FIFTH GRADE CURRICULUM MAP BLACKFORD COUNTY SCHOOLS

Transcription

1 FIFTH GRADE CURRICULUM MAP BLACKFORD COUNTY SCHOOLS

2 Add to Result Unknown Change Unknown Start Unknown Two bunnies sat on the grass. Three more bunnies hopped there. How many bunnies are on the grass now? Two bunnies were sitting on the grass. Some more bunnies hopped there. Then there were five bunnies. How many bunnies hopped over to the first two? Some bunnies were sitting on the grass. Three more bunnies hopped there. Then there were five bunnies. How many bunnies were on the grass before? Take from =? Five apples were on the table. I ate two apples. How many apples are on the table now? 5 2 =? 2 +? = 5 Five apples were on the table. I ate some apples. Then there were three apples. How many apples did I eat? 5 -? = 3? + 3 = 5 Some apples were on the table. I ate two apples. Then there were three apples. How many apples were on the table before?? 2 = 3 Put Together/ Take Apart Compare Total Unknown Addend Unknown Both addends Unknown Three red apples and two green apples are on the table. How many apples are on the table? =? Five apples are on the table. Three are red and the rest are green. How many apples are green? 3 +? = 5, 5 3 =? Grandma has five flowers. How many can she put in her red vase and how many in her blue vase? 5 = 0 + 5, 5 = = 1 + 4, = 2 + 3, 5 = Difference Unknown Bigger Unknown Smaller Unknown Difference Unknown Bigger Unknown Smaller Unknown ( How many more? version): Lucy has two apples. Julie has five apples. How many more apples does Julie have than Lucy? ( How many fewer? version): Lucy has two apples. Julie has five apples. How may fewer apples does Lucy have than Julie? 2 +? = 5, 5 2 =? (Version with more ): Julie has 3 more apples than Lucy. Lucy has two apples. How many apples does Julie have? (Version with fewer ): Lucy has three fewer apples than Julie. Lucy has two apples. How many apples does Julie have? =?, =? Julie has three more apples than Lucy. Julie has five apples. How many apples does Lucy have? (Version with fewer ): Lucy has three fewer apples than Julie. Julie has five apples. How many apples does Lucy have? 5 3 =?,? + 3 = 5

3 Addition Strategies Name Clarification Work Sample Counting All Counting On Student counts every number Students are not yet able to add on from either addend, they must mentally build every number Transitional strategy Student starts with 1 number and counts on from this point ,2,3,4,5,6,7,8,9,10,11,12, ,10,11,12,13,14,15 Doubles/ Near Doubles Making Tens Making Friendly Numbers/ Landmark Numbers Student recalls sums for many doubles (8 + 1) (8 + 8) = 17 Student uses fluency with ten to add quickly (7 + 1) (1 + 9) = 17 Friendly number are number that are easy to use in mental computation Student adjusts one or all addends by adding or subtracting to make friendly numbers Student then adjusts the answer to compensate (48 + 2) = =71 Compensation Breaking Each Number into its Place Value Adding up in Chunks Student manipulates the numbers to make them easier to add Student removes a specific amount from one addend and gives that exact amount to the other addend Strategy used as soon as students understand place value Student breaks each addend into its place value (expanded notations) and like place value amounts are combined Student works left to right to maintain the magnitude of the numbers Follows place value strategy Student keeps one addend whole and adds the second addend in easy to use chunks More efficient than place value strategy because student is only breaking apart one addend = = = (30 + 4) + (30 + 8) = = = ( ) = = 73

4 Adding up Subtraction Strategies Name Clarification Sample Student adds up from the number being subtracted to the whole 14 7 The larger the jumps, the more efficient the strategy 7 8,9,10,11,12,13,14 (+1 each jump) Student uses knowledge of basic facts, doubles, making ten, and counting on Counting Back Place Value Keeping a Constant Difference Adjusting the Create and Easier Number Strategy used by students who primarily view subtraction as taking away Student starts with the whole and removes the subtracting in parts Student needs the ability to decompose numbers in east to remove parts Student breaks each number into its place value (expanded notation) Student groups like place values and subtracts Student understands that adding or subtracting the same amount from both numbers maintains the distance between the numbers Student manipulates the numbers to create friendlier numbers Strategy requires students to adjust only one of the numbers in a subtraction problem Student chooses a number to adjust, subtracts, then adjusts the final answer to compensate Students must understand part/whole relationships to reason through this strategy 7 + 3= = ( ) 65, 55, 45, 35, (30 + 2) = = ( ) ( ) = = = = = = = = = 63 I added 1 to make an easier number = 64 I have to add 1 to my final answer because I took away 1 too many.

