Grade 4 Mathematics Common Core Standards

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1 Domain: Operations and Algebraic thinking 4.OA. Cluster: Use the four operations with whole numbers to solve problems 4.OA.1. Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations. Depth of Knowledge: 1, 2 Essential Question: Can I construct, model, or illustrate equivalent forms of the same multiplication equation? (3) interprets products of whole numbers. (3) represents and solves problems involving multiplication and division as well as solving problems involving the four operations. (3) knows what a multiplicative comparison is and is able to identify and verbalize which quantity is being multiplied and which number tells how many times. interpret a multiplication equation as a comparison. connect mathematical statements and number sentences or equations. represent an unknown number in a word problem with a symbol. identify and verbalize which quantity is being multiplied and which number tells how many times. distinguish whether a word problem involves multiplicative comparison or additive comparison. identify strategies to use when multiplying two numbers together. MP.2. Reason abstractly and quantitatively. MP.4. Model with mathematics. Use drawings or equations with a symbol for the unknown number to represent the problem Model how to solve word problems that involve multiplicative and additive comparisons Present multistep word problems with whole numbers and whole-number answers using the four operations Drawing pictures or using models will help students understand what the problem is asking Model checking for a reasonable answer using mental math and estimation strategies Build arrays for equations using the Commutative Property of Multiplication USD #233, Olathe, Kansas BOE Approved (Feb 2013)

2 Vocabulary: multiplication, factors, product, array, commutative property of multiplication, zero property of multiplication, identity property of multiplication, inverse operation, fact family, repeated addition, equation, comparison Sample Task: Sally is five years old. Her mom is eight times older. How old is Sally s mom? ASSESSMENT: Pedro has invited 8 of his friends to a summer party. He asked each of them to bring 7 pieces of candy. Create a representation of the total number of candy pieces the friends will share. Write the equation that represents the illustration you created. Solve for the answer. District: Resources: counters number lines arrays USD #233, Olathe, Kansas BOE Approved (Feb 2013)

3 Domain: Operations and Algebraic thinking 4.OA. Cluster: Use the four operations with whole numbers to solve problems 4.OA.2. Multiply or divide to solve word problems 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. Depth of Knowledge: 1, 2 Essential Question: How can I use multiplication and division fact families to show the relationship between division and multiplication? Can I explain how one is the inverse of the other. (3) interprets whole number quotients of whole numbers. (3) represents and solves problems involving multiplication and division as well as solving problems involving the four operations. (3) knows what a multiplicative comparison is and is able to identify and verbalize which quantity is being multiplied and which number tells how many times. multiply or divide to solve word problems involving multiplicative comparison. identify and verbalize which quantity is being multiplied and which number tells how many times. draw pictures and write related number sentences to solve problems. represent an unknown number in a word problem with a symbol. Sample Task: A blue scarf costs $3. A red scarf costs 6 times as much. How much does the red scarf cost? A book costs $18. That is three times more than a DVD. How much does a DVD cost? MP.2. Reason abstractly and quantitatively. MP.4. Model with mathematics. MP.5. Use appropriate tools strategically. MP.7. Look for and make use of structure. Use drawings or equations with a symbol for the unknown number to represent the problem Model word problems to help students understand what the problem is asking Model checking for a reasonable answer using mental math and estimation strategies Resources: counters number lines arrays USD #233, Olathe, Kansas BOE Approved (Feb 2013)

4 Vocabulary: multiplication, factors, product, division, dividend, divisor, quotient, array, repeated addition, repeated subtraction, equation, comparison, symbol ASSESSMENT: Helen raised $12 for the food bank last year and she raised 6 times as much money this year. How much money did she raise this year? Sandra raised $15 for the PTA and Nita raised $45. How many times as much money did Nita raise as compared to Sandra? Nita raised $45 for the PTA, which was 3 times as much money as Sandra raised. How much money did Sandra raise? District: USD #233, Olathe, Kansas BOE Approved (Feb 2013)

5 Domain: Operations and Algebraic thinking 4.OA. Cluster: Use the four operations with whole numbers to solve problems 4.OA.3. Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Depth of Knowledge: 1, 2 (3) uses multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities. Vocabulary: multiplication, factors, product, array, commutative property of multiplication, repeated addition, equation, comparison, operation, estimation, reasonable, remainder, addend, sum, difference, divisor, dividend, quotient, rounding, remainder, compatible numbers, breaking apart solve multistep word problems using all four operations. represent an unknown number in a word problem with a symbol. use and discuss various estimation strategies. assess the reasonableness of answers using estimation strategies. Sample Task: On a vacation, your family travels 267 miles on the first day, 194 miles on the second day, and 34 miles on the third day. How many miles did they travel in all? Your class is collecting bottled water for a service project. The goal is to collect 300 bottles of water. On the first day, Max brings MP.1. Make sense of problems and persevere in solving them. MP.2. Reason abstractly and quantitatively. MP.4. Model with mathematics. MP.5. Use appropriate tools strategically. MP.6. Attend to precision. MP.7. Look for and make use Use drawings or equations with a symbol for the unknown number to represent the problem Present multistep word problems with whole numbers and whole-number answers using the four operations Teach and model multiple estimation strategies (front-end estimation with adjusting, clustering around an average, rounding and adjusting, using friendly or compatible numbers, using benchmark numbers that are easy to compute) Model assessing the reasonableness of answers using mental computation and USD #233, Olathe, Kansas BOE Approved (Feb 2013)

