): o Provide application of the skills/concepts o Have more than one right answer which promotes student discourse o Increase the rigor in the classroom, by changing from teacher-centered to student-centered learning o Are referred to at the beginning, middle, and end of the lesson o Require you to make a decision o Promote critical thinking and problem solving o Encourage interdependence o Are open-ended Academic Vocabulary are: o Unfamiliar vocabulary that are essential to understanding new content within explicit instruction o Not necessarily the bold words in the chapter. o Cumulative and continuously used throughout the year. o Integrated into word walls, a research-based strategy that will facilitate vocabulary acquisition. Common Board Configuration Elements (specific layouts may vary by sites, but must include each of these): Purpose: For the student to know what is being taught and what the student will learn o Date o Benchmark o Measurable, student-friendly objective o Essential Question o Bell work o Agenda (Specific daily schedule) o Homework o Exit Strategy/Card Lessons that infuse reading, writing, and discussion are imperative components of every subject area. There should be daily: o Teacher to student and student to student discourse utilizing academic vocabulary. o Reading and authentic writing 2 June 11, 2010…DRAFT **Problem solving to be embedded throughout the year** Preface o Writing that includes higher-order thinking o Incorporation of effective reading and writing instructional strategies Maps are organized to include the following: o Pacing o Objective o Essential questions, content and understanding, benchmarks, and assessment o Appendix/ resources 3 June 11, 2010…DRAFT **Problem solving to be embedded throughout the year** Elementary Mathematics Fourth Grade Pacing Guide First Nine Weeks Second Nine Weeks Third Nine Weeks Fourth Nine Weeks Big Idea #1: Multiplication Big Idea #2: Decimals and Fractions Big Idea #3: Area of 2-dimensional Finding Sums of Decimal Amounts shapes Use and Represent Whole Numbers (3 Multiply by 2-Digit and 3-Digit Whole Multiplication to Estimate Quotients weeks) Numbers (3 weeks) Decimal Place Value and Number Sense (2 weeks) Fractions and Division Multiplication and Division Concepts Model Division by 1-Digit and 2-Digit and Facts (2 weeks) Division (3 weeks) Understand Area (2 weeks) Divisibility Rules Algebra: Expressions, Equations, and Factors, Multiples, and Fractions (2 Angles and Two-Dimensional Shapes Factor Whole Numbers Patterns (2 Weeks) weeks) (3 weeks) Fractions and Mixed Numbers Multiply by 1-Digit Whole Numbers (2 Understand Decimal Place Value (2 Transformations and Symmetry (1 weeks) weeks) week) Order of Operations Relate Two-Dimensional Shapes and Addition Properties Three-Dimensional Shapes (1 Week) Compare and Order Numbers Temperature Points on a Grid Points, Lines, and Angles Measuring Angles Line Relationships Fractions and Area Congruent Three-Dimensional Shapes 4 June 11, 2010…DRAFT **Problem solving to be embedded throughout the year** Elementary Mathematics Fourth Grade Curriculum Map Use and Represent Whole Numbers (3 weeks) Objectives: 1. Use appropriate symbols to compare various equivalent forms of numbers through the millions period. 2. Build and represent numbers through the millions period two or more different ways. 3. Estimate sums and differences through the millions period and justify reasonableness of estimate. 4. Place numbers through the millions period on a number line. Academic Vocabulary: millions period, million, ten million, hundred million. Essential Questions Essential Content & Understanding Essential Skills and Benchmarks Assessment How does place value 1. Use and represent numbers through millions MA.4.A.6.1 Chapter Test affect numbers? Recognize differences in numbers, distances, Use and represent numbers Unit Test (Textbook) etc. through millions in various When is an estimate an Place value charts contexts, including estimation of Sample Resources: appropriate answer to Standard form relative sizes of amounts or Navigating through Numbers & a mathematical Expanded form distances. Operations: pgs. 15-21 problem? Word form Number lines http://www.linkslearning.org/ “make a list” Teachers/1_Math/6_Learning_Resour 2. **Present data through the millions period in real- ces/1_Illustrated_Lessons/3_Place_V world situations: alue/index.html Tables Graphs http://www.archtech.org/java/b10bl ocks/description.html Lists Charts 3. **Identify, compare, and or order numbers through the millions place in real-world contexts 4. **Find answers to real-world problems that involve adding and subtracting numbers through millions 5. **Estimations of numbers through millions and determine reasonableness of estimate. Practice with standard units Using number lines Using place value Benchmark numbers 6. **Use the following Inequality symbols 5 June 11, 2010…DRAFT **Problem solving to be embedded throughout the year** Elementary Mathematics Fourth Grade Curriculum Map appropriately (>,<, ≤, ≥, ≠) 7. Exact answer versus estimation in real-world situations Compatible numbers Place Value 8. **Finding numbers or ranges of numbers that are most appropriate or reasonable 6 June 11, 2010…DRAFT **Problem solving to be embedded throughout the year** Elementary Mathematics Fourth Grade Curriculum Map Multiplication and Division Concepts and Facts. (2 weeks) Objectives: 1) Describe various models for multiplication in problem solving situations. 2) Recall basic multiplication and related division facts. 3) Interpret situational story problems to create expressions, equations, and visual representations. 