5 Common Multiplication and Division Situations Unknown Product 3 X 6 =? Group Size Unknown (How many in each group) Number of Groups Unknown (How many groups?) There are 3 bags with 6 plums in each bag. How many plums are there in all? If 18 plums are shared equally into 3 bags, then how many plums will be in each bag? If 18 plums are to be packed 6 to a bag, then how many bags are needed? Measurement example: You need 3 Measurement example: You have Measurement example: You Equal lengths of string, each 6 inches long. 18 inches of string, which you will have 18 inches of string, which Groups How much string will you need cut into 3 equal pieces. How long you will cut into pieces that are altogether? will each piece of string be? 6 inches long. How many pieces of string will you have? There are 3 rows of apples with 6 apples in each row. How many apples If 18 apples are arranged into 3 equal rows, how may apples will be If 18 apples are arranged into equal rows of 6 apples, how are there? in each row? many rows will there be? Arrays, Area example: What is the area of a Area example: A rectangle has area Area example: A rectangle has Area 3 cm by 6cm rectangle? 18 square centimeters. If one side area 18 square centimeters. If is 3 cm long, how long is a side next one side is 6cm long, how long is to it? a side next to it? A blue hat costs $6. A red hat cost 3 A red hat costs $18 and that is 3 A red hat costs $18 and a blue times as much as the blue hat. How times as much as a blue hat costs. hat costs $6. How many times much does the red hat cost? How much does the blue bat cost? as much does the red hat cost as Measurement example: A rubber Measurement example: A rubber the blue hat? band is 6 cm long. How long will the band is stretched to be 18 cm long Measurement example: A rubber band be when it is stretched and that is 3 times as long as it was rubber band was 6 cm long at to be 3 times as long? at first. How long was the rubber first. Now it is stretched to be band at first? 18 cm long. How many times as long is the rubber band now as it was at first? General a x b =? a x? = p and p a =?? x b = p and p b =? Compare

6 Repeated Addition/Skip Counting Multiplication Strategies Name Clarification Student Work Sample Beginning strategy for students who are just learning multiplication 6 15 Connection to an array model provides an essential visual model = = = = = 90 Friendly Numbers/Landmark Numbers Partial Products Breaking Factors into Smaller Factors Doubling and Halving Students who are comfortable multiplying by multiples of Add 1 group of = 150 We must now take off 1 group of = 135 strategy based on the distributive property and is the precursor for our standard U.S. algorithm student must understand that the factors in a multiplication problem can be broken into addends student can then u se friendlier numbers to solve more difficult problems Strategy relies on students understand of breaking factors into smaller factors Associate property Used by students who have an understanding of the concept of arrays with different dimensions but the same area Student can double and halve numbers with ease Student doubles one factor and halves the other factor (10 + 5) = = = (3 4) 25 3 (4 25) (4 25) + (4 25) + (4 25) = = = = 200

7 Repeated Subtraction/Sharing Division Strategies Name Clarification Student Work Sample Early strategy students use when they are developing multiplicative reasoning Repeated subtraction is one of the least efficient division strategies Presents opportunities to make connections to multiplication Multiplying Up Partial Quotients Proportional Reasoning Strategy is a natural progression from repeated subtraction Student uses strength in multiplication to multiply up to reach the dividend Students relying on smaller factors and multiples will benefit from discussions related to choosing more efficient factors Maintains place value Allows students to work their way toward the quotient by using friendly numbers such as ten, five, and two As the student chooses larger numbers, the strategy becomes more efficient Students who have a strong understand of factors, multiples, and fractional reasoning Students experiences with doubling and halving to solve multiplication problems can launch an investigation leading to the idea that you can divide the dividend and the divisor by the same number to create a friendlier problem = = = 5 = = = = 0 I took out 6 groups of = = = = = = = = = = ) = = 24

8 Problem Solving Strategies Focus By Grade Level Kindergarten First Second Third Fourth Fifth Sixth: Grade Level Strategies Use Objects Review Previous Grades Draw a Picture Use a Number Sentence Review Previous Grades Find a Pattern Make a Table Review Previous Grades Work Backwards Make It Simpler Review Previous Grades Make an Organized List Guess and Check Review Previous Grades Use Logical Reasoning Students should know all strategies that will be used all year.

9 Weeks 1-9 Pacing Guide: 1 st Quarter Week 1 Week 2 Week 3 Week 4 Week 5 Week 6 Week 7 Week 8 Week 9 5.C.1: Multiply multi-digit whole numbers fluently using a standard algorithmic approach. 5.C.3: Compare the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication. 5.C.2: Find whole-number quotients and remainders with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Describe the strategy and explain the reasoning used. 5.AT.1: Solve real-world problems involving multiplication and division of whole numbers (e.g. by using equations to represent the problem). In division problems that involve a remainder, explain how the remainder affects the solution to the problem. 5.NS.2: Explain different interpretations of fractions, including: as parts of a whole, parts of a set, and division of whole numbers by whole numbers. 5.NS.1: Use a number line to compare and order fractions, mixed numbers, and decimals to thousandths. Write the results using >, =, and < symbols. 5.C.4: Add and subtract fractions with unlike denominators, including mixed numbers. 5.AT.2: Solve real-world problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators (e.g., by using visual fraction models and equations to represent the problem). Use benchmark fractions and number sense of fractions to estimate mentally and assess whether the answer is reasonable. 5.C.4: Add and subtract fractions with unlike denominators, including mixed numbers. 5.C.5: Use visual fraction models and numbers to multiply a fraction by a fraction or a whole number. 5.AT.3: Solve real-world problems involving multiplication of fractions, including mixed numbers (e.g., by using visual fraction models and equations to represent the problem). 5.C.6: Explain why multiplying a positive number by a fraction greater than 1 results in a product greater than the given number. Explain why multiplying a positive number by a fraction less than 1 results in a product smaller than the given number. Relate the principle of fraction equivalence, a/b = (n a)/(n b), to the effect of multiplying a/b by 1. 5.C.7: Use visual fraction models and numbers to divide a unit fraction by a non-zero whole number and to divide a whole number by a unit fraction. 5.AT.4: Solve real-world problems involving division of unit fractions by non-zero whole numbers, and division of whole numbers by unit fractions (e.g., by using visual fraction models and equations to represent the problem). Review of all fractions

