Grade 7: Unit Test A (Ratios Proportional Relationships)

Transcription

1 Grade 7 s for Unit Assessments Grade 7: Unit Test A (Ratios Proportional Relationships) RP.1 Apply and extend previous understandings of equivalent ratios RP.1 Compute unit rates associated with ratios of fractions RP.1 Apply and extend previous understandings of equivalent ratios RP.1 Compute unit rates associated with ratios of fractions RP.1 Compute unit rates associated with ratios of fractions RP.2 Recognize and represent proportional relationships between quantities RP.2d RP.2b 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 (l, r) where r is the unit rate. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams and verbal descriptions of proportional relationships RP.2c Represent proportional relationships by equations RP.2c Solve problems involving scale drawings of geometric figures RP.2b Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams and verbal descriptions of proportional relationships RP.2c Represent proportional relationships by equations RP RP NS RP RP RP.3 problems involving taxes and gratuities (tips). problem involving simple interest. Solve real-world and mathematical problems involving the four operations with rational numbers. problems involving percent increase and decrease. problems involving markups and markdowns. problems involving markups and markdowns RP.2c Represent proportional relationships by equations. digitsmath.com 1

2 digits Grade 7 Standards for Unit Assessments Grade 7: Unit Test A (continued) RP.2 Recognize and represent proportional relationships between quantities RP NS.3 problems involving commissions and fees. Solve real-world and mathematical problems involving the four operations with rational numbers RP.1 Compute unit rates associated with ratios of fractions RP.1 Apply and extend previous understandings of equivalent ratios G.1 Solve problems involving scale drawings of geometric figures RP.2c Represent proportional relationships by equations RP.2a RP.3 Decide whether two quantities are in a proportional relationship by testing for equivalent ratios in a table. problems involving percent increase and decrease RP.1 Compute unit rates associated with ratios of fractions RP.1 Apply and extend previous understandings of equivalent ratios. digitsmath.com 2

3 digits Grade 7 Standards for Unit Assessments Grade 7: Unit Test B (Rational s) NS.1a Apply and extend previous understandings of rational numbers, including opposites and absolute value as a distance from zero NS.1b Recognize additive inverses as pairs of numbers that have a sum of NS.1b Use absolute value understanding to find 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 NS.1 Use horizontal or vertical number line diagrams to represent addition and subtraction NS.1b Interpret sums of rational numbers by describing real-world contexts NS.1c NS.1b NS.2a NS.2 Find the distance between two rational numbers on the number line using the absolute value of their difference, and apply this principle in real-world contexts. Use absolute value understanding to find 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. Understand that multiplication 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 multiplying signed numbers. Apply and extend previous understandings of multiplication and division of fractions to multiply and divide rational numbers NS.2b Understand that if p and q are integers, then (p/q) = ( p)/q = p/( q) NS NS NS.3 Apply and extend previous understandings of multiplication and division of fractions to multiply and divide rational numbers. Solve real-world and mathematical problems involving the four operations with rational numbers. Solve real-world and mathematical problems involving the four operations with rational numbers NS.2d Convert a rational number to a decimal using long division NS.2d Convert a rational number to a decimal using long division NS NS.3 Apply and extend previous understandings of fractions, decimals, and percents to use them interchangeably to solve real-world and mathematical problems. Apply and extend previous understandings of fractions, decimals, and percents to use them interchangeably to solve real-world and mathematical problems NS.2d Convert a rational number to a decimal using long division RP NS.3 problems involving percent error. Apply and extend previous understandings of fractions, decimals, and percents to use them interchangeably to solve real-world and mathematical problems. digitsmath.com 3

4 digits Grade 7 Standards for Unit Assessments Grade 7: Unit Test B (continued) NS.1c NS.1c Find the distance between two rational numbers on the number line using the absolute value of their difference, and apply this principle in real-world contexts. Find the distance between two rational numbers on the number line using the absolute value of their difference, and apply this principle in real-world contexts NS.1a Describe situations in which opposite quantities combine to make NS NS.2b Apply and extend previous understandings of multiplication and division of fractions to multiply and divide rational numbers. 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 NS.1b Recognize additive inverses as pairs of numbers that have a sum of NS.1 Use horizontal or vertical number line diagrams to represent addition and subtraction NS.2d Convert a rational number to a decimal using long division NS.2d Apply properties of operations as strategies to multiply and divide rational numbers NS.2a Understand that multiplication 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 multiplying signed numbers. digitsmath.com 4

5 digits Grade 67 Standards for Mathematical Unit Assessments Content (continued) Grade 7: Unit Test C (Expressions and Equations) EE EE EE EE EE EE EE EE EE.4a EE EE.4b EE EE EE.4b EE.4b EE EE EE.4a Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Solve word problems leading to equations of the form p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of this form fluently. Graph the solution set of the inequality and interpret it in the context of the problem. problem, and construct simple inequalities to solve problems by problem, and construct simple inequalities to solve problems by 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. 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. Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. Solve word problems leading to equations of the form p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of this form fluently. digitsmath.com 5