4) Model division as: a) The inverse of multiplication b) Partitioning c) Successive subtraction Academic Vocabulary: multiply, divide, factor, product, dividend, divisor, quotient, inverse operations, fact family, square number, multiple Essential Questions Essential Content & Understanding Essential Skills and Benchmarks Assessment How is multiplication 1. Develop quick recall of basic multiplication and MA.4.A.1.1 Chapter Test and division relevant in division facts through 12 Use and describe various models Unit Test (Textbook) daily situations? Continuous until mastery for multiplication in problem- Orally solving situations, and Sample Resources: How are properties Written demonstrate recall of basic http://www.naturalmath.com/mult/ helpful when solving Mastery achieved when recall is 5 sec. or less multiplication and related division mathematical 2. Use real-world problems using models in problem facts with ease. Navigating through Numbers & problems? solving situations Operations: pgs. 72-79; 108-113; Arrays 128-133; 141-146 Equal intervals on a number line M.A.4.A.4.2 *Splitting Arrays* applet on CD Facts from 0x0 through 12x12 Describe mathematics Patterns relationships using expressions, Square numbers equations, and visual 3. Properties of multiplication representations Multiplying with zeros M.A.4.A.6.2 Zero Property Use models to represent division Identity Property as: Commutative Property The inverse of Distributive Property multiplication Associate Property As partitioning **Use vocabulary terms factors and multiples As successive subtraction **Number being factored must be less than or equal to 7 June 11, 2010…DRAFT **Problem solving to be embedded throughout the year** Elementary Mathematics Fourth Grade Curriculum Map 100 **Multiple number must be 1-12, 25, 50, 100 M.A.4.A.6.4 Determine factors and multiples for specific whole numbers 8 June 11, 2010…DRAFT **Problem solving to be embedded throughout the year** Elementary Mathematics Fourth Grade Curriculum Map Chapter 3—Algebra: Expressions, Equations and Patterns (2 weeks) Objectives: 1. Use a pattern (numeric or non-numeric) to determine the expression or equation that can be used to find the value of the variable (or rule). 2. Extend patterns (numeric or non-numeric) to determine the “rule”. Academic Vocabulary: Distributive Property, numerical expression, algebraic expression, variable, function, equation Essential Questions Essential Content & Understanding Essential Skills and Benchmarks Assessment How can understanding 1. Generate algebraic rules to describe patterns using M.A.4.A.4.1 Chapter Test mathematical basic operations (+. -. X, ÷) Generate algebraic rules and use Unit Test (Textbook) properties help you **Include any of the four operations but will use only all four operations to describe solve mathematical one operation in each numeric pattern patterns, including nonnumeric Sample Resources: problems? 2. Numeric: growing or repeating patterns Navigating through Numbers & Using numbers (3,6,9,12,15,18,…n) Operations: pgs. 22-26 th How are algebraic rules What is the n number? useful in describing Write an expression to determine input. Navigating through Numbers & patterns? Review and extend finding input/output Operations: pgs. 72-79; 108-113; Example: S=12 + r 128-133; 141-146 S r *Splitting Arrays* applet on CD 17 ____ 23 ____ Navigating through Algebra: pgs. 12- ___ 7 14; 15-17; 18-22; 27-30; 61-63 Mental math/ multiplication- *Function Machine* applet on CD division patterns 3. Non-numeric Sample Resources: Shapes http://www.illuminations.nctm.org/le 4. Example: n ssonplans/3-5/variablemach/ 5. Identify and describe the algebraic rule for index.html determining the number of sides of a geometric A lesson plan that provides an shape: Shape + 1 = n introduction to the use of variables. Balance Equations **Extend a pattern beyond its next step **Repeated pattern should be shown with at least three examples of the repeated pattern 9 June 11, 2010…DRAFT **Problem solving to be embedded throughout the year** Elementary Mathematics Fourth Grade Curriculum Map **May use graphics, tables, or lists to describe patterns 6. Addition and subtraction 4 + S = 12. 7. Multiplication Example: draw diagram to show 5ℓ + 2 centimeters where ℓ is the length of the pencil and 2cm is length of the eraser 8. Basic Division 12/ F = 3 9. Algebraic expressions with two operations Solve and Evaluate algebraic expressions using two operations. Write expressions using variable for missing numbers Example: 10 + 5 – x = 12 (with and without parenthesis). **Use rules or relationships that involve only one operation or one-step function. **May include only one variable **A relationship must be defined in words, or at least four examples of the relationship must be provided 10 June 11, 2010…DRAFT **Problem solving to be embedded throughout the year** Elementary Mathematics Fourth Grade Curriculum Map Multiply by 1-digit Whole Numbers and Multiply by 2-digit and 3-digit Whole Numbers (5 Weeks) Objectives: 1. Determine factors and multiples of numbers through 100. 2. Demonstrate fluency of basic facts when solving multi-digit multiplication problems. 3. Derive partial products from invented and standard algorithm for multi-digit multiplication problems. 