6 Essential Question: How can mental math and estimation help when determining if an answer is reasonable? in 3 packs with 6 bottles in each container. Sarah wheels in 6 packs with 6 bottles in each container. About how many bottles of water still need to be collected? ASSESSMENT: A 17-inch long piece of rope is cut into 2-inch pieces. How many 2- inch pieces are there? How much of the rope is left? Draw a picture or diagram that illustrates the problem. Write an equation using a symbol for the unknown variable. Solve the equation. Use mental math or estimation to determine the reasonableness of your answer. Write an explanation of how you know you are right. District: estimation strategies Resources: counters number lines arrays rounding models USD #233, Olathe, Kansas BOE Approved (Feb 2013)

7 Domain: Operations and Algebraic thinking 4.OA. Cluster: Gain familiarity with factors and multiples 4.OA.4. Find all factor pairs for a whole number in the range Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range is a multiple of a given one-digit number. Determine whether a given whole number in the range is prime or composite. Depth of Knowledge: 1 Essential Question: How can patterns found in multiplication help us to solve problems? (3) determines the unknown whole number in multiplication or division equations relating three whole numbers. Vocabulary: fact families, factor, factor pairs, array, multiple, prime, composite, multiplication, division, equation, comparison, odd, even find factor pairs for a whole number. identify multiples of a number. understand the concept of factors and multiples as it relates to multiplication. identify if a number is prime or composite. use strategies to find factors or multiples of a whole number. Sample Task: Find the factors/factor pairs for 96. Find the first five multiples of 8. ASSESSMENT: Students at Creek Elementary are going to an assembly. Each class arranges its chairs in a rectangular MP.2. Reason abstractly and quantitatively. MP.7. Look for and make use of structure. Model finding factors of a number using a variety of strategies (e.g. factor rainbows, area models) Model finding multiples by skip counting Model strategies to determine whether a number is prime or composite (e.g. building arrays, using hundreds chart, using blocks) Resources: counters number lines arrays graph paper square tiles hundreds board blocks USD #233, Olathe, Kansas BOE Approved (Feb 2013)

8 How can you determine if a number is prime or composite? form. What are all the possible arrangements for the following classes? Miss Franklin 30 students Mr. Clark 27 students Ms. Rodriguez 31 students Mrs. Smith 13 students District: USD #233, Olathe, Kansas BOE Approved (Feb 2013)

9 Domain: Operations and Algebraic thinking 4.OA. Cluster: Generate and analyze patterns 4.OA.5. Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. For example, given the rule Add 3 and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way. Depth of Knowledge: 2, 3 (3) have familiarity with number and shape patterns, have an understanding of the four operations, and can solve math operations and sequences with an unknown. Vocabulary: pattern, odd, even, repeat, pattern rule, shape pattern, sequence, alternate investigate different patterns to find rules. identify features of a pattern that were not explicit in the rule. justify the reason for the features in a pattern. generate a number or shape pattern that follows a given rule. Sample Task: Rule: Create a pattern that starts at 1 and multiplies each number by 3. Stop when you have 6 numbers. ASSESSMENT: The table below shows a list of numbers. For every number listed in the table, multiply it by 2 and add 1. Record the result on the MP.2. Reason abstractly and quantitatively. MP.4. Model with mathematics. MP.5. Use appropriate tools strategically. MP.6. Attend to precision MP.7. Look for and make use of structure. MP.8. Look for and express regularity in repeated reasoning. Provide multiple opportunities using various methods for creating patterns (e.g. T-Chart, Number Patterns, Shape Patterns) Resources: manipulatives e.g. pattern blocks USD #233, Olathe, Kansas BOE Approved (Feb 2013)

10 Essential Question: How does looking for relationships in the pattern help you find the rule? right. How does finding the pattern help you to continue the sequence of numbers? What do you notice about the numbers you entered into the table? Sherri noticed that all the numbers she entered are odd. Does an even number multiplied by 2 result in an even or odd number? Why do you think this is? Does an odd number multiplied by 2 result in an even or odd number? Why do you think this is? Does an even number plus 1 result in an even or odd number? Why do you think this is? Does an odd number plus 1 result in an even or odd number? Why do you think this is? Explain why the numbers you entered in the table are all odd. USD #233, Olathe, Kansas BOE Approved (Feb 2013)

