Grade 7 Mathematics Item Specification C1 TA

Transcription

1 Grade 7 Mathematics Item Specification C1 TA Task Model 1 7.RP.1 Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. 7.RP.2b Recognize and represent proportional relationships between quantities. b. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. Evidence Required: 1. The student computes unit rates and finds the constant of proportionality of proportional relationships in various forms. Development Note: The graphical representations of real-world situations are in claims 2 and 3. Prompt Features: The student is prompted to give the constant of proportionality (unit rate) of two proportional quantities. The described ratio should involve ratios of fractions. Context should be familiar to students 12 to 14 years old. Item difficulty can be adjusted via these example methods: o Mixed number fractions increase the difficulty compared to fractions which are not mixed numbers. o Unit rates can be whole numbers or fractions. TM1a Stimulus: The student is presented with a verbal description of a real-world situation with a proportional relationship in a context. Example Stem: David uses cup of apple juice for every carrot juice to make a fruit drink. cup of Enter the number of cups of apple juice David uses for 1 cup of carrot juice. Rubric: (1 point) The student enters the correct number (e.g., 2 1 ). 4 Version 2.0

2 Grade 7 Mathematics Item Specification C1 TA Task Model 1 7.RP.1 Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. 7.RP.2b Recognize and represent proportional relationships between quantities. b. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. Prompt Features: The student is prompted to give the constant of proportionality (unit rate) of two proportional quantities. Context should be familiar to students 12 to 14 years old. Tables should be labeled and contain two to four sets of data. Item difficulty can be adjusted via these example methods: o Values can be whole numbers and/or fractions with or without mixed numbers. o Unit rate can be a whole number or fraction. TM1b Stimulus: The student is presented with a table or diagram of a proportional relationship in a context. Example Stem 1: This table shows a proportional relationship between the number of cups of sugar and flour used for a recipe. Cups of Sugar Cups of Flour Enter the number of cups of sugar used for 1 cup of flour. Example Stem 2: This table shows a proportional relationship between the number of cups of sugar and flour used for a recipe. Cups of Sugar Cups of Flour Evidence Required: 1. The student computes unit rates and finds the constant of proportionality of proportional relationships in various forms. Enter the number of cups of sugar used for 1 cup of flour. Rubric: (1 point) The student enters the correct number 2 1 (e.g., ; ). 5 3 Development Note: The graphical representations of real-world situations are in claims 2 and 3. 5 Version 2.0

3 Grade 7 Mathematics Item Specification C1 TA Task Model 1 7.RP.1 Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. 7.RP.2b Recognize and represent proportional relationships between quantities. b. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. Prompt Features: The student is prompted to give the constant of proportionality (unit rate) of two proportional quantities. Context should be familiar to students 12 to 14 years old. Tables should be labeled and contain two to four sets of data. Item difficulty can be adjusted via these example methods: o Values can be whole numbers and/or fractions with or without mixed numbers. o Unit rate can be a whole number or fraction. TM1c Stimulus: The student is presented with a table or diagram of a proportional relationship in a context. Example Stem 1: This diagram shows how much apple juice is mixed wit h c arrot juic e for a rec ipe. Enter the number of cups of apple juice used for 1 cup of carrot juice. Example Stem 2: This diagram shows how much apple juice is mixed wit h c arrot juic e for a rec ipe. Evidence Required: 1. The student computes unit rates and finds the constant of proportionality of proportional relationships in various forms. Enter the number of cups of apple juice used for 1 cup of carrot juice. Rubric: (1 point) The student enters the correct number 5 (e.g., 2; ). 3 Development Note: The graphical representations of real-world situations are in claims 2 and 3. 6 Version 2.0

4 Grade 7 Mathematics Item Specification C1 TA Task Model 1 7.RP.1 Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. 7.RP.2b Recognize and represent proportional relationships between quantities. b. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. Evidence Required: 1. The student computes unit rates and finds the constant of proportionality of proportional relationships in various forms. Development Note: The graphical representations of real-world situations are in claims 2 and 3. Prompt Features: The student is prompted to give the constant of proportionality (unit rate) of two proportional quantities. Context should be familiar to students 12 to 14 years old. Item difficulty can be adjusted via these example methods: o The equation should come in the following forms: y = rx, where r is the unit rate and [coefficient1][variable1] = [coefficient2][variable2]. o Unit rates include whole numbers, positive fractions, and mixed numbers. o Coefficients include whole numbers, fractions, and exclude the number one. TM1d Stimulus: The student is presented with an equation of a proportional relationship. Example Stem 1: For a drink recipe, the amount of papaya juice is proportional to the amount of carrot juice. This equation represents the proportional relationship between the number of quarts of papaya juice (p) and carrot juice (c) in a recipe. 2p = 8c Enter the number of quarts of papaya juice used for 1 quart of carrot juice. Example Stem 2: For a drink recipe, the amount of papaya juice is proportional to the amount of carrot juice. This equation represents the proportional relationship between the number of quarts of papaya juice (p) and carrot juice (c) in a recipe. ( )p = ( )c Enter the number of quarts of papaya juice used for 1 quart of carrot juice. Rubric: (1 point) The student enters the correct number (e.g., 4; ). 7 Version 2.0

5 Grade 7 Mathematics Item Specification C1 TA Task Model 2 Multiple Choice, multiple correct response 7.RP.2a Recognize and represent proportional relationships between quantities. a. Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin. 2. The student determines whether two quantities, shown in various forms, are in a proportional relationship. Prompt Features: The student is prompted to identify tables of values that represent proportional relationships. Tables should be labeled and have four to five sets of data. All tables within an item should follow the same format. All graphs within an item should follow the same format. Item difficulty can be adjusted via these example methods: o Table values are whole numbers or fractions. o Fractions may be mixed numbers. o For graphs, distractors should include graphs with the equation in the form of y = x 2 and the equation in the form of y = mx + b (where b 0) TM2a Stimulus: The student is presented with one table per answer choice. Example Stem 1: Select all tables that represent a proportional relationship between x and y. A. B. C. D Answer Choices: Answer choices should be tables showing a relationship between two quantities. There should be one to two tables showing proportional relationships. Distractors should be tables that do not show a proportional relationship, which may include a relationship following an equation in the form of y = mx + b (where b 0) or y = x 2. Rubric: (1 point) Student selects all the correct tables. (e.g., A and C). Multiple Choice, multiple correct response 8 Version 2.0

6 Grade 7 Mathematics Item Specification C1 TA Task Model 2 Multiple Choice, multiple correct response Example Stem 2: Select all tables that represent a proportional relationship between x and y. A RP.2a Recognize and represent proportional relationships between quantities. a. Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin. 2. The student determines whether two quantities, shown in various forms, are in a proportional relationship. B. C. D Answer Choices: Answer choices should be tables showing a relationship between two quantities. There should be one to two tables showing proportional relationships. Distractors should be tables that do not show a proportional relationship, which may include a relationship following an equation in the form of y = mx + b (where b 0) or y = x 2. Rubric: (1 point) Student selects all the correct tables. (e.g., A and D). Multiple Choice, multiple correct response 9 Version 2.0

7 Grade 7 Mathematics Item Specification C1 TA Task Model 2 Multiple Choice, multiple correct response 7.RP.2a Recognize and represent proportional relationships between quantities. a. Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin. Prompt Features: The student is prompted to identify which graphs represent proportional relationships. Context should be familiar to students 12 to 14 years old. Item difficulty can be adjusted via these example methods: o Unit rate is a whole number or fraction. o Distractors should inc lude graphs with the equation in the form of y = x 2 and the equation in the form of y = mx + b (where b 0) TM2b Stimulus: The student is presented with one table or one graph per answer choice. Example Stem: Select all the graphs that show a proportional relationship. A) 2. The student determines whether two quantities, shown in various forms, are in a proportional relationship. B) 10 Version 2.0