10 Week 10 Week 11 Week 12 Week 13 Week 14 Week 15 Weeks Pacing Guide: 2 nd Quarter 5.C.8: Add, subtract, multiply, and divide decimals to hundredths, using models or drawings and strategies based on place value or the properties of operations. Describe the strategy and explain the reasoning. 5.NS.3: Recognize the relationship that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right, and inversely, a digit in one place represents 1/10 of what it represents in the place to its left. 5.AT.5: Solve real-world problems involving addition, subtraction, multiplication, and division with decimals to hundredths, including problems that involve money in decimal notation (e.g. by using equations to represent the problem). 5.NS.5: Use place value understanding to round decimal numbers up to thousandths to any given place value. 5.NS.6: Understand, interpret, and model percents as part of a hundred (e.g. by using pictures, diagrams, and other visual models). Review of all decimal operations 5.G.1: Identify, describe, and draw triangles (right, acute, obtuse) and circles using appropriate tools (e.g., ruler or straightedge, compass and technology). Understand the relationship between radius and diameter. 5.G.2: Identify and classify polygons including quadrilaterals, pentagons, hexagons, and triangles (equilateral, isosceles, scalene, right, acute and obtuse) based on angle measures and sides. Classify polygons in a hierarchy based on properties. 5.M.1: Convert among different-sized standard measurement units within a given measurement system, and use these conversions in solving multi-step real-world problems. Week 16 Review perimeter (grades 3 and 4) 5.M.3: Develop and use formulas for the area of triangles, parallelograms and trapezoids. Solve real-world and other mathematical problems that involve perimeter and area of triangles, parallelograms and trapezoids, using appropriate units for measures. Week 17 Week 18 5.M.2: Find the area of a rectangle with fractional side lengths by modeling with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas. 5.M.4: Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths or multiplying the height by the area of the base. 5.M.5: Apply the formulas V = l w h and V = B h for right rectangular prisms to find volumes of right rectangular prisms with wholenumber edge lengths to solve real-world problems and other mathematical problems. 5.M.6: Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the non-overlapping parts, applying this technique to solve real-world problems and other mathematical problems.

11 Weeks Pacing Guide: 3 rd Quarter Week 19 Week 20 Week 21 Week 22 Week 23 Week 24 Countdown Week 25 Countdown Week 26 ISTEP Week 27 5.DS.2: Understand and use measures of center (mean and median) and frequency (mode) to describe a data set. 5.DS.1: Formulate questions that can be addressed with data and make predictions about the data. Use observations, surveys, and experiments to collect, represent, and interpret the data using tables (including frequency tables), line plots, bar graphs, and line graphs. Recognize the differences in representing categorical and numerical data. 5.AT.6: Graph points with whole number coordinates on a coordinate plane. Explain how the coordinates relate the point as the distance from the origin on each axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x- coordinate, y-axis and y-coordinate). 5.AT.7: Represent real-world problems and equations by graphing ordered pairs in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. 5.AT.8: Define and use up to two variables to write linear expressions that arise from real-world problems, and evaluate them for given values. 5.C.9: Evaluate expressions with parentheses or brackets involving whole numbers using the commutative properties of addition and multiplication, associative properties of addition and multiplication, and distributive property. 5.NS.4: Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Review of all fractions

12 Weeks Pacing Guide: 4 th Quarter Week 28 Week 29 Week 30 Week 31 ISTEP round 2 Week 32 Prepare for 6 th grade Week 33 Week 34 Week 35 Review Geometry Standards Review Measurement Standards Review Algebra/Graphing standards 6.NS.3: Compare and order rational numbers and plot them on a number line. Write, interpret, and explain statements of order for rational numbers in real-world contexts. 6.NS.6: Identify and explain prime and composite numbers 6.NS.7: Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers from 1 to 100, with a common factor as a multiple of a sum of two whole numbers with no common factor. 6.C.2: Compute with positive fractions and positive decimals fluently using a standard algorithmic approach. 6.C.1: Divide multi-digit whole numbers fluently using a standard algorithmic approach. Week 36 6.C.1: Divide multi-digit whole numbers fluently using a standard algorithmic approach.

