# Scott County Public Schools th. Grade Mathematics. Pacing Guide and Curriculum Map

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1 Scott County Public Schools th Grade Mathematics Pacing Guide and Curriculum Map TO CREATE A COLLABORATIVE CULTURE WITH A FOCUS ON STUDENT LEARNING

3 Scott County Pacing Guide Fifth Grade Mathematics 1st Nine Weeks 5.OA: Write and interpret numerical expressions 5.OA.1 5.OA.2 5.OA: Analyze patterns and relationships 5.OA.3 5.NBT: Perform operations with multi-digit whole numbers and with decimals to hundredths 5.NBT.5 5.NBT.6 5.NBT: Understand the place value system 5.NBT.1 5.NBT.2 5.NBT.3a 5.NBT.3b 5.NBT.4 2nd Nine Weeks 5.NBT: Perform operations with multidigit whole numbers and with decimals to hundredths 5.NBT.7 5.NF: Use equivalent fractions as a strategy to add and subtract fractions 5.NF.1 5.NF: Apply and extend previous understandings of multiplication and division to multiply and divide fractions 5.NF.3 5.NF.5b 5.NF: Use equivalent fractions as a strategy to add and subtract fractions 5.NF.1 5.NF.2 5.NF: Apply and extend previous understandings of multiplication and division to multiply and divide fractions 5.NF.4a 5.NF.4b 5.NF.5a 5.NF.5b 3rd Nine Weeks 5.NF: Apply and extend previous understandings of multiplication and division to multiply and divide fractions 5.NF.6 5.NF.3 5.NF.7 5.MD: Convert like measurement units within a given measurement system 5.MD.1 5.MD: Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition 5.MD.3ab 5.MD.4 5.MD.5a 5.MD.5b 5.MD.5c 4th Nine Weeks 5MD: Represent and interpret data 5.MD.2 5.G: Graph points on the coordinate plane to solve real-world and mathematical problems 5.G.1 5.G.2 5.G: Classify two-dimensional figures into categories based on their properties 5.G.3 5.G.4 Key CC OA NBT NF MD G Counting and Cardinality Operations and Algebraic Thinking Number and Operations in Base Ten Number and Operations Fractions Measurement and Data Geometry Page 3 of 40

4 1 st 2 nd 3 rd 4 th 5.OA.1 K R S P Operations and Algebraic Thinking Write and interpret numerical expressions Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. 1 K Use order of operations including parentheses, brackets, or braces. State Student Friendly Success Criteria I can use multiplication/division and addition/subtraction to solve basic problems. 2 K I can use parentheses in the order of operations to solve basic problems. 3 K I can use brackets in the order of operations to solve basic problems. 4 K I can use braces in the order of operations to solve basic problems. 5 R Evaluate expressions using the order of operations (including using parentheses, brackets, or braces). I can evaluate equations using the order of operations. (Including parentheses, brackets, or braces) This means I can solve equations using the algorithm: PBBEMDAS (Please Brother Bob Excuse My Dear Aunt Sally) Parentheses, Brackets, Braces, Exponents, Multiplication or Division, Addition or Subtraction. * = defined in glossary Order of operations parenthesis brackets braces numerical expression evaluate interpret Page 4 of 40

5 1 st 2 nd 3 rd 4 th 5.OA.2 K R S P Operations and Algebraic Thinking Write and interpret numerical expressions Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating 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. State Student Friendly Success Criteria 1 K Write numerical expressions for given numbers with operation words. 2 K Write operation words to describe a given numerical expression. 3 R Interpret numerical expressions without evaluating I can write numerical expressions for given numbers with operation words. I can write operation words to describe a given numerical expression (addition, subtraction, multiplication, division). I can interpret key words to tell what operation to use and write a numerical expression. This means I can read a word problem and then combine number and operation signs (+, -, x, ) to show the problem. 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 numerical expressions interpret Page 5 of 40