8 Grade 7 Mathematics Item Specification C1 TA Task Model 2 Multiple Choice, multiple correct response C) 7.RP.2a Recognize and represent proportional relationships between quantities. a. Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin. 2. The student determines whether two quantities, shown in various forms, are in a proportional relationship. D) Answer Choices: Distractors should be graphs that do not show a proportional relationship, which may show a nonlinear relationship or a relationship following an equation in the form of y = mx + b (where b 0) or y = x 2. Rubric: (1 point) Student selects all the correct graphs (e.g., B and C). Multiple Choice, multiple correct response 11 Version 2.0

9 Grade 7 Mathematics Item Specification C1 TA Task Model 3 7.RP.2c Recognize and represent proportional relationships between quantities. c. Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn. 3. The student represents proportional relationships between quantities using equations. Development Note: The verbal descriptions and table representations will be in claim 2. Prompt Features: The student is prompted to give an equation that represents the proportional relationship between two given quantities. Context should be familiar to students 12 to 14 years old. Graph is linear and begins at (0, 0) or a set of plotted points which includes (0, 0). Tables should be labeled, represent the relationship between two variables, and have 3-5 sets of data. For graphs, axes are labeled and include whole numbers and/or fractions. r, the unit rate, is a whole number or fraction. Item difficulty can be adjusted via these example methods: o The graph of the line that intersects at point (1, r) where r is the unit rate in rational number form. o Scaling of the graph may be fractional or in units other than multiples of 2 or 10. o Table values are whole numbers or fractions. o Fractions are not mixed numbers. TM3 Stimulus: The student is presented with two quantities in a contextual proportional relationship given in a graph or table. Example Stem 1: This graph shows a proportional relationship between the number of hours (h) a business operates and the total cost of electricity (c). Find the constant of proportionality (r). Using the value for r, enter an equation in the form of c = rh that represents the relationship between the number of hours (h) and the total cost (c). 12 Version 2.0

10 Grade 7 Mathematics Item Specification C1 TA Task Model 3 Example Stem 2: This graph shows a proportional relationship between x and y. 7.RP.2c Recognize and represent proportional relationships between quantities. c. Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn. 3. The student represents proportional relationships between quantities using equations. Development Note: The verbal descriptions and table representations will be in claim 2. Find the constant of proportionality (r). Using the value for r, enter an equation in the form of y = rx. Example Stem 3: This table shows a proportional relationship between x and y. x y Find the constant of proportionality (r). Using the value for r, enter an equation in the form of y = rx. Rubric: (1 point) Student enters the correct equation (e.g., c = 10h; y = 2x; y = 12x). 13 Version 2.0

11 Grade 7 Mathematics Item Specification C1 TA Task Model 4 Matching Tables 7.RP.2d Recognize and represent proportional relationships between quantities. d. Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate. 4. The student interprets specific values from a proportional relationship in the context of a problem situation. Prompt Features: The student is prompted to select specific values from a proportional relationship in the context of a problem situation. Context should be familiar to students 12 to 14 years old. Graph is linear and begins at (0, 0) or a set of plotted points which includes (0, 0). Graph axes are labeled and inc lude whole numbers and/or fractions. r, the unit rate, is a whole number or fraction. Items difficulty can be adjusted via these example methods: o One answer choice which assesses the interpretation of a single point on the graph that is not the unit rate is easier than an answer choice that compares the interpretation of two different points. TM4 Stimulus: The student is presented with a graph of a proportional relationship where specific values may be emphasized. Example Stem: This graph shows a proportional relationship between the number of hours (h) a business operates and the total cost (c) of electricity. Select True or False for each statement about the graph. 14 Version 2.0

12 Grade 7 Mathematics Item Specification C1 TA Statement True False Point A represents the total cost of electricity when operating the business for 6 hours. The total cost of electricity is $8 when operating the business for 80 hours. The total cost of electricity is $10 when operating the business for 1 hour. Rubric: (1 point) Student determines each statement as being either true or false (e.g., T, F, T). Each statement is a sentence describing one of the points in the context. False statements should be statements that use the wrong values or switch the values when interpreting the graph. More difficult statements are about points beyond the visible portion of the graph. Matching Tables 15 Version 2.0

13 Grade 7 Mathematics Item Specification C1 TA Task Model 5 7.RP.3 Use proportional relationships to solve mult ist ep rat io and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error. 5. The student computes with percentages in context. Prompt Features: The student is prompted to compute with percentages in a real-world context that requires multiple steps to solve. Context of problems should be familiar to students 12 to 14 years old. For items asking for a percentage, the percent symbol (%) should not be required for full credit. For items asking for a dollar amount, the dollar sign ($) should not be required for full credit. Item difficulty can be adjusted via these example methods: o 1-3 step(s) problem. o Multiplying by a percent which should include benchmark percentages, i.e. 25%, 50%, etc. o Divide two numbers or by a perc ent whic h should include benchmark percents, 25%, 50%, etc. TM5 Stimulus: The student is presented with a real-world context involving adding or subtracting a percent to the whole (simple interest, tax, commission, markup, markdowns, tips, coupons, and discounts). Example Stem 1: Dave buys a baseball for $15 plus an 8% tax. Mel buys a football for $20 plus an 8% tax. Enter the difference in the amount Dave and Mel paid, including tax. Round your answer to the nearest cent. Rubric: (1 point) Student gives the correct difference in the amount between David and Mel (e.g., 5.40). Example Stem 2: A bicycle is originally priced at $80. The store owner gives a discount and the bicycle is now priced at $60. Enter the percentage discount for the cost of the bicycle. Rubric: (1 point) Student gives the correct percentage discount (e.g., 25). Example Stem 3: Dave has a 32 ounc e energy drink. He drinks 10 ounces. Enter the percentage of ounces Dave has left from his energy drink. Round your answer to the nearest hundredth. Rubric: (1 point) Student gives the correct percentage (e.g., 68.75). 16 Version 2.0

14 Grade 7 Mathematics Item Specification C1 TB Task Model 1 Graphing 7.NS.1b Understand p + q as the number located a distance q from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts. Prompt Features: The student is prompted to construct a model on the number line that corresponds to given information. Item difficulty can be adjusted via these met hods: Mathematical operations involving addition and subtraction are easier when the terms are positive. Terms consisting of integers are easier than terms which include rational numbers such as decimals, fractions or mixed numbers. A number line containing whole number scaling is easier than one containing rational number scaling. TM1a Stimulus: The student is presented with a scaled number line including a labeled point at a rational number. Example Stem: What numbers are located exactly 3 5 units from point P on the number line? Use the Add Point tool to plot the location of these numbers on the number line. Evidence Required: 1. The student interprets rational number values on a number line, including modeling addition and subtraction expressions. Tools: None Interaction: Add Point and Delete tools should be provided for students to plot points on the number line containing snap-to regions at every tic mark. Rubric: (1 point) The student plots the exact location of both points 7 (e.g., and 1). 3 Graphing 6 Version 2.0

15 Grade 7 Mathematics Item Specification C1 TB Task Model 1 Multiple Choice, multiple correct response DOK Level 1 7.NS.1b Understand p + q as the number located a distance q from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts. 1. The student interprets rational number values on a number line, including modeling addition and subtraction expressions. Tools: None Prompt Features: The student is prompted to identify the sum or difference of rational numbers given a number line. At least one of the numbers must be a negative rational number. At least one of the numbers must be negative. Rational numbers are in the same form. Item difficulty can be adjusted via these methods: o Terms consisting of integers are easier than terms which include rational numbers such as decimals, fractions or mixed numbers. o A number line containing whole number scaling is easier than one containing rational number scaling. TM1b Stimulus: The student is presented with a number line with two labeled points at least 3 units apart. Example Stem: Select all expressions that show the distance between P and Q. A. 5 ( 8) B. C. D. 5 + ( 8) Answer Choice: Answer choices should involve using absolute value signs, such 5+8 Distractors should include using a wrong operation, number, or sign(s). Rubric: (1 point) Student selects all correct expressions and no incorrect expressions (e.g., A and B). Multiple Choice, mult iple c orrect response 7 Version 2.0

