MAT-09.NO Domain 

(NO) Number and Operations  Learners will develop a foundational understanding of the number system, operations, and computational fluency to create connections and solve problems within and across concepts.

Sub-Categories

• (CC) Counting and Cardinality 
  Learners will understand the relationship between numerical symbols, names, quantities, and counting sequences.
• (NBT) Number Base Ten 
  Learners will understand the place value structure of the base-ten number system and represent, compare, and perform operations with multi-digit whole numbers and decimals.
• (NF) Number Fractions 
  Learners will understand fractions and equivalency to represent, compare, and perform operations of fractions and decimals.
• (NS) Number System 
  Learners will expand their knowledge of the number system to create connections and solve problems within and across concepts.
• (O) Operations
  Learners will expand their computational fluency to create connections and solve problems within and across concepts.

Calculation Method for Domains

Domains are larger groups of related standards. The Domain Grade is a calculation of all the related standards. Click on the standard name below each Domain to access the learning targets and rubrics/ proficiency scales for individual standards within the domain.

9th Grade (MAT) Targeted Standard    (NO) Number and Operations  Learners will develop a foundational understanding of the number system, operations, and computational fluency to create connections and solve problems within and across concepts.

Proficiency Scale

Progressions

Exponents

• MAT-05.NO.NBT.07 Explain patterns in the number of zeros of the product when multiplying a number by powers of 10. Explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10.
  
• MAT-06.AR.EE.01 Write, read, and evaluate numerical expressions, including expressions with whole number exponents and grouping symbols.
  
• MAT-08.AR.EE.01 Explain the relationship between repeated multiplication and the properties of integer exponents. Apply a single exponent property to generate equivalent numeric and algebraic expressions that include numerical coefficients.
  
• MAT-09.NO.01 Explain how the definition of rational exponents follows from extending the properties of integer exponents; rewrite simple expressions involving radicals and rational exponents using the properties of exponents.
  
• MAT-09.NO.02 Perform basic operations on simple radical expressions to write a simplified equivalent expression.
  
• MAT-09.AR.06 Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear, quadratic, and exponential functions.
  
• MAT-09.AR.04 Create linear and exponential equations in two or more variables to represent relationships between quantities. Graph equations on coordinate axes with proper labels and scales.
  
• MAT-09.AR.F.06 Write a function defined by an expression in different but equivalent forms to reveal and explain the different properties of the function.
  
• MAT-0.AR.F.08 Identify situations that can be modeled with linear, quadratic, and exponential functions. Justify the most appropriate model for a situation based on the rate of change over equal intervals. Include situations in which a quantity grows or decays. 
  
• MAT-12.NO.01 Rewrite complex expressions involving radicals and rational exponents using the properties of exponents.
  
• MAT-12.NO.02 Perform basic operations on advanced radicals and simplify radicals to write equivalent expressions.
  
• MAT-12.AR.07 Create equations and inequalities and use them to solve problems. Include equations arising from linear and quadratic functions and simple rational and exponential functions.
  
• MAT-12.AR.08 Create equations in two or more variables to represent relationships between quantities. Graph equations on coordinate axes with appropriate labels and scales.
  
• MAT-12.AR.F.03 Write a function defined by an expression in different but equivalent forms to reveal and explain the different properties of the function.
  
• MAT-12.AR.F.06 Apply the inverse relationship between exponents and logarithms to solve problems.
  
• MAT-12.AR.F.15 Use properties of logarithms to express the solution to abct = d where a, c, and d are real numbers and b is a positive real number. Evaluate the logarithm using technology when appropriate.

9th Grade (MAT) Targeted Standard    (NO) Number and Operations  Learners will develop a foundational understanding of the number system, operations, and computational fluency to create connections and solve problems within and across concepts.