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14 Weeks 1-3: Problem Solving: Should be embedded within daily instruction: Make sense of problems and persevere in solving them. PS.1 Reason abstractly and quantitatively PS.2 Construct viable arguments and critique the reasoning of others PS.3 Model with Mathematics PS.4 Use appropriate tools strategically PS.5 Attend to precision PS.6 Look for and make sure of structure PS. 7 Look for and express regularity in repeated reasoning. PS.8 Level 1: identify, list, label, illustrate, measure, state, tell, use, match Level 2: graph, classify, cause/effect, estimate, compare, infer, construct, summarize, interpret, estimate DOK (Depth of Knowledge) Level 3: Revise, critique, construct, investigate, cite evidence, conclusions, assess Level 4: Design, connect, synthesize, critique, analyze, create, prove, apply concepts Critical Standards (check plus) for 3 weeks: 5.C.1: Multiply multi-digit whole numbers fluently using a standard algorithmic approach. 5.C.2: Find whole-number quotients and remainders with up to four-digit dividends and two- digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Describe the strategy and explain the reasoning used. 5.AT.1: Solve real-world problems involving multiplication and division of whole numbers (e.g. by using equations to represent the problem). In division problems that involve a remainder, explain how the remainder affects the solution to the problem. Spiral Review of Current Curriculum 4.C.4: Multiply fluently within C.3: Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Describe the strategy and explain the reasoning. 4.AT.2: Recognize and apply the relationships between addition and multiplication, between subtraction and division, and the inverse relationship between multiplication and division to solve real-world and other mathematical problems. 4.AT.4: Solve real-world problems with whole numbers involving multiplicative comparison (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem), distinguishing multiplicative comparison from additive comparison. [In grade 4, division problems should not include a remainder.]

15 Week 1: 5.C.1: Multiply multi-digit whole numbers fluently using a standard algorithmic approach. 5.C.3: Compare the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication. (memory of all multiplication facts is a third grade standard) Multiply numbers fluently Compare size of a product with another Use correct comparison symbols Algorithmic approach Compare Equal to Factors Fluently Greater than Less than Multiply Product

16 Week 2: 5.C.2: Find whole-number quotients and remainders with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Describe the strategy and explain the reasoning used. Determine quotients Determine quotients with remainders Divide by 1 digit Divide by 2 digits Use strategies based upon place value Use strategies based upon properties of operations Understand the relationship between multiplication and division Describe the strategy that was used Explain the reasoning Use Your Head Dividend Divisor Operations Place value Properties Quotient Reasoning Strategy

17 Week 3: 5.AT.1: Solve real-world problems involving multiplication and division of whole numbers (e.g. by using equations to represent the problem). In division problems that involve a remainder, explain how the remainder affects the solution to the problem. Solve real-world multiplication problems of whole numbers Solve real-world division problems of whole numbers Use equations to represent problem Explain how remainder affects the solution Dividend Division Divisor Equation Factor Multiplication Product Quotient Remainder

18 Weeks 4-6: Problem Solving: Should be embedded within daily instruction: Make sense of problems and persevere in solving them. PS.1 Reason abstractly and quantitatively PS.2 Construct viable arguments and critique the reasoning of others PS.3 Model with Mathematics PS.4 Use appropriate tools strategically PS.5 Attend to precision PS.6 Look for and make sure of structure PS. 7 Look for and express regularity in repeated reasoning. PS.8 Level 1: identify, list, label, illustrate, measure, state, tell, use, match Level 2: graph, classify, cause/effect, estimate, compare, infer, construct, summarize, interpret, estimate DOK (Depth of Knowledge) Level 3: Revise, critique, construct, investigate, cite evidence, conclusions, assess Level 4: Design, connect, synthesize, critique, analyze, create, prove, apply concepts Critical Standards (check plus) for 3 weeks: 5.C.4: Add and subtract fractions with unlike denominators, including mixed numbers. 5.AT.2: Solve real-world problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators (e.g., by using visual fraction models and equations to represent the problem). Use benchmark fractions and number sense of fractions to estimate mentally and assess whether the answer is reasonable. 5.C.5: Use visual fraction models and numbers to multiply a fraction by a fraction or a whole number. Spiral Review of Current Curriculum 4.C.5: Add and subtract fractions with common denominators. Decompose a fraction into a sum of fractions with common denominators. Understand addition and subtraction of fractions as combining and separating parts referring to the same whole. 4.C.6: Add and subtract mixed numbers with common denominators (e.g. by replacing each mixed number with an equivalent fraction and/or by using properties of operations and the relationship between addition and subtraction). 4.AT.5: Solve real-world problems involving addition and subtraction of fractions referring to the same whole and having common denominators (e.g., by using visual fraction models and equations to represent the problem).