16 Grade 7 Mathematics Item Specification C1 TB Task Model 1 Drag and Drop 7.NS.1c Understand subtraction of rational numbers as adding the additive inverse, p q = p + ( q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts. 1. The student interprets rational number values on a number line, including modeling addition and subtraction expressions. Tools: None Prompt Features: The student is prompted to construct a model on the number line that corresponds to given expression. At least one of the numbers must be negative. Item difficulty can be adjusted via these example methods: o Terms consisting of integers are easier than terms which include rational numbers such as decimals, fractions or mixed numbers. o The number line mat use rational numbers such as fractions or decimals. TM1c Stimulus: The student is presented with a scaled number line and an expression involving the sum or difference of two rational numbers in the same form. Example Stem: Drag the expression into the box that has a sum or difference between 8 and 8. You may use the number line and Add Arrow tool to model the problem. The number line will not be scored. Interaction: The student drags an expression to the answer box above the number line and may or may not use the Add Arrow tool and number line. Rubric: (1 point) Student chooses the correct expression [e.g., 1 + ( 8)]. Drag and Drop 8 Version 2.0

17 Grade 7 Mathematics Item Specification C1 TB Task Model 1 Multiple Choice, single correct response DOK Level 1 7.NS.1c Understand subtraction of rational numbers as adding the additive inverse, p q = p + ( q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts. 1. The student interprets rational number values on a number line, including modeling addition and subtraction expressions. Prompt Features: The student is prompted to identify a model on the number line that corresponds to given information. At least one of the numbers must be negative. Item difficulty can be adjusted via these example methods: o Terms consisting of integers are easier than terms which include rational numbers such as decimals, fractions or mixed numbers. o The number line may use rational numbers such as fractions or decimals. TM1d Stimulus: The student is presented with a scaled number line and an expression involving the sum or difference of two rational numbers. Example Stem: Which number line model represents the sum of ( )? A. B. Tools: None C. D. Answer Choices: Answer choices are number lines modeling addition or subtraction expressions. Distractors should inc lude number line models with arrows facing in the wrong direction, arrows placed incorrectly, and arrows of incorrect length. Rubric: (1 point) Student selects correct number line model (e.g., D). Multiple Choice, single correct response 9 Version 2.0

18 Grade 7 Mathematics Item Specification C1 TB Task Model 2 DOK Level 1 7.NS.1d Apply properties of operations as strategies to add and subtract rational numbers. 2. The student applies properties of operations as strategies to add and subtract rational numbers. Tools: None Prompt Features: The student is prompted to identify the sum or difference of rational numbers. Numbers can be presented on a vertical number line if more than three points with labels are graphed. Item difficulty can be adjusted via these methods: o Mathematical operations involving addition and subtraction are easier when the terms are positive. o Terms consisting of integers are easier than terms which include rational numbers such as decimals, fractions or mixed numbers. o A number line containing whole number scaling is easier than one containing rational number scaling. TM2a Stimulus: The student is presented with a real-world context problem involving the addition or subtraction of rational numbers written in the same form on a number line. Example Stem: The number line shows four elevations in Death Valley National Park. Enter the difference, in feet, between the elevation at Zabriskie Point and Furnace Creek. Rubric: (1 point) Correct answer will be a rational number (e.g., 826). 10 Version 2.0

19 Grade 7 Mathematics Item Specification C1 TB Task Model 2 DOK Level 1 7.NS.1d Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. d. Apply properties of operations as strategies to add and subtract rational numbers. 2. The student applies properties of operations as strategies to add and subtract rational numbers. Tools: None Prompt Features: The student is prompted to apply properties of operations as strategies to add and subtract rational numbers. Quotients must not result in a repeating decimal. At least one of the numbers must be negative. Item difficulty can be adjusted via these methods: o Terms consisting of integers are easier than terms which include rational numbers such as decimals, fractions or mixed numbers. o Use of parentheses in mathematical operations. TM2b Stimulus: The student is presented with an expression involving the sum or difference of rational numbers Example Stem: Enter the value of 4 Rubric: (1 point) Student accurately computes the value of the expression, which is a rational number (e.g., or 16 ) Version 2.0

20 Grade 7 Mathematics Item Specification C1 TB Task Model 3 Matching Tables DOK Level 1 7.NS.2a Understand that mult iplic at ion is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as ( 1)( 1) = 1 and the rules for mult iplying signed numbers. Interpret products of rational numbers by describing real-world contexts. 3. The student applies properties of operations as strategies to multiply and divide rational numbers. Tools: None Development Note: Interpreting products of rational numbers by describing real-world contexts will be assessed in Claim 2. Prompt Features: The student is prompted to mult iply rational numbers in a real-world context. Item difficulty can be adjusted via these methods: o Mathematical operations involving addition and subtraction are easier when the terms are positive. o Terms consisting of integers are easier than terms which include rational numbers such as decimals, fractions or mixed numbers. o Use of parentheses in mathematical operations. TM3a Stimulus: The student is presented with a verbal description of a real-world situation with multiplication of rational numbers. Example Stem: Is the given expression equal to -3(4 + 2b)? Select Yes or No for each expression. Expression Yes No 6b 12 6b b Rubric: (1 point) The student selects Yes for all correct expressions and No for all incorrect expressions (e.g., Y, N, N). Expressions will be in the form px + q or q + px. Distractors will be inc orrect expressions where one term is not multiplied or is given an incorrect sign. Matching Tables 12 Version 2.0

21 Grade 7 Mathematics Item Specification C1 TB Task Model 3 Multiple Choice, multiple correct response DOK Level 1 Prompt Features: The student is prompted to identify equivalent representations of fractions involving negative signs. TM3b Stimulus: The student is presented with an expression of the form p p or where p and q are integers, and q 0. q q 7.NS.2b Apply and extend previous understandings of mult iplic at ion and division and of fractions to multiply and divide rational numbers. b. Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then (p/q) = ( p)/q = p/( q). Interpret quotients of rational numbers by describing real-world contexts. 3. The student applies properties of operations as strategies to multiply and divide rational numbers. Example Stem: Select all values equal to A. B. C. D. E Answer Choices: Answer choices are rational numbers in the form of fractions. Distractors should include incorrect values which may be of the form p, q p, q p, q p, q p, q p q. Rubric: (1 point) Student selects all the correct expressions (e.g., B, C, and E). Multiple Choice, mult iple c orrec t response Tools: None 13 Version 2.0

22 Grade 7 Mathematics Item Specification C1 TB Task Model 3 DOK Level 1 7.NS.2c Apply and extend previous understandings of mult iplic at ion and division and of fractions to multiply and divide rational numbers. c. Apply properties of operations as strategies to multiply and divide rational numbers. Prompt Features: The student is prompted to determine the value of a multiplication or division expression with rational numbers. Quotients must not result in a repeating decimal. Rational numbers may be in different forms (integer, fraction/mixed number, decimal). Item difficulty can be adjusted via these methods: o Mathematical operations involving addition and subtraction are easier when the terms are positive. o Terms consisting of integers are easier than terms which include rational numbers such as decimals, fractions or mixed numbers. o Use of parentheses in mathematical operations. TM3c Stimulus: The student is presented with an expression involving products or quotients of rational numbers Example Stem: Enter the value of The student applies properties of operations as strategies to multiply and divide rational numbers. Rubric: (1 point) Student accurately calculates the product or quotient, which is a rational number (e.g., or ). Tools: None 14 Version 2.0