4. Use the distributive property to solve multi-digit multiplication problems fluently. Academic Vocabulary: Partial product, compatible numbers Essential Questions Essential Content & Understanding Essential Skills and Benchmarks Assessment What strategies can be 1. Multiply multi-digit whole numbers through MA.4.A.1.2—Multiply multi-digit whole Chapter Test used to multiply multiples 4 digits fluently numbers through four digits fluently, Unit Test (Textbook) of 10, 100, 1000 by a one- **Factors may not exceed three digits demonstrating understanding of the digit number? by three digits or four digits by two standard algorithm, and checking for Sample Resources: digits reasonableness of results, including Navigating through Numbers & How can the distributive **One digit must be zero in a three digit solving real-world problems. Operations: pgs. 72-79; 108-113; property help solve multi- by three digit multiplication problem M.A.4.A.1.1 128-133; 141-146 digit multiplication 2. Use the Distributive Property (Example: 13 x Use and describe various models for *Splitting Arrays* applet on CD problems? 14 can be thought of as (10 + 3)x (10 + multiplication in problem-solving 4)…10 x 10 and 10 x 4 then (3 x 10 ) and (3 x situations, and demonstrate recall of Justify your procedure for 4) a.k.a. partial products basic multiplication and related division finding products of multi- 3. Provide several classroom experiences with facts with ease. digit multiplication base ten blocks demonstrating standard MA.4.A.4.2 problems. algorithm’s derivation Describe mathematics relationships using 4. Develop understanding of standard expressions, equations, and visual algorithm. representations. 5. Check for reasonableness M.A.4.A.6.4 6. Find errors in multiplication problems to Determine factors and multiples for check understanding of partial products and specific whole numbers standard algorithm. M.A.4.A.6.6. Use inverse operation to check for correct Estimate and describe reasonableness of answer estimates; determine the solve read-world word problems appropriateness of an estimate versus an 7. **Solve multi-digit whole-number exact answer multiplication problems or supply partial products in real-world situations. 11 June 11, 2010…DRAFT **Problem solving to be embedded throughout the year** End of First Quarter Elementary Mathematics Fourth Grade Curriculum Map Model Division by 1-digit and 2-digit Divisors ( 3 weeks) Objectives: 1. Use models to represent division as: a. The inverse of multiplication b. Partitioning c. Successive subtraction 2. Translate situational story problems into division expressions or equations from models (such as array, equal-sized groups, area) Academic Vocabulary: Remainder, successive subtraction Essential Questions Essential Content & Understanding Essential Skills and Benchmarks Assessment 1. Use models to represent division MA.4.A.6.2 Chapter Test How can models be Inverse of multiplication Use models to represent division as: Unit Test (Textbook) used to Fact families for multiplication and division The inverse of multiplication Represent division’s a. (e.g. 13 x 14 = 182 and 182 ÷ 13 = 14) As partitioning Sample Resources: different modalities? As successive subtraction As successive subtraction http://www.beaconlearningcenter.co b. (Example: Find quotient 184 ÷ 13 by M.A.4.A.1.2 m/lessons/ repeatedly subtracting 13 and Multiply multi-digit whole numbers Lesson plans submitted by Florida counting number of groups of 13 through four digits fluently, Teachers that are linked to the subtracted before reaching zero) demonstrating understanding of the Sunshine State Standards. As partitioning (separating) using base-ten standard algorithm, and checking for What problem solving blocks or counters reasonableness of results, including strategies can be used 2. Divisibility rules solving real-world problems. to solve division 3. **Include only whole numbers and whole- M.A.4.A.4.2 problems? number remainders Describe mathematics relationships 4. **Translate a word problem to a using expressions, equations, and visual multiplication or division expression or representations. equation (from arrays, equal-sized groups, M.A.4.A.6.4 area, or visual representations) Estimate and describe reasonableness of estimates; determine the appropriateness of an estimate versus an exact answer 12 June 11, 2010…DRAFT **Problem solving to be embedded throughout the year** Elementary Mathematics Fourth Grade Curriculum Map Factors, Multiples, and Fractions (2 weeks) Objectives: 1. Determine factors and multiples for specific whole numbers. 2. Apply knowledge of factors and multiples to generate equivalent fractions. 3. Apply knowledge of factors and multiples to simplify fractions. 4. Explain why fractions, including fractions greater than one, are equivalent. Academic Vocabulary: common factor, common multiple, equivalent fractions, simplest form, common denominator, benchmark Essential Questions Essential Content & Understanding Essential Skills and Benchmarks Assessment How can arrays be use 1. Determine factors and multiples M.A.4.A.6.4 Chapter Test to find the factors of a Determine divisibility rules for 2, 3, 5, 9,10 Determine factors and multiples for Unit Test (Textbook) number? Find missing factors in patterns of multiples specific whole numbers Use array and number lines to find factors M.A.4.A.6.3 Sample Resources: and multiples Generate equivalent fractions and http://www.pen.k12.va.us/VDOE/Inst How can common Use arrays to find prime and composite simplify fractions ruction/Math/FractionsDecimalsPerc factors be found? Skip counting ent.pdf 2. Find square numbers/square Arrays creating squares Navigating through Numbers and How can you find multiplication tables Operations: *Fraction Models* common multiples? 3. Find common denominators for fractions applet on CD Two-color counters Circle fractions Navigating through Geometry: pgs. 88-89 Cuisenaire Rods Virtual Manipulatives 3. Generate equivalent fractions Generate rules for finding equivalent fractions and simplifying fractions using: Previous knowledge of factors/primes Models (student made) Fraction bars Number line Fraction Tiles Linear Models Area models Set models 13 June 11, 2010…DRAFT **Problem solving to be embedded throughout the year** Elementary Mathematics Fourth Grade Curriculum Map 4. **Rename fractions as mixed numbers or vice versa 5. **Common factors of the numerator and denominator must be less that or equal to 10 6. **Responses may or may not be in lowest terms. 