19 Week 4: 5.NS.2: Explain different interpretations of fractions, including: as parts of a whole, parts of a set, and division of whole numbers by whole numbers. 5.NS.1: Use a number line to compare and order fractions, mixed numbers, and decimals to thousandths. Write the results using >, =, and < symbols. (decimals will be during week 11) Explain different interpretations of fractions Explain fractions as parts of a whole Explain fractions as parts of a set Explain division of whole numbers by whole numbers Use a number line to compare fractions Use a number line to order fraction Use a number line to compare mixed numbers Use a number line to compare decimals (week 11) Use a number line to order mixed numbers Use a number line to order decimals (week 11) Use correct comparison symbols Deducing Decimals Dealing With Decimals Compare Denominator Division Equal to Fraction Greater than Interpretations Less than Mixed number Number line Numerator Order Part of set Part to whole Whole numbers

20 Week 5: 5.C.4: Add and subtract fractions with unlike denominators, including mixed numbers. 5.AT.2: Solve real-world problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators (e.g., by using visual fraction models and equations to represent the problem). Use benchmark fractions and number sense of fractions to estimate mentally and assess whether the answer is reasonable. Add fraction with unlike denominators Add mixed numbers with unlike denominators Subtract fractions with unlike denominators Subtract mixed numbers with unlike denominators Solve real-world problems involving addition of fractions Solve real-world problems involving subtraction of fractions Use a visual fraction model to represent the problem Use equations to represent the problem Use benchmark fraction to estimate answer Assess whether the answer is reasonable when adding fractions Assess whether the answer is reasonable when subtracting fractions Fraction Time Royal Rugs Fractions With Pattern Blocks Part 4: Fraction Action Part 5: Fraction Action Part 9: Fraction Action Benchmark fraction Denominator Equation Estimate Fraction Mixed number Model Number sense Numerator Reasonable Unit fraction Visual fraction

21 Week 6: 5.C.4: Add and subtract fractions with unlike denominators, including mixed numbers. 5.C.5: Use visual fraction models and numbers to multiply a fraction by a fraction or a whole number. Add fractions with unlike denominators Add mixed numbers with unlike denominators Subtract fractions with unlike denominators Subtract mixed numbers with unlike denominators Use visual fraction models to multiply a fraction by a fraction Use visual fraction models to multiply a fraction by a whole number Fraction Time Royal Rugs Fractions With Pattern Blocks Part 4: Fraction Action Part 5: Fraction Action Part 9: Fraction Action Denominator Fraction Mixed number Multiply Numerator Visual fraction model

22 Weeks 7-9: Problem Solving: Should be embedded within daily instruction: Make sense of problems and persevere in solving them. PS.1 Reason abstractly and quantitatively PS.2 Construct viable arguments and critique the reasoning of others PS.3 Model with Mathematics PS.4 Use appropriate tools strategically PS.5 Attend to precision PS.6 Look for and make sure of structure PS. 7 Look for and express regularity in repeated reasoning. PS.8 Level 1: identify, list, label, illustrate, measure, state, tell, use, match Level 2: graph, classify, cause/effect, estimate, compare, infer, construct, summarize, interpret, estimate DOK (Depth of Knowledge) Level 3: Revise, critique, construct, investigate, cite evidence, conclusions, assess Level 4: Design, connect, synthesize, critique, analyze, create, prove, apply concepts Critical Standards (check plus) for 3 weeks: 5.C.7: Use visual fraction models and numbers to divide a unit fraction by a non-zero whole number and to divide a whole number by a unit fraction. Spiral Review of Current Curriculum

23 Week 7: 5.AT.3: Solve real-world problems involving multiplication of fractions, including mixed numbers (e.g., by using visual fraction models and equations to represent the problem). 5.C.6: Explain why multiplying a positive number by a fraction greater than 1 results in a product greater than the given number. Explain why multiplying a positive number by a fraction less than 1 results in a product smaller than the given number. Relate the principle of fraction equivalence, a/b = (n a)/(n b), to the effect of multiplying a/b by 1. Solve real-world problems involving multiplication of fractions Solve real-world problems involving multiplication of mixed numbers Use visual fraction models to represent a problem Use equations to represent a problem Explain why multiplying a positive number by a fractions great than 1 results in a product great than the given number Explain why multiplying a positive number by a fraction less than 1 results in a product smaller than the given number Understand fraction equivalence Fraction Time Royal Rugs Fair Squares and Cross Products Part 6: Fraction Action Denominator Equation Equivalence Explain Fraction Mixed number Numerator Product Represent Visual fraction model

24 Week 8: 5.AT.4: Solve real-world problems involving division of unit fractions by non-zero whole numbers, and division of whole numbers by unit fractions (e.g., by using visual fraction models and equations to represent the problem). 5.C.7: Use visual fraction models and numbers to divide a unit fraction by a non-zero whole number and to divide a whole number by a unit fraction. Solve real-world problems in division of fractions Solve real-world problems in division of whole numbers by unit fractions Use visual fraction models to represent the problem Use equations to represent the problem Use visual fraction models to divide fractions Divide and Conquer Division Equation Non-zero whole number Unit fraction