23 Grade 7 Mathematics Item Specification C1 TB Task Model 4 DOK Level 1 7.NS.2d Apply and extend previous understandings of mult iplic at ion and division and of fractions to multiply and divide rational numbers. d. Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats. 4. The student converts from a fractional form of rational numbers to a decimal form of rational numbers. Tools: None Prompt Features: The student is prompted to convert a rational number to a decimal equivalent. Quotients must not result in a repeating decimal. The number is given in fraction form. Item difficulty can be adjusted via these methods: o Mathematical operations involving addition and mult iplic at ion are easier t han operat ions involving subtraction and division. o Terms consisting of integers are easier than terms which include rational numbers such as decimals, fractions or mixed numbers. o The number of differing mathematical operations increases difficulty. o Use of parentheses in mathematical operations. TM4 Stimulus: The student is presented with a rational number. Example Stem: Enter the decimal equivalent of 8 5. Rubric: (1 point) Student gives the correct decimal equivalent (e.g., 0.625). 15 Version 2.0

24 Grade 7 Mathematics Item Specification C1 TB Task Model 5 7.NS.3 Solve real-world and mat hemat ic al problems involving the four operations with rational numbers. 5. The student solves real-world and mat hemat ic al problems involving the four operations with rational numbers. Tools: None Prompt Features: The student is prompted to solve real-world and mat hemat ic al problems involving t he four operat ions wit h rat ional numbers. Rational numbers may be in any form. Quotients must not result in a repeating decimal. Item difficulty can be adjusted via these methods: o Mathematical operations involving addition and mult iplic at ion are easier t han operat ions involving subtraction and division. o Terms consisting of integers are easier than terms which include rational numbers such as decimals, fractions or mixed numbers. o The number of differing mathematical operations increases difficulty. o Use of parentheses in mathematical operations. TM5a Stimulus: The student is presented with a mathematical expression involving a combination of addition/subtraction and mult iplic at ion/division wit h rat ional numbers. Example Stem: Enter the value of [ ]. Development Note: Solving multioperation real-world problems with rational numbers will be assessed in Claim 2. Rubric: (1 point) Student accurately calculates the value, which is a rational number (e.g., or 3 ). TM5b Stimulus: The student is presented with a one-step real-world problem involving addition, subtraction, mult iplic at ion, or division with rational numbers. Example Stem: Mark buys a wooden board that is 7 feet long. The cost of the board is $0.50 per foot, including tax. What is the total cost, in dollars, of Mark s board? Rubric: (1 point) Correct answer will be a single numeric value. (e.g., 3.75). 16 Version 2.0

25 Grade 7 Mathematics Item Specification C1 TC Task Model 1 Multiple Choice, single correct response DOK Level 1 7.EE.1 Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. 1. The student adds and subtracts linear expressions with rational coefficients. Tools: None Prompt Features: The student is prompted to identify the sum or difference of linear expressions with rational coefficients. Stimulus: The student is presented with two or more linear expressions. Item difficulty can be adjusted via these methods: o Expressions have integer coefficients. o Expressions include decimal coefficients or terms. o Expressions include coefficients or terms which are fractions or mixed numbers. o Expressions include exactly one variable. o Expressions include more than one variable. TM1a Example Stem 1: Select the expression equivalent to (3x + 2) + ( 6x + 3). A. 3x + 5 B. 3x +5 C. 9x + 5 D. 9x + 5 Example Stem 2: Select the expression equivalent to (2.1x + 4.3) ( 3x 7). A. 0.9x 2.7 B. 0.9x C. 5.1x 2.7 D. 5.1x Answer Choices: Each answer choice should be expressions in the form px + q, where p and q are integers or rational numbers, depending on the level of difficulty. Distractors will inc lude inc orrect calculations based on negative sign(s) and incorrectly combining terms. Rubric: (1 point) The student identifies the equivalent expression (e.g., A; D). Multiple Choice, single correct response 4 Version 2.0

26 Grade 7 Mathematics Item Specification C1 TC Task Model 1 DOK Level 1 7.EE.1 Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. 1. The student adds and subtracts linear expressions with rational coefficients. Tools: None Prompt Features: The student is prompted to identify the sum or difference of linear expressions with rational coefficients. Stimulus: The student is presented with a linear equation including a sum or difference where combining like terms of one side of the equation gives rise to the solution for n without further manipulat ion. Item difficulty can be adjusted via these methods: o Expressions have integer coefficients. o Expressions include decimal coefficients or terms. o Expressions include coefficients or terms which are fractions or mixed numbers. o Expressions include exactly one variable. o Expressions include more than one variable. TM1b Example Stem 1: Enter the value of n so that the expression ( y + 5) + (7y 9) is equivalent to (ny 4). Example Stem 2: Enter the value of n so that the expression ( y + 5.3) + (7.2y 9) is equivalent to 6.2y + n. Rubric: (1 point) The student enters the correct value for the variable (e.g., 6; 3.7). 5 Version 2.0

27 Grade 7 Mathematics Item Specification C1 TC Task Model 2 Multiple Choice, multiple correct response DOK Level 1 7.EE.1 Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. 2. The student factors linear expressions with rational coefficients. Tools: None Prompt Features: The student is prompted to identify the factors of a linear expression. Stimulus: The student is presented with a linear expression with rational coefficients. Item difficulty can be adjusted via these methods: o Expressions have only positive rational coefficients or terms. o Expressions include negative rational coefficients or terms. TM2a Example Stem: Select all expressions equivalent to 72x A. 12(6x 5) B. 12( 6x 5) C. 6( 12x + 10) D. 6( 12x 10) Answer Choices: Answer choices will be expressions in the form p(qx + r) or p(r + qx), where p, q, and r are rational numbers. Distractors will inc lude misuse of the distributive property, incorrect calculations based on negative sign(s), and incorrectly combining terms. Rubric: (1 point) The student selects all of the equivalent expressions (e.g., A and C). Multiple Choice, multiple correct response 6 Version 2.0

28 Grade 7 Mathematics Item Specification C1 TC Task Model 2 DOK Level 1 7.EE.1 Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. 2. The student factors linear expressions with rational coefficients. Tools: None Prompt Features: The student is prompted to enter the factor of a linear expression given an equation containing two variables. Stimulus: The student is presented with two linear expressions. Item difficulty can be adjusted via these methods: o Expressions have only positive rational coefficients or terms. o Expressions include negative rational coefficients or terms. o Should contain one or more rational coefficient(s). o Coefficients are rational numbers sharing a common factor with other terms. TM2b Example Stem 1: Enter the value of p so that the expression 3(n + 5) is equivalent to (n + p)3. Example Stem 2: Enter the value of p so that the expression 5 1 n is equivalent to p(5 2n). 6 3 Rubric: (1 point) The student enters the correct value for p (e.g., 5; 6 1 ). 7 Version 2.0

29 Grade 7 Mathematics Item Specification C1 TC Task Model 3 Multiple Choice, single correct response DOK Level 1 Prompt Features: The student is prompted to identify equivalent expressions with rational coefficients that involve expanded form. Stimulus: The student is presented with a linear expression. Item difficulty can be adjusted via these methods: o Expressions have positive or negative integer coefficients or terms. o Expressions include rational coefficients or terms. 7.EE.1 Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. 3. The student expands linear expressions with rational coefficients. Tools: None TM3a Example Stem 1: Which expression is equivalent to 15x + 6? A. ( 3)x ( 3)2 + ( 3)4x B. 3(-5x + 6) C. (3)x ( 3)2 ( 3)4x D. 3(5x + 6) Example Stem 2: Which expression is equivalent to 0.8(10.8x x)? A. 11.2x + 16 B. 11.2x 16 C. 8.64x 16.8 D. 8.64x Answer Choices: Answer choices should be expressions in the form px + q or p + qx, where p and q are integers or rational numbers, depending on the level of difficulty. Distractors will inc lude misuse of the distributive property; incorrect calculations are based on negative sign(s), and incorrectly combining terms. Rubric: (1 point) The student selects the equivalent expression (e.g., A; A). Multiple Choice, single correct response 8 Version 2.0

