# DRAFT. Grade 5 Mathematics Item Specifications

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1 DRAFT Grade 5 Mathematics Item Specifications

2 The draft Florida Standards Assessment (FSA) Test Item Specifications (Specifications) are based upon the Florida Standards and the Florida Course Descriptions as provided in CPALMs. The Specifications are a resource that defines the content and format of the test and test items for item writers and reviewers. Each grade-level and course Specifications document indicates the alignment of items with the Florida Standards. It also serves to provide all stakeholders with information about the scope and function of the FSA. Item Specifications Definitions Also assesses refers to standard(s) closely related to the primary standard statement. Clarification statements explain what students are expected to do when responding to the question. Assessment limits define the range of content knowledge and degree of difficulty that should be assessed in the assessment items for the standard. Acceptable response mechanisms describe the characteristics from which a student must answer a question. defines types of stimulus materials that can be used in the assessment items. 2 P a g e J u n e 3 0,

3 Content Standard MAFS.5.OA Operations and Algebraic Thinking MAFS.5.OA.1 Write and interpret numerical expressions. MAFS.5.OA.1.1 Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Assessment Limits Whole numbers and simple fraction expressions (single digit denominators, fraction multiplied by a whole number). Expressions should not be more complex than those used in associative or distributive property situations. Calculator No Acceptable Mechanisms Multiple Choice Multi-Select Graphic Drag and Drop, Hot Spot No context Example Use two operations inside the grouping symbols. Use more than one set of grouping symbols with one operation inside the grouping symbols. Use only whole numbers. Evaluate the expression 6 x (4 + 3 x 2) Evaluate the expression (6 + 3) x (4 + 2). Use one operation inside the grouping symbols. Use only whole numbers. easier Evaluate the expression 6 x (4 + 2) more Use fractions. Use more than one set of grouping symbols with two operations inside the grouping symbols. difficult Evaluate the expression x (4 + 8 x 2) 9. Evaluate the expression (6 + 3 x 3) (4 x 2 + 2). Sample Item Stem Mechanism Notes, Comments An expression is shown. 6 x (4 + 2) What is the value of the expression? An expression is shown x 2 12 Create an equivalent expression that includes a set of parentheses so that the value of the expression is 2. An expression is shown. 6 x (4 + 2 x 4) P a g e J u n e 3 0,

4 What is the value of the expression? An expression is shown. x [4 + 6 x 3] 9 What is the value of the expression? A numerical expression is evaluated as shown. Multiple Choice x {6 x 1 + 7} + 11 Line 1: x {6 x 8} + 11 Line 2: x Line 3: Line 4: 35 In which line does a mistake first appear? A. Line 1 B. Line 2 C. Line 3 D. Line 4 4 P a g e J u n e 3 0,

5 Content Standard MAFS.5.OA Operations and Algebraic Thinking MAFS.5.OA.1 Write and interpret numerical expressions. MAFS.5.OA.1.2 Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation "add 8 and 7, then multiply by 2" as 2 (8 + 7). Recognize that 3 ( ) is three times as large as , without having to calculate the indicated sum or product. Assessment Limits Whole numbers only. Simple fraction expressions. Do not use nested parentheses. Use numeric expressions only. Multiplication cross symbol is the only acceptable symbol for multiplication. Do not use the c-dot. When grouping symbols are part of the expression, the associative property or distributive property should be found in that expression. Calculator No Acceptable Mechanisms Multiple Choice Natural Language No context Example Use 4 numbers with expressions that do not require grouping (Multiply 3 and 4, then add 5). Use 3 numbers with expressions that require grouping (Add 3 and 4, then multiply by 5). easier Use only 3 numbers. Use direct words for the operations (add, subtract, multiply, divide, plus, minus, times). Use only whole numbers. Expressions that do not require grouping. more difficult Use 5 numbers with expressions that do not require grouping ( Multiply 3 and 4, then add 5 ). Use 4 numbers with expressions that require grouping (Add 3 and 4, then multiply by 5). Use indirect words for the operations (double, triple, sum, product) Include a fraction. Sample Item Stem Mechanism Notes, Comments An expression is described in words. Divide 10 by 2, then subtract 3. Create the expression using numbers and symbols. 5 P a g e J u n e 3 0,

6 An expression is described in words. Subtract 6 from 9, then divide by 3. Create the expression using numbers and symbols. An expression is described in words. Add 5 and 14, triple the sum, and then add four-fifths. Create the expression using numbers and symbols. An expression is shown (9 4) Multiple Choice Which statement describes this expression? A. Half the difference of 9 and 4 added to 18 B. Subtract half the quantity of 9 and 4 from 18 C. The sum of 18 and half the product of 9 and 4 D. Half of 9 added to 18 minus 4 An expression is shown. 3 x 4 x Multiple Choice Which statement describes this expression? A. Three more than 5 subtracted from the sum of 3, 4, and 5 B. The product of 3, 4, and 5 subtracted from 5 plus 3 C. Multiply 3, 4, and 5, then subtract 5 and add 3. D. Three added to 5, then subtracted from the product of 3, 4, and 5 6 P a g e J u n e 3 0,

