M ATHEMATICS C URRICULUM M AP Fifth Grade 2010 Table of Contents Overview: I. II. III. IV. V. Best Practices Assessment Fifth Grade Vocabulary Timeline Important ISAT Concepts Units by Standard: Unit 1: Multiply Whole Numbers Unit 2: Divide Whole Numbers Unit 3: Algebra Expressions and Equations Unit 4: Decimals Overview Unit 5: Add and Subtract Decimals Unit 6: Multiplying Decimals Unit 7: Divide Decimals by Whole Numbers Unit 8: Fraction Concepts Unit 9: Add and Subtract Fractions Unit 10: Add or Subtract Mixed Numbers Unit 11: Multiply Fractions Unit 12: Divide Fractions Unit 13: Ratio, Percents, and Probability Unit 14: Geometric Figures Unit 15: Plane and Solid Figures Unit 16: Perimeter Unit 17: Area Unit 18: Volume Unit 19: Number Concepts Unit 20: Data Grouping Unit 21: Customary and Metric Measurements Unit 22: Graph and Integers Unit 23: Coordinate Plane and Order Pairs Unit 24: Patterns * The asterisk next to a document represents an adapted document. Best Practices Small Group Modeling Guided Practice Independent Practice Plans and teaches lessons to support full implementation of mathematics core standards. Establishes physical classroom environment to support mathematics learning Establishes classroom climate or culture focused on studentācentered learning Supports mathematical communication (student’s ability to explain mathematical process) Common Math vocabulary Uses assessment to support student learning and to guide planning. Relating Concepts to real life situations Incorporate word problems within units Use concrete examples and have students draw representations of concepts * The asterisk next to a document represents an adapted document. Assessment Core Practice- Independent Wrkst. Activities- Showing understanding Quizzes Pre- Post Test Common Assessment Observations MAP Assessment ISAT Assessment * The asterisk next to a document represents an adapted document. Fifth Grade Vocabulary Abbreviations Acute Angle Approximately Approx. Equal to ( ≈) Arc Arithmetic Average Base Bisect Characteristic Chord Circle Circumference Column Combination Compare Composite Number Congruent Symbols Coordinate Graph Correspond Cubic Units Data Decimeter Degrees (C) (F) Diagonals Diagram Difference Digits Dimensions Dividend Divisor Elapsed Time Equilateral Triangle Estimate Exact Expression Factors Gallon Greatest Common Factor Half Heptagon Intersect Intersecting Lines Irregular Polygon Isosceles Triangle Least Common Multiple Liter (l) Lowest Terms Mean (Average) Median Midpoint Miles Per Hour (MPH) Mode Multiple Multiplication (x or •) Nonagon Nth Term (exponents) Numeral Numerical Obtuse Angle Order of Operations Parallelogram Per Percent (%) Perpendicular (symbol) Pint (pt) Polygon Proportion Product Quadrilateral Quart (qt) Quotient Range Ratio Reflection Right Angle (symbol) Rotation Round Row Scale Drawing Scalene Triangle Sequence Slides Square Units Stem-and-leaf plot Ton (t) Triangle * The asterisk next to a document represents an adapted document. Fifth Grade- Concepts 4.NBT.1 4.OA.2 4.OA.3 4.NBT.1 Unit Review CCS Title Number Computations Skill(s) 1. 2. 3. 4. 5. 6. 7. 8. 1. 2. 3. 4. 5. 6. 7. 1. 2. 3. 4. 5. 6. 7. 8. 1. 2. 3. 4. 5. 6. 5.NBT.1 5.NBT.2 5.NBT.5 5.NF.5A 1 Multiply Whole Numbers 5.NBT.2 5.NBT.6 2 Divide Whole Numbers 5.OA.1 5.OA.2 3 Algebra Expressions and Equations 4 Decimals Overview ISAT CONCEPT 5.NBT.3 Duration 1. Rounding 2. Estimation Place Value Patterns in Place Value Place Value with Expanded Form Estimate Products Multiply by 10’s and 100’s Find Patterns Choose correct methods Comparing Factors Estimate with 1-Digit Divisors Divide by 1-Digit Divisors Write the remainder as a Mixed Number Zeros in Division Patterns in Division Estimate with 2-Digit Divisors Divide by 2-Digit Divisors Order of Operations Write Expressions Evaluate Expressions Properties Write Equations Solve Equations- Missing Numbers- Variables Functions Inequalities Decimal Place Value Verbal, Written, and Numerical Representation Create Models/Drawing to represent place value Equivalent Decimals Compare and Order Decimals Predict and Draw Conclusions * The asterisk next to a document represents an adapted document. 5.NBT.3 5.NBT.4 5 Add and Subtract Decimals 5.NBT.7 6 Multiplying Decimals 7 Divide Decimals by Whole 1. Divide Decimals 2. Estimate Quotients Numbers ISAT CONCEPT 5.NBT.7 ISAT CONCEPT 5.NF.1 5.NF.2 8 Fraction Concepts 9 Add and Subtract Fractions ISAT CONCEPT 5.NF.1 5.NF.2 5.NF.1 5.NF.2 10 Add or Subtract Mixed Numbers 1. 2. 3. 1. 2. 3. 4. 1. 2. 3. 4. 5. 6. 7. 8. 1. 2. 3. 4. 5. 6. 1. 2. 3. 4. 5. Round Decimals Add and Subtract Decimals Estimate Sums and Differences Multiply Decimals Estimate Products Divide Decimals with Whole Numbers Evaluate Answers for reasonableness Understand Fractions Equivalent Fractions Simplest Form Understand Mixed Numbers Improper Fractions Compare and Order Fractions Compare and Order Mixed Numbers Relate Fractions to Decimals Add and Subtract Like Fractions Model Addition of Unlike Fractions Model Subtraction of Unlike Fractions Estimate Sums and Differences of Fractions Add and Subtract Unlike Fractions- Common Denominators Compare Strategies Model Addition of Mixed Numbers Model Subtraction of Mixed Numbers Estimate Sums and Differences of Mixed Numbers Add and Subtract Mixed Numbers Subtraction with Renaming * The asterisk next to a document represents an adapted document. 5.NF.4a 5.NF.5b 5.NF.6 11 Multiply Fractions 5.NF.3 5.NF.7a 5.NF.7b 5.NF.7c 12 Divide Fractions 1. 2. 3. 4. 1. 2. 3. 4. 5. ISAT CONCEPT 13 Ratio, Percents, and Probability 1. 2. 3. 4. 5. 6. 5.G.3 5.G.4 14 Geometric Figures 15 Plane and Solid Figures 1. 2. 3. 4. 5. 6. 7. 8. 1. 2. 3. 4. 5. 6. ISAT CONCEPT 5.G.3 5.G.4 ISAT CONCEPT Model Multiplication of Fractions Multiplication of Fractions Multiplication of Fractions and Whole Numbers Multiply with Mixed Numbers Model Fraction Division Write Remainders as Mixed Numbers Divide Whole Numbers by Fractions Divide Fractions by Whole Numbers Divide Fractions Understand and Express Ratios Ratios and Rates Understand Percents Percents (relate to fractions and decimals) Understand Probability Understand Predictions of Probability (likeliness) Points, Lines, and Angles Measure and Draw Angles Polygons Compare Relationships of Polygons Circles Congruent and Similar Figures Symmetry Diagonals of Polygons Classifying Triangles Classifying Quadrilaterals (2D) Draw and Model Quadrilaterals and Triangles Solid Figures (3D) Nets of Solid Figures Vertices, Faces, Edges * The asterisk next to a document represents an adapted document. ISAT CONCEPT 16 Perimeter 1. 