# Casey County Schools- 5 th Grade Math Curriculum Map

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1 Week(s) Standard I can statement(s) Critical Vocabulary Weeks NBT.1 Recognize 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 1/10 of what it represents in the place to its left. I can determine the place value of a whole number and a decimal number. I can recognize that a digit in one place is 10 times the digit to its right. I can recognize that a digit in one place is 1/10 times the digit to its left. digit place value right left base ten numerals place value names Resources Lesson 1-1 Lesson 1-3 Lesson 1-2 Lesson 1-4 Formative Assessment(s) (this will be left blank for you to fill in as you assess your students in each class) 5.NBT.3a Read, write, and compare decimals to thousandths: a. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, 5.NBT.3a Read, write, and compare decimals to thousandths: a. Read and write decimals to I can read and write whole numbers and decimals to the thousandths place. I can read and write decimals to the thousandths using expanded form. November 2015 Page 1

2 thousandths using base-ten numerals, number names, and expanded form, Lesson 1-5 e.g., = (1/10) + 9 (1/100) + 2 (1/1000). b. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. I can compare two decimals using >, =, and < symbols to record the results of comparisons between decimals. I can compare two decimals to the thousandths based on the place value of each digit. Weeks NBT.4 Use place value understanding to round decimals to any place. I can use knowledge of base ten and place value to round decimals to any place. Digits Rounding Lesson NBT.5 Fluently multiply multi-digit whole numbers using the standard algorithm. I can fluently multiply multi-digit whole numbers using the standard algorithm. Product Factors Multiples Lesson 3-3/3-9 November 2015 Page 2

3 5.NBT.2 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 wholenumber exponents to denote powers of 10. I can identify and use strategies based on the properties of operations to multiply. Weeks NBT.6 Find wholenumber quotients of whole numbers with up to four-digit dividends and twodigit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the I can find wholenumber quotients of whole numbers with up to four-digit dividends and twodigit divisors. I can divide using a rectangular array and area model. Dividend Divisor Quotient Operations Lessons 4-1/4-7 Lessons 5-1/5-8 Fall Break November 2015 Page 3

4 calculation by using equations, rectangular arrays, and/or area models. Week 10 5.NBT.7 Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. I can add and subtract decimals to hundredths using concrete models or drawings. I can add and subtract decimals using strategies based on place value, I can identify and use the properties of operations to add and subtract decimals. I can add and subtract decimals using the relationship between addition and subtraction. Decimal Point Decimal Lesson 2-1, 2-3/2-7 Week NBT.7 Add, subtract, multiply, and divide decimals to hundredths, I can multiply and divide decimals to hundredths using concrete models or Topics 6 and 7 November 2015 Page 4

5 using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. drawings. I can multiply and divide decimals using strategies based on place value, I can identify and use the properties of operations to multiply and divide decimals. I can multiply and divide decimals using the relationship between addition and subtraction. Weeks Review Domain 1 Common Core Coach Domain Assessments Week OA.1 Use I can use order of Numerical Expression Lesson 8-2/8-4 parentheses, operations including Evaluate brackets, or braces parenthesis, brackets, Operation Words in numerical or braces to evaluate Order of Operations expressions, and an expression. Parenthesis, brackets, evaluate and braces expressions with these symbols. Thanksgiving Christmas Break 5.OA.2 Write simple expressions that record calculations I can write numerical expressions for given numbers with Lesson 8-1,8-8/8-9 November 2015 Page 5

6 with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation add 8 and 7, then multiply by 2 as 2 x (8+7). Recognize that 3 x ( ) is three times as large as , without having to calculate the indicated sum of product. operation words. I can write operation words to describe a given numerical expression. I can interpret numerical expressions without evaluating them. Week 19 Week 20 Review 5.OA.3 Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms for two patterns, and graph I can generate two numerical patterns using two given rules. I can form ordered pairs consisting of corresponding terms for the two patterns. I can graph generated ordered pairs on a coordinate plane Numerical Expression Evaluate Operation Words Order of Operations Parenthesis, brackets, and braces Lessons 8-5/8-7 November 2015 Page 6

7 the ordered pairs on a coordinate plane. For example, given the rule Add 3 and the starting number 0, and the given rule Add 6 and the starting number 0, generate the terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so. Weeks NF.1 Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For I can determine a common denominator of two fractions. I can add fractions with unlike denominators by finding equivalent fractions with common denominators. Numerator Denominator Simplify Fractions (less than a whole) Unlike/like denominator Mixed numbers Benchmark (0, 1/8, ¼, 1/2, 1) Unit Fraction 9-1, 9-2, 9-5/ , 10-4/10-7 November 2015 Page 7

8 example, 2/3 + 5/4 = 8/ /12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd) I can subtract fractions with unlike denominators by finding equivalent fractions with unlike denominators. 5.NF.2 Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g. by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of I can solve addition and subtraction problems involving fractions (including mixed numbers) with like and unlike denominators using an equivalent fraction strategy. I can solve word problems involving addition and subtraction of fractions with unlike denominators by November 2015 Page 8

9 answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7<1/2. using visual fraction models or equations to represent the problem. I can evaluate the reasonableness of an answer, using fractional number sense, by comparing it to a benchmark fraction. Weeks NF.3 Interpret a fraction as division of the numerator by the denominator (a/b = a b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For I can interpret fractions as division. I can find the correct solution using a division strategy and interpret the solution in the context of the problem. I can interpret the remainder as a fractional part November 2015 Page 9

10 example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50- pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? 5.NF.4 Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. a. Interpret the I can multiply a whole number by a fraction. I can multiply two fractions. 11-2/11-4/11-6 November 2015 Page 10