14 June 11, 2010…DRAFT **Problem solving to be embedded throughout the year** Elementary Mathematics Fourth Grade Curriculum Map Understanding Decimal Place Value (2 weeks)Objectives: Objectives: 1. Name decimal (to the thousandths place) and fraction numbers between whole numbers. 2. Describe decimals as an extension of the base ten system. 3. Identify place value of digits to the right of the decimal to the thousandths place. 4. Relate commonly used fractions and decimals with models and on a number line. Academic Vocabulary: decimal, decimal point, tenths, hundredths, thousandths Essential Questions Essential Content & Understanding Essential Skills and Benchmarks Assessment How does placement of 1. Decimals through Thousandths MA.4.A.2.1 Chapter Test decimals affect place Use area model (graph paper) to represent Use decimals through the thousandths Unit Test (Textbook) value? decimals place to name numbers between whole Use base 10 blocks to represent tenths and numbers. Sample Resources: hundredths http://www.linkslearning.org/ What does a decimal MA.4.A.2.2 represent? Name and locate values between whole Teachers/1_Math/6_Learning_Resour Describe decimals as an extension of the ces/1_Illustrated_Lessons/3_Place_V numbers using a number line base-ten number system **Identify decimals and/or fractions from a alue/index.html How can decimals and graphical representation or a number line MA.4.A.2.3 Students work with place value fractions be related on 2. Decimals as extension of base-ten number Relate equivalent fractions and using whole numbers as well as a number line? system decimals with and without models, decimals. This interactive, computer- including locations on a number based lesson includes activities and Know that the relationship between adjacent line assessments places in whole numbers is or can be described by a ten-to-one rule Sample Resources: **Identify the place value of a digit to the http://www.archtech.org/java/b10bl right of the decimal point ocks/description.html 3. Relate equivalent fractions and decimals Visual representations of base-10 Models fractions and decimals with number place value and multi-digit line operations, a valuable tool for Fraction bars teachers to use in class or for Fraction kits (students made) students to use on their own. Fraction tiles **Identify decimals that are equivalent to commonly used fractions or mixed numbers **May include mixed numbers and/or 15 June 11, 2010…DRAFT **Problem solving to be embedded throughout the year** End of Second Quarter Elementary Mathematics Fourth Grade Curriculum Map fractions **May assess translating the following commonly used fractions or mixed numbers to decimals (or their decimal equivalents): 1/10, ¼, ½, ¾, all fifths, tenths, hundredths, and thousandths. (eg. 0.2, 0.20, 0.200, and 2/10 are all equivalent. Also, 0.5 = ½, 3/5, = 0.6, 3/2 = 1.5, or 7 ½ = 7.5. 4. Use coins as basis for understanding place value of tenths and hundredths 16 June 11, 2010…DRAFT **Problem solving to be embedded throughout the year** End of Second Quarter Elementary Mathematics Fourth Grade Curriculum Map Decimal Place Value and Number Sense (3 weeks) Objectives: 1. Compare and order decimals on a number line. 2. Relate halves, fourths, tenths, and hundredths to decimals. 3. Relate halves, fourths, tenths, and hundredths to percents. 4. Estimate fraction and decimal amounts in real-world problems. 5. Justify reasonableness of estimates. Academic Vocabulary: decimals, not equal to ( ≠ ), greater than ( > ), less than ( < ), greater than or equal to ( ≥ ), less than or equal to ( ≤ ) percent Essential Questions Essential Content & Understanding Essential Skills and Benchmarks Assessment How are comparing and 1. Compare and order decimals MA.4.A.2.4 Chapter Test estimating decimals Relate decimals to fractions Compare and order decimals, and Unit Test (Textbook) and fractions used in Number lines estimate fractions and decimal amounts everyday life? Representative drawings in real-world problems. Sample Resources: http://askeric.org/cgi- Making charts How can models be MA.4.A.6.5 bin/printlessons.cgi/Virtual/Lessons/ Benchmark decimals: used to compare Relate halves, fourths, tenths, and Mathematics/Number_Sense/NUS02 1. 5ths as decimals (e.g., 3/5 = decimals? hundredths to decimals and 00.html 0.6) Percents. An activity in which students 2. halves as decimals (e.g. 7 ½ = arrange themselves into decimal 7.5) numbers. **Compare and order mixed numbers and decimals through the thousandths http://funbrain.com/football/index.h place with no more than five digits tml **Compare and order decimals, Power Football provides fractions, and/or mixed numbers interactive practice with the decimal between two numbers concepts. 2. Estimate fraction and decimal amounts http://www.pen.k12.va.us/VDOE/Inst Using number lines ruction/Math/FractionsDecimalsPerc Dollar amounts, money and cents, to ent.pdf hundredths Real-world setting Navigating through Numbers & **Identify a fraction or decimal that is Operations: pgs. 41-48 closest to another number or a *Fraction Models* applet on CD benchmark fraction, eg., 7/16 of a 17 June 11, 2010…DRAFT **Problem solving to be embedded throughout the year** Elementary Mathematics Fourth Grade Curriculum Map circle is closer to ½ than 1/3 3. May include fractions with denominators of 1 through 12, 16, 20, 25, 50, 100, and 1000 4. Relate common fractions to decimals and percents using: Models Symbols (Such as ¼ = 0.25 = 25%) **Convert a percent to a fractions or a decimal **Convert a fraction or a decimal to a percent **Fractions: ¼. ½. ¾. all tenths, and all hundredths may be converted to percents (e.g., ¼ = 25%, or ¾ = 75%) or vice versa. 