25 Week 9: Review of all fractions Add fractions with unlike denominators Add mixed numbers with unlike denominators Subtract fractions with unlike denominators Subtract mixed numbers with unlike denominators Use a number line to order fractions Use a number line to order mixed numbers Multiply fractions Divide fractions Denominator Fraction Mixed number Numerator

26 Weeks 10-12: Problem Solving: Should be embedded within daily instruction: Make sense of problems and persevere in solving them. PS.1 Reason abstractly and quantitatively PS.2 Construct viable arguments and critique the reasoning of others PS.3 Model with Mathematics PS.4 Use appropriate tools strategically PS.5 Attend to precision PS.6 Look for and make sure of structure PS. 7 Look for and express regularity in repeated reasoning. PS.8 Level 1: identify, list, label, illustrate, measure, state, tell, use, match Level 2: graph, classify, cause/effect, estimate, compare, infer, construct, summarize, interpret, estimate DOK (Depth of Knowledge) Level 3: Revise, critique, construct, investigate, cite evidence, conclusions, assess Level 4: Design, connect, synthesize, critique, analyze, create, prove, apply concepts Critical Standards (check plus) for 3 weeks: 5.C.8: Add, subtract, multiply, and divide decimals to hundredths, using models or drawings and strategies based on place value or the properties of operations. Describe the strategy and explain the reasoning. Spiral Review of Current Curriculum 5.AT.5: Solve real-world problems involving addition, subtraction, multiplication, and division with decimals to hundredths, including problems that involve money in decimal notation (e.g. by using equations to represent the problem).

27 Week 10: 5.C.8: Add, subtract, multiply, and divide decimals to hundredths, using models or drawings and strategies based on place value or the properties of operations. Describe the strategy and explain the reasoning. 5.NS.3: Recognize the relationship that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right, and inversely, a digit in one place represents 1/10 of what it represents in the place to its left. Add decimals to hundredths Subtract decimals to hundredths Multiply decimals to hundredths Divide decimals to hundredths Use various strategies for illustration of operation Use strategies based on place values Describe the strategy used to solve the problem Use reasoning to justify answer Understand relationship of place value of decimal Use Your Head Pack and Post Operation: Decimals Operation: Decimals Addition Decimals Division Hundredth Models Multiplication Operations Place value Property Reasoning Represents Strategy Subtraction

28 Week 11: 5.NS.1: Use a number line to compare and order fractions, mixed numbers, and decimals to thousandths. Write the results using >, =, and < symbols. 5.NS.5: Use place value understanding to round decimal numbers up to thousandths to any given place value. 5.AT.5: Solve real-world problems involving addition, subtraction, multiplication, and division with decimals to hundredths, including problems that involve money in decimal notation (e.g. by using equations to represent the problem). (focus on decimals) Deducing Decimals Compare Decimal notation Use a number line to compare fractions Dealing With Decimals Decimals Use Your Head Use a number life to order fractions Equal to Use a number line to compare mixed numbers Equation Use a number line to order mixed numbers Estimate Use a number line to compare decimals to thousandths Fractions Use a number line to order decimals to thousandths Greater than Use correct comparison symbols when comparing Less than Solve real-world problems involving addition of decimals to hundredths Mixed numbers Solve real-world problems involving subtraction of decimals to hundredths Number line Order Solve real-world problems involving multiplication of decimals to hundredths Place value Solve real-world problems involving division of decimals to hundredths Round Symbol Tenths Thousandths

29 Week 12: 5.NS.6: Understand, interpret, and model percent as part of a hundred (e.g. by using pictures, diagrams, and other visual models). Review of all decimal and percent operations Understand percent as part of a hundred Interpret percent as part of a hundred Model percent as part of a hundred Use visual models to display percent Percent

30 Weeks 13-15: Problem Solving: Should be embedded within daily instruction: Make sense of problems and persevere in solving them. PS.1 Reason abstractly and quantitatively PS.2 Construct viable arguments and critique the reasoning of others PS.3 Model with Mathematics PS.4 Use appropriate tools strategically PS.5 Attend to precision PS.6 Look for and make sure of structure PS. 7 Look for and express regularity in repeated reasoning. PS.8 Level 1: identify, list, label, illustrate, measure, state, tell, use, match Level 2: graph, classify, cause/effect, estimate, compare, infer, construct, summarize, interpret, estimate DOK (Depth of Knowledge) Level 3: Revise, critique, construct, investigate, cite evidence, conclusions, assess Level 4: Design, connect, synthesize, critique, analyze, create, prove, apply concepts Critical Standards (check plus) for 3 weeks: 5.M.1: Convert among different-sized standard measurement units within a given measurement system, and use these conversions in solving multi-step real-world problems. Spiral Review of Current Curriculum 4.M.2: Know relative sizes of measurement units within one system of units, including km, m, cm; kg, g; lb, oz; l, ml; hr, min, sec. Express measurements in a larger unit in terms of a smaller unit within a single system of measurement. Record measurement equivalents in a two-column table. 4.M.3: Use the four operations (addition, subtraction, multiplication and division) to solve real-world problems involving distances, intervals of time, volumes, masses of objects, and money. Include addition and subtraction problems involving simple fractions and problems that require expressing measurements given in a larger unit in terms of a smaller unit.