11 District: USD #233, Olathe, Kansas BOE Approved (Feb 2013)

12 Domain: Number and Operations Base Ten 4.NBT. Cluster: Generalize place value understanding for multi-digit whole numbers 4.NBT.1. Recognize that in a multidigit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that = 10 by applying concepts of place value and division. Depth of Knowledge: 1, 2 Essential Question: How does understanding the place a digit is in and its value help you to understand a multi-digit number? (2) understands that the three digits of a three-digit number represent amounts of hundreds, tens, and ones, e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. (3) uses place value understanding to round whole numbers to the nearest 10 or 100. Vocabulary: place value (0 to 1,000,000), greater than (>), less than (<), equal to (=), compare, ones, tens, hundreds, thousands, ten thousands, hundred thousands, millions, digit recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. understand place value related to multiplying and dividing by multiples of ten. Sample Task: How is the 2 in the number 582 similar to the 2 in the number 528? How is the 2 in the number 582 different from the 2 in the number 528? ASSESSMENT: Given two numbers (e.g., 2,000 and 20) explain the relationship between the numbers, digits, MP.2. Reason abstractly and quantitatively. MP.6. Attend to precision. MP.7. Look for and make use of structure. Provide multiple opportunities in the classroom setting and use real-world context for students to read and write multi-digit whole numbers Provide opportunities for students to compare numbers with the same number of digits (e.g. 453, 698, and 215), numbers that have the same number in the leading digit position (e.g. 45, 495, and 41,223), and numbers that have different numbers of digits and different leading digits (e.g. 312, 95, and 5, 245) Resources: rounding model place value flip chart USD #233, Olathe, Kansas BOE Approved (Feb 2013)

13 places, and values. District: USD #233, Olathe, Kansas BOE Approved (Feb 2013)

14 Domain: Number and Operations Base Ten 4.NBT. Cluster: Generalize place value understanding for multi-digit whole numbers 4.NBT.2. Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. Depth of Knowledge: 1, 2 Essential Question: What is the difference between standard, written, and expanded form? (K-3) can read and write numbers in base-ten numerals, number names, and expanded form <1000, can use manipulatives to show and compare numbers. Vocabulary: place value (0 to 1,000,000), greater than (>), less than (<), equal to (=), compare, ones, tens, hundreds, thousands, ten thousands, hundred thousands, millions, expanded form, digit, standard form, written form read and write multi-digit whole numbers. have a deeper understanding of place value as it relates to the value of numbers (e.g. 285 could also be 28 tens + 5 ones or 1 hundred, 18 tens, and 5 ones). use place value to compare two multi-digit whole numbers using appropriate symbols. understand the difference between standard, written, and expanded form. Sample Task: Write the number 465 in standard, written, and expanded form. MP.2. Reason abstractly and quantitatively. MP.4. Model with mathematics. MP.6. Attend to precision. MP.7. Look for and make use of structure. Model various ways to write numbers (e.g. standard, written, and expanded) Model comparing numbers, focusing on the place value Resources: place value flipchart USD #233, Olathe, Kansas BOE Approved (Feb 2013)

15 ASSESSMENT: Arrange these numbers in order, beginning with the smallest Arrange these numbers in order, beginning with the greatest District: USD #233, Olathe, Kansas BOE Approved (Feb 2013)

16 Domain: Number and Operations Base Ten 4.NBT. Cluster: Generalize place value understanding for multi-digit whole numbers 4.NBT.3. Use place value understanding to round multi-digit whole numbers to any place. Depth of Knowledge: 1, 2 Essential Question: What strategies help you round numbers? (2) reads and writes numbers to 1000 using base ten numerals, number names, and expanded form. (3) uses place value understanding to round whole numbers to the nearest 10 or 100. Vocabulary: place value (0 to 1,000,000), greater than (>), less than (<), equal to (=), compare, ones, tens, hundreds, thousands, ten thousands, hundred thousands, millions, expanded form, digit, rounding identify the value of digits in multi-digit numbers. understand place value and be able to apply this understanding when working with numbers. use place value to round multidigit whole numbers to any place. utilize a strategy to help him/her round numbers. Sample Task: Draw a number line to show 368 rounded to the nearest hundred. ASSESSMENT: Your class is collecting bottled water for a service project. The goal is to collect 300 bottles of water. On the first day, Max brings MP.2. Reason abstractly and quantitatively. MP.6. Attend to precision. Model the vertical addition method 4, Model various rounding strategies This standard refers to place value understanding, which extends beyond an algorithm or procedure for rounding. The expectation is that students have a deep understanding of place value and number sense and can explain and reason about the answers they get when they round. Students should have numerous experiences using a number line and a hundreds chart as tools to support their work with rounding. USD #233, Olathe, Kansas BOE Approved (Feb 2013)