6 1 st 2 nd 3 rd 4 th 5.OA.3 K R S P Operations and Algebraic Thinking Analyze patterns and relationships Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. From ordered pairs consisting of corresponding terms for two patterns, and graph 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. State Student Friendly Success Criteria 1 K Generate two numerical patterns using two given rules. 2 From ordered pairs I can generate (create) two numerical patterns using two given rules. I can define corresponding terms. 3 consisting of I can form ordered pairs K corresponding terms for the consisting of two patterns corresponding terms for the two patterns. 4 I can generate ordered Graph generated ordered pairs on a coordinate plane. K 5 pairs on a coordinate plane. I can graph ordered pairs on a coordinate plane. 7 I can analyze the relationships between corresponding terms in the two numerical patterns. R Analyze and explain the relationship between corresponding terms in the two numerical patterns. 8 I can explain the relationship between corresponding terms in the two numerical patterns. This mean I can write an ordered pair in the (x,y) pattern. This means I can find the rule in a series of numbers, write the ordered pairs, and then graph the values on a coordinate plane. This means I can explain the relationship between at least two numbers. generate numerical patterns corresponding terms coordinate grid (graph) ordered pairs x-coordinate y-coordinate x-axis y-axis Page 6 of 40

7 1 st 2 nd 3 rd 4 th 5.NBT.5 K R S P Number and Operations in Base Ten Perform operations with multi-digit whole numbers and with decimals to hundredths Fluently multiply multi-digit whole numbers using the standard algorithm. State Student Friendly Success Criteria 1 K Fluently multiply multidigit whole numbers using the standard algorithm I can multiply four-digit by two-digit whole numbers using the standard algorithm (a step by step process). This means I can use the steps to multiply starting with the ones place. algorithm product factors addends distributive property equation variable partial product Page 7 of 40

8 1 st 2 nd 3 rd 4 th 5.NBT.6 K R S P Number and Operations in Base Ten Perform operations with multi-digit whole numbers and with decimals to hundredths Find whole-number quotients of whole numbers 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. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. State Student Friendly Success Criteria 1 K Find whole-number quotients of whole numbers with up to fourdigit dividends and twodigit divisors 2 I can divide up to four-digit dividends and two-digit divisors to find a quotient. Use strategies based on place value, the properties 3 R of operations, and/or the I can solve division relationship between multiplication and division to solve division problems 4 R Illustrate and explain division calculations by using equations, rectangular arrays, and/or area models. I can solve division problems using the inverse operation of multiplication. problems using the distributive property, associative property, commutative property, identity and property of zero. I can explain division problems by using equations, rectangular arrays, and/or area models. This means I can use words or pictures to explain how I solved division problems. division dividend divisor quotient/remainder associative property commutative property distributive property inverse operation rectangular array equation area models mixed numbers Page 8 of 40

9 1 st 2 nd 3 rd 4 th 5.NBT.1 K R S P Number and Operations in Base Ten Understand the place value system 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. State Student Friendly Success Criteria 1 K Recognize that in a multidigit 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 identify the value of any digit based on its place value. I can understand that in a multi-digit whole number each digit is ten times the digit to the right. This means I know the hundreds place is ten times greater than the tens place. digit/multi-digit Page 9 of 40

10 1 st 2 nd 3 rd 4 th 5.NBT.2 K R S P Number and Operations in Base Ten Understand the place value system 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. State Student Friendly Success Criteria 1 K Represent powers of 10 using whole number exponents 2 K Fluently translate between powers of ten written as ten raised to a whole number exponent, the expanded form, and standard notation (10 3 = 10 x 10 x 10 = 1000) 3 R Explain the patterns in the number of zeros of the product when multiplying a number by powers of R Explain the relationship of the placement of the decimal point when a decimal is multiplied or divided by a power of 10. I can represent powers of 10 using whole number exponents. I can fluently translate between powers of ten. I can explain the patterns in the number of zeros of the product when multiplying by 10. I can explain the relationship of the placement of the decimal point when a decimal is multiplied or divided by a power of 10. This means I can explain how to multiply a whole number by a power of 10 (add on zeros at the end of the whole number. For example, 12 x 10 = 120, 12 x 100 = 1,200) This means I can: Decide which direction to move the decimal point Find the number of places to move the decimal point in the product Write the product decimal point exponents explain Page 10 of 40

11 1 st 2 nd 3 rd 4 th 5.NBT.3a K R S P Number and Operations in Base Ten Understand the place value system Read, write, and compare decimals to thousandths: a. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., = 3 x x x x (1/10) + 9 x (1/100) + 2 x (1/1000). State Student Friendly Success Criteria 1 I can read and write decimals to thousandths using base-ten numerals in standard form. 2 Read and write decimals to I can read and write K thousandths using base-ten decimals to thousandths numerals, number names, using base-ten numerals in and expanded form word form. 3 I can read and write decimals to thousandths using base-ten numerals in expanded form. place value decimals decimal point base ten system base-ten numerals (standard form) number name (word form) expanded form tenth hundredth thousandth Page 11 of 40