7 Content Standard MAFS.5.OA Operations and Algebraic Thinking MAFS.5.OA.2 Analyze patterns and relationships. MAFS.5.OA.2.3 Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule Add 3 and the starting number 0, and given the rule Add 6 and the starting number 0, generate 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. Assessment Limits Whole numbers and fractions with denominators less than 10. Quadrant I on coordinate plane. Acceptable operations: addition, subtraction, multiplication, and division. The rule should be no more complex than one finds in an application of the associative or distributive property. Examples should not contain nested grouping symbols. Calculator No Acceptable Mechanisms Graphic Drawing/Graphing Multiple Choice Multi-Select Natural Language Table Allowable Example Use two one-step patterns that use different operations. easier more difficult Michael uses the rule multiply by 2. John uses the rule add 10. Use two patterns which use the same operation. Michael uses the rule multiply by 2. John uses the rule multiply by 10. Use at least one multi-operation pattern. Michael uses the rule multiply by 2, then add 4. John uses the rule subtract 2, then multiply by 3. 7 P a g e J u n e 3 0,

8 Sample Item Stem Mechanism Notes, Comments Michael and John are creating patterns. Table Each pattern starts at 1. Michael uses the rule multiply by 2. John uses the rule multiply by 4. Complete the table to show the next two numbers in each pattern. Michael's Pattern John's Pattern Term Number Term Number Michael and John are creating patterns. Michael uses the rule multiply by 2 and starts at 5. John uses the rule add 8 and starts at 16. For which term is Michael s number equal to John s number? Michael and John are creating patterns. Each pattern starts at 1. Graphic Drawing/Graphing Michael uses the rule multiply by 2, then add 3. John uses the rule multiply by 2, then add 4. Use the Add Point tool to plot the ordered pairs that are created from the first three terms of the sequences. 8 P a g e J u n e 3 0,

9 Michael and John each created a numeric pattern. Both patterns start with 0. Multiple Choice The terms in Michael s pattern are always two times the same terms in John s pattern. What could be the rules for the two patterns? A. Michael: Add 2 John: Add 0 B. Michael: Add 6 John: Add 3 C. Michael: Multiply by 2 John: Multiply by 0 D. Michael: Multiply by 6 John: Multiply by 3 9 P a g e J u n e 3 0,

10 Content Standard MAFS.5.NBT Number and Operations in Base Ten MAFS.5.NBT.1 Understand the place value system. MAFS.5.NBT.1.1 Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and of what it represents in the place to its left. Assessment Limits Whole numbers up to millions and decimals to thousandths. Calculator No Acceptable Multi-Select Mechanisms Allowable Example Working with numbers to the right of the decimal. Identifying number patterns across only one place value. Working with numbers only to the left of the decimal. easier more Working with numbers to the right and left of the decimal. Identifying number patterns across several place values. difficult Sample Item Stem Notes, Comments Mechanism An expression is shown. 3,400 x What is the value of the expression? An equation is shown.? x = What is the missing number? An equation is shown x? = 3.4 What is the value of the missing number? How many times larger is the value 0.34 than the value ? 10 P a g e J u n e 3 0,

11 Which statements about the values and 3.40 are true? Multi-Select o is of 340 o is 100 times more than 340 o 3.40 is 100 times more than o is of 3.4 o is of 340 One coin weighs 11 grams. How many grams do 10 coins weigh? Ten coins weigh 25 grams. How many grams does 1 coin weigh? 11 P a g e J u n e 3 0,

12 Content Standard MAFS.5.NBT Number and Operations in Base Ten MAFS.5.NBT.1 Understand the place value system. MAFS.5.NBT.1.2 Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use wholenumber exponents to denote powers of 10. Assessment Limits Whole number exponents with a base of 10. Calculator No Acceptable Multiple Choice Mechanisms Multi-Select Natural Language No context Example Working with numbers to the right of the decimal. Working with numbers to the left of the decimal. easier Generally, multiplication is easier. more difficult Working with numbers to the right and left of the decimal. Generally, division is more difficult. Sample Item Stem Mechanism Notes, Comments What is the value of 10 2? What is 5.23 x 10²? What is ²? What is x 10²? An equation is shown. What is the value of the missing exponent? 12 P a g e J u n e 3 0,

13 Which is equivalent to multiplying a number by 10 3? A. Adding 10 three times B. Adding 3 ten times C. Multiplying by 10 three times D. Multiplying by 3 ten times When dividing a number by 10 3, how is the decimal point moved? A. 3 places to the right B. 3 places to the left C. 4 places to the right D. 4 places to the left David multiplies and divides original numbers by powers of 10 to create new numbers. Multiple Choice Multiple Choice Multi-Select Original number New number , , , ,760 Which original numbers were multiplied by 10 3 to create the new numbers? 13 P a g e J u n e 3 0,