2. 3. 4. 5. 6. 5.NF.4b 5.NF.5a 5.NF.6 17 Area 5.MD.3a 5.MD.3b 5.MD.4 5.MD.5a 5.MD.5b 5.MD.5c 18 Volume 1. Model Multiplication of Area 2. Area of Square and Rectangles using square units 3. Area of Square and Rectangles using formula 4. Compare Perimeter to Area 5. Area of Triangles 6. Area of Parallelograms 7. Estimate Area 8. Relate and Compare Perimeter, Volume, Area 1. Model Multiplication of Volume 2. Find Volume Using square units 3. Solve Volume as Multiplication and Addition 4. Estimate Volume 5. Compare Volume 6. Volume as the Associative Property 7. Relate and Compare Perimeter, Volume, Area ISAT CONCEPT 19 Number Concepts ISAT CONCEPT 20 Data Grouping ISAT CONCEPT 1. 2. 3. 4. 5. 6. 7. 1. 2. Find Perimeter Perimeter Formulas Estimate and Measure Perimeter Circumference Polygon Sides Compare Perimeters Multiples and Least Common Multiples Divisibility Factors and Greatest Common Factors Prime and Composite Numbers Understand Exponents Exponents and Square Numbers Prime Factorization Mean, Median, Mode, and Range Compare the data and Concepts of the mean, median, mode, and range. * The asterisk next to a document represents an adapted document. 21 Customary and Metric Measurements 22 Graphs and Integers 5.MD.2 5.G.1 5.G.2 23 Coordinate Planes and Ordered Pairs 5.OA.3 24 Patterns 5.MD.1 ISAT CONCEPT 5.OA.3 5.MD.2 5.G.1 5.G.2 ISAT CONCEPT ISAT CONCEPT 1. 2. 3. 4. 5. 6. 7. 1. 2. 3. 4. 5. 6. 7. 8. 9. 1. 2. 3. 4. 1. 2. 3. 4. 5. 6. Customary Lengths Metric Lengths Customary Capacity and Weight Metric Capacity and Mass Estimate or Actual Measurement Elapsed Time Temperature Make Bar Graphs and Pictographs Make Histograms Make Circle Graphs Make a Stem-and-Leaf Graph Make Line Graphs Understand integers Compare and Order Integers Choose the Appropriate Graph Relationships of Graphs Create a Coordinate Plane Graph Ordered Pairs Graph Relationships Graph Integers on Coordinate Plane Transformations Tessellations Create a Geometric Pattern Numeric Patterns Find a Pattern Input/ Output- Rules/Sequencing /X- and YCharts * The asterisk next to a document represents an adapted document. Review: Number Computations Approximate Duration of Study: 1 - 2 weeks CCS Supports 4.NBT.1 Supports 4.OA.2 4.OA.3 Essential Question How do we round numbers? How does rounding vary depending on the place value that is being rounded to? How do we estimate an answer? Concepts Rounding Estimation Skills Round two and three digit numbers to the tens place value. Round two and three digit numbers to the hundreds place value. Round two and three digit numbers to the thousands place value. Estimate the sum. Estimate the difference. Estimate the product. Estimate the quotient. Assessments Helpful Strategies and Resources Pretest Pretest* Posttest Posttest* Quiz Quiz * SMART Notebook- Rounding BrainPOP- Rounding SMART Notebook- Estimation SMART Notebook- Estimation Quiz Template BrainPOP- Estimation Vocabulary: Rounding, Estimation, Place Value, Expanded Form, Powers of Ten, Product, Quotient, Sum and Difference. Timeline * The asterisk next to a document represents an adapted document. Unit 1: Multiply Whole Numbers CCS Supports 5.NBT.1 5.NBT.2 5.NBT.1 4.NBT.1 5.NBT.2 5.NBT.5 Essential Question How do we determine the place value of a number? Concept How do we compare relationships between place values? Place Value Patterns How do I demonstrate the patterns between numbers, quantities and place value using the power of ten? How can we use the concept of Place Value Approximate Duration of Study: 1 ½ - 2 weeks Skills Assessments Determine the place value of any given whole digit number through the billions. Relationship of digits in a multi-digit number The ones place is ten times as much as the place value to the right. Expanded Form Separate any given whole number by place value using powers of tens. e.g. 5,678 (5x1,000)+(6x100)+(7x10)+(8x1) Multiplying by Explain the patterns of zeros in Power of Ten whole numbers. (Patterns) Explain the patterns of the placement of decimal points Whole Number Multiplying Solve two digit multiplication. Solve three digit multiplication. Pretest Pretest* Posttest Posttest* Quiz Quiz * Helpful Strategies and Resources Literature: Amanda Beans Amazing Dream How Much is a Million? Hershey’s Milk Chocolate Multiplication Book Anno Mysterious Multiplying Jar The Grapes of Math Master Pieces Math Fables Math Curse Math for all Seasons Six Sick Sheep If you Made a Million Manipulative: Money Place Value Flip Charts SMART Notebook- Place Value SMART Notebook- Multiplying by Tens SMART Notebook- Multiplying by Tens GAME Manipulative: Base Ten SMART Notebook- Two and Three Digit Multiplication * The asterisk next to a document represents an adapted document. 1 of 2 SMART Notebook- Two Digit Multiplication- Lattice Method SMART Notebook- Two Digit Multiplication multiplication to solve problems? 5.NF.5a How can we interpret Comparing multiplication as Factors scaling (resizing)? Evaluate the factors to estimate the product (size), without multiplying SMART Notebook- Estimate/Comparing Product Lesson/Activity Manipulative: Scale Vocabulary: Round, Compare, Digit, Expanded Form, and Place Value. Billion, Period, Estimate, Millions, Product, Difference, Sum, Distributive Property, and Multiple. Timeline 2 of 2 * The asterisk next to a document represents an adapted document. Unit 2: Divide Whole Numbers CCS 5.NBT. 2 5.NBT. 6 Essential Question How do I demonstrate the patterns between numbers, quantities and place value using the power of ten? Concept How does division relate to placing everyday items into groups? Whole Number Division Dividing by Power of Ten (zeros) Approximate Duration of Study: 1 ½ - 2 weeks Skills Assessments Explain the patterns of the zeros in whole numbers. Explain the placement of decimal points Find whole number quotients with four digit dividends and two digit divisors. Use place value to solve division problems. Use properties of operation to solve division problems. Use relationships of multiplication and division to solve division problems Follow the steps of division a write the remainder as the numerator and the divisor is the denominator. Pretest Pretest* Posttest Posttest* Quiz Quiz * Helpful Strategies and Resources SMART Notebook- Explanation of Division Riddle: Does McDonald’s Serve Burgers? (Divide, Multiply, Subtract, Bring Down) Manipulatives: Money Red/Yellow Discs SMART Notebook- Long Division Game BrainPOP- Long Division How do we write a Writing the remainder as mixed remainder number without the “r” as a mixed symbol to represent the number remainder? How do we estimate the Estimate Estimate the quotient of a given quotient? division problem. Vocabulary: Estimate, Dividend, Divisor, Quotient, Mixed Number, and Remainder. * The asterisk next to a document represents an adapted document. Unit 3: Algebra Expressions and Equations CCS 5.OA.1 Essential Question How do we apply numerical expressions? 