17 in 3 packs with 6 bottles in each container. Sarah wheels in 6 packs with 6 bottles in each container. About how many bottles of water still need to be collected? District: Resources: rounding model place value flipchart number cards number lines hundreds chart graph paper USD #233, Olathe, Kansas BOE Approved (Feb 2013)

18 Domain: Number and Operations Base Ten 4.NBT. Cluster: Use place value understanding and properties of understanding to perform multi-digit arithmetic 4.NBT.4. Fluently add and subtract multi-digit whole numbers using the standard algorithm. Depth of Knowledge: 1, 2 Essential Question: How does understanding place value help you when you are adding or subtracting whole numbers? (3) knows addition facts. (3) knows subtraction facts. (3) fluently adds and subtracts within 1000 using strategies and algorithms based on place value, properties of operation, and/or the relationship between addition and subtraction. Vocabulary: add, addition, addend, sum, subtraction, difference, place value, digit, regroup understand the role place value plays in adding and subtracting whole numbers. add and subtract multi-digit whole numbers. Sample Task: ASSESSMENT: District: MP.2. Reason abstractly and quantitatively. MP.5. Use appropriate tools strategically. MP.7. Look for and make use of structure. MP.8. Look for and express regularity in repeated reasoning. Model adding and subtracting, using regrouping when necessary Model the importance of lining up the digits according to their place value Model examples of addition and subtraction problems that have been done incorrectly and ask students to provide feedback as to where the mistake was made and make corrections Provide students with opportunities to talk through their understanding of addition and subtraction algorithms (e.g. Think, Pair, Share and Showdown) USD #233, Olathe, Kansas BOE Approved (Feb 2013)

19 Resources: graph paper USD #233, Olathe, Kansas BOE Approved (Feb 2013)

20 Domain: Number and Operations Base Ten 4.NBT. Cluster: Use place value understanding and properties of understanding to perform multi-digit arithmetic 4.NBT.5. Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Depth of Knowledge: 1, 2 Essential Question: What is a standard procedure for multiplying multi-digit numbers? (3) knows multiplication facts. (3) multiplies one-digit whole numbers by multiples of 10 and the range (e.g. 9 x 80 and 5 x 60) using strategies based on place value and properties of operations. Vocabulary: multiply, multiplication, factors, product, array, distributive property, equation, digit understand the role place value plays in the process of multiplication. multiply a whole number of up to four digits by a one-digit number. multiply two two-digit numbers. utilize various multiplication strategies. Sample Task: There are 25 dozen cookies in the bakery. What is the total number of cookies in the bakery? ASSESSMENT: MP.2. Reason abstractly and quantitatively. MP.3. Construct viable arguments and critique the reasoning of others. MP.4. Model with mathematics. MP.5. Use appropriate tools strategically. MP.7. Look for and make use of structure. Model multiplication using various strategies (e.g. partial products, area model, breaking apart, matrix model, traditional, lattice) Model the importance of lining up the digits according to their place value Model examples of multiplication problems that have been done incorrectly and ask students to provide feedback as to where the mistake was made and make corrections Provide students with opportunities to talk through their understanding of USD #233, Olathe, Kansas BOE Approved (Feb 2013)

21 District: multiplication algorithms (e.g. Think, Pair, Share and Showdown) Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models Resources: base ten blocks graph paper arrays USD #233, Olathe, Kansas BOE Approved (Feb 2013)

22 Domain: Number and Operations Base Ten 4.NBT. Cluster: Use place value understanding and properties of understanding to perform multi-digit arithmetic 4.NBT.6. 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. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Depth of Knowledge: 1, 2 Essential Question: What strategy can you use to divide? (3) knows multiplication facts. (3) knows division facts. (3) fluently divides within 100, using strategies such as the relationship between multiplication and division. (3)understands place value and properties of operations. (3) knows how to use basic multiplication and division facts fluently and is fluent in basic subtraction facts. (3) knows how to model with an array. Vocabulary: dividend, divisor, quotient, remainder, repeated understand the role place value plays in the process of division. find whole-number quotients and remainders. explain his/her calculations using various division strategies. Sample Task: A fourth grade teacher bought four new pencil boxes. She has 260 pencils. She wants to put the pencils in the boxes so that each box has the same number of pencils. How many pencils will there be in each box? MP.2. Reason abstractly and quantitatively. MP.3. Construct viable arguments and critique the reasoning of others. MP.4. Model with mathematics. MP.5. Use appropriate tools strategically. MP.7. Look for and make use of structure. Model division using various strategies (e.g. traditional, open array, area model) Model the importance of lining up the digits (e.g. the digit in the quotient is above the correct digit in the dividend) Model examples of division problems that have been done incorrectly and ask students to provide feedback as to where the mistake was made and make corrections Provide students with opportunities to talk through their understanding of division algorithms (e.g. Think, Pair, Share and USD #233, Olathe, Kansas BOE Approved (Feb 2013)