12 1 st 2 nd 3 rd 4 th 5.NBT.3b K R S P Number and Operations in Base Ten Understand the place value system Read, write, and compare decimals to thousandths: b. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. State Student Friendly Success Criteria 1 K Use >, =, and < symbols to record the results of comparisons between decimals. 2 R Compare two decimals to the thousandths on the place value of each digit I can compare decimals using >, =, and < symbols. I can compare two decimals to the thousandths place. This means I can align numbers with a decimal point and compare the digits starting with the greatest/least place value. compare place value decimal point decimal greatest to least (>) least to greatest (<) equal to (=) greatest place value (<, >, =) digits Page 12 of 40

13 1 st 2 nd 3 rd 4 th 5.NBT.4 K R S P Number and Operations in Base Ten Understand the place value system Use place value understanding to round decimals to any place. State Student Friendly Success Criteria 1 K Use knowledge of base ten and place value to round decimals to any place I can round decimals to the thousandths place using the base ten system. place value rounding base ten system Page 13 of 40

14 1 st 2 nd 3 rd 4 th 5.NBT.7 K R S P Number and Operations in Base Ten Perform operations with multi-digit whole numbers and with decimals to hundredths. 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. State Student Friendly Success Criteria 1 K Add, subtract, multiply, I can add decimals to and divide decimals to hundredths using models hundredths using concrete and/or drawings. 2 K models or drawings and I can subtract decimals to strategies based on place hundredths using models value, properties of and/or drawings. 3 K operations, and/or the I can multiply decimals to relationship between hundredths using models addition and subtraction. and/or drawings. 4 K I can divide decimals to hundredths using models and/or drawings. 5 K I can use the properties of operations and/or inverse operations to solve problems using decimals. 6 R Relate the strategy to a I can write and explain the This means I can draw, use written method and explain strategy I used to solve words, or create a model to the reasoning used to solve operations using decimals. explain how to solve decimal operation problems using decimals. calculations. concrete model grid hundredths thousandths inverse operation addition identity property of 0 commutative property of addition associative property of addition multiplicative identity property of 1 commutative property of multiplication associative property of multiplication Page 14 of 40

15 1 st 2 nd 3 rd 4 th 5.NF.1 K R S P Number and Operations Fractions Use equivalent fractions as a strategy to add and subtract fractions. 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 example, 2/3 + 5/4 = 8/ /12 = 23/12. (In general, a/b + c/d = (ad + bc) /bd) State Student Friendly Success Criteria 1 K Generate equivalent fractions to find the like denominator 2 R Solve addition and subtraction problems involving fractions (including mixed numbers) I can generate (create) equivalent fractions to find like denominators. I can solve addition and subtraction problems involving fractions with like denominators. 3 R with like and unlike I can solve addition and denominators using an equivalent fraction strategy subtraction problems involving fractions with unlike denominators. 4 R I can solve addition and subtraction problems involving mixed numbers with like and unlike denominators. This means I can convert fractions with unlike denominators to fractions with like denominators before adding and subtracting. This means I can convert a mixed number to an improper fraction, find a common denominator, and then solve. numerator denominator (like/unlike) common denominator least common denominator (LCD) least common multiple (LCM) fraction mixed number generate equivalent convert simplest form simplify Greatest Common Factor (GCF) improper fraction Page 15 of 40

16 1 st 2 nd 3 rd 4 th 5.NF.3 K R S P Number Operations Fractions Apply and extend previous understandings of multiplication and division to multiply an divide fractions. 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 example, interpret ¾ as the result of dividing 3 by 4, noting that ¾ multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size ¾. 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? State Student Friendly Success Criteria 1 K Interpret a fraction as division of the numerator by the denominator (a/b = a b). I can interpret (show) that a fraction is the numerator divided by the denominator. interpret fractions numerator denominator inverse operation Page 16 of 40