5.OA.2 Supports 5.OA.1 5.OA.2 Concept Evaluate Expressions Written Expressions How do you write an equation? How do you solve equations for missing numbers? Parentheses Braces Brackets Write numerical expressions in words “add 8 and 7, then multiply by 2” Write a written numerical expression in numbers. “2 x (8+7)” Interpret Expression Understand an expression without evaluating. Write equations Solve a story problem by writing an equation. Create an equation from a set a data (numbers or written). Solve Equations with Missing Numbers (Variables) Solve for a missing number in addition. Solve for a missing number in subtraction. Solve for a missing number in multiplication. Solve for a missing number in division. How do you determine the important information within a problem to create an equation? ISAT CONCEPT Approximate Duration of Study: 1 ½ - 2 weeks Skills Assessments Pretest Pretest* Posttest Posttest* Quiz Quiz * Helpful Strategies and Resources SMART Notebook- Order of Operations SMART Notebook- Parentheses BrainPOP- Order of Operations Manipulative: Order of Operations Literature: Anno’s Magic Seeds BrainPop- Equations w/Variables SMART Notebook- Variables SMART Notebook- Expressions and Variables 1 of 2 * The asterisk next to a document represents an adapted document. ISAT CONCEPT How do you insert an Functions Given an algebraic expression with a amount of a variable variable, insert the variable amount to solve the equation? to solve the equation. How do you compare Inequalities Compare whole numbers using the numbers using the greater than, less than, and equal appropriate inequality signs. symbol? Vocabulary: Parentheses, Braces, Brackets, Numeral, Expression, Equation, Evaluate, Function, Variable, Inequality, Order of Operations, and Solution. Timeline 2 of 2 * The asterisk next to a document represents an adapted document. Unit 4: Decimals Overview CCS Essential Question How do we represent decimals? Concept Skills Approximate Duration of Study: 1 ½ weeks Assessments Helpful Strategies and Resources SMART Notebook- Reading Decimals to the Tenths Pretest Name numbers in digit SMART Notebook- Introduction to Decimals Pretest* form to the thousandths SMART Notebook- Decimal Place Value Posttest place BrainPOP- Decimals Posttest* Read numbers to the Literature: Quiz thousandths place in Two Ways to Count to Ten Quiz * words Piece = Part = Portion Write numbers to the thousandths place in words Write numbers in words in expanded form Interpret verbal representation into written form Equivalent Create equivalent decimals decimals by attaching zeros in place values to the left of the final decimal digit. Compare BrainPOP-Decimals Compare two digit Decimals decimals to the thousandths place Order Decimals Compare decimals and order them from least to greatest and/or greatest to least. Vocabulary: Decimal, Equivalent, Hundredth, Tenth, Thousandth, Digit, Round, and Expanded Form. 5.NBT.3 Representation of Decimals Timeline * The asterisk next to a document represents an adapted document. Unit 5: Add and Subtract Decimals CCS Essential Question How do we add and subtract decimals? Concept How do we determine where the decimal point goes? Subtract Decimals 5.NBT.4 How do we round decimals? Rounding Decimals 5.NBT.7 How do we multiply decimals? Representing Decimals 5.NBT.7 Add Decimals Approximate Duration of Study:1 – 1 ½ weeks Skills Assessments Align the decimal points to add decimals. Insert zero the left of the final decimal digit to hole place value if needed (understand adding zeros does not change the value of the decimal number). Align the decimal points to subtract decimals. Subtraction rules apply, make sure the largest decimal value is on top. Insert zero the left of the final decimal digit to hole place value if needed (understand adding zeros does not change the value of the decimal number). Borrowing rules of subtraction still apply when subtracting decimals. Round decimals to all places Helpful Strategies and Resources Pretest Pretest* Posttest Posttest* Quiz Quiz * BrainPOP-Rounding Decimals Using all operations to the hundredths create models, drawings, and strategies using place value. Using all operations to the hundredths use How do we the properties of operations to solve. know where Using all operations to the hundredths to put the show relationships between addition and decimal subtraction. point? Using all above strategies develop a written method and explain using reasoning. Vocabulary: Compare, Decimal, Decimal Point, Equivalent Decimals, Expanded Form, Hundredth, Round, Tenth, and Thousandth. * The asterisk next to a document represents an adapted document. Timeline Unit 6: Multiplying Decimals Approximate Duration of Study: 1 - 1 ½ weeks CCS 5.NBT.7 Essential Question Where is the decimal point inserted in the product? ISAT CONCEPT Supports 5.NBT.7 Concept Multiplying Decimals Skills Solve for the product of decimal numbers following the same rules of multiplication of whole numbers. Understand that the decimal point in the product is determined by the total number of decimal place values in both addends. Estimate the product of decimals in any given multiplication problem. Assessments Helpful Strategies and Resources Pretest Pretest* Posttest Posttest* Quiz Quiz * How can you Estimate use estimate to get an approximate product? Vocabulary: Decimal, Decimal Point, Equivalent Decimals, Expanded Form, Hundredth, Product, Round, Tenth, and Thousandth. Timeline * The asterisk next to a document represents an adapted document. Unit 7: Divide Decimals by Whole Numbers Approximate