14 Content Standard MAFS.5.NBT Number and Operations in Base Ten MAFS.5.NBT.1 Understand the place value system. MAFS.5.NBT.1.3 Read, write, and compare decimals to thousandths. MAFS.5.NBT.1.3a Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., = ( ) + 9 ( ) + 2 ( ). Assessment Limits MAFS.5.NBT.1.3b Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. Decimals to thousandths. Calculator No Acceptable Mechanisms Graphic Drag and Drop Matching Item Multiple Choice Multi-Select Allowable Example Hundredths or thousandths place. Limit to tenths place. easier To the thousandths place with a zero in the tenths or hundredths place. more difficult Sample Item Stem Mechanism Notes, Comments What is nine-tenths in decimal form? What is two hundred sixty-five thousandths in decimal form? 14 P a g e J u n e 3 0,

15 Grade 5 Mathematics Item Specifications Select the decimal form for each number name. Matching Item Sixty-five thousandths Six hundred five thousandths A number in expanded form is shown. 4 x x ( ) What is the number in decimal form? A number in expanded form is shown. 3 x x ( ) + 6 x ( ) + 5 x ( ) What is the number in decimal form? Select all the expressions that show written in expanded form. Multi-Select 2 x x ( ) + 5 x ( ) + 9 x ( ) 2 x x ( ) + 9 x ( ) 2 x x ( ) + 59 x ( ) 20 x ( ) + 59 x ( ) 20 x ( ) + 5 x ( ) + 9 x ( ) Select all the statements that correctly compare the two numbers. Multi-Select o > o < o > o < o > P a g e J u n e 3 0,

16 Grace, Logan, and Kevin are growing bean plants. They each measured the height of their plant. Graphic Drag and Drop Drag the measurements to order them from least to greatest. Grace 2.1 inches Logan 2.3 inches Kevin 2.0 inches A number in expanded form is shown. 4 x x ( ) + 9 x x ( ) What is the number in decimal form? 16 P a g e J u n e 3 0,

17 Content Standard MAFS.5.NBT Number and Operations in Base Ten MAFS.5.NBT.1 Understand the place value system. Assessment Limits Calculator MAFS.5.NBT.1.4 Use place value understanding to round decimals to any place. Decimals to thousandths. No Acceptable Mechanisms Matching Item Multiple Choice Multi-Select Table Allowable Example Round a decimal number by one digit to the nearest hundredth. Round a decimal number by one digit to the nearest tenth or ones place. easier Round a decimal number by more than one digit to the nearest hundredth, tenth, or ones place. more difficult Sample Item Stem Notes, Comments Mechanism Select all the numbers that round to 4.3 when rounded to the nearest tenth. Multi-Select o 4.25 o 4.24 o 4.21 o 4.35 o 4.34 o 4.31 What is rounded to the nearest hundredth? Select the value of each decimal number when it is rounded to the nearest whole number. Matching Item P a g e J u n e 3 0,

18 Numbers are rounded to the nearest tenth and hundredth, as shown in the table. Table Complete the table to show the numbers that could be rounded. Number Rounded to Nearest Tenth Rounded to Nearest Hundredth P a g e J u n e 3 0,

19 Content Standard MAFS.5.NBT Number and Operations in Base Ten MAFS.5.NBT.2 Perform operations with multi-digit whole numbers and with decimals to hundredths. Assessment Limits MAFS.5.NBT.2.5 Fluently multiply multi-digit whole numbers using the standard algorithm. Multiplication should not exceed 5 digits by 2 digits. Calculator No Acceptable Mechanisms Allowable Example Include multiplication by two-digit numbers with no carrying required. Multiplication by a one-digit number with limited carrying required. easier Include only multiplication by a one-digit number. Use small digits that do not require carrying. more Include multiplication by a two-digit number with carrying. Increase the amount of carrying required. difficult Sample Item Stem Mechanism Notes, Comments Multiply 213 x 12. Multiply 423 x 79. A multiplication problem is shown. What is the missing digit? A multiplication problem is shown. What is the missing digit? 19 P a g e J u n e 3 0,

20 Content Standard MAFS.5.NBT Number and Operations in Base Ten MAFS.5.NBT.2 Perform operations with multi-digit whole numbers and with decimals to hundredths. Assessment Limits MAFS.5.NBT.2.6 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. Only 3-digit or 4-digit dividend and 2-digit divisor. Calculator No Acceptable Graphic Drag and Drop Mechanisms Multi-Select Natural Language Allowable Example Include 2-digit divisors that are not multiples of 5. Zero is not included in the middle of the quotient. 2-digit divisor includes multiples of 5. easier more difficult Quotient includes a zero in the middle of nonzero values (ex: 1, = 104). Quotient requires the student to look at the dividend or part of the dividend as a whole (ex: , because 15 does not divide into the first two digits of 105, 10). Sample Item Stem Mechanism Notes, Comments An expression is shown. 2, What is the value of the expression? An expression is shown What is the value of the expression? Select all the expressions that have a value of 34. Multi-Select o o o o o P a g e J u n e 3 0,