30 Grade 7 Mathematics Item Specification C1 TC Task Model 3 DOK Level 1 7.EE.1 Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. Prompt Features: The student is prompted to enter the unknown value of an equivalent expression to the expanded form of a linear expression with rational coefficients. Stimulus: The student is presented with two equivalent linear expressions. Item difficulty can be adjusted via these methods: o Expressions have positive or negative integer coefficients or terms. o Expressions include rational coefficients or terms. o One expression has two variables. TM3b Example Stem: Enter the value of b when the expression 14.1x + b is equivalent to 4.7(3x 3.5). 3. The student expands linear expressions with rational coefficients. Rubric: (1 point) The student enters the value for b. (e.g., 16.45) Tools: None 9 Version 2.0

31 Grade 7 Mathematics Item Specification C1 TC Task Model 4 Multiple Choice, multiple correct response 7.EE.1 Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. 4. The student generates equivalent linear expressions using a combination of addition and subtraction, factoring, and expansion. Tools: None Prompt Features: The student is prompted to identify a linear expression that is equivalent to a given linear expression. Stimulus: The student is presented with a linear expression. Item difficulty can be adjusted via these methods: o Expressions have only positive rational coefficients or terms. o Expressions include negative rational coefficients or terms. o Only addition/subtraction of expressions is required. o Factoring/expansion of expressions is required. TM4 Example Stem 1: Select all expressions that are equivalent to 3x + 5( 4x + 12) (x 3). A. 18x + 63 B. 18x 63 C. 3x 20x + 60 x + 3 D. 3x +20x +60 x 3 Example Stem 2: Select all expressions that are equivalent to 0.75x (x ) + (x 2.1). A. 2x + 1 B. x + 1 C. x x D. x x 2.1 Answer Choices: Distractors will inc lude misuse of the distributive property, incorrect calculations based on negative sign(s), and incorrectly combining terms. Rubric: (1 point) The student selects all the appropriate expressions (e.g., A and C; A and D). Multiple Choice, multiple correct response 10 Version 2.0

32 Grade 7 Mathematics Item Specification C1 TD Task Model 1 Multiple Choice, multiple correct response DOK Level 1 7.EE.3 Solve multi-step, real-life, and mat hemat ic al problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using ment al c omput ation and estimation strategies. 1. The student identifies equivalency between two rational numbers. Tools: None Prompt Features: The student is prompted to determine whether two numeric expressions are equivalent. Item difficulty can be adjusted via these example methods: o Terms within the expressions can be integers, decimals, fractions, or mixed numbers. o Terms within the expressions may use any or all of the four arithmetic operations with or without parentheses. o Higher difficulty level problems need to include mixed numbers and the use of parentheses. TM1a Stimulus: The student is presented with a multi-step numeric expression involving rational numbers in at least two of these three forms: fraction, decimal, whole number. Example Stem: Select all expressions equivalent to 2.3 ( ) 9. A. 2.3 (1.25) 9 B ( ) C ( ) D. 2.3 (9 1.25) Answer Choices: Each answer choice is an expression following the same stimulus guidelines. Distractors inc lude expressions with misapplic at ion of propert ies of operat ions, sign mist akes, or computation errors. Rubric: (1 point) The student selects all the appropriate expressions (e.g., A and C). Multiple Choice, multiple correct response 5 Version 2.0

33 Grade 7 Mathematics Item Specification C1 TD Task Model 1 Drag and Drop DOK Level 1 7.EE.3 Solve multi-step, real-life, and mat hemat ic al problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. 1. The student identifies equivalency between two rational numbers. Tools: None Prompt Features: The student is prompted to identify equivalent numeric expressions containing rational numbers in any form. Each expression should be a multi-step numeric expression with rational numbers. Item difficulty can be adjusted via these example met hods: o Terms within the expressions can be integers, decimals, fractions, or mixed numbers. o Terms within the expressions may use any or all of the four arithmetic operations with or without parentheses. o Higher difficulty level problems need to include mixed numbers and the use of parentheses. TM1b Stimulus: The student is presented with a list of numeric expressions in the background image and palette at the bottom. Example Stem: Place each numeric expression into one of the empty cells to make true equations. Interaction: Students drag and drop expressions into the table. One column of the table has expressions in it already. Each expression may only be used once. Rubric: (1 point) The student makes t rue equat ions by dragging all four expressions into the cells (e.g., ). 8 4, 25, 5 5, 2 Drag and Drop 6 Version 2.0

34 Grade 7 Mathematics Item Specification C1 TD Task Model 2 DOK Level 1 7.EE.3 Solve multi-step, real-life, and mat hemat ic al problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using ment al c omput ation and estimation strategies. Prompt Features: The student is prompted to determine the value of a numeric expression. Item difficulty can be adjusted via these example methods: Terms within the expressions can be integers, decimals, fractions, or mixed numbers. Terms within the expressions may use any or all of the four arithmetic operations with or without parentheses. TM2a Stimulus: The student is presented a multi-step numeric expression involving rational numbers in at least two of these three forms: fraction, decimal, or whole number. Example Stem: Enter the value of 2.3 (4 + 12). Rubric: (1 point) The student accurately calculates the value of the expression (e.g., 27.8). 2. The student applies properties of operations to evaluate numeric expressions, including converting between different forms of rational numbers. Tools: None 7 Version 2.0

35 Grade 7 Mathematics Item Specification C1 TD Task Model 2 DOK Level 1 7.EE.3 Solve multi-step, real-life, and mat hemat ic al problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using ment al c omput ation and estimation strategies. 2. The student applies properties of operations to evaluate numeric expressions, including converting between different forms of rational numbers. Tools: None Prompt Features: The student is prompted to convert between forms of rational numbers or use place value understanding. Item difficulty can be adjusted via these example methods: Terms within the expressions can be integers, decimals, fractions, or mixed numbers. Terms within the expressions may use any or all of the four arithmetic operations with or without parentheses. TM2b Stimulus: The student is presented a rational equation with an unknown. Example Stem 1: Enter the number that makes the equation true = + Example Stem 2: Enter the number that makes the equation true = + Example Stem 3: Enter the number that makes the equation true = + Rubric: (1 point) The student enters the correct number (e.g., 31; 310; 310). 8 Version 2.0

36 Grade 7 Mathematics Item Specification C1 TD Task Model 3 7.EE.4a Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width? 3. The student solves word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Prompt Features: The student is prompted to identify an equation or solution that represents a real-world problem. Contexts must be familiar to students years old. Item difficulty can be adjusted via these example methods: o Expressions have only positive rational coefficients or terms. o Expressions include negative rational coefficients or terms. TM3 Stimulus: The student is presented with a real-world situation that leads to an equation of the form px + q = r or p(x + q) = r, where p, q, and r are rational numbers. Example Stem 1: A coach buys a uniform (u) and a basketball for each of the 15 players on the team. Each basketball costs $9.00. The coach spends a total of $420 for uniforms (u) and basketballs. Enter an equation that models t he sit uation wit h u, the cost of 1 uniform. Rubric: (1 point) Student enters a correct equation (e.g., 15u = 420). Example Stem 2: A coach buys a uniform and a basketball for each of the 15 players on the team. Each basketball costs $9. The coach spends a total of $420 for uniforms and basketballs. Enter the cost of 1 uniform. Round to the nearest cent. Rubric: (1 point) The student enters a correct solution (e.g., 19). 9 Version 2.0