23 subtraction, equation, digit ASSESSMENT: District: Showdown) Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models Resources: graph paper base ten blocks arrays area models USD #233, Olathe, Kansas BOE Approved (Feb 2013)

24 Domain: Number and Operations Fractions 4.NF. Cluster: Extend understanding of fraction equivalence and ordering 4.NF.1. Explain why a fraction a/b is equivalent to a fraction (n x a)/(n x b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. Depth of Knowledge: 1, 2 Essential Question: How can you use a model to represent and generate equivalent fractions? (3) understands a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understands a fraction a/b as the quantity formed by a parts of size 1/b. Vocabulary: numerator, denominator, fractions, equivalent, equivalent fractions, benchmark fractions use visual models to generate equivalent fractions. make comparisons of fractions with different numerators and denominators. Sample Task: Name 3 equivalent fractions to ½. ASSESSMENT: District: MP.2. Reason abstractly and quantitatively. MP.4. Model with mathematics. MP.7. Look for and make use of structure. MP.8. Look for and express regularity in repeated reasoning. Teach visual models to generate equivalent fractions Emphasize how the number and size of the parts can differ even though the two fractions themselves are the same size Resources: fraction models area models linear models (number lines) USD #233, Olathe, Kansas BOE Approved (Feb 2013)

25 Domain: Number and Operations Fractions 4.NF. Cluster: Extend understanding of fraction equivalence and ordering 4.NF.2. Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. Depth of Knowledge: 1, 2 (3) Understands a fraction as a number on the number line; represents fractions on a number line diagram. (3)benchmark fractions on a number line. Vocabulary: numerator, denominator, fractions, equivalent, equivalent fractions, benchmark fractions, compare, greater than, less than, equal to compare fractions by creating visual fraction models. compare fractions by finding common denominators or numerators. recognize that he/she must consider the size of the whole when comparing fractions. Sample Task: Melissa used a 12 x 12 grid to represent 1 and Nancy used a 10 x 10 grid to represent 1. Each girl shaded grid squares to show ¼. How many grid squares did Melissa shade? How many grid squares did Nancy shade? Why did they need to shade different numbers of grid squares? MP.2. Reason abstractly and quantitatively. MP.4. Model with mathematics. MP.5. Use appropriate tools strategically. MP.7. Look for and make use of structure. Teach visual models to generate equivalent fractions Emphasize how the number and size of the parts can differ even though the two fractions themselves are the same size Model taking two fractions with unlike denominators, creating equivalent fractions with common denominators, and comparing the numerators Resources: graph paper fraction models linear models (number lines) area model USD #233, Olathe, Kansas BOE Approved (Feb 2013)

26 Essential Question: How can you compare two fractions with different numerators? How can you compare two fractions with different denominators? ASSESSMENT: District: USD #233, Olathe, Kansas BOE Approved (Feb 2013)

27 Domain: Number and Operations Fractions 4.NF. Cluster: Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers 4.NF.3. Understand a fraction a/b with a > 1 as a sum of fractions 1/b. a. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. b. Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model. Examples: 3/8=1/8+1/8+1/8; 3/8=1/8+2/8; (3) explains equivalence of fractions in special cases and compare fractions by reasoning about their size. Vocabulary: unit fraction, mixed numbers, numerator, denominator, fraction, decompose, equivalent understand addition and subtraction of fractions by only adding or subtracting the numerators (not the denominators). understand that adding fractions is joining parts and subtracting fractions is separating parts. decompose a fraction into a sum of fractions (3/8 = 1/8 + 1/8 + 1/8). add and subtract mixed numbers with like denominators. solve word problems involving adding and subtracting fractions with like denominators. show his/her thinking using MP.1. Make sense of problems and persevere in solving them. MP.2. Reason abstractly and quantitatively. MP.4. Model with mathematics. MP.5. Use appropriate tools strategically. MP.6. Attend to precision. MP.7. Look for and make use of structure. MP.8. Look for and express regularity in repeated reasoning. Model adding and subtracting mixed numbers by drawing pictures and using fraction models Model converting mixed numbers to improper fractions and vice versa Model representing whole numbers as fractions Resources: fraction models USD #233, Olathe, Kansas BOE Approved (Feb 2013)

28 2 1/8= /8=8/8+8/8 +1/8. c. Add and subtract mixed numbers with like 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. d. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem Depth of Knowledge: 1, 2 concrete representations. before moving to abstract thinking. Sample Task: Timothy has 4 1/8 pizzas left over from his soccer party. After giving some pizza to his friend, he has 2 4/8 of a pizza left. How much pizza did Timothy give to his friend? ASSESSMENT: District: Essential Question: Can you illustrate adding and subtracting of fractions and mixed numbers or decomposing fractions and mixed numbers using number lines, fraction strips, area models, set models, or rulers? USD #233, Olathe, Kansas BOE Approved (Feb 2013)