5. Real world problem solving using percent off, etc. **May include graphic models of fractions, decimals, or percents 18 June 11, 2010…DRAFT **Problem solving to be embedded throughout the year** Elementary Mathematics Fourth Grade Curriculum Map Understanding Area (2 Weeks) Objectives: 1. Describe and model area as the number of same-sized units that cover a region in the plane. 2. Use appropriate units of measure when solving area problems. 3. Justify the formula for the area of the rectangle “area = base x height”. 4. Select appropriate tools (customary and metric) to measure area in real-world situations. 5. Estimate area and justify reasonableness of estimate. 6. Identify real-world uses of the area formula. Academic Vocabulary: area, square unit (sq un), base, height, formula Essential Questions Essential Content & Understanding Essential Skills and Benchmarks Assessment How can real world 1. Determine area and focus on countable MA.4.G.3.1 Chapter Test problems be solved square units: Describe and determine area as the Unit Test (Textbook) using area? Geo boards number of same-sized units that cover a Tiles region in the plane, recognizing that a Sample Resources: How can the area of a Grid paper unit square is the standard unit for Navigating through Measurement: non-standard shape be Snap cubes measuring area pgs. 53-57; 62-65 found? Tables MA.4.G.3.2 2. **Determine the area of a figure or a region Justify the formula for the area of the www.shodor.org/intgeractivate/lesso How can the area of a on a plane by using countable units rather rectangle “area = base X height” ns/lpa.html complex shape be than multiplying dimensions. MA.4.G.3.3 This lesson is designed to examine found? 3. **Estimate areas of irregular geometric Select and use appropriate units, both the mathematical concepts of length, shapes customary and metric, strategies, and perimeter, and area. 4. **Include countable units that estimate to a measuring tools to estimate and solve whole unit or half unit real-world area problems www.funbrain.com/poly/ 5. **Use one-to-one scale Activities involving area and 6. ** show shapes on a grid, with grid lines perimeter extended through the shape, and without. 7. Area formula Navigating through Measurement: Derive relationship between counting units pgs. 58-61 to find area and finding area by multiplying *Stuck on Stickers* applet on CD 8. **Identify situations that require the use of the area formula in real-world contexts 9. **Identify the number of square units of a rectangle as the base times the height 19 June 11, 2010…DRAFT **Problem solving to be embedded throughout the year** Elementary Mathematics Fourth Grade Curriculum Map 10. **Derive or explain the area of a rectangle in order to solve real-world problems 11. **Responses should include units. 12. Select and use appropriate measuring tools and strategies decompose area of composite shape into two rectangles and determine area of both shapes and then combine together Use customary and metric measuring tools to measure base and height to determine area. 13. Solving real world problems involving above units Recognize difference in measurement units Use appropriate metric units Identify appropriate measurement tools 14. **Solve problems involving the area of a rectangle or a composite shape 15. **Include figures with whole-number dimensions of 100 or fewer units. 16. Find errors in measuring and area situations, including incorrect units of measurement 20 June 11, 2010…DRAFT **Problem solving to be embedded throughout the year** Elementary Mathematics Fourth Grade Curriculum Map Angles and Two-Dimensional Shapes (3 Weeks) Objectives: 1. Identify acute, obtuse, and right angles. 2. Identify benchmark angle measurements of 45°, 90°, 180°, and 360°. 3. Classify angles of 2-D shapes using benchmark angles. 4. Use appropriate geometric notation for angles and degrees. Academic Vocabulary: angle, right angle, degree (° ), vertex, clockwise, counterclockwise, acute angle, obtuse angle, reflex angle Essential Questions Essential Content & Understanding Essential Skills and Benchmarks Assessment How can angles be 1. Classify angles using plane figures MA.4.G.5.1 Chapter Test classified, measured, identify angles in environment Classify angles of two-dimensional Unit Test (Textbook) and drawn using Review lines, rays, and line shapes using benchmark angles (i.e. Sample Resources: benchmark angles? relationships 45°, 90°, 180°, and 360°). Navigating through Geometry: pgs. Set right angles as identifiers 15-21 Use protractor to draw angles of various degrees making sure to emphasize the benchmark angles. Use geo boards or square dot paper to draw shapes with angles **Classify angles by the following terms: acute, obtuse, right, or straight **Identify the benchmark angle measurements of 45°, 90°, 180°, and/or 360°. **Use the geometric notation for angle and degrees ( <, ° ) 21 June 11, 2010…DRAFT **Problem solving to be embedded throughout the year** Elementary Mathematics Fourth Grade Curriculum Map Transformations and Symmetry (1 Week) Objectives: 1. Identify different types of transformations (i.e. reflection, rotation, translation). 2. Describe the results of a transformation on an object. 3. Use transformations to create new shapes. 