21 An expression is shown. 1, What is the value of the expression? 21 P a g e J u n e 3 0,

22 Content Standard MAFS.5.NBT Number and Operations in Base Ten MAFS.5.NBT.2 Perform operations with multi-digit whole numbers and with decimals to hundredths. Assessment Limits MAFS.5.NBT.2.7 Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Decimals within hundredths place in all numbers involved (divisors, dividends, quotients and likewise for other operations). Calculator No Acceptable Multi-Select Mechanisms Natural Language Allowable Example Include multiplication and division. Permit value up to the hundredths place. Include limited carrying and/or borrowing. easier more difficult Restrict the operations to addition and subtraction. Restrict decimals to tenths. Include values that do not require carrying or borrowing. Use multiple operations in a single problem. Increase the amount of carrying and/or borrowing required. Sample Item Stem Mechanism Notes, Comments An expression is shown What is the value of the expression? An expression is shown. 5.2 x 10.3 What is the value of the expression? An expression is shown x 0.6 What is the value of the expression? 22 P a g e J u n e 3 0,

23 Allen ran 5.4 miles on Monday and 3.2 miles on Tuesday. How many miles did Allen run altogether? During the first race, 12 people ran a 1.5 mile race. During the second race, 4 people ran a 2.2 mile race. How many more total miles were run during the first race compared to the second race? 23 P a g e J u n e 3 0,

24 Content Standard MAFS.5.NF Numbers and Operations Fractions MAFS.5.NF.1 Use equivalent fractions as a strategy to add and subtract fractions. Assessment Limits Calculator Acceptable Mechanisms MAFS.5.NF.1.1 Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example,. (In general, ( ).) Improper fractions and mixed numbers included. Least common denominator is not necessary to calculate sums of fractions. Do not use the terms simplify or lowest terms. Denominators should be one-digit or two-digit. No Graphic Hot Spot Multiple Choice Multi-Select No context Example Addition or subtraction of two fractions, where the denominator of one is not a multiple of the other. Addition or subtraction of a fraction and a mixed number, or two mixed numbers, where the denominator of one fraction is a multiple of the other. easier Addition or subtraction of two fractions, where the denominator of one is a multiple of the other. more difficult Addition or subtraction of a fraction and a mixed number, or two mixed numbers, where the denominator of one fraction is not a multiple of the other. Add/subtract three fractions/mixed numbers (use sparingly, and all items that use this parameter should be labeled hard ). Add or subtract two mixed numbers where regrouping into the whole number is necessary. Sample Item Stem Mechanism Notes, Comments An expression is shown. What is the value of the expression? An expression is shown. What is the value of the expression? 24 P a g e J u n e 3 0,

25 An expression is shown. What is the value of the expression? An equation is shown. What is the missing number? An equation is shown. What is the missing number? An equation is shown. What is the missing number? 25 P a g e J u n e 3 0,

27 27 P a g e J u n e 3 0,

28 Javon, Sam, and Antoine are baking cookies. Javon has cup of flour, Sam has 1 cups of flour, and Antoine has 1 cups of flour. How many cups of flour do they have altogether? Richard and Gianni each bought a pizza. The pizzas are the same size. Richard cut his pizza into 12 slices. Gianni cut his pizza into 6 slices, and ate 2 slices. Together, Richard and Gianni ate of one pizza. How many slices of his pizza did Richard eat? Jasmine has cup of flour in a mixing bowl. She adds more flour. Multiple Choice Jasmine claims that she now has cup of flour in the mixing bowl. Which statement explains why Jasmine s claim is incorrect? A. 7 is not a multiple of 2 B. 1 is less than 3 C. is less than D. is not a multiple of 28 P a g e J u n e 3 0,

29 Content Standard MAFS.5.NF Numbers and Operations Fractions MAFS.5.NF.2 Apply and extend previous understandings of multiplication and division to multiply and divide fractions. Assessment Limits Calculator Acceptable Mechanisms MAFS.5.NF.2.3 Interpret a fraction as division of the numerator by the denominator ( ). 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 as the result of dividing 3 by 4, noting that multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size. 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? Quotients in division problems should not be equivalent to a whole number. Do not use the term simplify or lowest terms. Only use whole numbers for the divisor and dividend of a fraction. No Multiple Choice Natural Language Table Allowable Example Use of double-digit divisors or dividends that share common factors. Simple fractions with single-digit divisor and dividend. easier more Division with a double- or single-digit dividend and/or divisor as well as improper fraction/quotients. difficult Sample Item Stem Mechanism Notes, Comments An expression is shown. 9 3 What is the quotient expressed as a fraction? 29 P a g e J u n e 3 0,

30 A fraction is shown. Multiple Choice Which expression is equivalent to this fraction? A B C D. D Joe has an 8-foot-long board. He needs to cut it into 9 equal length parts. How many feet long should each section of the board be? Joe has a 6-foot-long board. He needs to cut it into 15 equal length parts. How many feet long should each section of the board be? Joe has a 28-foot-long board. He needs to cut it into 24 equal length parts. How many feet long should each section of the board be? An expression is shown. Table Between which two consecutive whole numbers does this value lie? Enter your numbers in the boxes. Between and 30 P a g e J u n e 3 0,