Proficiency Scale

Progressions

Addition and Subtraction

• MAT-01.NO.NBT.03 Add within 100 using a two-digit number and a one-digit number. Use concrete models, drawings, and strategies that reflect an understanding of place value.
• MAT-02.NO.NBT.03 Add within 100 using place value strategies and/or the relationship between addition and subtraction.
• MAT-01.NO.NBT.04 Subtract multiples of 10 within 100 using concrete models, drawings, and strategies that reflect an understanding of place value.
• MAT-01.NO.NBT.05 Mentally add or subtract 10 to or from a given two-digit number and explain the reasoning used.
• MAT-02.NO.NBT.04 Subtract within 100 using place value strategies and/or the relationship between addition and subtraction.
• MAT-02.NO.NBT.05 Mentally add or subtract 10 or 100 to or from a given number between 100 and 900.
• MAT-03.NO.NBT.03 Add and subtract within 1000 using place value strategies, algorithms, and/or the relationship between addition and subtraction.
• MAT-04.NO.NBT.04 Add and subtract multi-digit whole numbers to the one million place using strategies flexibly, including the algorithm.
• MAT-05.NO.NBT.05 Use concrete models, drawings, place value strategies, properties of operations, and/or relationships to add, subtract, and multiply decimals to hundredths.
• MAT-07.NO.O.01 Add, subtract, multiply, and divide integers using visual models and properties of operations in multi-step authentic and mathematical problems, including authentic problems.
• MAT-07.NO.O.02 Add, subtract, multiply, and divide non-negative fractions in multi-step problems, including authentic problems.
• MAT-07.NO.O.03 Add, subtract, multiply, and divide non-negative decimals to the hundredth place in multi-step problems using strategies or procedures, including authentic problems.
• MAT-08.NO.O.02 Add, subtract, multiply, and divide rational numbers using strategies or procedures.
• MAT-09.NO.02 Perform basic operations on simple radical expressions to write a simplified equivalent expression.
• MAT-09.AR.11 Add, subtract, and multiply polynomials.
• MAT-12.NO.03 Demonstrate that the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational, and that the product of a nonzero rational number and an irrational number is irrational.
• MAT-12.AR.13 Add, subtract, and multiply polynomials beyond quadratics. Understand that polynomials form a system comparable to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication.
• MAT-12.NO.11 Represent addition, subtraction, multiplication, conjugation, powers, and roots of complex numbers geometrically on the complex and/or polar plane; use properties of this representation for computation.
• MAT-12.NO.17 Add and subtract vectors. Represent vector subtraction graphically by connecting the tips of the appropriate order and using the components to perform vector subtraction.
• MAT-12.NO.19 Represent data in a matrix. Perform operations (i.e., addition, subtraction, multiplication) on matrices of appropriate dimensions to solve problems and in context. Know that matrix multiplication is not commutative.

Multiplication and Division

• MAT-03.NO.NBT.04 Multiply one-digit whole numbers by multiples of 10 within 100.
• MAT-04.NO.NBT.05 Multiply a whole number up to four digits by a one-digit whole number and multiply two two digit numbers. Show and justify the calculation using equations, rectangular arrays, and models.
• MAT-05.NO.NBT.04 Multiply multi-digit whole numbers using strategies flexibly, including the algorithm.
• MAT-05.NO.NBT.07 Explain patterns in the number of zeros of the product when multiplying a number by powers of 10. Explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10.
• MAT-04.NO.NBT.06 Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors using place value strategies. Show and justify the calculation by using equations, rectangular arrays, and models.
• MAT-05.NO.NBT.05 Use concrete models, drawings, place value strategies, properties of operations, and/or relationships to add, subtract, and multiply decimals to hundredths.
• MAT-05.NO.NBT.06 Find whole-number quotients and remainders with up to four-digit dividends and two-digit divisors using place value strategies. Show and justify the calculation using equations, rectangular arrays, and/or area models.
• MAT-06.NO.O.01 Divide multi-digit whole numbers up to four-digit dividends and two-digit divisors using strategies or procedures.
• MAT-07.NO.O.01 Add, subtract, multiply, and divide integers and positive rational numbers using visual models and properties of operations in multi-step problems, including authentic problems.
• MAT-07.NO.O.02 Add, subtract, multiply, and divide non-negative fractions in multi-step problems, including authentic problems.
• MAT-07.NO.O.03 Add, subtract, multiply, and divide non-negative decimals to the hundredth place in multi-step problems using strategies or procedures, including authentic problems.
• MAT-08.NO.O.01 Evaluate mentally the square roots of perfect squares up to 225 and cube roots of perfect cubes up to 1000.
• MAT-08.NO.O.02 Add, subtract, multiply, and divide rational numbers using strategies or procedures.
• MAT-09.NO.02 Perform basic operations on radicals and simplify radicals to write equivalent expressions.
• MAT-09.AR.11 Add, subtract, and multiply polynomials.
• MAT-12.NO.03 Demonstrate that the sum or product of two rational numbers is rational, that the sum of a rational number and an irrational number is irrational, and that the product of a nonzero rational number and an irrational number is irrational.
• MAT-12.AR.13 Add, subtract, and multiply polynomials beyond quadratics. Understand that polynomials form a system comparable to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication.
• MAT-12.NO.11 Represent addition, subtraction, multiplication, conjugation, powers, and roots of complex numbers geometrically on the complex and/or polar plane; use properties of this representation for computation.
• MAT-12.NO.19 Represent data in a matrix. Perform operations (i.e., addition, subtraction, multiplication) on matrices of appropriate dimensions to solve problems and in context. Know that matrix multiplication is not commutative.