Duration of Study: 1 - 1 ½ weeks CCS 5.NBT.7 Essential Question How do we divide decimals? Concept Representing Decimals How do we know where to put the decimal point? Divide Decimals by Whole Numbers ISAT CONCEPT Supports 5.NBT.7 Skills Assessments Using all operations to the hundredths create models, drawings, and strategies using place value. Using all operations to the hundredths use the properties of operations to solve. Using all operations to the hundredths show relationships between addition and subtraction. Using all above strategies develop a written method and explain using reasoning. Solve for the quotient of decimal numbers following the same rules of division of whole numbers. Understand that the decimal is aligned vertically in the answer to the dividend in the division problem. Estimate the quotient of decimals in any given division problem. Helpful Strategies and Resources Pretest Pretest* Posttest Posttest* Quiz Quiz * How can you Estimate use estimate to get an approximate product? Vocabulary: Decimal, Decimal Point, Equivalent Decimals, Expanded Form, Hundredth, Quotient, Round, Tenth, and Thousandth. * The asterisk next to a document represents an adapted document. Unit 8: Fraction Concepts CCS Essential Question ISAT How do we identify the CONCEPT parts of a fraction? Supports 5.NF.1 5.NF.2 Concept Fraction Properties How do we use equivalent fractions? How do we change a fraction to be equivalent? How do you convert an improper fraction into a mixed number? How do we simplify fractions? How do we use simplified and reduced fractions? How do we use pictures to compare fractions/mixed numbers? How do we order fractions/mixed numbers? Equivalent Fractions Improper Fractions Simplify/ Reduce Fractions Compare Fractions Order Fractions Approximate Duration of Study: 2 – 2 ½ weeks Skills Assessments Pretest Identify the numerator as the top Pretest* number in a fraction. Posttest Identify the denominator as the Posttest* bottom number in a fraction. Identify the parts of a mixed number Quiz Quiz * (whole number and fraction). Create a fraction that is equal to a given fraction. Understand an improper fraction has a larger numerator than denominator. Convert an improper fraction to a mixed number using long division. Use division to reduce fractions. Use fractions that are equivalent to one to simplify. Helpful Strategies and Resources BrainPOP-Converting Fractions to Decimals Literature: Piece = Part = Portion The Hershey’s Chocolate Fraction Book Fraction Action BrainPOP-Reducing Fractions Lesson: Reducing Fractions Solve using pictures to determine the appropriate equality sign. Solve using a number line to determine the appropriate equality sign. Solve using pictures to determine the appropriate order from least to greatest and greatest to least. Solve using a number line to determine the appropriate order 1 of 2 * The asterisk next to a document represents an adapted document. from least to greatest and greatest to least. Compare Solve using pictures to determine the Mixed appropriate equality sign. Numbers Solve using a number line to determine the appropriate equality sign. Order Mixed Solve using pictures to determine the Numbers appropriate order from least to greatest and greatest to least. Solve using a number line to determine the appropriate order from least to greatest and greatest to least. Vocabulary: Numerator, Denominator, Mixed Numbers, Greatest, Least, Equality Signs Timeline 2 of 2 * The asterisk next to a document represents an adapted document. Unit 9: Add and Subtract Fractions Approximate Duration of Study: 1 ½ - 2 weeks CCS 5.NF.1 5.NF.2 Essential Question How do we convert fractions to common denominators? How do we use fraction conversions in our daily life (cooking, slices, etc.)? How can we demonstrate fractions through story problems? Concept Skills Unlike Denominators (changing to common denominators) Solve for the sum of two fractions with unlike denominators. Solve for the difference of two fractions with unlike denominators. Story Problems (Addition/ Subtraction Common Denominators) Use fraction models to represent the problem. Use equations to represent the problem. Assessments Helpful Strategies and Resources Pretest Pretest* Posttest Posttest* Quiz Quiz * Games:Adding Fractions BrainPOP-Adding and Subtractions Fractions Estimate mentally using benchmark fractions and number sense to assess the reasonableness of an answer. Story Problems Use fraction models to represent the problem. Use equations to represent the problem. (Addition/ Estimate mentally using Subtraction benchmark fractions and Unlike number sense to assess the Denominators) reasonableness of an answer. Vocabulary: Sum, Difference, Equivalent, Numerator, Denominator, Common Denominator, Mixed Number, and Factors. Benchmark Fraction: Benchmark fractions are common fractions that you can judge other numbers against. Normally, 1/4, 1/2, 3/4, and often 1/10 (because of its relationship with decimals) are referred to as benchmark fractions. Read more: http://wiki.answers.com/Q/What_is_benchmark_fraction#ixzz174UgbnsV Timeline * The asterisk next to a document represents an adapted document. Unit 10: Add or Subtract Mixed Numbers Approximate Duration of Study: 1 ½ - 2 weeks CCS 5.NF.1 Essential Question How do we solve for the sum of mixed numbers? How do we solve for the difference in mixed numbers? 5.NF.2 How can we demonstrate fractions through story problems? Concept Add/Subtract Mixed Numbers Estimation Story Problems Skills Align mixed numbers vertically to solve for the sum/difference. Borrow using regrouping in order to subtract mixed numbers from whole numbers. Estimate the sum by rounding the mixed numbers before solving. Estimate the difference by rounding the mixed number before solving. (borrow using regrouping if needed). Use mixed numbers models to represent the problem. Use equations to represent the problem. Assessments Helpful Strategies and Resources Pretest Pretest* Posttest Posttest* Quiz Quiz * BrainPOP-Mixed Numbers Estimate mentally using mixed numbers and number sense to assess the reasonableness of an answer. Story Problems Use mixed number models to represent the problem. Use equations to represent the problem. Estimate mentally using mixed numbers and number sense to assess the reasonableness of an answer. Vocabulary: Sum, Difference, Equivalent, Numerator, Denominator, Common Denominator, Mixed Number, Estimation, Regrouping, and Factors. Timeline * The asterisk next to a document represents an adapted document. Unit 11: Multiply Fractions Approximate Duration of Study: 1 ½ weeks CCS 5.NF.4a Essential Question How do we multiply fractions? 