17 1 st 2 nd 3 rd 4 th 5.NF.5b K R S P Number and Operations-Fractions Apply and extend previous understandings of multiplication and division to multiply and divide fractions Interpret multiplication as scaling (resizing), by: b. Explaining why multiplying a given number by a fraction greater than 1 results in a 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 x a)/(n x b) to the effect of multiplying a/b by 1 State Student Friendly Success Criteria 1 K Know that multiplying whole numbers and fractions result in products greater than or less than one depending upon the factors 2 R Draw a conclusion multiplying a fraction greater than one will result in a product greater than the given number 3 R Draw a conclusion that when you multiply a fraction by one (which can I can show that multiplying whole numbers and fractions results in products greater than or less than one depending on the factors I can explain that multiplying a fraction by anything greater than one will give me a product greater than my original number I can explain that when you multiply a fraction by one (can be represented by a This means if I multiply a whole number by a proper fraction, my answer will be less than the whole number. This means if I multiply a whole number by an improper fraction, my answer will be greater than the whole number. This means I can show that when multiply a fraction y a number greater than one gets a number greater than the original number by using pictures, models, or equations conclusion explain Page 17 of 40

18 be written as various fraction, i.e. 2/2, 3/3, etc) the resulting fraction is equivalent 4 R Draw a conclusion that when you multiply a fraction by a fraction, the product will be smaller than the given number whole number or a fraction) you will get an equivalent fraction I can explain that when you multiply two fractions together you get a product smaller than the given factors. Page 18 of 40

19 1 st 2 nd 3 rd 4 th 5.NF.1 K R S P Number and Operations Fractions Use equivalent fractions as a strategy to add and subtract fractions. 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 example, 2/3 + 5/4 = 8/ /12 = 23/12. (In general, a/b + c/d = (ad + bc) /bd) State Student Friendly Success Criteria 1 K Generate equivalent fractions to find the like denominator 2 R Solve addition and subtraction problems involving fractions (including mixed numbers) I can generate (create) equivalent fractions to find like denominators. I can solve addition and subtraction problems involving fractions with like denominators. 3 R with like and unlike I can solve addition and denominators using an equivalent fraction strategy subtraction problems involving fractions with unlike denominators. 4 R I can solve addition and subtraction problems involving mixed numbers with like and unlike denominators. This means I can convert fractions with unlike denominators to fractions with like denominators before adding and subtracting. This means I can convert a mixed number to an improper fraction, find a common denominator, and then solve. numerator denominator (like/unlike) common denominator least common denominator (LCD) least common multiple (LCM) fraction mixed number generate equivalent convert simplest form simplify Greatest Common Factor (GCF) improper fraction Page 19 of 40

20 1 st 2 nd 3 rd 4 th 5.NF.2 K R S P Number and Operations Fractions Use equivalent fractions as a strategy to add and subtract fractions. 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 answers. For example, recognize an incorrect result 2/5 + ½ = 3/7, by observing that 3/7 < ½. State Student Friendly Success Criteria 1 K Generate equivalent fractions to find like denominators. 2 R Solve word problems involving addition and subtraction of fractions with unlike denominators referring to the same whole (e.g. by using visual fraction models or equations to represent the problem) 3 R Evaluate the reasonableness of an answer, using fractional number sense, by comparing it to a benchmark fraction. I can generate (create) equivalent fractions to find like denominators. I can solve word problems using addition and subtraction of fractions with unlike denominators referring to the same whole. I can evaluate a fraction and determine if it is closer to 0, ½, or 1. This means I can illustrate a model or create equations to show how different size fractional parts fit together to equal a whole. fractions numerator denominator (like/unlike) common denominator least common denominator benchmarks (0, ½, 1) estimate inverse operations Page 20 of 40

21 1 st 2 nd 3 rd 4 th 5.NF.4a K R S P Number and Operations Fractions Apply and extend previous understandings of multiplication and division to multiply and divide fractions. Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. a. Interpret the product (a/b) x q as a parts of a partition of q into b equal parts; equivalently, as a results of a sequence of operations a x q / b. For example, use a visual fraction model to show (2/3) x 4 = 8/3, and create a story context for this equation. Do the same with (2/3) x (4/5) = 8/15. (In general, (a/b) x (c/d) = ac/bd.) State Student Friendly Success Criteria 1 K Multiply fractions by whole numbers. 2 R Interpret the product of a fraction times a whole n number as total number of parts of the whole. (for example ¾ x 3 = ¾ + ¾ + ¾ = 9/4) 3 R Determine the sequence of operations that result in the total number of parts of the whole (for example ¾ x 3 = (3x3) /4=9/4) 4 K Multiply fractions by fractions I can multiply fractions by whole numbers. I can explain a fraction by a whole number to find the product. I can use the order of operations to solve a multiplication problem using fractions as total parts of a whole. I can multiply fractions by fractions. 5 R Interpret the product of a I can interpret if I multiply This means I can write an equation for the problem, rename the whole number as an improper fraction, multiply the numerators and the denominators, use models to check, and convert the improper fraction to a mixed number in simplest form. improper fractions mixed number Page 21 of 40