37 Grade 7 Mathematics Item Specification C1 TD Task Model 4 7.EE.4b Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. 4. The student solves word problems leading to inequalities of the form px + q > r and px + q < r, where p, q, and r are specific rational numbers. Prompt Features: The student is prompted to give an inequality that represents a real-world problem. Contexts must be familiar to students years old. Item difficulty can be adjusted via these methods: o Inequalities have only positive rational coefficients or terms. o Inequalities include negative rational coefficients or terms. o Boundary value of solution set is an integer. TM4 Stimulus: The student is presented with a real-world situation that leads to an inequality in the form of px + q > r or px + q < r, where p, q, and r are rational numbers. Example Stem 1: Linda has $26. She earns $6 for 1 hour (h) of babysitting. She wants to buy a ski pass for $80. Enter an inequality that shows the number of hours (h) Linda could babysit to be able to buy the ski pass. Rubric: (1 point) The student enters a correct inequality (e.g., 6h ). Example Stem 2: Linda has $26. She earns $6 for 1 hour of babysitting. She wants to buy a ski pass for $80. Development Notes: Interpreting the remainder in terms of the context will be assessed in Claim 2. Enter the minimum number of hours Linda must babysit to be able to buy the ski pass. Rubric: (1 point) The student enters a correct solution (e.g., 9). 10 Version 2.0

38 Grade 7 Mathematics Item Specification C1 TD Task Model 5 Multiple Choice, single correct response 7.EE.4b Use variables to represent quantities in a real-world or mat hemat ic al problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. b. Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r, are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. 5. The student graphs the solution set of an inequality on a number line. Prompt Features: The student is prompted to identify the graph of the solution set of a mathematical problem. Item difficulty can be adjusted via these example met hods: Constants are integers; coefficient is one. Constants are integers; boundary value of solution set is an integer. Boundary value of solution set is a frac tion/mixed number, or decimal. TM5a Stimulus: The student is presented with an inequality of the form px + q > r or px + q < r, where p, q, and r are rational numbers. Example Stem: Which number line shows the solution to the inequality 3x 5 < 2? A. B. C. D. Answer Choices: The answer choices will be horizontal lines, each showing a graph of an inequality. Distractors will inc lude c ommon mist akes made when graphing inequalit ies suc h as a ray point ing the wrong direction, rays with closed and/or open circles, incorrect solution to the inequality by not performing the correct operation t o both sides of the inequality, and forgetting to switch the inequality symbol when dividing/multiplying by a negative number. Rubric: (1 point) The student selects the correct number line (e.g., A). Multiple Choice, single correct response 11 Version 2.0

39 Grade 7 Mathematics Item Specification C1 TD Task Model 5 Drag and Drop 7.EE.4b Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Give an inequality for the number of sales you need to make, and describe the solutions. Prompt Features: The student is prompted to identify the solution set of an inequality on a number line. Contexts must be familiar to students years old. Drag elements should not replace (preset palette). Drag elements should inc lude: closed and open circles with arrows going to the left and right directions. Appropriate tick marks should be spac ed and labeled throughout the number line. Each tick mark should have snap regions that can fit the circles and arrows. Item difficulty can be adjusted via these methods: o Inequalities can have positive or negative rational coefficients or terms. o Constants are integers; boundary value of solution set can be an integer divided by a positive coefficient. o Boundary value of solution set can be an integer, fraction, mixed number or decimal. TM5b Stimulus: The student is presented with an inequality of the form px + q > r or px + q < r, where p, q, and r are rational numbers, or a situation that can be modeled with an inequality. Example Stem: Drag the c orrect arrow to the number line to represent the solution of the inequality 3x + 7 > The student graphs the solution set of an inequality on a number line. Interaction: The student will drag an arrow from a set of preset images to a number line to represent the solution of an inequality. Snap-to feature should be used at each tick mark. Rubric: (1 point) The student graphs the inequality by placing an arrow on the number line. Drag and Drop 12 Version 2.0

40 Grade 7 Mathematics Item Specification C1 TE Task Model 1 Graphing 7.G.1 Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. 1. The student creates scale drawings. Prompt Features: The student is prompted to create a scale drawing of a polygon on a grid using drawing tools. Item difficulty can be adjusted via these example methods: Figures may consist of polygons such as quadrilaterals, trapezoids or parallelograms. Lengths and angles may be posit ive int egers or rat ional numbers. Scale factor may be a positive rational number. Inclusion of extraneous information. TM1a Stimulus: The student is presented with a simple polygon on a grid and a scale factor. Example Stem: A scale factor of 2 is applied to this figure. Use the Connect Line tool to draw the resulting figure. Interaction: The student is given the Connect Line, Add Point, and Delete tools to draw the polygon on a grid. Rubric: (1 point) Student draws the correct figure with correct dimensions. Allow for correct scoring regardless of orientation of the figure (see one example of a correct response below). Response Types: Graphing 4 Version 2.0

41 Grade 7 Mathematics Item Specification C1 TE Task Model 1 7.G.1 Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. Prompt Features: The student is prompted to give the area of an actual figure based on a scale drawing and scale factor. Item difficulty can be adjusted via these example methods: Types of polygons (square, rectangle, parallelogram, or right triangle). Linear dimensions can be a combination of rational numbers. Area can be a combination of rational numbers. TM1b Stimulus: The student is presented with a polygon (square, rectangle, parallelogram, or right triangle) on a grid and the scale factor at which it was created. Example Stem: The scale drawing of the right triangle shown was drawn using a scale factor of. 1. The student creates scale drawings. 2. The student solves problems involving scale drawings using proportional reasoning. Each square on the grid is 3 units in length. What is the area of the actual figure, in square units, on which this scale drawing is based? Rubric: (1 point) Student enters the correct area (e.g., 2700). 5 Version 2.0

42 Grade 7 Mathematics Item Specification C1 TE Task Model 2 DOK Level 1 7.G.1 Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. 2. The student solves problems involving scale drawings using proportional reasoning. Prompt Features: The student is prompted to give the length of one or more sides of a polygon or the scale factor being applied based on a scale drawing. Scale factor and side lengths may be posit ive rat ional numbers. Item difficulty can be adjusted via these example methods: o Types of polygons (square, rectangle, parallelogram, or right triangle). o Linear dimensions can be a combination of rational numbers. o Lengths of corresponding sides of similar polygons are not all labeled. o Inclusion of extraneous information. TM2a Stimulus: The student is presented with two polygons and a scale factor. A side length is given and the corresponding side is labeled with a variable. Example Stem: Figure A is a scale image of Figure B, as shown. The scale that maps Figure A onto Figure B is of x. 1 1 : 3. Enter the value 2 Rubric: (1 point) Student gives the correct value of the variable, which is a single numeric answer. Units, if given, should be assumed from the stem (e.g., 17.5). 6 Version 2.0

43 Grade 7 Mathematics Item Specification C1 TE Task Model 2 DOK Level 1 7.G.1 Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. TM2b Stimulus: The student is presented with two polygons with lengths of some or all corresponding sides given or indicated by a grid. Example Stem: Figure B is a scale image of Figure A, as shown. 2. The student solves problems involving scale drawings using proportional reasoning. Enter the scale factor applied to Figure A to produce Figure B. Rubric: (1 point) Student gives the correct scale factor, which is a single numeric answer. The keypad should only contain numbers (e.g., 3). 7 Version 2.0

44 Grade 7 Mathematics Item Specification C1 TE Task Model 2 7.G.1 Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. Prompt Features: The student is prompted to give the length of one side of an actual figure based on a scale drawing. Context should be familiar to year olds. Scale factor may be given in a key. Item difficulty can be adjusted via these example methods: o Numbers can be rational. o Combinations of area and length are provided. o Extra information is provided. o Unit conversion is used. o Scale factor may be a positive rational number. TM2c Stimulus: The student is presented with information about the area and/or dimensions of a scale drawing, including the scale factor. Example Stem: The front side of a playhouse is shown in this scale drawing. The height of the door in the drawing is 1.8 inches. 2. The student solves problems involving scale drawings using proportional reasoning. The scale that maps the drawing to the actual playhouse is 1 inch to 2.5 feet. Using the scale given, enter the actual height of the playhouse door, in feet. Rubric: (1 point) Correct answer is a single numeric answer (e.g., 4.5). 8 Version 2.0