4. Rotate figures with rotational symmetry from point of rotation according to descriptors of rotation. Academic Vocabulary: transformation, translation, reflection, rotation, line symmetry, line of symmetry, tessellation Essential Questions Essential Content & Understanding Essential Skills and Benchmarks Assessment How can shapes be 1. Identify and describe the results of MA.4.G.5.2 Chapter Test transformed? translations, reflections, and rotations Identify and describe the results of Unit Test (Textbook) Transformations translations, reflections, and How does a reflection Rotational symmetry rotations of 45, 90, 180, 270, and 360 Sample Resources: transform a shape? Line symmetry degrees, including figures with line Navigating through Geometry: pgs. Identify degree of change of transformed and rotational symmetry 55-58; 77-79 How can a line of figures *Tangram Challenges* applet on CD symmetry be found? **Include no more than two transformations 2. Identify shapes that can produce tessellations 3. Creates tessellations 4. Explain how to manipulate shapes to create different shapes using transformations to a partner while they try to recreate the shape being described. 22 June 11, 2010…DRAFT **Problem solving to be embedded throughout the year** Elementary Mathematics Fourth Grade Curriculum Map Relate Two-Dimensional Shapes and Three-Dimensional Shapes (2 Weeks) Objectives: 1. Identify 2-D shapes that compose a 3-D Shape from different orientations (top, bottom, side). 2. Compose 3-D shapes from 2-D view of that shape. 3. Recreate and describe 2-D and 3-D objects viewed from different orientations using appropriate academic vocabulary. Academic Vocabulary: dimension, face, base, two-dimensional, three-dimensional Essential Questions Essential Content & Understanding Essential Skills and Benchmarks Assessment What are different 1. Build three-dimensional objects from objects MA.4.G.5.3 Chapter Test ways geometry is used with two-dimensional representations using: Identify and build a three- Unit Test (Textbook) in our world? blocks dimensional object from a two- tiles dimensional representation of that Sample Resources: How are two- unifix cubes object and vice versa. Navigating through Geometry: pgs. dimensional shapes 2. Identify 11-14; 22-25; 26-30; 31-34; 80-82; 83- and three-dimensional Geometric shapes 85; 90-94 shapes related? faces edges *Exploring Geometric Solids* vertices *Shape Sorter* & *Pattern Patch* **Identify a three-dimensional object applet on CD from two-dimensional object Navigating through Measurement: **Identify one or more of the two- pgs. 77-82 dimensional views of a three-dimensional object **Include drawings of views from the top, sides, front, or base of an object 3. Create nets to identify 2-dimensional shapes composing 3-dimensional solids 4. **Three-dimensional objects represented in items must be made from cubes 5. **Two-dimensional views should show lines indicating square units 23 June 11, 2010…DRAFT **Problem solving to be embedded throughout the year** End of Third Quarter Elementary Mathematics Fourth Grade Curriculum Map Remediate Extend Use Big Idea Projects “Getting Ready for First Grade” Create small groups based on needs assessment and re-visit Finding Sums of Decimal Amounts skills not yet mastered Multiplication to Estimate Quotients Fractions and Division Divisibility Rules Factor Whole Numbers Fractions and Mixed Numbers Order of Operations Addition Properties Compare and Order Numbers Temperature Points on a Grid Points, Lines, and Angles Measuring Angles Line Relationships Fractions and Area Congruent Three-Dimensional Shapes **Resources for Big Idea Projects & Getting Ready for First Grade can be found in the “Planning Guide – End of Year Resources”** 24 June 11, 2010…DRAFT **Problem solving to be embedded throughout the year** End of Fourth Quarter Fourth Grade Math Curriculum Map Appendix Scope and Sequence Correlated to Textbook Pages State Approved Benchmarks with Access Points Resources 25 Fourth Grade Scope & Sequence First Nine Weeks Chapter 1: Use and Represent Whole Numbers (3 weeks) Chapter 2: Multiplication and Division Concepts and Facts (2 weeks) Chapter 3: Algebra: Expressions, Equations, and Patterns (2 Weeks) Chapter 4: Multiply by 1-Digit Whole Numbers (2 weeks) Second Nine Weeks Chapter 5: Multiply by 2-Digit and 3-Digit Whole Numbers (3 weeks) Chapter 6: Model Division by 1-Digit and 2-Digit Division (3 weeks) Chapter 7: Factors, Multiples, and Fractions (2 weeks) Chapter 8: Understand Decimal Place Value (2 weeks) Third Nine Weeks Chapter 9: Decimal Place Value and Number Sense (2 weeks) Chapter 10: Understand Area (2 weeks) Chapter 11: Angles and Two-Dimensional Shapes (3 weeks) Chapter 12: Transformations and Symmetry (1 week) Chapter 13: Relate Two-Dimensional Shapes and Three-Dimensional Shapes (1 Week) June 11, 2010… DRAFT 26 State Approved Fourth Grade Math Standards Benchmark Coding Scheme MA. 4. A. 1. 