31 Content Standard MAFS.5.NF Number and Operations Fractions MAFS.5.NF.2 Apply and extend previous understanding of multiplication and division to multiply and divide fractions. MAFS.5.NF.2.4 Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. MAFS.5.NF.2.4a Interpret the product ( ) as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a q b. For example, use a visual fraction model to show ( ), and create a story context for this equation. Do the same with ( ) ( ). (In general, ( ) ( ) ). MAFS.5.NF.2.4b 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. Assessment Limits Multiply whole numbers by fractions or fractions by fractions. Visual models: Any appropriate fraction model (e.g., circles, tape, polygons, etc.) Rectangle models only, tile with unit squares For tiling, the dimensions of the tile should be unit fractions with the same denominator as the given rectangular shape (see p. 13 of the progression document for demonstration). Do not use the term simplify or lowest terms. Calculator No Acceptable Mechanisms Graphic Drag and Drop, Drawing/Graphing, Hot Spot Multiple Choice Multi-Select Allowable Example Multiply two proper fractions, with denominator(s) between 5 and 10. Include a fraction multiplied by a whole number. easier Fractions with denominator less than or equal to 5. Include unit fractions. Items where the final answer is a step in the process. more difficult Multiply two fractions, which can include improper fractions. At least one fraction has a double-digit denominator. 31 P a g e J u n e 3 0,

32 Sample Item Stem Mechanism Notes, Comments An expression is shown. What is the value of the expression? An expression is shown. Multiple Choice Which expression is equivalent? An expression is shown. What is the value of the expression? A baker has 5 pounds of sugar. She divides them equally into 3 containers. She then uses 1 container to bake pies. Which expression shows how many pounds of sugar the baker used? A rectangle is shown with dimensions in inches (in.). Multiple Choice What is the area of the rectangle in square inches? 32 P a g e J u n e 3 0,

33 Select all the rectangles that have an area of square inches. Multi-Select 33 P a g e J u n e 3 0,

34 Content Standard MAFS.5.NF Number and Operations Fractions MAFS.5.NF.2 Apply and extend previous understandings of multiplication and division to multiply and divide fractions. MAFS.5.NF.2.5 Interpret multiplication as scaling (resizing), by: MAFS.5.NF.2.5a 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. MAFS.5.NF.2.5b 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 to the effect of multiplying by 1. Assessment Limits Base numbers should be large to discourage students from calculating products. Scaling is explored or demonstrated only in terms of quantity. Scaling geometric figures should not be assessed at this standard. Scaling quantities of any kind in 2 dimensions is strictly beyond the scope of this standard. Calculator No Acceptable Multiple Choice Multi-Select Mechanisms Natural Language Allowable Example Comparisons are made based on a mix of benchmark fractions, whole numbers, nonbenchmark fractions, and mixed numbers/improper fractions. Comparisons are made based strictly on benchmark unit fractions ( and ), whole numbers, easier more difficult and mixed numbers where the fractional part is a benchmark unit fraction. Comparisons are made based strictly on non-benchmark fractions and mixed numbers/improper fractions. ( ) ( ) 34 P a g e J u n e 3 0,

35 Sample Item Stem Mechanism Notes, Comments Two newspapers are comparing sales from Multiple Choice last year. The Post sold 34,859 copies. The Tribune sold 34,589 x copies. Which statement compares the numbers of newspapers sold? A. The Post sold half the number of newspapers that the Tribune sold. B. The Tribune sold half the number of newspapers that the Post sold. C. The Tribune sold twice the number of newspapers that the Post sold. D. The Post sold the same number of newspapers that the Tribune sold. Two newspapers are comparing sales from last year. Multiple Choice The Post sold 34,859 copies. The Tribune sold three-fourths as many copies as the Post. Which expression describes the number of newspapers the Tribune sold? A. 34,859 B. 34,859 C. 34,859 1 D. 34, P a g e J u n e 3 0,

36 Two newspapers are comparing sales from last year. Multiple Choice The Post sold 34,859 copies. The Tribune sold one-and-a-half times as many copies as The Post. Which expression describes the number of newspapers The Tribune sold? A. 34,859 1 B. 34,859 1 C. 34,859 D. 34,859 Select all the expressions that have a value greater than 1,653. Multi-Select A. 1,653 B. 1,653 4 C. 1, D. 1,653 E. 1,653 1 Logan multiplied 54,216 by a number. The product was less than 54,216. Multi-Select Select all the numbers that Logan could have multiplied. A. B. C. 1 D. E. 3 F. 36 P a g e J u n e 3 0,