45 Grade 7 Mathematics Item Specification C1 TE Task Model 2 7.G.1 Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. Prompt Features: The student is prompted to give the area of a polygon based on a scale drawing. Context should be familiar to year olds. Item difficulty can be adjusted via these example methods: o Dimensions can be a combination of positive rational numbers. o Scale factor may be a positive rational number. TM2d Stimulus: The student is presented with a scale drawing of a polygon (square, rectangle, or right triangle) with dimensions labeled and the dimension for one side of the actual polygon given. Example Stem: This scale drawing of a rectangular rug has dimensions 8 inches by 5 inches. The length of the longer side of the actual rug is 32 feet. 2. The student solves problems involving scale drawings using proportional reasoning. 8 in 5 in Enter the area, in square feet, of the actual rug. Rubric: (1 point) Correct answer is a single numeric answer. Units should be assumed from the stem (e.g., 640). ` 9 Version 2.0

46 Grade 7 Mathematics Item Specification C1 TE Task Model 3 Matching Tables 7.G.2 Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. 3. The student draws, constructs, or describes geometric shapes given certain conditions. Tools: None Prompt Features: Identify the type of triangles that can be constructed based on given information about the sides and angles of the triangle. Number of statements should be within three to five. Information given may either: o Describe a unique triangle o Be insuffic ient to determine a unique triangle (more than one triangle) o Be inc onsistent with the triangle inequality or the triangle angle sum theorem (no triangle) Item difficulty can be adjusted via these example methods: o Triangles may be right, acute, obtuse, equilateral, isosceles, or scalene. o Angle measures and unit lengths are composed of differing positive rational numbers. o Inclusion of extraneous information. TM3a Stimulus: The student is presented with side lengths and/or angle measures of a t riangle and st at ements about t he t ype of t riangle. Example Stem: A triangle has a 45 angle, a 60 angle, and a side 3 centimeters in length. Select True or False for each statement about this type of triangle. Statement True False The triangle might be an isosceles triangle. The triangle must be an acute triangle. The triangle must contain an angle measuring 75. Rubric: (1 point) Student selects True or False for each statement (e.g., F, T, T). Item Type: Matching Tables 10 Version 2.0

47 Grade 7 Mathematics Item Specification C1 TE Task Model 3 Graphing DOK Level 1 7.G.2 Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. Prompt Features: The student is prompted to generate geometric shapes based on given conditions. Item difficulty can be adjusted via these example methods: Figures may consist of triangles (right, acute, obtuse, equilateral, isosceles, scalene), quadrilaterals, trapezoids or parallelograms, or combinations of the above. Combinations of given side lengths and angles. Inclusion of extraneous information. TM3b Stimulus: The student is presented with a series of conditions regarding a triangle or quadrilateral. The conditions should determine a unique polygon, and measurements should be positive integers reasonable for display in the workspace provided. Example Stem: Use the Connect Line tool to draw a triangle with a 90 angle, a side with a length of 7 units, and a side with a length of 4 units. Each square on the grid is 1 unit in length. Interaction: The student is given the Connect Line, Add Point, and Delete tools to generate line segments on a grid. 3. The student draws, constructs, or describes geometric shapes given certain conditions. Rubric: (1 point) The student correctly constructs the figure described. Tools: None Graphing 11 Version 2.0

48 Grade 7 Mathematics Item Specification C1 TE Task Model 4 Multiple Choice, multiple correct response 7.G.3 Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right-rectangular prisms and right-rectangular pyramids. Prompt Feature: The student is prompted to identify a two-dimensional figure that results from slicing a given three-dimensional figure by a plane. Item difficulty can be adjusted via these example methods: Three-dimensional figures c an be right-rectangular prisms or right-rectangular pyramids. Slices may be horizontal planes, vertical planes, or planes that are not parallel to a face. Increasing number of possible answer choices. TM4 Stimulus: The student is presented with a three-dimensional figure and a description of how the figure is sliced by a plane. Example Stem: This figure is a square pyramid. 4. The student describes a two-dimensional figure resulting from slicing a three-dimensional figure by a plane. Tools: None Select all figures that can be formed by a vertical slice perpendicular to the base of the square pyramid. A. Isosceles Trapezoid B. Line segment C. Square D. Triangle Answer Choices: Answer choices will be names of polygons and can also include line segment as a choice. Rubric: (1 point) Student selects the correct figures (e.g., A, B, and D). Multiple Choice, multiple correct response 12 Version 2.0

49 Grade 7 Mathematics Item Specification C1 TF Task Model 1 DOK Level 1 7.G.4 Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. 1. The student solves real-life and mat hemat ic al problems for the circumference and area of circles. Prompt Features: The student is prompted to give the area of circles for mathematical problems. Context should be familiar to students years old. Unit label is a measurement of length. Item difficulty can be adjusted via these example methods: o Radius is a whole number, decimal, fraction, inc luding mixed numbers o Diameter is a whole number, decimal, fraction, including mixed numbers o Number of computational steps o Partial areas or circumferences TM1a Stimulus: The student is presented with the radius, diameter or circumference of a circle in a mathematical context. Example Stem: The radius of a circle is 7.5 centimeters. Enter the area of the circle, in square centimeters. Round your answer to the nearest hundredth. Rubric: (1 point) The student enters the correct area in a range of correct values (e.g., ). 4 Version 2.0

50 Grade 7 Mathematics Item Specification C1 TF Task Model 1 7.G.4 Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. 1. The student solves real-life and mat hemat ic al problems for the circumference and area of circles. Prompt Features: The student is prompted to give the area of circles for real-life problems. Context should be familiar to students years old. Unit label is a measurement of length. Item difficulty can be adjusted via these example methods: o Radius is a whole number, decimal, fraction, including mixed numbers. o Diameter is a whole number, decimal, fraction, including mixed numbers. o Number of computational steps. o Partial areas or circumferences. TM1b Stimulus: The student is presented with the radius, diameter or circumference of a circle in a real-life context. Example Stem 1: A circular table top has a radius of 3 feet. Enter the area, in square feet, of the table top. Round your answer to the nearest hundredth. Example Stem 2: Jill buys two circular pizzas. The small pizza has an 8-inch diameter. The medium pizza has a 12-inch diameter. How much greater, in square inches, is the area of the medium pizza than the small pizza? Round your answer to the nearest hundredth. Rubric: (1 point) The student enters the correct area in a range of correct values (e.g., ; ). 5 Version 2.0

51 Grade 7 Mathematics Item Specification C1 TF Task Model 1 7.G.4 Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. Prompt Features: The student is prompted to give the circumference of a circle. Unit label is a measurement of length. Item difficulty can be adjusted via these example methods: o Radius is a whole number, decimal, fraction, inc luding mixed numbers. o Diameter is a whole number, decimal, fraction, including mixed numbers. o Number of computational st eps. o Partial areas or circumferences. TM1c Stimulus: The student is presented with the radius or diameter of a circle in a real-life or mathematical context. Example Stem: The radius of a circle is 7 centimeters. 1. The student solves real-life and mat hemat ic al problems for the circumference and area of circles. Enter the circumference of the circle, in centimeters. Round your answer to the nearest hundredth. Rubric: (1 point) The student enters the correct circumference in a range of correct values (e.g., ). Prompt Features: The student is prompted to give the radius of a circle given its circumference. TM1d Stimulus: The student is presented with the circumference of a circle in a real-world or mat hemat ic al c ontext. Example Stem: The circumference of a circle is 31.4 inches. Enter the radius of the circle, in inches. Round your answer to the nearest whole number. Rubric: (1 point) The student enters the correct radius (e.g., 5). 6 Version 2.0