29 Domain: Number and Operations Fractions 4.NF. Cluster: Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers 4.NF.4. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. a. Understand a fraction a/b as a multiple of 1/b. For example, use a visual fraction model to represent 5/4 as the product 5 x (1/4), recording the conclusion by the equation 5/4 = 5 x (1/4). b. Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number. For example, use a visual fraction model to (3) can model addition of fractions using various models. (3)can add fractions referring to the same whole. (3)understands equivalent fractions. (4) can decompose a whole number or a fraction into unit fractions. Vocabulary: unit fraction, mixed numbers, improper fraction, numerator, denominator, fraction, equivalent, multiple, equation multiply a fraction by a whole number. solve word problems involving multiplication of a fraction by a whole number using visual fraction models. use and create visual fraction models to multiply a whole number by a fraction. Sample Performance Task: If each person at a party will eat 3/8 of a pound of roast beef and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie? MP.1. Make sense of problems and persevere in solving them. MP.2. Reason abstractly and quantitatively. MP.4. Model with mathematics. MP.5. Use appropriate tools strategically. MP.6. Attend to precision. MP.7. Look for and make use of structure. MP.8. Look for and express regularity in repeated reasoning. Model how to multiply a fraction by a whole number Resources: fraction models USD #233, Olathe, Kansas BOE Approved (Feb 2013)

30 express 3 x (2/5) as 6 x (1/5), recognizing this product as 6/5. (In general, n x (a/b) = (n x a) /b.) c. Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem. For example, if each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie? ASSESSMENT: Marsha has 120 stamps. She gave her sister half of the stamps and 3 more. How many stamps does Marsha have left? District: Depth of Knowledge: 1, 2 Essential Question: How do you multiply a fraction by a whole number? USD #233, Olathe, Kansas BOE Approved (Feb 2013)

31 Domain: Number and Operations Fractions 4.NF. Cluster: Understand decimal notation for fractions, and compare decimal fractions. 4.NF.5. Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100. For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100. Depth of Knowledge: 1, 2 Essential Question: Can you model addition of fractions with base-ten denominators? (3)can use a variety of models to represent addition of fractions with like denominators. (3)can add fractions with like denominators. (3)Understands equivalent fractions. (3) Understands a unit whole. Vocabulary: unit fraction, numerator, denominator, fraction, equivalent, decimal make equivalent fractions by converting a denominator of 10 to a denominator of 100. add a fraction with a denominator of 10 to a fraction with a denominator of 100. represent fractions using grids (in order to prepare for work with decimals in 4.NF.6 and 4.NF.7). understand the connection between fractions and decimals. Sample Task: MP.2. Reason abstractly and quantitatively. MP.4. Model with mathematics. MP.5. Use appropriate tools strategically. MP.7. Look for and make use of structure. Model creating equivalent fractions with denominators of 10 and 100 Model adding fractions with denominators of 10 and 100 Model representing a fraction in various ways - base ten blocks, grid paper, etc. (In order to prepare for work with decimals, students need experience with representing fractions using grids) Resources: decimal place value mats area models base ten blocks number lines USD #233, Olathe, Kansas BOE Approved (Feb 2013)

32 ASSESSMENT: A dime is 1/10 of a dollar and a penny is 1/100 of a dollar. What fraction of a dollar is 6 dimes and 3 pennies? Write your answer in both fraction and decimal form. District: USD #233, Olathe, Kansas BOE Approved (Feb 2013)

33 Domain: Number and Operations Fractions 4.NF. Cluster: Understand decimal notation for fractions, and compare decimal fractions. 4.NF.6. Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram. Depth of Knowledge: 1, 2 Essential Question: How can you represent a fraction as a decimal? How can you represent a decimal as a fraction? (3)understands that the value of each place is ten times the value of the place to its immediate right. (3) understands that fractions have many names in the form of equivalent fractions. (3) can use place value charts, illustrations or manipulatives to represent whole numbers. Vocabulary: tenths, hundredths, decimal, unit fraction, numerator, denominator, fraction, equivalent represent a fraction as a decimal or a decimal as a fraction. represent decimals on a place value model or number line. Sample Task: How can you express.45 as a fraction? How can you express 6/100 as a decimal? ASSESSMENT: Rewrite 0.62 as a fraction. District: MP.2. Reason abstractly and quantitatively. MP.4. Model with mathematics. MP.5. Use appropriate tools strategically. MP.7. Look for and make use of structure. Model making connections between fractions and the place value chart Model various ways to represent the same fraction (32/100, thirty-two hundredths, 0.32) Resources: place value chart number line USD #233, Olathe, Kansas BOE Approved (Feb 2013)