1 Subject Grade Level Body of Knowledge Big Idea / Supporting Benchmark Idea Body of Knowledge Key: A ~ Algebra C ~ Calculus D ~ Discrete Mathematics F ~ Financial Literacy G ~ Geometry P ~ Probability S ~ Statistics T ~ Trigonometry June 11, 2010… DRAFT 27 State Approved Fourth Grade Mathematics Standards Benchmark Body Of Cognitive Descriptor Idea Remarks/Examples Number Knowledge Complexity Use and describe various Given real-world problems and accompanying models that include models for equal-sized groups, arrays, area, and equal intervals on the number multiplication in line, students should be able to give the multiplication or division problem-solving basic fact associated with the situation. MA.4.A.1.1 situations, and Algebra BIG IDEA 1 The goal is to develop quick recall of multiplication facts and related Moderate demonstrate recall of division facts. basic multiplication and Basic multiplication facts include the factors 0 through 9. related division facts with ease. Related division facts include divisors 1 through 9 and dividends 0-81. Multiply multi-digit whole numbers through Place value and properties of operations and numbers should play four digits fluently, major roles in developing strategies for multiplying multi-digit whole demonstrating numbers. For example, 13 x 14 can be thought of as (10 + 3) x (10 + understanding of the 4). The Distributive Property can then be applied along with focus on MA.4.A.1.2 standard algorithm, and Algebra BIG IDEA 1 High decomposition of numbers to multiply 10 x 10 and 10 x 4 then 3 x 10 checking for and 3 x 4. These partial products are added to find the product of 13 x reasonableness of 14. This process should be connected to the standard algorithm. results, including solving real-world problems. June 11, 2010… DRAFT 28 State Approved Fourth Grade Mathematics Standards Benchmark Body Of Cognitive Descriptor Idea Remarks/Examples Number Knowledge Complexity 13 x 14 = (10 + 3) x (10 + 4) = 10 x 10 + 10 x 4 + 3 x 10 + 3 x 4 Students may use a place value mat to represent decimal numbers through the thousandths with objects, write the symbolic Use decimals through representation with numerals, and name the decimal represented with the thousandths place to words. MA.4.A.2.1 Algebra BIG IDEA 2 Low name numbers between whole numbers. Students can identify decimal numbers on a number line, write the symbolic representation with numerals, and name the decimal value with words. Describe decimals as an By fourth grade, students should know that the relationship between MA.4.A.2.2 extension of the base-ten Algebra BIG IDEA 2 adjacent places in whole numbers is described by a ten-to-one rule (…, High number system. 1000, 100, 10, 1, 0.1, 0.01,...). This relationship should be developed June 11, 2010… DRAFT 29 State Approved Fourth Grade Mathematics Standards Benchmark Body Of Cognitive Descriptor Idea Remarks/Examples Number Knowledge Complexity for decimals. Students can explore equivalency of fractions and decimals by using Relate equivalent rulers. fractions and decimals with and without MA.4.A.2.3 Algebra BIG IDEA 2 Moderate models, including locations on a number Models may include rulers, fraction circles, sets of similar objects, and line. drawings. Measurements (e.g., lengths) and dollar amounts provide useful contexts for estimating in the real world. Compare and order Students should understand the relationships and equivalencies decimals, and estimate between decimals and fractions. . A decimal number may have an MA.4.A.2.4 fraction and decimal Algebra BIG IDEA 2 Moderate equivalent fraction- one where the denominator is (or can be) a power amounts in real-world of 10, at this grade level 10, 100, or 1000. They should also be able to problems. represent 5ths as decimals (for example, 3/5= 0.6) and halves as decimals (for example, 7 ½ = 7.5). Example 1: A number pattern is: 3, 6, 9, 12, 15, 18... What is an algebraic rule to describe the nth number in the pattern? Generate algebraic rules and use all four Example 2: The triangle below is shape 1 and the square is shape 2. operations to describe This same pattern continues, in which each shape has one more side High MA.4.A.4.1 Algebra Algebra patterns, including than the previous shape. How many sides would shape n have, where n nonnumeric growing or can be any natural number? How do you know? repeating patterns. Example: Mr. Sims has 168 oranges. He wants to pack them into boxes with 28 in each box. How many boxes does he need? Use Describe mathematics pictures or diagrams to show what is happening in the problem. relationships using Record your solution with equations. MA.4.A.4.2 expressions, equations, Algebra Algebra High and visual representations. Example Alex is 4 years older than twice as old as Sam What June 11, 2010… DRAFT 30 State Approved Fourth Grade Mathematics Standards Benchmark Body Of Cognitive Descriptor Idea Remarks/Examples Number Knowledge Complexity expression gives Alex's age if you use the variable "S " to represent Sam's age? Regina received $50 from her grandmother as her birthday gift. Her grandfather told her that his Birthday gift will be to give her $5 each month, starting the month after her birthday. Regina decided to save her birthday gifts to buy her favorite music player. The table below illustrates the total amount of gift money that Regina will have received each month. Write an algebraic expression that can be used to show the total amount of money that Regina will have each month. Recognize and write algebraic expressions for MA.4.A.4.3 Algebra Algebra High functions with two operations. Month 0 1 2 … n Amount 50 50 + 5 50+5 + … ? of 5 Money Use and represent numbers through millions in various Number and Students should recognize the difference between distances such as MA.4.A.6.1 contexts, including Algebra Moderate Operations 100 feet and 1,000 feet or 10 km and 200 cm. estimation of relative sizes of amounts or distances. Use models to represent The inverse of multiplication: 4 x 45 = 180, 180 ÷ 4 = 45, and 180 ÷ division as: 45 = 4. Number and MA.4.A.6.2 the inverse of Algebra Moderate Operations multiplication as partitioning Partitioning: We can share 180 things (possibly represented by base- as successive ten blocks) evenly among 4 groups and determine the number of items June 11, 2010… DRAFT 31 State Approved Fourth Grade Mathematics Standards Benchmark Body Of Cognitive Descriptor Idea Remarks/Examples Number Knowledge Complexity subtraction in each group. Successive subtraction: We can find the quotient of 