31 Week 13: 5.G.1: Identify, describe, and draw triangles (right, acute, obtuse) and circles using appropriate tools (e.g., ruler or straightedge, compass and technology). Understand the relationship between radius and diameter. Identify types of triangles Describe the types of triangles Draw the types of triangles Draw circles using appropriate tools Understand radius Understand diameter Understand the relationship between radius and diameter Acute angle Acute triangle Compass Diameter Obtuse angle Obtuse triangle Protractor Radius Right angle Right triangle Straightedge

32 Week 14: 5.G.2: Identify and classify polygons including quadrilaterals, pentagons, hexagons, and triangles (equilateral, isosceles, scalene, right, acute and obtuse) based on angle measures and sides. Classify polygons in a hierarchy based on properties. Identify polygons Classify polygons based on properties Classifying Quadrilaterals Acute angle Acute triangle Categorize Classify Equilateral triangle Hexagon Hierarchy Isosceles triangle Obtuse angle Obtuse triangle Pentagon Polygon Properties Quadrilateral Right angle Right triangle Scalene triangle Solid figure Triangle

33 Week 15: 5.M.1: Convert among different-sized standard measurement units within a given measurement system, and use these conversions in solving multi-step real-world problems. Convert different-sized standard measurement units Solve multi-step problems Straw Planes Conversions Convert Standard measurement

34 Weeks 16-18: Problem Solving: Should be embedded within daily instruction: Make sense of problems and persevere in solving them. PS.1 Reason abstractly and quantitatively PS.2 Construct viable arguments and critique the reasoning of others PS.3 Model with Mathematics PS.4 Use appropriate tools strategically PS.5 Attend to precision PS.6 Look for and make sure of structure PS. 7 Look for and express regularity in repeated reasoning. PS.8 Level 1: identify, list, label, illustrate, measure, state, tell, use, match Level 2: graph, classify, cause/effect, estimate, compare, infer, construct, summarize, interpret, estimate DOK (Depth of Knowledge) Level 3: Revise, critique, construct, investigate, cite evidence, conclusions, assess Level 4: Design, connect, synthesize, critique, analyze, create, prove, apply concepts Critical Standards (check plus) for 3 weeks: 5.M.3: Develop and use formulas for the area of triangles, parallelograms and trapezoids. Solve real-world and other mathematical problems that involve perimeter and area of triangles, parallelograms and trapezoids, using appropriate units for measures. 5.M.5: Apply the formulas V = l w h and V = B h for right rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths to solve real-world problems and other mathematical problems. Spiral Review of Current Curriculum 4.M.4: Apply the area and perimeter formulas for rectangles to solve real-world problems and other mathematical problems. Recognize area as additive and find the area of complex shapes composed of rectangles by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts; apply this technique to solve real-world problems and other mathematical problems.

35 Week 16: 5.M.3: Develop and use formulas for the area of triangles, parallelograms and trapezoids. Solve real-world and other mathematical problems that involve perimeter and area of triangles, parallelograms and trapezoids, using appropriate units for measures. Review Perimeter (grades 3 and 4) Develop formulas for area of triangles Develop formulas for area of parallelograms Develop formulas for area of trapezoids Use formulas for area of triangles Use formulas for area of parallelograms Use formulas for area of trapezoids Solve real-world problems with perimeter Solve real-world problems with area Use appropriate units for measures Area Formulas Parallelogram Perimeter Trapezoid Triangle Unit

36 Week 17: 5.M.2: Find the area of a rectangle with fractional side lengths by modeling with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas. Find area of a rectangle Find area of a rectangle with fractional side Show the area is same by multiplying Represent fraction products as rectangular areas Area Fractional side Length Modeling Product Rectangle Unit squares

37 Week 18: 5.M.4: Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths or multiplying the height by the area of the base. 5.M.5: Apply the formulas V = l w h and V = B h for right rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths to solve real-world problems and other mathematical problems. 5.M.6: Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the non-overlapping parts, applying this technique to solve real-world problems and other mathematical problems. Find the volume of a right rectangular prism Show volume is same by multiplying side lengths Apply formula to find volume Find volume of sold figures of two prisms Luggage Limits Essential Math: Measurement of Rectangular Solids book Base Edge Face Height Length Non-overlapping Right rectangular prism Solid Unit cubes Vertex Vertices Volume Whole number

38 Weeks 19-21: Problem Solving: Should be embedded within daily instruction: Make sense of problems and persevere in solving them. PS.1 Reason abstractly and quantitatively PS.2 Construct viable arguments and critique the reasoning of others PS.3 Model with Mathematics PS.4 Use appropriate tools strategically PS.5 Attend to precision PS.6 Look for and make sure of structure PS. 7 Look for and express regularity in repeated reasoning. PS.8 Level 1: identify, list, label, illustrate, measure, state, tell, use, match Level 2: graph, classify, cause/effect, estimate, compare, infer, construct, summarize, interpret, estimate DOK (Depth of Knowledge) Level 3: Revise, critique, construct, investigate, cite evidence, conclusions, assess Level 4: Design, connect, synthesize, critique, analyze, create, prove, apply concepts Critical Standards (check plus) for 3 weeks: Spiral Review of Current Curriculum