22 fraction times a fraction as the total number of parts of the whole. two fractions together the product will be a smaller fraction. 6 R I can multiply mixed fractions. This means I can convert mixed fractions to improper fractions, then multiply, and convert back to a mixed fraction in simplest form. Page 22 of 40

23 1 st 2 nd 3 rd 4 th 5.NF.4b K R S P Number and Operations Fractions Apply and extend previous understandings of multiplication and division to multiply and divide. 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 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. State Student Friendly Success Criteria 1 K Find area of a rectangle with fractional side lengths using different strategies. (e.g. tiling with unit squares of the appropriate unit fraction side lengths, multiplying side lengths) 2 R Represent fraction products as rectangular areas. 3 R Justify multiplying fractional side lengths to find the area is the same as tiling a rectangle with unit squares of the appropriate unit fraction side lengths. 4 S Model the area of rectangles with fractional side lengths with unit I can multiply the fractional length times the fractional width to find the area of a rectangle. I can create a model or illustration of fractional products as rectangular areas. I can justify area by showing the multiplication of fractional sides and models. I can create a model to show the area of a rectangle using fractional This means I can show that the picture and the equation area equal. This means I can Break into tiles based on a fraction area of a rectangle multiplicative identity property of 1 commutative property of multiplication associative property of multiplication model tiling Page 23 of 40

24 squares to show the area of rectangles. lengths. Find length and width using multiplication of fractions Find area of rectangle unit fraction fraction model fractional side lengths Page 24 of 40

25 1 st 2 nd 3 rd 4 th 5.NF.5a K R S P Number and Operations Fractions Apply and extend previous understandings of multiplication and division to multiply and divide fractions. 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. State Student Friendly Success Criteria 1 K Know that scaling (resizing) involves multiplication. 2 R 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 indication multiplication. For example, a 2x3 rectangle would have an area twice the length of 3. I can show that scaling (resizing) involves the multiplication of fractions. For example: 6 ½ x ¾ = 13/2 x ¾ = 13 x 3 2x4 = 39/8 =4 7/8 I can compare the product of two whole numbers and know that it will be greater than the value of either of those factors. For example, a 2x3 rectangle would have an area twice the length of 3. scaling/resizing compare product factor Page 25 of 40

26 1 st 2 nd 3 rd 4 th 5.NF.6 K R S P Number and Operations Fractions Apply and extend previous understandings of multiplication and division to multiply and divide fractions. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction. State Student Friendly Success Criteria 1 K Represent word problems involving multiplication of fractions and mixed numbers (e.g., by using visual fraction models or equations to represent the problem.) 2 R Solve real world problems involving multiplication of fractions and mixed numbers. I can represent word problems with fractions and mixed numbers using pictures, models, and/or numbers. I can solve word problems by multiplying fractions and mixed numbers. This means I can read the problem, decide what to multiply, solve the problem, and decide if my answer makes since using mathematical proof or illustrations. represent visual models simplest forms convert properties of operations Page 26 of 40

27 1 st 2 nd 3 rd 4 th 5.NF.3 K R S P Number Operations Fractions Apply and extend previous understandings of multiplication and division to multiply and divide fractions. 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 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? State Student Friendly Success Criteria 1 K Interpret a fraction as division of the numerator by the denominator (a/b = a b). 2 R Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers (e.g., using visual fraction models or equations to represent the problem.) 3 R Interpret the remainder as a fractional part of the problem. I can interpret a fraction as a numerator divided by a denominator. I can solve a word problem using division and show the answer as a fraction or mixed number. I can explain how a remainder is a fractional part of the whole. This means I can use visual fraction models or equations to represent and solve a problem. interpret fractions numerator denominator inverse operation Page 27 of 40