34 Domain: Number and Operations Fractions 4.NF. Cluster: Understand decimal notation for fractions, and compare decimal fractions. 4.NF.7. Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model. Depth of Knowledge: 1, 2 Essential Question: How do you compare two decimals up to the hundredths place value? (3) can use a model to visually represent fractions. (3)can place decimal values on a number line. (3)can use the symbols >, =, < to compare whole numbers and fractions. (3) can write a decimal by looking at a visual model. Vocabulary: tenths, hundredths, decimal, unit fraction, numerator, denominator, fraction, equivalent, greater than, less than, equal to use symbols to compare two decimals to the hundredths place value. recognize that comparisons are valid only when the two decimals refer to the same whole. Sample Task: Draw a model to show that 0.3 < 0.5. ASSESSMENT: District: MP.2. Reason abstractly and quantitatively. MP.4. Model with mathematics. MP.5. Use appropriate tools strategically. MP.7. Look for and make use of structure. Model how to compare two decimals to the hundredths place value Model how to record the comparisons with the symbols <, >, or = and justify the conclusions Resources: fraction models area models USD #233, Olathe, Kansas BOE Approved (Feb 2013)

35 Domain: Measurement and Data 4.MD. Cluster: Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit 4.MD.1. Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. For example, know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36),... Depth of Knowledge: 1, 2 (2) measures the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes. (3) tells and writes time to the nearest minute and measures time intervals in minutes. Solves word problems involving addition and subtraction of time intervals in minutes. Vocabulary: kilometer (km), meter (m), centimeter (cm), mile (mi), yard (yd), foot (ft), inch (in), kilogram (kg), gram (g), pound (lb), ounce (oz), understand the difference between the two systems of measurement. understand the units of measurement for each system. understand the relationships between units of measurement. understand what operations to use to convert between units within the same system. Sample Task: Standard/Customary 5 quarts = cups Metric 8 liters = milliliters MP.2. Reason abstractly and quantitatively. MP.5. Use appropriate tools strategically. MP.6. Attend to precision Use measuring tools (e.g. measuring cups) to model the different units of measurement Use visuals (e.g. Gallon Man) to help students understand the relationship between units of measurement Model conversions using a T-Chart Use a number line diagram to teach elapsed time Resources: measuring tools (e.g. yardstick, ruler, measuring cups, meter stick) clock scale number lines USD #233, Olathe, Kansas BOE Approved (Feb 2013)

36 Essential Question: How do you know which measurement tool to use when measuring a(n)? How do you convert a larger unit to a smaller unit? liter (L), milliliter (ml), gallon (gal), quart (qt), pint (pt), cup (c), hour (hr), minute (min), second (sec), measurement, convert, conversion, time, length, width, capacity, distance, standard/ customary, metric, operation ASSESSMENT: District: USD #233, Olathe, Kansas BOE Approved (Feb 2013)

37 Domain: Measurement and Data 4.MD. Cluster: Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit 4.MD.2. Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. Depth of Knowledge: 1, 2 (3) adds, subtracts, multiplies, or divides to solve one-step word problems involving masses or volumes that are given in the same units. Vocabulary: kilometer (km), meter (m), centimeter (cm), mile (mi), yard (yd), foot (ft), inch (in), kilogram (kg), gram (g), pound (lb), ounce (oz), liter (L), milliliter (ml), gallon (gal), quart (qt), pint (pt), cup (c), hour (hr), minute (min), second (sec), measurement, convert, conversion, time, length, width, capacity, distance, standard/ understand the units of measurement for each system. understand which operations to use to solve word problems. understand what operations to use to convert between units within the same system. understand that some problems involve more than one step. Sample Task: At 7:00 a.m. Melisa wakes up to go to school. It takes her 8 minutes to shower, 9 minutes to get dressed and 17 minutes to eat breakfast. How many minutes does she have until the bus comes at 8:00 a.m.? MP.1. Make sense of problems and persevere in solving them. MP.2. Reason abstractly and quantitatively. MP.4. Model with mathematics. MP.5. Use appropriate tools strategically. MP.6. Attend to precision. Model how to use key words to help understand the problem and to determine which operation to use to solve the problem Model using various strategies to determine which operation to use to solve problems (e.g. bar diagram, drawing a picture, T- Chart) Model examples of choosing the appropriate measuring tool to use (e.g. Would I use a ruler or a scale to see how much my dog weighs?) Use measurement tools to model if an USD #233, Olathe, Kansas BOE Approved (Feb 2013)