5.NF.5b What are rules to multiplying fractions? How do we anticipate the product of fractions? Concept Skills Assessments Helpful Strategies and Resources Multiplying Fractions with Fractions Multiplying Whole Numbers to Fractions Multiply fractions with fractions e.g. (a/b x c/d =ac/bd) Multiply fractions with whole numbers e.g. (a/b x q = aq/b) Pretest Pretest* Posttest Posttest* Quiz Quiz * BRainPOP-Multiplying Fractions Multiplying Fractions Explain why multiplying a fraction greater than one by a given number will result in a larger product Explain why multiplying a fraction less than one by a given number will result in a smaller product Supports How do we Multiplying Mixed Multiply mixed numbers by 5.NF.4a multiply mixed Numbers converting them into improper 5.NF.5b numbers? fractions and following the steps of fraction multiplication. 5.NF.6 How does Real World Solve real world problems multiplication Problems of using fractions and mixed relate to real Multiplication numbers world scenarios? Use fraction models and equations to represent the problem Vocabulary: Product, Difference, Equivalent, Compare, Numerator, Denominator, Common Denominator, Mixed Number, and Factors. Timeline * The asterisk next to a document represents an adapted document. Unit 12: Divide Fractions CCS 5.NF.3 5.NF.7a Essential Question Can you interpret fractions as division? Concept Division Use division by dividing the numerator by denominator Mixed Number Quotients Write the quotient as a mixed number Can you create a Story problems of model to division represent division as a fraction? Interpret that a fraction times a whole number equals a new number. e.g. ¾ multiplied by 4 equals 3. Understand ¾ is 3 wholes beings shared by 4 people so that each person has to share a size of ¾. Be able to place the quotient as a mixed number or fraction on a number line. How do we divide fractions by whole numbers? Interpret and compute the quotient e.g. (1/3) ÷4 Create a visual fraction model and equations to represent the quotient Use the relationship of multiplication to support your quotient e.g. (1/3) ÷ 4 = 1/12 because (1/12) x 4 = 1/3 Divide unit fractions by whole numbers How do we model a division equation? 5.NF.7b Approximate Duration of Study: 1 week Skills Assessments How do we Timeline Divide whole Pretest Pretest* Posttest Posttest* Quiz Quiz * Helpful Strategies and Resources BrainPOP-Dividing Fractions Literature: A Remainder of One Interpret and compute the * The asterisk next to a document represents an adapted document. 1 of 2 divide whole numbers by fractions? numbers by unit fractions quotient e.g. 4 ÷(1/5) Create a visual fraction model and equations to represent How do we the quotient model a division Use the relationship of equation? multiplication to support your quotient e.g. 4 ÷ (1/5) = 20 because 20 x (1/5) = 4 Divide fractions by Interpret and compute the fractions quotient e.g. (1/5) ÷(1/5) Create a visual fraction model and equations to represent the quotient Use the relationship of multiplication to support your quotient 5.NF.7c How do you Division Problem Create a story to represent a create story Solving/Story sample division equation problems to Problems Solve story problems involving represent division of unit fractions by division non zero whole numbers and equations? division of whole numbers by unit fractions Create a visual fraction model and equations to represent the quotient e.g. How much chocolate will each person get if 3 people share ½ lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Vocabulary: Product, Quotient, Difference, Equivalent, Numerator, Denominator, Common Denominator, Mixed Number, and Factors. 2 of 2 Timeline * The asterisk next to a document represents an adapted document. Unit 13: Ratio, Percents, and Probability Approximate Duration of Study: 1 ½ weeks CCS ISAT CONCEPT Essential Question How do you express a ratio? Concept Assessments Pretest Understand Ratio Pretest* proportions Write ratios using a fraction Posttest How are ratios Posttest* and a colon used daily? Quiz Fractions, Decimals and Quiz * Percents Ratios and Rates Solve word problems and properly represent ratios How do I calculate Percents Understand a Percent a percent? Calculate a Percentage Find the percentage of How can I use whole numbers percentages at a Find the percentage of a restaurant? fraction Find the percentage of How will I use money percentages at a Relate percents to fractions store? and decimals Solve for percents through word problems How is probability Probability Understand Probability computed? Represent probability in multiple ways How can Compare/Relate Probability probability be to percentages and ratios used in everyday Solve for probability through life? word problems Vocabulary: Fractions, Ratio, Percent, Probability, Compare, Colon, Rates, and Proportions. Timeline Ratios Skills Helpful Strategies and Resources BrainPOP-Ratios Literature: Do you Wanna Bet? BrainPOP-Percents BrainPop-Basic Probability BrainPOP-Probability * The asterisk next to a document represents an adapted document. Unit 14: Geometric Figures CCS Essential Question ISAT How do you plot CONCEPT points in order outline a 2D shape? Supports 5.G.3 5.G.4 How do you indentify lines according to their properties? Concept 5.G.3 Angles 5.G.4 ISAT CONCEPT Supports 5.G.3 How do we classify angles? How do we measure using a protractor? How do you classify a polygon? How do you identify the properties of a circle? Approximate Duration of Study: 2 – 2 ½ weeks Skills Assessments Points Establish points to create 2D shapes. Label points using letters to name 2D shapes. Lines Identify figures as lines, rays, and line segment. Identify lines as oblique, horizontal or vertical. Identify pairs of lines as perpendicular, parallel, or intersecting. Name an angle (right, acute, or obtuse) Draw an angle (right, acute, or obtuse) Measure an angle (right, acute, or obtuse) Polygons Use the properties of lines, points, and angles to classify polygons. Name a polygon based on the polygons properties. Identify the total number of diagonals within a polygon. Evaluate a polygon to determine lines of symmetry. Circles Name the properties of a circle (circumference, radius, diameter, chord). Solve for the radius, circumference, and diameter using the appropriate Pretest Pretest* Posttest Posttest* Quiz Quiz * Helpful Strategies and Resources Literature: The Greedy Triangle The Black Dots What’s Your Angle Pythagoras? BrainPOP-Angles BrainPOP-Circles and Measuring Circles * The asterisk next to a document represents an adapted document. 