Multiplying and Dividing Fractions

• MAT-04.NO.NF.07 Solve problems by multiplying fractions and whole numbers using visual fraction models (proper and improper fractions limited to denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100).
• MAT-05.NO.NF.02 Explain why multiplying a given number by a fraction greater than one results in a product greater than the given number and explain why multiplying a given number by a fraction less than one results in a product smaller than the given number.
• MAT-05.NO.NF.04 Solve authentic word problems by multiplying fractions and mixed numbers using visual fraction models and equations.
• MAT-06.NO.O.03 Apply multiplication and division of fractions and decimals to solve and interpret problems using visual models, including authentic problems.
• MAT-07.NO.O.02 Add, subtract, multiply, and divide non-negative fractions in multi-step problems, including authentic problems.
• MAT-08.NO.O.02 Add, subtract, multiply, and divide rational numbers using strategies or procedures.
• MAT-09.NO.02 Perform basic operations of simple radical expressions to write a simplified equivalent expression.
• MAT-12.NO.03 Demonstrate that the sum or product of two rational numbers is rational, that the sum of a rational number and an irrational number is irrational, and that the product of a nonzero rational number and an irrational number is irrational.
• MAT-12.NO.02 Perform basic operations on advanced radicals and simplify radicals to write equivalent expressions.
• MAT-12.AR.5 Add, subtract, multiply, and divide rational expressions. Understand that rational expressions form a system analogous to rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression.
• MAT-12.NO.06 Know there is a complex number i such that i² = -1, and every complex number has the form a + bi with a and b real. Understand the hierarchal relationships among subsets of the complex number system.

Exponents

• MAT-05.NO.NBT.07 Explain patterns in the number of zeros of the product when multiplying a number by powers of 10. Explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10.
  
• MAT-06.AR.EE.01 Write, read, and evaluate numerical expressions, including expressions with whole number exponents and grouping symbols.
  
• MAT-08.AR.EE.01 Explain the relationship between repeated multiplication and the properties of integer exponents. Apply a single exponent property to generate equivalent numeric and algebraic expressions that include numerical coefficients.
  
• MAT-09.NO.01 Explain how the definition of rational exponents follows from extending the properties of integer exponents; rewrite simple expressions involving radicals and rational exponents using the properties of exponents.
  
• MAT-09.NO.02 Perform basic operations on simple radical expressions to write a simplified equivalent expression.
  
• MAT-09.AR.06 Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear, quadratic, and exponential functions.
  
• MAT-09.AR.04 Create linear and exponential equations in two or more variables to represent relationships between quantities. Graph equations on coordinate axes with proper labels and scales.
  
• MAT-09.AR.F.06 Write a function defined by an expression in different but equivalent forms to reveal and explain the different properties of the function.
  
• MAT-0.AR.F.08 Identify situations that can be modeled with linear, quadratic, and exponential functions. Justify the most appropriate model for a situation based on the rate of change over equal intervals. Include situations in which a quantity grows or decays. 
  
• MAT-12.NO.01 Rewrite complex expressions involving radicals and rational exponents using the properties of exponents.
  
• MAT-12.NO.02 Perform basic operations on advanced radicals and simplify radicals to write equivalent expressions.
  
• MAT-12.AR.07 Create equations and inequalities and use them to solve problems. Include equations arising from linear and quadratic functions and simple rational and exponential functions.
  
• MAT-12.AR.08 Create equations in two or more variables to represent relationships between quantities. Graph equations on coordinate axes with appropriate labels and scales.
  
• MAT-12.AR.F.03 Write a function defined by an expression in different but equivalent forms to reveal and explain the different properties of the function.
  
• MAT-12.AR.F.06 Apply the inverse relationship between exponents and logarithms to solve problems.
  
• MAT-12.AR.F.15 Use properties of logarithms to express the solution to abct = d where a, c, and d are real numbers and b is a positive real number. Evaluate the logarithm using technology when appropriate.