37 Content Standard MAFS.5.NF Number and Operations Fractions MAFS.5.NF.2 Apply and extend previous understandings of multiplication and division to multiply and divide fractions. Assessment Limits MAFS.5.NF.2.6 Solve real-world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Items should require student to interpret the context to determine operations. Calculator Acceptable Mechanisms easier No Multiple Choice Required Example Multiply a non-unit fraction by a non-unit fraction, proper or improper. Multiply a fraction by a whole number. Multiply a fraction by a unit fraction. Multiply a fraction by a mixed number. more difficult Sample Item Stem Mechanism Notes, Comments Roger has gallon of milk. He gives of it to a friend. How many gallons of milk does Roger have left? Roger has gallon of milk. He gives of it to a friend. How many gallons of milk does Roger have left? Roger has 2 gallons of milk. He gives of it to a friend. How many gallons of milk does Roger have left? 37 P a g e J u n e 3 0,

38 Roger has 6 gallons of milk. He uses of it to make hot chocolate. Then, he uses of the milk he has left to make cookies. How many gallons of milk does Roger have left after making hot chocolate and cookies? 38 P a g e J u n e 3 0,

39 Content Standard MAFS.5.NF Number and Operations Fractions MAFS.5.NF.2 Apply and extend previous understandings of multiplication and division to multiply and divide fractions. MAFS.5.NF.2.7 Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. MAFS.5.NF.2.7a Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for ( ), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that ( ) because ( ). MAFS.5.NF.2.7b Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for ( ),and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that ( ) because ( ). MAFS.5.NF.2.7c 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 lb. of chocolate equally? How many -cup servings are in 2 cups of raisins? Assessment Limits Division of unit fractions by a non-zero whole number, or Division of a non-zero whole number by a unit fraction. Calculator No Acceptable Graphic Drag and Drop, Drawing/Graphing, Hot Spot Mechanisms Multiple Choice Natural Language Allowable Example Either the whole number or the denominator of the fraction is between 5 and 10. Both the whole number and the denominator of the fraction are less than or equal to 5. easier Either the whole number or the denominator of the fraction is greater than or equal to 10. more difficult 39 P a g e J u n e 3 0,

40 Sample Item Stem Mechanism Notes, Comments An expression is shown. 5 What is the value of the expression? An expression is shown. 5 What is the value of the expression? An expression is shown. 12 What is the value of the expression? Julio has 4 pounds of candy. He wants to put the candy into bags so that each bag has pound. Multiple Choice Which expression shows how to calculate the number of bags of candy Julio can make? A. 3 B. 3 C. 3 D. 3 Julio wrote the division equation shown. 8 = 16 Multiple Choice Which multiplication equation can Julio use to show that his work is correct? A. 16 = 8 B = 32 C = D = P a g e J u n e 3 0,

41 Julio has 12 pounds of candy. He wants to put the candy into bags so that each bag has pound of candy. How many bags of candy can Julio make? Julio has 6 pounds of candy. He wants to put the candy into bags so that each bag has pound of candy. Graphic Hot Spot How many bags of candy can Julio make? A. Click on the number line to create sections that model the solution to this problem. B. Select the number of bags that Julio can make. 41 P a g e J u n e 3 0,

42 Content Standard MAFS.5.MD Measurement and Data MAFS.5.MD.1 Convert like measurement units within a given measurement system. Assessment Limits Calculator Acceptable Mechanisms easier more difficult MAFS.5.MD.1.1 Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real-world problems. Measurement values can be whole, decimal, and/or fractional values. Conversion is within the same system. Units of measurement include: kilometer, meter, centimeter, millimeter, liter, milliliter, kilogram, gram, milligram, mile, yard, foot, inch, gallon, quart, pint, cup, ton, pound, and ounce. No Multi-Select Multiple Choice Table Allowable Example Michael is measuring and converting distances in and around his school using whole numbers and decimals. Whole-number values. One-step conversions. Measurement conversions are from larger to smaller units. Whole, decimal, and fractional values. Multi-step conversions. Measurement conversions can go in either direction. Conversions of non-adjacent units that are separated by two or more (i.e., cups to gallons). Sample Item Stem Mechanism Notes, Comments Michael is helping with the school play by measuring fabric for the costumes. He needs 9 yards of fabric. He has 12 feet of fabric. How many more feet of fabric does he need? Michael is helping with the school play by measuring fabric for the costumes. He needs 11.5 yards of fabric. He has 13.5 feet of fabric. How many more feet of fabric does he need? 42 P a g e J u n e 3 0,

43 Michael is helping with the school play by measuring fabric for the costumes. He needs 46 feet of fabric. He has 12.5 yards of fabric. How many more yards of fabric does he need? 43 P a g e J u n e 3 0,

44 Content Standard MAFS.5.MD Measurement and Data MAFS.5.MD.2 Represent and interpret data. Assessment Limits Calculator Acceptable Mechanisms easier more difficult MAFS.5.MD.2.2 Make a line plot to display a data set of measurements in fractions of a unit ( ). Use operations on 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. Measurement units are limited to halves, quarters, and eighths. Division is limited to a whole number divided by a unit fraction or a unit fraction divided by a whole number. No Graphic Hot Spot Multiple Choice Table Allowable Example For line plot construction or identification, all data are at four or five specific measures. For problem solving, if one operation is used, it is subtraction or multiplication. If multiple operations are used, they are addition and subtraction. For line plot construction or identification, all data are at two or three specific measures. For problem solving, addition is used. For line plot construction or identification, all data are at more than five specific measures. For problem solving, if one operation is used, it is division. If multiple operations are used, one must be multiplication or division. 44 P a g e J u n e 3 0,