39 Week 19: 5.DS.2: Understand and use measures of center (mean and median) and frequency (mode) to describe a data set. Understand mean to describe a data set Understand median to describe a data set Understand mode to describe a data set Data Data set Frequency Mean Median Mode

40 Week 20: 5.DS.1: Formulate questions that can be addressed with data and make predictions about the data. Use observations, surveys, and experiments to collect, represent, and interpret the data using tables (including frequency tables), line plots, bar graphs, and line graphs. Recognize the differences in representing categorical and numerical data. Formulate questions that can be addressed with data Make predictions about data Use observations to interpret the data Use surveys to interpret the data Use experiments to collect data Use experiments to represent data using tables Understand the types of graphs Recognize the differences in categorical data Recognize the differences in numerical data Bar graph Categorical data Data Experiment Formulate Frequency Frequency table Interpret Line graph Line plot Numerical data Observations Predictions Represent Survey Tables

41 Week 21: 5.AT.6: Graph points with whole number coordinates on a coordinate plane. Explain how the coordinates relate the point as the distance from the origin on each axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate) 5.AT.7: Represent real-world problems and equations by graphing ordered pairs in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Graph ordered pairs on a coordinate plane Explain how coordinates relate distance from the origin Understand the x-axis and y-axis Understand the x-coordinate and y-coordinate Represent real-world problems by graphing ordered pairs in first quadrant Represent equations by graphing ordered pairs in the first quadrant Interpret coordinate values of points Mark My Words Space Shuttle Coordinates Captain Kid s Grid Hurkle Hide and Seek Plotting Planes Willie the Wheel Man Sticking Around Just Drop It! Coordinate Coordinate plane Equation Ordered pair Origin Quadrant Points Value x-axis x-coordinate y-axis y-coordinate

42 Weeks 22-24: Problem Solving: Should be embedded within daily instruction: Make sense of problems and persevere in solving them. PS.1 Reason abstractly and quantitatively PS.2 Construct viable arguments and critique the reasoning of others PS.3 Model with Mathematics PS.4 Use appropriate tools strategically PS.5 Attend to precision PS.6 Look for and make sure of structure PS. 7 Look for and express regularity in repeated reasoning. PS.8 Level 1: identify, list, label, illustrate, measure, state, tell, use, match Level 2: graph, classify, cause/effect, estimate, compare, infer, construct, summarize, interpret, estimate DOK (Depth of Knowledge) Level 3: Revise, critique, construct, investigate, cite evidence, conclusions, assess Level 4: Design, connect, synthesize, critique, analyze, create, prove, apply concepts Critical Standards (check plus) for 3 weeks: 5.C.9: Evaluate expressions with parentheses or brackets involving whole numbers using the commutative properties of addition and multiplication, associative properties of addition and multiplication, and distributive property. Spiral Review of Current Curriculum

43 Week 22: 5.AT.8: Define and use up to two variables to write linear expressions that arise from real-world problems, and evaluate them for given values. Define two variables to write linear expressions Use two variables to write linear expressions Solve real-world problems using linear expressions Evaluate expressions for given values Define Evaluate Expression Linear Expression Variable

44 Week 23: 5.C.9: Evaluate expressions with parentheses or brackets involving whole numbers using the commutative properties of addition and multiplication, associative properties of addition and multiplication, and distributive property. 5.NS.4: Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Evaluate expressions with parentheses Evaluate expressions with brackets Use the commutative property of addition Use the commutative property of multiplication Use associative property of addition Use associative property of multiplication Use distributive property Explain patterns in number of zeros by multiplying by power of 10 Explain patterns of the decimal point when it is multiplied by power of 10 Use whole number exponents for powers of 10 Associative property Bracket Commutative property Cubed Distributive property Exponent Expression Order of operation Parentheses Power Product Squared

45 Week 24: Countdown The next two weeks determine which standards will need more practice.

46 Weeks 25-27: Problem Solving: Should be embedded within daily instruction: Make sense of problems and persevere in solving them. PS.1 Reason abstractly and quantitatively PS.2 Construct viable arguments and critique the reasoning of others PS.3 Model with Mathematics PS.4 Use appropriate tools strategically PS.5 Attend to precision PS.6 Look for and make sure of structure PS. 7 Look for and express regularity in repeated reasoning. PS.8 Level 1: identify, list, label, illustrate, measure, state, tell, use, match Level 2: graph, classify, cause/effect, estimate, compare, infer, construct, summarize, interpret, estimate DOK (Depth of Knowledge) Level 3: Revise, critique, construct, investigate, cite evidence, conclusions, assess Level 4: Design, connect, synthesize, critique, analyze, create, prove, apply concepts Critical Standards (check plus) for 3 weeks: Spiral Review of Current Curriculum