28 1 st 2 nd 3 rd 4 th 5.NF.7abc K R S P Number and Operations Fractions Apply and extend previous understandings of multiplication and division to multiply and divide fractions. Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.* *Students 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 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) = 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 represent the problem. For example, 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? State Student Friendly Success Criteria 1 K Know the relationship between multiplication and division. I can tell that division is the opposite of multiplication (fact families). 2 K I can define reciprocal. 3 R Interpret division of a unit fraction by a whole number and justify your answer using the relationship between multiplication and division, and by creating I can divide a fraction by a whole number and prove the answer using multiplication. This means that I can solve problems such as 3 x 4 = 12 so therefore 12/3 = 4 and 12/4 = 3. This means I can prove my answer is correct by creating story problems, visual models, and/or other multiplication strategies by multiplying the quotient reciprocal unit fraction justify Page 28 of 40

29 story problems, using visual models, and relationship to multiplication, etc. 4 R Interpret division of a whole number by a unit fraction and justify your answer using the relationship between multiplication and division, and by representing the quotient with a visual fraction model. 5 R Solve real world problems involving division of unit fractions by whole numbers other than 0 and division of whole numbers by unit fractions using strategies such as visual fractions models and equations. I can divide a whole number by a fraction with an equation and a fraction model. I can solve a word problem involving division of unit fractions by whole numbers. and divisor. This means I can *write an equation for the problem. *write the reciprocal. *multiply by the reciprocal. *create a fraction model to show the quotient. This means I can use models and equations to solve division problems with fractions. Page 29 of 40

30 1 st 2 nd 3 rd 4 th 5.MD.1 K R S P Measurement and Data Convert like measurement units within a given measurement system. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5cm to 0.05m), and use these conversions in solving multi-step, real world problems. State Student Friendly Success Criteria 1 K Recognize units of measurement within the same system. 2 K Divide and multiply to change units. 3 R Convert units of measurement within the same system. I can identify units of measurement within the same system. I can divide and multiply to change units. I can convert metric lengths and weights. 4 R I can convert customary lengths and weights. 5 R Solve multi-step, real world problems that involve converting units. I can solve multi-step word problems that involve converting units. This means I can multiply by powers of 10 and move the decimals as necessary. This means that I can convert between metric units (m, cm, mm, kg, ml, etc) by multiplying or dividing. This means that I can convert between inches, feet, yards, ounces, pounds and miles and pints, gallons, quarts, cups, etc., by multiplying or dividing. convert Measurement System customary units metric units capacity length weight (mass) Page 30 of 40

31 1 st 2 nd 3 rd 4 th 5.MD.3ab K R S P Measurement and Data Geometric measurement: understand concepts of volume and relate volume and relate volume to multiplication and to addition. 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 volume of n cubic units. State Student Friendly Success Criteria 1 K 2 K 3 K Recognize that volume is the measurement of the space inside a solid threedimensional figure. Recognize a unit cube has 1 cubic unit of volume and is used to measure volume of three-dimensional shapes. Recognize any solid figure packed without gaps or overlaps and filled with (n) unit cubes indicates the total cubic units or volume. I can define volume as the space inside of a solid 3D shape. I can identify that a unit cube is the same as 1 cubic unit of volume in a 3D shape. I can find the volume of any solid figure by counting the number of unit cubes. I can identify the volume is the same as the number of total unit cubes. volume attribute cubic unit cube rectangular prism gaps overlaps 3-deminsional Unit cube Page 31 of 40

32 1 st 2 nd 3 rd 4 th 5.MD.4 K R S P Measurement and Data Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition. Measure volumes by counting unit cubes, using cubic cm, cubic in., cubic ft., and improvised units. State Student Friendly Success Criteria 1 K Measure volume by counting unit cubes, cubic cm, cubic in., cubic ft., and improvised units. I can measure the volume of a solid by counting the units and recording it as units cubes. unit cubes cubed cubic units of measure (cm., in., ft., etc.) improvised unit (non-standard) Page 32 of 40

33 1 st 2 nd 3 rd 4 th 5.MD.5a K R S P Measurement and Data Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition. 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 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, equivalently by multiplying the height by the area of the base. Represent threefold whole-number procedures as volumes, e.g., to represent the associative property of multiplication. 1 K Identify a right rectangular prism. 2 R Develop volume formula for a rectangle prism by comparing volume when filled with cubes to volume by multiplying the height by the area of the base, or when multiplying the edge lengths (LxWxH). 3 K Multiply the three dimensions in any order to calculate volume (Commutative and associative properties). 4 S Find the volume of a right rectangular prism with whole number side lengths by packing it with unit cubes. State Student Friendly Success Criteria I can identify a right rectangular prism by its characteristics. I can develop a formula to find volume. I can calculate the volume of a three dimensional shape by using the formula: LxWxH (associative and commutative properties of multiplication) I can find the volume of a right rectangular prism using the formula LxWxH and compare it to the number of cubes I counted. This means I can fill a 3D shape with cubes and then count the number of cubes in the height, width, and length to find the formula (This will lead to LxWxH). * = defined in glossary volume right rectangular prism volume (length x width x height = volume cubed) Page 33 of 40