11 product (a/b) x q as a parts of a partition of q into b equal parts; equivalently, as a result of a sequence of operations a x q / b. For example, use a visual fraction model to show (2/3) 4 = 8/3, and create a story context for this equation. Do the same with (2/3) (4/5) = 8/15. (In general, (a/b) (c/d) = ac/bd.) 5.NF.4b Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. b. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show I can find the area of a rectangle with fractional side lengths by tiling. I can find the area of a rectangle with fractional side lengths by multiplying November 2015 Page 11

12 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.NF.5a Interpret multiplication as scaling (resizing), by: a. Comparing 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.NF.5b Interpret multiplication as scaling (resizing), by: b. Explaining why multiplying a given number by a fraction greater than 1 results in a I can 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. I can recognize that multiplying whole numbers and fractions result in products greater than or less than one depending upon the factors November 2015 Page 12

13 product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n a)/(n b) to the effect of multiplying a/b by 1. 5.NF.6 Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. 5.NF.7abc Apply and I can solve realworld problems involving multiplication of fractions and mixed numbers November 2015 Page 13

14 extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. 1 1Students able to multiply fractions in general can develop strategies to divide fractions in general, by reasoning about the relationship between multiplication and division. But division of a fraction by a fraction is not a requirement at this grade. a. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) divided by 4, and use a visual fraction model to show the quotient. Use relationships I can divide a unit fraction by a whole number by using a story context or using a visual model November 2015 Page 14

15 between multiplication and division to explain that (1/3) 4 = 1/12 because (1/12) x 4 = 1/3. b. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 (1/5) = 20 because 20 x (1/5) = 4. c. 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 I can divide a whole number by a unit fraction by using a story context or using a visual model. I can solve real world problems by dividing fractions and using visual models and equations November 2015 Page 15

16 Weeks represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb. of chocolate equally? How many 1/3 cup servings are in 2 cups of raisins? 5.MD.3ab Recognize volume as an attribute of solid figures and understands concepts of volume measurement. a. A cube with side length 1 unit, called a unit cube, is said to have one cubic unit of volume, and can be used to measure volume. b. A solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a I can recognize that volume is the measurement of the space inside a solid three-dimensional figure. I can recognize a unit cube has 1 cubic unit of volume and is used to measure volume of three-dimensional shapes. I can recognize any solid figure packed without gaps or overlaps and filled with (n) unit cubes indicates the total cubic units or volume. Volume Gaps Overlaps 3-D Solid figures Unit cube/cubic Units Improvised Units Right rectangular prism Additive Irregular (compound) V=lxwxh Shapes/Figures Area models Rectangular arrays 12-1/12-2/12-4 November 2015 Page 16

17 volume of n cubic units. 5.MD.4 Measure volumes by counting unit cubes, using cubic cm, cubic in., cubic ft., and improvised units. 5.MD.5a Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume. a. Find the volume of a right rectangular prism with wholenumber 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, equivalently by I can measure volume by counting unit cubes, cubic cm, cubic in., cubic ft., and improvised units. I can find the volume of a right rectangular prism with whole number side lengths by packing it with unit cubes /12-5 November 2015 Page 17

18 multiplying the height by the area of the base. Represent threefold wholenumber procedures as volumes, e.g., to represent the associative property of multiplication. 5.MD.5b Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume. b. Apply the formulas V=l x w x h and V=B x h for rectangular prisms to find volumes of right rectangular prisms with whole-number lengths in the context of solving real world and I can apply the volume formulas to right rectangular prisms in the context of real world mathematical problems. Volume = length x width x height Volume = area of base x height 12-5 November 2015 Page 18

19 mathematical problems. 5.MD.5c Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume. c. Recognize volume as additive. Find volumes of solid figures composed of two nonoverlapping right rectangular prisms by adding the volumes of the nonoverlapping parts, applying this technique to solve real world problems. I can recognize volume as additive. I can solve real world problems by decomposing a solid figure into two nonoverlapping right rectangular prisms and adding their volumes Weeks MD.1 Convert among differentsized standard measurement units I can convert units of measurement within the same system by multiplying and Customary system Metric system Convert Units for length, Topic 13 November 2015 Page 19

20 within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. dividing. weight/mass, capacity, and time Week 32 5.MD.2 Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations of fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. I can make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). I can solve problems involving information presented in line plots which use fractions of a unit (1/2, 1/4, 1/8) by adding, subtracting, multiplying, and dividing fractions. Line plots Origin Graph/plot 14-1/14-4 Weeks G.1 Use a pair of I can define the x-axis coordinate 16-1/16-2/16-3/16-6 November 2015 Page 20

21 perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x- axis and x- coordinate, y-axis coordinate system. I can identify the x- and y-axis. I can locate the origin on the coordinate system. I can identify coordinates of a point on a coordinate system. I can recognize and describe the connection between the ordered pair and the x- and y-axis (from the origin). y-axis coordinate intersection 1 st quadrant Ordered pairs Corresponding terms Coordinate plane system Relationship between rules November 2015 Page 21

22 Week 35 and y-coordinate). 5.G.2 Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. 5.G.3 Understand that attributes belonging to a category of twodimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. I can graph points in the first quadrant. I can represent real world and mathematical problems by graphing points in the first quadrant. I can interpret coordinate values of points in real world context and mathematical problems I can recognize that some twodimensional shapes can be classified into more than one category based on their attributes. I can recognize if a two-dimensional shape is classified into a category, that it belongs to all subcategories of that category. 16-4/16-5 Topic 15 November 2015 Page 22

23 5.G.4 Classify twodimensional figures in a hierarchy based on properties. I can recognize the hierarchy of twodimensional shapes based on their attributes. I can analyze properties of twodimensional figures in order to place into a hierarchy. I can classify twodimensional figures into categories and/or subcategories based on their attributes. November 2015 Page 23

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