6 digits Grade 7 Standards for Unit Assessments Grade 7: Unit Test C (continued) EE EE EE.4a EE.4a EE.4b EE.4b Solve word problems leading to equations of the form px + q = r, where p, q, and r are specific rational numbers. Solve equations of this form fluently. Solve word problems leading to equations of the form px + q = r, where p, q, and r are specific rational numbers. Solve equations of this form fluently. 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. 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 EE.4b EE EE EE EE EE.1 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. problem, and construct simple inequalities to solve problems by Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. digitsmath.com 6

7 digits Grade 7 Standards for Unit Assessments Grade 7: Unit Test D (Geometry) EE G G G G G EE.4 Use facts about adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure. Use facts about adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure. Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Use facts about vertical angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure. Use facts about adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure G.4 Solve problems using the formula for the circumference of a circle G.4 Solve problems using the formula for the area of a circle G.4 Give an informal derivation of the relationship between the circumference and area of a circle G.4 Solve problems using the formula for the circumference of a circle G G G G G G G.6 Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Construct triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. Construct triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids. Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids. Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids. Solve real-world and mathematical problems involving area of two-dimensional objects and surface area of three-dimensional digitsmath.com 7

8 digits Grade 7 Standards for Unit Assessments Grade 7: Unit Test D (continued) G G G G G G G.6 Solve real-world and mathematical problems involving area of two-dimensional objects and volume of three-dimensional Solve real-world and mathematical problems involving area of two-dimensional objects and surface area of three-dimensional Solve real-world and mathematical problems involving area of two-dimensional objects and volume of three-dimensional Solve real-world problems involving surface area and volume of a three-dimensional object composed of right prisms. Give an informal derivation of the relationship between the circumference and area of a circle. Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids. Solve real-world and mathematical problems involving area of two-dimensional objects and volume of three-dimensional G.4 Solve problems using the formula for the circumference of a circle G G.5 Use facts about complementary angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure. Solve real-world and mathematical problems involving area of two-dimensional objects and volume of three-dimensional G.2 Name parts of a geometric figure using appropriate letters and symbols G.6 Solve real-world and mathematical problems involving area of two-dimensional objects and surface area of three-dimensional digitsmath.com 8

9 digits Grade 7 Standards for Unit Assessments Grade 7: Unit Test E (Statistics) SP SP SP SP SP SP SP SP SP SP SP SP SP SP SP SP SP SP SP.1 Understand that statistics can be used to gain information about a population by examining a sample of the population. Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Understand that statistics can be used to gain information about a population by examining a sample of the population. Understand that statistics can be used to gain information about a population by examining a sample of the population. Understand that statistics can be used to gain information about a population by examining a sample of the population. Understand that statistics can be used to gain information about a population by examining a sample of the population. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. Use measures of center and measures of variability for numerical data from random samples. Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability. Understand that generalizations about a population from a sample are valid only if the sample is representative of that population. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. Understand that generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that generalizations about a population from a sample are valid only if the sample is representative of that population. Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Understand that statistics can be used to gain information about a population by examining a sample of the population. digitsmath.com 9

10 digits Grade 7 Standards for Unit Assessments Grade 7: Unit Test E (continued) SP SP SP SP SP SP SP SP.2 Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions Differentiate between single and multiple populations SP SP.4 Understand that generalizations about a population from a sample are valid only if the sample is representative of that population. digitsmath.com 10

11 digits Grade 7 Standards for Unit Assessments Grade 7: Unit Test F (Probability) SP.5 Identify the probability of a chance event using a number between 0 and 1 to express the likelihood of the event occurring SP.7 Develop a probability model and use it to find probabilities of events SP SP.7 Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy SP.7 Develop a probability model and use it to find probabilities of events SP SP.8b SP.8b SP.8a SP.8a Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy. Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs. Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs SP.8c Design and use a simulation to generate frequencies for compound events SP SP SP.6 Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability SP.6 Develop a probability model and use it to find probabilities of events SP SP.7a SP.7b SP.7b SP.8b Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability. Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events. Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process. Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process. Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. digitsmath.com 11

12 Grade 7 s for Unit Assessments Grade 7: Unit Test F (continued) SP.8b SP.8b SP.8 Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. Identify the outcomes in a sample space that compose a compound event described in everyday language. Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation SP.8c Design and use a simulation to generate frequencies for compound events SP SP SP.8b SP.7 Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy. Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy SP.8c Design and use a simulation to generate frequencies for compound events SP.8 Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. PearsonSchool.com Copyright Pearson Education, Inc., or its affiliates. All rights reserved. PDF.1112.DI.PC.RH Mat122413