34 1 st 2 nd 3 rd 4 th 5.MD.5b K R S P Measurement and Data Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume. b. Apply the formula V = l x w x h and V = B x h for rectangular prisms to find volume of right rectangular prisms with whole-number lengths in the context of solving real world and mathematical problems. State Student Friendly Success Criteria 1 K Know that B is the area of the Base I know that B stands for the area of the base. 2 Apply the following I can find the volume of a formulas to right right rectangular prism rectangular prisms having using length x width x whole number edge lengths height. 3 in the context of real world I can find the volume of a R mathematical problems: right rectangular prism using area of base x height. Volume = length x width x height Volume = area of base x height This means to find B I calculate L x W. base = area squared (length x width = area squared) volume formula: (base x height = volume cubed) apply Page 34 of 40

36 1 st 2 nd 3 rd 4 th 5.MD.2 K R S P Measurement and Data Represent and Interpret Data 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. State Student Friendly Success Criteria 1 K Identify benchmark fractions (1/2, 1/4, 1,8). 2 K Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). 3 R 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. I can identify benchmark fractions (1/2, 1/4, 1,8). I can make a line plot between 0 and 1 using benchmark fractions. I can solve computational problems using fractions on a line plot. This means I can read a line plot and correctly use addition, subtraction, multiplication, and/or division with fractions and/or whole numbers. line plot benchmark fractions (0, ½, 1) identify Page 36 of 40

37 1 st 2 nd 3 rd 4 th 5.G.1 K R S P Geometry Graph points on the coordinate plane to solve real-world and mathematical problems. Use a pair of 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 and y-coordinate. State Student Friendly Success Criteria 1 K Define the coordinate system. I can define the coordinate system. 2 K Identify the x- and y- axis. I can identify the x and y axis. 3 K Locate the origin on the I can identify and locate coordinate system. the origin as (0,0) on the 4 K Identify coordinates of a point on a coordinate system. 5 K Recognize and describe the connection between the ordered pair and the x- and y- axis (from the origin). coordinate plane. I can identify the ordered pairs of numbers for a point on a coordinate plane. I can find a point on a coordinate plane and correctly go left/right then up/down. perpendicular number lines axis coordinate system intersection origin locate coordinates (ordered pairs) x-axis y-axis corresponding coordinates given point in a plane (exact location) Page 37 of 40

38 1 st 2 nd 3 rd 4 th 5.G.2 K R S P Geometry Graph points on the coordinate plane to solve real-world and mathematical problems. 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. State Student Friendly Success Criteria 1 K Gap Skill I can locate the first quadrant. 2 K Graph points in the first I can graph points in the quadrant. first quadrant. 3 R Represent real world and I can graph an ordered pair mathematical problems by in the first quadrant to graphing points in the first show real world quadrant. mathematical situations. 4 R Interpret coordinate values of points in real world context and mathematical problems. I can find distances from one location to another on a map or other real world examples. 5 R I can find distances between two locations when given the coordinate values on a map or other real world. ordered pairs graph first quadrant coordinate values exact location scale coordinate grid Page 38 of 40

39 1 st 2 nd 3 rd 4 th 5.G.3 K R S P Geometry Classify 2-dimensional figures into categories based on their properties. Understand that attributes belonging to a category of two-dimensional 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. State Student Friendly Success Criteria 1 K Recognize that some 2- dimensional shapes can be classified into more than one category based on their attributes. 2 K Recognize if a 2- dimensional shape is classified into a category, that it belongs to all subcategories of that category. I can identify 2D shapes based on their attributes. I can classify 2D shapes in all categories and subcategories. For example: a square is a quadrilateral, rhombus, parallelogram, and a rectangle. This means I can identify all categories that a shape could be grouped in. 2 dimensional (2-D) plane figure Polygons: triangle square pentagon hexagon heptagon octagon nonagon decagon circle center point classify categories subcategories attributes angles parallel lines right angles degrees Quadrilateral: parallelogram rhombus rectangle square trapezoid kite Page 39 of 40

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