9th Grade (MAT) Targeted Standard    (NO) Number and Operations  Learners will develop a foundational understanding of the number system, operations, and computational fluency to create connections and solve problems within and across concepts.

Proficiency Scale

Progressions

Unit Size and Scale

• MAT-06.NO.NS.02 Write, interpret, and explain statements of order for rational numbers on a number line diagram and in authentic contexts.
  
• MAT-09.NO.03 Choose and interpret the scale and the origin in graphs and data displays.
  
• MAT-09.NO.04 Define appropriate quantities and units for the purpose of descriptive modeling.
  
• MAT-09.NO.05 Choose a level of accuracy or precision appropriate to limitations on measurement when reporting quantities.
  
• MAT-09.AR.04 Create linear and exponential equations in two or more variables to represent relationships between quantities. Graph equations on coordinate axes with appropriate labels and scales.
  
• MAT-10.GM.14 Verify experimentally and justify the properties of dilations given by a center and a scale factor.
  
• MAT-10.GM.26 Recognize that the radian measure of an angle is the ratio of the length of the arc to the length of the radius of a circle.
  
• MAT-12.NO.04 Use units to understand problems and to guide the solution of multi-step problems (e.g., unit analysis). Choose and interpret units consistently in formulas. Choose and interpret the scale and the units in graphs and data displays.
  
• MAT-12.NO.05 Choose a level of accuracy or precision appropriate to limitations on measurement when reporting quantities.
  
• MAT-12.AR.08 Create equations in two or more variables to represent relationships between quantities. Graph equations on coordinate axes with appropriate labels and scales.

Unit Rate

• MAT-06.AR.RP.02 Describe and calculate a unit rate when given a ratio relationship between two quantities using rate language and visual models.
• MAT-06.AR.RP.05 Convert measurement units within and between measurement systems using ratio reasoning given conversion factors.
• MAT-06.AR.RP.04 Calculate a percent of a quantity as a rate per 100. Solve problems involving finding the whole, given a part, and the percent.
• MAT-07.AR.RP.01 Calculate unit rates associated with ratios of rational numbers, including ratios of lengths, areas, and other quantities measured in like or different units.
• MAT-09.NO.03 Choose and interpret the scale and the units in graphs and data displays.
• MAT-09.NO.04 Define appropriate quantities and units for the purpose of descriptive modeling.
• MAT-09.AR.F.05 Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.
• MAT-09.AR.F.06 Write a function defined by an expression in different but equivalent forms to reveal and explain the different properties of the function.
• MAT-12.NO.04 Use units to understand problems and to guide the solution of multi-step problems (e.g., unit analysis). Choose and interpret units consistently in formulas. Choose and interpret the scale and the units in graphs and data displays.
• MAT-12.AR.F.02 Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.

Units of Measurement

• MAT-03.GM.M.02 Measure and estimate liquid volumes and masses of objects using standard units. Solve one step authentic word problems involving masses or volumes given in the same units.
• MAT-04.GM.M.01 Know the relative sizes of measurement units within one system of units, including km, m, cm; kg, g; lb., oz.; l, ml; hr., min., sec. Record measurement equivalents in a two-column table.
• MAT-04.GM.M.03 Identify and use the appropriate tools, operations, and units of measurement, both customary and metric to solve problems involving time, length, weight, mass, and capacity.
• MAT-04.GM.M.02 Generate simple conversions from a larger unit to a smaller unit to solve authentic problems within a single system of measurement, both customary and metric systems.
• MAT-05.GM.M.01 Generate conversions among different-sized standard measurement units within a given measurement system, both customary and metric systems. Use these conversions in solving multi-step, authentic word problems.
• MAT-06.AR.RP.05 Convert measurement units within and between measurement systems using ratio reasoning given conversion factors.
• MAT-10.GM.36 Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; scaling a model).
• MAT-09.NO.03 Choose and interpret the scale and the origin in graphs and data displays.
• MAT-09.NO.04 Define appropriate quantities and units for the purpose of descriptive modeling.
• MAT-09.NO.05 Choose a level of accuracy or precision appropriate to limitations on measurement when reporting quantities.
• MAT-12.NO.04 Use units to understand problems and to guide the solution of multi-step problems (e.g., unit analysis). Choose and interpret units consistently in formulas. Choose and interpret the scale and the units in graphs and data displays.
• MAT-12.NO.05 Choose a level of accuracy or precision appropriate to limitations on measurement when reporting quantities.