38 Essential Question: How do you determine which operation to use when converting measurements in a measurement word problem? customary, metric, operation ASSESSMENT: District: amount is reasonable (e.g. When baking cookies, would you use a cup of sugar or a gallon of sugar?) Model how to solve multi-step word problems Resources: measuring tools (e.g. yardstick, ruler, measuring cups, meter stick) clock scale number lines USD #233, Olathe, Kansas BOE Approved (Feb 2013)

39 Domain: Measurement and Data 4.MD. Cluster: Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit 4.MD.3. Apply the area and perimeter formulas for rectangles in real world and mathematical problems. For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor. Depth of Knowledge: 1, 2 Essential Question: How can you determine when to use area or perimeter when solving a problem? What formula did you use to solve the problem? (3) understands the visual concept of area and perimeter. (3) understand how to use addition to find perimeter. (3) understand the square unit as the unit of measurement for area. (3) understand how to use multiplication to find area. (3) understand that a division problem can be set up using a variable for an unknown factor. Vocabulary: area, perimeter, length, width, unit, square unit understand the concept of area. understand the concept of perimeter. generalize his/her understanding of area and perimeter by connecting the concepts to mathematical formulas. apply the area and perimeter formulas to various problems. MP.2. Reason abstractly and quantitatively. MP.4. Model with mathematics. MP.5. Use appropriate tools strategically. MP.6. Attend to precision. MP.7.Look for and make use of structure. Model the concepts of area and perimeter using visual representations (e.g. graph paper, linking cubes, drawing pictures, floor tiles, geoboards) Connect the visual models with the formulas for area and perimeter Area l x w Perimeter 2l + 2w or 2(l+w) Make connections with real-world examples (e.g. getting new carpet for your house, putting a border up in a bedroom, getting a fence for a garden) USD #233, Olathe, Kansas BOE Approved (Feb 2013)

40 Sample Task: Mrs. Rutherford is covering the miniature golf course with an artificial grass. How many 1-foot squares of carpet will she need to cover the entire course? Resources: tile blocks graph paper geoboards linking cubes ASSESSMENT: District: USD #233, Olathe, Kansas BOE Approved (Feb 2013)

41 Domain: Measurement and Data 4.MD. Cluster: Represent and interpret data 4.MD.4. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots. For example, from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection. Depth of Knowledge: 1, 2 Essential Question: How do you use a line plot to represent and interpret data? (3) generates measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Shows the data by making a line plot, where the horizontal scale is marked off in appropriate units whole numbers, halves, or quarters. Vocabulary: line plot, number line, data, halves, fourths, quarters, whole, fraction, numerator, denominator, length use data to construct a line plot in fraction units. interpret information in a line plot. solve problems using information presented in a line plot. Sample Task: Students measure objects in their desk to the nearest ½, ¼, or 1/8 inch. They display their data collected on a line plot. How many objects measured ¼ inch? ½ inch? If you put all the objects together end to end what would be the total length of all the objects? Kelly and Mike have an insect collection. They have measured the lengths of all their insects. MP.2. Reason abstractly and quantitatively. MP.4. Model with mathematics. MP.5. Use appropriate tools strategically. MP.6. Attend to precision. MP.7. Look for and make use of structure. Model how to represent fractions on a number line Model using data to create line plots Model interpreting the data on line plots Model solving problems involving addition and subtraction of fractions on a line plot Resources: number lines fraction strips USD #233, Olathe, Kansas BOE Approved (Feb 2013)

42 Their data shows that 4 insects are 1/8 inch long, 6 are 1/4 inch long, 8 are 1/2 inch long, 2 are 1/6 inch long, 1 is 1/12 inch long, and 5 are 1/3 inch long. Create a line plot that shows the data. How much longer is the longest insect from the shortest insect? ASSESSMENT: District: USD #233, Olathe, Kansas BOE Approved (Feb 2013)

43 Domain: Measurement and Data 4.MD. Cluster: Geometric measurement: understand concepts of angle and measure angles 4.MD.5. Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement Depth of Knowledge: 1, 2 Essential Question: How can you determine the types of angles in geometric shapes? (3) understand the basic fractional parts of a circle. (3) can use models, manipulatives, and pictures to represent fractional parts of a circle. (4) understand the definition and components of ray. Vocabulary: angle, shape, ray, endpoint, acute, right, obtuse, straight, angle measurement, degree, protractor recognize that geometric shapes are formed by angles. recognize that angles are made when two rays share a common endpoint. understand concepts of angle measurement. understand the different types of angles (acute, right, obtuse, straight). understand that the length of the ray does not affect the size of the angle. determine if the measure of the angle is reasonable based on the relationship of the angle to a right angle. MP.6. Attend to precision. MP.7. Look for and make use of structure. Model the connection between angles (measure of rotation) and circular measurement (360 degrees) Model drawing different types of angles and discussing their characteristics Resources: protractor USD #233, Olathe, Kansas BOE Approved (Feb 2013)

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