45 Sample Item Stem Mechanism Notes, Comments Kelly has strips of ribbon with lengths as shown. Multiple Choice Ribbon Lengths (inches) Which line plot represents these data? 45 P a g e J u n e 3 0,

46 Kelly has strips of ribbon with lengths as shown. Ribbon Lengths (inches) 12 Graphic Hot Spot Click on the graph to create a line plot that represents these data. A line plot with Kelly s lengths of ribbons is shown. What is the total length, in inches, of the longest and shortest pieces of ribbon? 46 P a g e J u n e 3 0,

47 A line plot with Kelly s lengths of ribbons is shown. What is the total length, in inches, for all pieces of ribbon? A line plot with Kelly s lengths of ribbons is shown. She adds another ribbon so that the difference between the longest and shortest piece of ribbon is 1 inches. What length of ribbon, in inches, could Kelly have added? A line plot with Kelly s lengths of ribbons is shown. She uses the shortest ribbon and buys another of the longest ribbon. Table How much longer is the total length, in inches, of ribbon now? 47 P a g e J u n e 3 0,

48 A line plot with Kelly s lengths of ribbons is shown. She adds two more ribbons so that the total length of ribbon that Kelly has is 200 inches. Table Ribbon Lengths (inches) Complete the table to show two possible lengths of ribbon, in inches, Kelly could have added. 48 P a g e J u n e 3 0,

49 Content Standard MAFS.5.MD Measurement and Data MAFS.5.MD.3 Geometric measurement: understand concepts of volume and relate volume to multiplication and division. MAFS.5.MD.3.3 Recognize volume as an attribute of solid figures and understand concepts of volume measurement. MAFS.5.MD.3.3a 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. MAFS.5.MD.3.3b 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. Also Assessed: MAFS.5.MD.3.4 Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. Assessment Limits Right rectangular prisms with whole-number side lengths. Graphics include unit cube. Labels can include cubic units (i.e. cubic centimeters, cubic feet, etc.) or exponential units (i.e., cm 3, ft 3, etc.). Calculator No Acceptable Matching Item Mechanisms Multiple Choice Multi-Select Allowable Example A rectangular prism(s) with unit cubes is shown. Decrease dimensional values (<= 6). easier One prism given. Increase dimensional values (> 6). more Increase number of prisms given (3 or more). difficult 49 P a g e J u n e 3 0,

50 Sample Item Stem Mechanism Notes, Comments Ellen is shopping for boxes. Which attribute should she use to determine the amount the box will hold? Multiple Choice A. Area B. Perimeter C. Length D. Volume For which solid object can the volume be found just by counting the number of cubes? Multiple Choice 50 P a g e J u n e 3 0,

51 A rectangular prism is shown. What is the volume of the prism in cubic inches? A rectangular prism is shown. What is the volume of the prism in cubic centimeters? 51 P a g e J u n e 3 0,

52 Several rectangular prisms are shown. Multi-Select Which prisms have a volume between 20 and 40 cubic units? 52 P a g e J u n e 3 0,

53 Content Standard MAFS.5.MD: Measurement and Data MAFS.5.MD.3 Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition. MAFS.5.MD.3.5 Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume. MAFS.5.MD.3.5a 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 products as volumes, e.g., to represent the associative property of multiplication. MAFS.5.MD.3.5b Apply the formulas V = l w h and V = b h for rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths in the context of solving real world and mathematical problems. Assessment Limits Calculator Acceptable Mechanisms easier more difficult MAFS.5.MD.3.5c Recognize volume as additive. Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the non-overlapping parts, applying this technique to solve real world problems. Whole number side lengths. Right rectangular prisms. No more than two non-overlapping prisms non-overlapping means that two prisms may share a face, but they do not share the same volume. No Graphic Drawing/Graphing Matching Item Multiple Choice Multi-Select Allowable Example Volumes between 50 and 100 square units. Volumes greater than 100 square units where at least one of the side lengths is a multiple of 10. Volumes under 50 square units. Volumes greater than 50 where at least one side length is 10. Volumes greater than 100, where no side length is a multiple of 10. The student is presented with multiple prisms to evaluate (i.e., multi-select items where each option is a prism). 53 P a g e J u n e 3 0,