Displaying Data

• MAT-01.DPS.D.01 Collect, organize and represent data with up to three categories using picture and bar graphs.
• MAT-02.DPS.D.01 Formulate questions and collect, organize, and represent data, with up to four categories using single unit scaled pictures and bar graphs.
• MAT-03.DPS.D.01 Formulate questions to collect, organize, and represent data with more than four categories using scaled pictures and bar graphs.
• MAT-04.DPS.D.01 Formulate questions to collect, organize, and represent data to reason with math and across disciplines.
• MAT-02.DPS.D.02 Generate data and create line plots marked in whole number units.
• MAT-03.DPS.D.02 Generate data and create line plots marked in whole numbers, halves, and fourths of a unit.
• MAT-04.DPS.D.02 Generate data and create line plots to display a data set of fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots.
• MAT-05.DPS.D.01 Generate data and create line plots to display a data set of fractions of a unit (1/2, 1/4, 1/8). Use grade-level operations for fractions to solve problems involving information presented in line plots.
• MAT-06.DPS.DA.04 Display numerical data in plots on a number line, including dot plots and histograms. Describe any overall patterns in data, such as gaps, clusters, and skews.
• MAT-09.NO.03 Choose and interpret the scale and the units in graphs and data displays.
• MAT-09.NO.05 Choose a level of accuracy or precision appropriate to limitations on measurement when reporting quantities.
• MAT-10.DPS.01 Represent data with plots on the real number line (dot plots, histograms, and box plots).
• MAT-10.DPS.03 Represent data on two quantitative variables on a scatter plot and describe how the variables are related.
• MAT-10.DPS.10 Construct and interpret two-way frequency tables of data for two categorical variables. Use the two-way table as a sample space to decide if events are independent and approximate conditional probabilities.
• MAT-12.NO.04 Use units as a way to understand problems and to guide the solution of multi-step problems (e.g., unit analysis). Choose and interpret units consistently in formulas. Choose and interpret the scale and the units in graphs and data displays.
• MAT-12.DPS.04 Represent data on a scatter plot for two quantitative variables and describe how the variables are related.

9th Grade (MAT) Targeted Standard    (NO) Number and Operations  Learners will develop a foundational understanding of the number system, operations, and computational fluency to create connections and solve problems within and across concepts.

Proficiency Scale

Progressions

Unit Size and Scale

• MAT-06.NO.NS.02 Write, interpret, and explain statements of order for rational numbers on a number line diagram and in authentic contexts.
  
• MAT-09.NO.03 Choose and interpret the scale and the origin in graphs and data displays.
  
• MAT-09.NO.04 Define appropriate quantities and units for the purpose of descriptive modeling.
  
• MAT-09.NO.05 Choose a level of accuracy or precision appropriate to limitations on measurement when reporting quantities.
  
• MAT-09.AR.04 Create linear and exponential equations in two or more variables to represent relationships between quantities. Graph equations on coordinate axes with appropriate labels and scales.
  
• MAT-10.GM.14 Verify experimentally and justify the properties of dilations given by a center and a scale factor.
  
• MAT-10.GM.26 Recognize that the radian measure of an angle is the ratio of the length of the arc to the length of the radius of a circle.
  
• MAT-12.NO.04 Use units to understand problems and to guide the solution of multi-step problems (e.g., unit analysis). Choose and interpret units consistently in formulas. Choose and interpret the scale and the units in graphs and data displays.
  
• MAT-12.NO.05 Choose a level of accuracy or precision appropriate to limitations on measurement when reporting quantities.
  
• MAT-12.AR.08 Create equations in two or more variables to represent relationships between quantities. Graph equations on coordinate axes with appropriate labels and scales.

Unit Rate

• MAT-06.AR.RP.02 Describe and calculate a unit rate when given a ratio relationship between two quantities using rate language and visual models.
• MAT-06.AR.RP.05 Convert measurement units within and between measurement systems using ratio reasoning given conversion factors.
• MAT-06.AR.RP.04 Calculate a percent of a quantity as a rate per 100. Solve problems involving finding the whole, given a part, and the percent.
• MAT-07.AR.RP.01 Calculate unit rates associated with ratios of rational numbers, including ratios of lengths, areas, and other quantities measured in like or different units.
• MAT-09.NO.03 Choose and interpret the scale and the units in graphs and data displays.
• MAT-09.NO.04 Define appropriate quantities and units for the purpose of descriptive modeling.
• MAT-09.AR.F.05 Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.
• MAT-09.AR.F.06 Write a function defined by an expression in different but equivalent forms to reveal and explain the different properties of the function.
• MAT-12.NO.04 Use units to understand problems and to guide the solution of multi-step problems (e.g., unit analysis). Choose and interpret units consistently in formulas. Choose and interpret the scale and the units in graphs and data displays.
• MAT-12.AR.F.02 Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.