1 of 2 5.G.4 equations. 5.G.4 What is the Congruent/S Compare shapes and classify them as difference of figures imilar either congruent or similar. being congruent or Figures similar? Vocabulary: Two- Dimensional Shapes, Lengths, Degrees, Angles, Sides, Quadrilateral, Square, Parallelogram, Rhombus, Trapezoid, Rectangle, Angles, Degrees, Classify, Chord, Radius, Diameter, Circumference, Simple, and Complex. Timeline 2 of 2 * The asterisk next to a document represents an adapted document. Unit 15: Plane and Solid Figures CCS Essential Question How can the characteristics of shapes helps us categorize multiple figures? Concept 5.G.4 How can we sequentially order shapes according the properties from simplest to most complex? Classify and Compare Quadrilaterals ISAT CONCEPT Supports 5.G.3 How can we name triangles according to properties? Categorize Triangles 5.G.3 ISAT CONCEPT Categorize Quadrilaterals Approximate Duration of Study: 1 ½ - 2 weeks Skills Assessments Understand that a twodimensional shape can be classified using different categorization (side lengths, degrees of angles, number of sides) e.g. All rectangles have right angles, a square is rectangle, so all squares have right angles. Organize two-dimensional shapes as being classified as more than one figure in order from simplest to most complex. e.g. shape, quadrilateral, parallelogram, rhombus, square Identify triangles using properties of side lengths and angles (Isosceles, Scalene, Equilateral, Right, Obtuse, and Acute). Understand that a threedimensional shape can be classified using different categorization (faces, edges, vertices, and face shape). Helpful Strategies and Resources Pretest Pretest* Posttest Posttest* Quiz Quiz * BrainPOP-Classifying Triangles How can the Categorize 3D properties of a 3D shapes shapes be SupportS analyzed to 5.G.3 establish a 5.G.4 classification? Vocabulary: Two- Dimensional Shapes, Lengths, Degrees, Angles, Sides, Quadrilateral, Square, Parallelogram, Rhombus, Trapezoid, Rectangle, Angles, Degrees, Classify, Acute Angle, Obtuse Angle, Right Angle, Equilateral, Scalene, Isosceles, Simple, and Complex. Timeline * The asterisk next to a document represents an adapted document. Unit 16: Perimeter Approximate Duration of Study: 1 week CCS ISAT CONCEPT Essential Question How do you solve for the perimeter? Supports 5.NF.4b 5.NF.5a 5.NF.6 Supports 5.G.3 5.G.4 Concept Skills Assessments Helpful Strategies and Resources Perimeter of polygons Understand the concept of the perimeter of polygons Use addition to solve for the perimeter Use the formulas: (l + l + w + w) or (2 x l) + (2 x w) Pretest Pretest* Posttest Posttest* Quiz Quiz * Literature: Cut Down to Size at High Noon Sir Cumfrence and the Great Knight of Angleland How does the perimeter relate to architecture? Circumference of Circles Understand the concept of the perimeter of circles Use formulas: (π • d) or (2πr) Vocabulary: Perimeter, Circumference, Diameter, Radius, Length, Width, and Sum. Timeline * The asterisk next to a document represents an adapted document. Unit 17: Area Approximate Duration of Study: 2- 2 1/2 weeks CCS 5.NF.4b Essential Question How do we solve for the area of a rectangle? Concept Skills Area- Unit Squares Solve for the area of a rectangle with fractional sides using unit squares Recognize that the area is the same using different strategies. (Unit squares/Lengths of sides) Record the product as a rectangle area Area- Side Lengths Solve for the area of a rectangle with fractional side lengths Record the product as a rectangle area How do we solve for the area of a rectangle? Area-Triangle 5.NF.5a How can we interpret multiplication as scaling (resizing)? Comparing Sizes Solve for the area of a triangle with whole number side lengths Solve for the area of a triangle with fractional side lengths Record the product as a triangular area Evaluate the factors to estimate the product (size), without multiplying 5.NF.6 How does multiplication relate to real world scenarios? Real World Problems of Multiplication ISAT CONCEPT Supports 5.NF.4b Assessments Helpful Strategies and Resources Pretest Pretest* Posttest Posttest* Quiz Quiz * BrainPOP-Area of Polygons Solve real world problems using fractions and mixed numbers Use fraction models and equations to represent the problem Vocabulary: Product, Compare, Congruent, Similar, All Shapes, Sides, Length, Width, Surface Area ,and Base. Timeline * The asterisk next to a document represents an adapted document. Unit 18: Volume Approximate Duration of Study: 1 – 1 ½ weeks CCS 5.MD.3a Essential Question How do we solve for volume? Concept Identifying Volume Problems What types of shapes can we solve for the volume? Skills Volume is solved when evaluating solid figures To recognize that we need three measurements (length, width, height) to solve for the volume Unit Cube How do we identify a Measurement cube that consists of 1 unit cube? 5.MD.3b How can we solve for Unit Cube the volume of a solid Measurement figure using addition? Understand that units(square) can be used to measure volume 5.MD.4 Measuring solid figures (unit cubes only) Measure volume by counting unit cubes Solve Volume Use unit cubes to fill a rectangle to find the side lengths. 5.MD.5a When we solve for volume are there patterns? Is the unit of measurement relevant to solving for the problem? How can we use unit cubes to find the side lengths of a shape? How can we compare using unit cubes or side length to solve for the volume? Compare Volume Assessments Helpful Strategies and Resources Pretest Pretest* Posttest Posttest* Quiz Quiz * BrainPOP-Volume of Cylinders BrainPOP-Volume of Prisms Understand that the sum of unit cubes within a solid figure is the volume Use cubic cm, cubic in, cubic ft, and improvised units. Relate volume of unit cubes to the multiplication of edge lengths (l x w x h) Relate the volume of unit cubes to multiplying an edge length and the area of the base(b x h) 1 of 2 Timeline * The asterisk next to a document represents an adapted document. How can we represent the volume using three different strategies? 