52 Grade 7 Mathematics Item Specification C1 TF Task Model 1 7.G.4 Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. 1. The student solves real-life and mat hemat ic al problems for the circumference and area of circles. Prompt Features: The student is prompted to give a fractional part of the area of a circle for both real-life and mathematical problems. Context should be familiar to students years old. Unit label is a measurement of length. Item difficulty can be adjusted via these example methods: o Radius is a whole number, decimal, fraction, including mixed numbers. o Diameter is a whole number, decimal, fraction, including mixed numbers. o Number of computational steps. o Partial areas or circumferences. TM1e Stimulus: The student is presented with the radius, diameter or circumference of a circle in a real-life or mathematical context. Example Stem 1: A corner shelf has a radius of 10.5 inches and represents of a circle, as shown. Enter the area of the shelf, in square inches. Round your answer to the nearest hundredth. Example Stem 2: The circumference of the circle is approximately centimeters. The shaded region is of the whole circle. Enter the area of the shaded region, in square centimeters. Round your answer to the nearest hundredth. Rubric: (1 point) The student enters the correct area in a range of correct values (e.g., ; ). 7 Version 2.0

53 Grade 7 Mathematics Item Specification C1 TF Task Model 2 Matching Tables DOK Level 1 7.G.5 Use facts about supplementary, complementary, vertical, and adjacent angles in a mult i-step problem to write and solve simple equations for an unknown angle in a figure. 2. The student solves real-life and mat hemat ic al problems involving angle measure including problems requiring writing and solving equations. Prompt Features: The student solves real-life and mathematical problems involving angle measure including problems requiring writing and solving equations. Measures of certain angles in the figure can be shown. Measures of angles shown in the figure should be less than 180. Angle measures can be whole numbers or decimals to the tenths place. TM2a Stimulus: The student is given a figure involving supplementary, complementary, vertical, and/or adjacent angles that contains a missing angle measure. Example Stem: Lines XU and WY intersect at point A. Based on the diagram, determine whether each statement is true. Select True or False for each statement. Statement True False An angle supplementary to WAU measures 50. An angle complementary to WAX measures 40. The angle vertical to YAU measures 50. Rubric: (1 point) Student correctly identifies each statement as being either true or false (e.g., T, T, T). True choices will be correct angle measures such as False choices will be incorrect angle measure about the computation and comparative statements of the angles. Matching Tables 8 Version 2.0

54 Grade 7 Mathematics Item Specification C1 TF Task Model 2 Matching Tables 7.G.5 Use facts about supplementary, complementary, vertical, and adjacent angles in a mult i-step problem to write and solve simple equations for an unknown angle in a figure. 2. The student solves real-life and mat hemat ic al problems involving angle measure including problems requiring writing and solving equations. Prompt Features: The student solves real-life and mathematical problems involving angle measure including problems requiring writing and solving equations. Measures of certain angles in the figure can be shown. Measures of angles shown in the figure should be less than 180. Angle measures can be whole numbers or decimals to the tenths place. TM2b Stimulus: The student is given a figure involving supplementary, complementary, vertical, and/or adjacent angles that contains a missing angle measure. Example Stem: Lines XU and WY intersect at point A. Based on the diagram, determine whet her eac h st atement is t rue. Select True or False for each statement. Statement True False m XAZ = 180 m ZAY m YAU m WAZ = m WAY m ZAY m WAU = m XAZ m ZAY Rubric: (1 point) Student correctly identifies each statement as being either true or false (e.g., T, T, F). Matching Tables 9 Version 2.0

55 Grade 7 Mathematics Item Specification C1 TF Task Model 2 7.G.5 Use facts about supplementary, complementary, vertical, and adjacent angles in a mult i-step problem to write and solve simple equations for an unknown angle in a figure. Prompt Features: The student gives the solution to a multi-step problem involving supplementary, complementary, vertical, and/or adjacent angles. Variables used represent missing angle measure. Angles in the figure can be identified by variables. Item difficulty can be adjusted via these example methods: o Angle measures are whole numbers. o Angle measures are decimals. o Angle measures include variables. TM2c Stimulus: The student is provided a figure showing supplementary, complementary, vertical, and/or adjacent angles. Example Stem: Consider this figure. 2. The student solves real-life and mat hemat ic al problems involving angle measure including problems requiring writing and solving equations. Enter the measure of YVZ, in degrees. Rubric: (1 point) The student enters the correct value (e.g., 56). 10 Version 2.0

56 Grade 7 Mathematics Item Specification C1 TF Task Model 2 Matching Tables 7.G.5 Use facts about supplementary, complementary, vertical, and adjacent angles in a mult i-step problem to write and solve simple equations for an unknown angle in a figure. Prompt Features: The student solves an equation for an unknown angle in a figure involving supplementary, complementary, vertical, and/or adjacent angles. Variables used represent missing angle measure. Angles in the figure can be identified by variables. Item difficulty can be adjusted via these example methods: o Angle measures are whole numbers. o Angle measures are decimals. o Angle measures include variables. TM2d Stimulus: The student is provided a figure showing supplementary, complementary, vertical, and/or adjacent angles. Example Stem: The base of a hexagon lies on ray AB as shown. 2. The student solves real-life and mat hemat ic al problems involving angle measure including problems requiring writing and solving equations. Based on the diagram, determine whether each equation is true. Select True or False for each statement. Statement True False Rubric: (1 point) The student correctly determines each statement as being either true or false (e.g., T, T, F). Matching Tables 11 Version 2.0

57 Grade 7 Mathematics Item Specification C1 TF Task Model 3 7.G.6 Solve real-world and mat hemat ic al problems involving area, volume and surface area of twoand threedimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. 3. The student solves real-life and mat hemat ic al problems for the area of two-dimensional objects composed of polygons. Prompt Features: The student is prompted to identify the area of two-dimensional figures composed of triangles, quadrilaterals, and/or other polygons for both real-life and mathematical problems. Context should be familiar to students years old. Dimensions of figures c an be explic itly labeled or indicated by a grid. Item difficulty can be adjusted via these example methods: o Dimensions c an inc lude whole numbers, decimals, and fractions including mixed numbers or any combination o Figures can be composed of triangles, quadrilaterals, or polygons TM3 Stimulus: The student is presented with a real-life or mathematical problem involving a figure composed of triangles, quadrilaterals, and/or other polygons. Example Stem 1: This is the floor plan of Julie s bedroom. Enter the amount of carpet, in square feet, needed to completely cover Julie s bedroom floor. Rubric: (1 point) The student enters the correct area (e.g., ). 12 Version 2.0

58 Grade 7 Mathematics Item Specification C1 TF Task Model 3 Example Stem 2: The figure shown is created by joining three rectangles. 7.G.6 Solve real-world and mat hemat ic al problems involving area, volume and surface area of twoand threedimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. 3. The student solves real-life and mat hemat ic al problems for the area of two-dimensional objects composed of polygons. Enter the area of the figure, in square centimeters. Round to the nearest hundredth. Rubric: (1 point) The student enters the correct area (e.g., 46.75). 13 Version 2.0

59 Grade 7 Mathematics Item Specification C1 TF Task Model 4 7.G.6 Solve real-world and mat hemat ic al problems involving area, volume and surface area of twoand threedimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. Prompt Features: The student is prompted to give the surface area or volume of three-dimensional objects. Context should be familiar to students years old. Item difficulty can be adjusted via these example methods: o Dimensions c an inc lude whole numbers, decimals, and fractions including mixed numbers or any combination. o Figures can be composed of cubes and right prisms or any combination. TM4 Stimulus: The student is presented with three-dimensional objects composed of cubes and/or right prisms. Example Stem 1: The figure shows a set of concrete stairs to be built. 4. The student solves real-life and mat hemat ic al problems for the volume and surface area of three-dimensional objects composed of right prisms and cubes. Enter the amount of concrete, in cubic feet, needed to build the stairs. Round your answer to the nearest hundredth. Example Stem 2: The figure shown is created by joining two right rectangular prisms. Enter the volume of the figure, in cubic centimeters. 14 Version 2.0

60 Grade 7 Mathematics Item Specification C1 TF Example Stem 3: The figure shows the dimensions for a package to be shipped. Enter the minimum amount of wrapping paper, in square inches, needed to cover the package. Round your answer to the nearest whole inch. Rubric: (1 point) Student provides a correct surface area or volume (e.g., 5.82; 72; 174). 15 Version 2.0