180 ÷45 by repeatedly subtracting 45 and counting the number of groups of 45 subtracted before reaching zero. The area model is a useful model for exploring the inverse relationship between multiplication and division. Generate equivalent Earlier work with models of equivalent fractions in grade 3 should Number and MA.4.A.6.3 fractions and simplify Algebra help students to develop conceptual understanding for the rules for Moderate Operations fractions. generating equivalent fractions and simplifying fractions. Multiples and factors should be explored as students determine common denominators for fractions. Determine factors and Number and Use models to identify square numbers to 100. MA.4.A.6.4 multiples for specified Algebra Moderate Operations whole numbers. Example: You have 28 chairs. Show all of the ways you can arrange these chairs into arrays. Draw the arrays. Record the dimensions of the arrays. Relate halves, fourths, Relate common fractions to equivalent decimals and percents such as: tenths, and hundredths Number and MA.4.A.6.5 Algebra 1/4 = 0.25 = 25%. These representations should be related through Moderate to decimals and Operations both models and symbols. percents. MA.4.A.6.6 Estimate and describe Algebra Number and An example in which an estimate is more appropriate than an exact High June 11, 2010… DRAFT 32 State Approved Fourth Grade Mathematics Standards Benchmark Body Of Cognitive Descriptor Idea Remarks/Examples Number Knowledge Complexity reasonableness of Operations answer is in estimating the amount of food needed for a party. You estimates; determine the know the number of people you invited, but still you need to estimate appropriateness of an the amount of food and drink to buy. estimate versus an exact answer. Describe and determine area as the number of same-sized units that Geoboards, tiles, and grid paper provide helpful contexts for this cover a region in the MA.4.G.3.1 Geometry BIG IDEA 3 exploration. The focus is on countable units rather than multiplying Moderate plane, recognizing that a dimensions. unit square is the standard unit for measuring area. The students should be able to justify the formula for the area of the rectangle by explaining how counting units to find area of a rectangle is related to finding the area by multiplying. Justify the formula for MA.4.G.3.2 the area of the rectangle Geometry BIG IDEA 3 Moderate "area = base x height". The idea of the area of a rectangle as "base x height" rather than "length x width" is useful in connecting to other area formulas. Students should recognize that the area of a piece of paper might be measured in square inches, the area of a room might be measured in Select and use square feet, and the area of a large piece of land might be measured in appropriate units, both square miles. Alternately, these measurements might be in square customary and metric, centimeters, square meters, and square kilometers, respectively. MA.4.G.3.3 strategies, and Geometry BIG IDEA 3 Moderate measuring tools to estimate and solve real- world area problems. Example: Students find the area of a composite shape. An L-shaped region may be decomposed into rectangular regions. June 11, 2010… DRAFT 33 State Approved Fourth Grade Mathematics Standards Benchmark Body Of Cognitive Descriptor Idea Remarks/Examples Number Knowledge Complexity Example: Find the area of the polygon in the picture. Explain or show how you found the area. Use pictures of real world objects or diagrams of shapes with angles and ask students to classify the given angles by using benchmark Classify angles of two- angles. dimensional shapes Geometry MA.4.G.5.1 using benchmark angles Geometry and Low (45°, 90°, 180°, and Measurement 360°) Use protractor to draw the angles of 45, 90, 180, and 360 degrees. Identify and describe the results of translations, reflections, and rotations Geometry Paper folding, mirrors, and computer technology may be helpful in MA.4.G.5.2 of 45, 90, 180, 270, and Geometry and developing student understanding of these concepts. Simple Moderate 360 degrees, including Measurement tessellation of plane may provide engaging opportunities for practice. figures with line and rotational symmetry. June 11, 2010… DRAFT 34 State Approved Fourth Grade Mathematics Standards Benchmark Body Of Cognitive Descriptor Idea Remarks/Examples Number Knowledge Complexity Example: A cylinder is composed of 2 bases (circles) & a rectangle. A cube is composed of six squares. A sphere is not easily decomposed into basic two dimensional shapes. Identify and build a three-dimensional object Geometry MA.4.G.5.3 from a two-dimensional Geometry and Moderate representation of that Measurement Provide nets for students to construct 3-dimensional objects. Challenge object and vice versa. students to create their own nets using grid paper. June 11, 2010… DRAFT 35

DOCUMENT INFO

Shared By:

Categories:

Tags:
Fourth grade, 4th Grade, Social Studies, grade students, Grade Level, fourth grade math, language arts, Multiplication and Division, third grade, fourth-grade students

Stats:

views: | 80 |

posted: | 8/18/2011 |

language: | English |

pages: | 35 |

OTHER DOCS BY cuiliqing

Docstoc is the premier online destination to start and grow small businesses. It hosts the best quality and widest selection of professional documents (over 20 million) and resources including expert videos, articles and productivity tools to make every small business better.

Search or Browse for any specific document or resource you need for your business. Or explore our curated resources for Starting a Business, Growing a Business or for Professional Development.

Feel free to Contact Us with any questions you might have.