54 Sample Item Stem Mechanism Notes, Comments A shipping box in the shape of a rectangular prism has the dimensions shown. What is the volume of the box in cubic feet? Select all the shipping boxes that are shaped like rectangular prisms that have a volume of 384 cubic feet (ft). o 6 ft x 8 ft x 8 ft o 4 ft x 12 ft x 24 ft o 4 ft x 6 ft x 16 ft o 4 ft x 8 ft x 12 ft o 3 ft x 10 ft x 20 ft A shipping box in the shape of a rectangular prism has a volume of 48 cubic feet, a length of 4 feet, and a width of 3 feet. What is the height, in feet, of the box? A shipping box in the shape of a rectangular prism has a height of 6 feet (ft) and a volume of 96 ft 3. Use the Connect Line tool to draw a possible base for the box. Multi-Select Graphic Drawing/Graphing 54 P a g e J u n e 3 0,

55 Content Standard MAFS.5.G Geometry MAFS.5.G.1 Graph points on the coordinate plane to solve real-world and mathematical problems. Assessment Limits Calculator Acceptable Mechanisms MAFS.5.G.1.1 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). Whole numbers. Use only points located in the first quadrant of the coordinate plane. Plotting points given the ordered pair is aligned to MAFS.5.G.2. No Graphic Drawing/Graphing Multiple Choice Multi-Select No context Example Give coordinates of one point and direction to another point. Same coordinate values for both x and y. easier Different coordinate values for both x and y. more difficult Sample Item Stem Mechanism Notes, Comments Point M is 3 units away from the origin in the direction of the x-axis, and 3 units away in the direction of the y-axis. Multiple Choice What could be the coordinates of point M? A. (0, 3) B. (3, 3) C. (3, 6) D. (6, 6) 55 P a g e J u n e 3 0,

56 Point M is 3 units away from the origin on the x-axis. Multiple Choice What could be the coordinates of point M? A. (0, 3) B. (3, 0) C. (3, 3) D. (3, 6) Point M is 3 units away from the origin in the direction of the x-axis, and 5 units away in the direction of the y-axis. Multiple Choice What could be the coordinates of point M? A. (3, 5) B. (5, 3) C. (3, 8) D. (5, 8) Point T is 6 units away from the origin on the x-axis. Multi-Select Select all coordinates that could represent point T. o (0, 6) o (6, 0) o (-6, 6) o (-6, 0) o (0, -6) A point is located as described. 4 units away from the origin in the direction of the x-axis, and 4 units away from the origin in the direction of the y-axis Use the Add Point tool to plot the point. A point is 3 units away from the origin on the y-axis. Graphic Drawing/Graphing Graphic Drawing/Graphing Use the Add Point tool to plot the point. 56 P a g e J u n e 3 0,

57 A point is located as described. 3 units away from the origin in the direction of the x-axis, and 4 units away from the origin in the direction of the y-axis Graphic Drawing/Graphing Use the Add Point tool to plot the point. 57 P a g e J u n e 3 0,

58 Content Standard MAFS.5.G Geometry MAFS.5.G.1 Graph points on the coordinate plane to solve real-world and mathematical problems. Assessment Limits Calculator Acceptable Mechanisms easier more difficult MAFS.5.G.1.2 Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Whole numbers. Use only points located in the first quadrant of the coordinate plane. Mathematical and real-world problems must have axes scaled to whole numbers (not letters). No Graphic Drag and Drop, Drawing/Graphing Multi-Select Multiple Choice Matching Item Allowable Example Give coordinates of one point and direction to another point. Generally includes some points that are on an axis. Give actual coordinates or points plotted. Generally includes some points that have the same x-and y-coordinate. Give only directions, no coordinates. Give distances from both axes (assuming that distances are different if distances are the same, this should be medium difficulty). Generally includes some points that have different x-and y-coordinates. 58 P a g e J u n e 3 0,

59 Sample Item Stem Mechanism Notes, Comments Which point is located at (5, 1) on the Multiple Choice coordinate grid? A. Point A B. Point B C. Point C D. Point D Use the Add Point tool to plot the point (3, 4). Point A has the coordinates (3, 5). Point B is located 5 units above point A. Drag points A and B to show their locations in the coordinate plane. Point A is located on the x-axis. Point B is located 5 units above point A. Drag points A and B to show their locations in the coordinate plane. Point A is located 5 units below and 4 units to the left of point B. Graphic Drawing/Graphing Graphic Drag and Drop Graphic Drag and Drop Graphic Drag and Drop Drag points A and B to show their locations in the coordinate plane. 59 P a g e J u n e 3 0,

60 The location of the park in Dan s town is shown in the coordinate plane. Graphic Drawing/Graphing Dan left home, went 3 units up and 4 units right, and got to the park. Use the Connect Line tool to plot a point that indicates the location of Dan s house. Some locations in Dan s town are shown in the coordinate plane. Multi-Select Dan moved from one location to another by traveling 1 unit left and 5 units up. Which ways could he have travelled? A. From home to the park B. From the park to the library C. From home to the library D. From school to the park 60 P a g e J u n e 3 0,

61 Sonia s trip is shown in the coordinate plane. Multi-Select Select all the true statements. o Sonia travelled 3 miles. o Sonia travelled 5 miles. o Sonia travelled 6 miles. o Sonia s trip lasts 7 hours. o Sonia s trip lasts 5 hours. 61 P a g e J u n e 3 0,

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