5.MD.5b 5.MD.5c Can volume be represented through the associative property? How can we apply the multiple formulas of volume to real world problems? How can we recognize volume as an additive? How can we apply addition to solving for the volume in real world situations? Representation of Volume Represent solving for the volume in three different ways e.g. unit cubes, l x w x h, (base area)b x h Represent the volume through the associative property Apply Formulas to Real World Problems Volume as Addition Solve using V = l x w x h for rectangular prisms using whole numbers Solve using V = B (base area) x H for rectangular prisms using whole numbers Find the volume of two nonoverlapping rectangular prisms by adding the volumes of the separate parts. e.g. “T- shaped” prism Apply additive strategies of volume to real world situations. Vocabulary: Base, Area, Formula, Associative Property, Solid Figure, Unit Cube, One cubic unit, Threefold whole-numbers, Volume, Product, Prisms, and Variables. Timeline 2 of 2 * The asterisk next to a document represents an adapted document. Unit 19: Number Concepts Approximate Duration of Study: 1- 1 ½ weeks CCS ISAT CONCEPT Supports 5.NBT.1 5.NBT.2 5.NBT.5 5.NF.5A Essential Question How do you solve for multiples? Concept Skills Assessments Multiples Find multiples and least common multiples How can we use multiples and division to determine divisibility? Divisibility How do we identify factors? Factors Use to division and multiples to be able to list all numbers that are divisible by the given number. Find all factors of whole numbers Solve and understand the greatest common factors (GCF); between two or three numbers Connect factors to reducing and simplifying fractions How can factors help us reduce and simplify fractions? What is the difference between a prime and composite number? How do we solve for exponents? How will exponent terminology support our understanding of polygons? Helpful Strategies and Resources Pretest Pretest* Posttest Posttest* Quiz Quiz * BrainPOP-Factoring Prime and Composite Identify prime and composite numbers Prime Factorization BrainPop-Prime Numbers Exponents Solve for exponents Represent exponents using expanded form from standard form Represent exponents in standard form from expanded form Understand exponent terminology (e.g. squared, cubed, powers) BrainPOP-Exponents Vocabulary: Multiples, Factors, Composite, Prime, Factorization, Squared, Cubed, Powers, Standard Form, Expanded Form. Timeline * The asterisk next to a document represents an adapted document. Unit 20: Data Grouping Approximate Duration of Study: 2 days CCS ISAT CONCEPT Essential Question How do I solve for the mean, median, mode, and range? How does the mean, median, mode, and range compare to each other? Concept Skills Mean, Median, Mode, and Range Solve for the mean, median, mode, and range separately Solve for the mean, median, mode, and range for one set of data. Comparing Mean, Median, Mode, and Range Compare the mean, median, mode, and range Identify the similarities and differences of ell concepts (mean, median, mode, and range) Assessments Helpful Strategies and Resources Pretest Pretest* Posttest Posttest* Quiz Quiz * BrainPOP-Mean, Median, Mode and Range Vocabulary: Mean. Median, Mode, Range, Average, Product, Quotient, Sum, and Difference. Timeline * The asterisk next to a document represents an adapted document. Unit 21: Customary and Metric Measurements CCS 5.MD.1 ISAT CONCEPT Essential Question How do you convert measurements within the same unit? Concept Approximate Duration of Study: 1 ½ - 2 weeks Skills Assessments Convert Metric Lengths Convert different size measurements within a given measurement system e.g. 5 cm to 0.05 m Solve multi- step problems Solve real world problems How do you convert measurements within the same unit? Customary Lengths (ft./in./yds.) How do you convert measurements within the same unit? Convert Metric Weight How do you convert measurements within the same unit? Customary Mass How do we measure time that has past? Elapsed Time Convert different size measurements within a given measurement system e.g. 5 ft to 60 in. Solve multi- step problems Solve real world problems Convert different size measurements within a given measurement system (lb., oz.,tons, etc.) Solve multi- step problems Solve real world problems Convert different size measurements within a given measurement system (grams, kg, etc.) Solve multi- step problems Solve real world problems Evaluate two set times and be able to determine the amount of time in between. Solve time in the past a future. Supports 5.MD.1 How do we establish Pretest Pretest* Posttest Posttest* Quiz Quiz * Helpful Strategies and Resources ISAT rulers BrainPOP-Metric Units SMART Notebook – Converting Measurement SMART Notebook - Conversions Literature: Millions to Measure Jim and The Beanstalk Weighting the Elephant BrainPOP-Customary Units BrainPOP-Metric vs. Customary BrainPOP-Elapsed TIme 1 of 2 * The asterisk next to a document represents an adapted document. a time that needs to be met in the future? Solve for time over years, months, weeks, days, hours, minutes, and seconds. Solve multi- step problems Solve real world problems How do you read a Temperature Read a thermometer. thermometer? Convert between Celsius and Fahrenheit. How do we convert Solve multi- step problems temperature? Solve real world problems Vocabulary: All Metric System Units, All Customary Units, Celsius, Fahrenheit, Thermometer, Elapsed Time, Convert, Ruler, Fractional Parts, Decimals, and Place Value. Timeline 2 of 2 * The asterisk next to a document represents an adapted document. Unit 22: Graphs and Integers CCS 5.MD.2 ISAT CONCEPT Essential Question How do you represent data using a multiple graphs? Supports 5.MD.2 5.G.2 Concept Line Graph Bar Graph Pictographs Histograms Circle Graphs Stem-and-Leaf Real World Graphing Approximate Duration of Study: 1 ½ - 2 weeks Skills Assessments Make a graph to display a data set of measurements of whole and fractional numbers (1/2, 1/4, 1/8) Make a graph to display a data set of measurements of positive and negative whole numbers Use operations to solve problems involving information presented in the graph. Represent points in the first quadrant (whole positive numbers) to interpret data of a real world problem Interpret coordinate points in the context of the situation. Pretest Pretest* Posttest Posttest* Quiz Quiz * Helpful Strategies and Resources SMART Notebook – Line Plots & Integers Vocabulary: Ordered Pairs, Coordinates, Quadrants, Patterns, Sequences, Axes, Pair of perpendicular number lines, Origin, Coordinate System, Coordinates, X- Axis and Y- Axis, X- Coordinate and Y- Coordinate. Timeline * The asterisk next to a document represents an adapted document. Unit 23: Coordinate Planes and Ordered Pairs Approximate Duration of Study: 1 ½ - 2 weeks CCS 5.G.1 Essential Question How do we configure a coordinate plane? Concept Create a Coordinate Plane/Graph Intersect a pair of line perpendicularly Understand that these lines define a coordinate system and create axes. Identify the origin Ordered Pairs/ Coordinates Understand that the first number is how far to travel from the origin in the direction of one axes Understand that the second number is how far to travel in the direction of second axes Identify the names of the two axes and the two coordinates. e.g. x-axis and y- axis, x- coordinate and y- coordinate Generate two number patterns using a given rule X-value add 3, Y-value add 6. What are the parts of a coordinate plane? How can we represent numbers in a coordinate plane? What are ordered pairs? What do the numbers in an ordered pair represent? 5.OA.3 What are the relationships between corresponding terms? Skills Functions and Patterns of Ordered Pairs Assessments Helpful Strategies and Resources Pretest Pretest* Posttest Posttest* Quiz Quiz * BrainPOP-Coordinate Plane SMART Notebook – Coordinate Planes SMART Notebook – Coordinate Plane SMART Notebook – Ordered Pairs SMART Notebook – Ordered Pairs SMART Notebook – Coordinate Planes SMART Notebook – Coordinate Graphing Why are the relationships relevant? How can we use ordered pair to develop relationships in numbers? 1 of 2 * The asterisk next to a document represents an adapted document. Find ordered pair relationships (rule) What are ordered pairs? Ordered Pairs/ Coordinates Compare two sequences of numbers to develop pattern. Add 3, starting at 0 and Add 6 starting at 0, then identify that the sequence is twice the corresponding term. What do the numbers in an ordered pair represent? 5.G.2 SMART Notebook – Coordinate Grids Real World Graphing Represent points in the first quadrant (whole positive numbers) to interpret data of a real world problem Interpret coordinate points in the context of the situation. Vocabulary: Integers, Ordered Pairs, Coordinates, Quadrants, Patterns, Sequences, Axes, Pair of Perpendicular Lines, Number Lines, Origin, Coordinate System, Coordinates, X- Axis and Y- Axis, X- Coordinate and Y- Coordinate. Timeline 2 of 2 * The asterisk next to a document represents an adapted document. Unit 24: Patterns Approximate Duration of Study: 1 week CCS ISAT CONCEPT Essential Question How do we classify the movement of a shape/object? Concept Transformations (Movement of Objects) Tessellations Patterns ISAT CONCEPT How do we determine a rule using an input/output chart? Skills Identify the movement of an object as a translation (slide), rotation (turns), reflections (flip). Assessments Helpful Strategies and Resources Pretest Pretest* Posttest Posttest* Quiz Quiz * BrainPOP- Transformations SMART Notebook- Transformations SMART Notebook - Transformations Arrange 2D shapes on a flat plane to create a pattern of plane figures that fills the plane with no overlaps and no gaps. Identify the pattern and continue the pattern using geometric figures. Identify the pattern and continue the pattern using whole numbers. Input/ Output Sequences SMART Notebook – Function Compare the input to the output Machine and determine a rule. SMART Notebook – Function Man Insert a digit(s) into an input and solve for the output. Determine the input when only given the output and the rule. Vocabulary: Transformations, Tessellations, Ordered Pairs, Relevancy, Corresponding Terms, Term, Patterns, X-Value, Y-Value, Sequence, and Rule. Timeline * The asterisk next to a document represents an adapted document. Important ISAT Concepts 1. 2. 3. 4. 5. 6. 7. 8. Shapes i. Faces/Edges/Vertices/Corners ii. 3-Demential Shapes iii. Congruent Shapes iv. Flat 3D shape v. Similar Figures vi. Naming Shapes (Pentagon) vii. Balance weight of shapes- pictures Rounding i. Basic rounding ii. Estimating Rounding Estimation Transformations (translations) Algebra i. All operations ii. N = 5 put into equation Decimals i. Naming decimals ii. Ordering Decimals iii. Least to greatest Coordinate graphing i. X and Y chart (1/2 amounts) ii. Graphing Ordered Pairs Rules/Sequencing i. Input/output Timeline * The asterisk next to a document represents an adapted document. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. ii. Sequence Rules iii. 4 family members older/younger find the order Mean/median/mode/range Probability and Ratio i. Probability of number shaded ii. Ex. Dice rolled 50 times of getting 2 Measurement i. ISAT RULERS ii. Measuring lengths with rulers iii. Measurement of a line (Fractions/Number Line) Exponents Fractions and Improper i. Converting (fraction – decimal) ii. Reducing Volume/Perimeter/Area i. Square units ii. Ex. Perimeter Length of paper chip or ant Time – Elapsed Time Properties i. Associative Property parenthesis ii. Communitive Property Angles/Degrees i. Acute/Obtuse/Straight ii. 90 degrees & 45 degrees Graphs i. Reading a bar graph ii. Pictograph Timeline * The asterisk next to a document represents an adapted document. 19. Measurement i. Convert Inches to feet ii. Pool water is measured in gallons 20. Combinations i. Ex. 5 ice creams 3 cones Quick Review Concepts - Factors - Multiplication Dot - Writing numbers in words Random Question Examples Time/Temp/went up and down Total amount shared by a number equals Bought two at $5.50 and four at $.50 / give change Purchase 3 items, 1 item, 2 item and change 1/6 of 50 Calculator Practice 1. Changing improper to proper fractions 2. Reducing fractions 3. Simplifying improper fractions 4. Parentheses 5. Estimating 6. Exponent Timeline * The asterisk next to a document represents an adapted document.