Units of Measurement

• MAT-03.GM.M.02 Measure and estimate liquid volumes and masses of objects using standard units. Solve one step authentic word problems involving masses or volumes given in the same units.
• MAT-04.GM.M.01 Know the relative sizes of measurement units within one system of units, including km, m, cm; kg, g; lb., oz.; l, ml; hr., min., sec. Record measurement equivalents in a two-column table.
• MAT-04.GM.M.03 Identify and use the appropriate tools, operations, and units of measurement, both customary and metric to solve problems involving time, length, weight, mass, and capacity.
• MAT-04.GM.M.02 Generate simple conversions from a larger unit to a smaller unit to solve authentic problems within a single system of measurement, both customary and metric systems.
• MAT-05.GM.M.01 Generate conversions among different-sized standard measurement units within a given measurement system, both customary and metric systems. Use these conversions in solving multi-step, authentic word problems.
• MAT-06.AR.RP.05 Convert measurement units within and between measurement systems using ratio reasoning given conversion factors.
• MAT-10.GM.36 Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; scaling a model).
• MAT-09.NO.03 Choose and interpret the scale and the origin in graphs and data displays.
• MAT-09.NO.04 Define appropriate quantities and units for the purpose of descriptive modeling.
• MAT-09.NO.05 Choose a level of accuracy or precision appropriate to limitations on measurement when reporting quantities.
• MAT-12.NO.04 Use units to understand problems and to guide the solution of multi-step problems (e.g., unit analysis). Choose and interpret units consistently in formulas. Choose and interpret the scale and the units in graphs and data displays.
• MAT-12.NO.05 Choose a level of accuracy or precision appropriate to limitations on measurement when reporting quantities.

9th Grade (MAT) Targeted Standard    (NO) Number and Operations  Learners will develop a foundational understanding of the number system, operations, and computational fluency to create connections and solve problems within and across concepts.

Proficiency Scale

Progressions

Unit Size and Scale

• MAT-06.NO.NS.02 Write, interpret, and explain statements of order for rational numbers on a number line diagram and in authentic contexts.
  
• MAT-09.NO.03 Choose and interpret the scale and the origin in graphs and data displays.
  
• MAT-09.NO.04 Define appropriate quantities and units for the purpose of descriptive modeling.
  
• MAT-09.NO.05 Choose a level of accuracy or precision appropriate to limitations on measurement when reporting quantities.
  
• MAT-09.AR.04 Create linear and exponential equations in two or more variables to represent relationships between quantities. Graph equations on coordinate axes with appropriate labels and scales.
  
• MAT-10.GM.14 Verify experimentally and justify the properties of dilations given by a center and a scale factor.
  
• MAT-10.GM.26 Recognize that the radian measure of an angle is the ratio of the length of the arc to the length of the radius of a circle.
  
• MAT-12.NO.04 Use units to understand problems and to guide the solution of multi-step problems (e.g., unit analysis). Choose and interpret units consistently in formulas. Choose and interpret the scale and the units in graphs and data displays.
  
• MAT-12.NO.05 Choose a level of accuracy or precision appropriate to limitations on measurement when reporting quantities.
  
• MAT-12.AR.08 Create equations in two or more variables to represent relationships between quantities. Graph equations on coordinate axes with appropriate labels and scales.

Units of Measurement

• MAT-03.GM.M.02 Measure and estimate liquid volumes and masses of objects using standard units. Solve one step authentic word problems involving masses or volumes given in the same units.
• MAT-04.GM.M.01 Know the relative sizes of measurement units within one system of units, including km, m, cm; kg, g; lb., oz.; l, ml; hr., min., sec. Record measurement equivalents in a two-column table.
• MAT-04.GM.M.03 Identify and use the appropriate tools, operations, and units of measurement, both customary and metric to solve problems involving time, length, weight, mass, and capacity.
• MAT-04.GM.M.02 Generate simple conversions from a larger unit to a smaller unit to solve authentic problems within a single system of measurement, both customary and metric systems.
• MAT-05.GM.M.01 Generate conversions among different-sized standard measurement units within a given measurement system, both customary and metric systems. Use these conversions in solving multi-step, authentic word problems.
• MAT-06.AR.RP.05 Convert measurement units within and between measurement systems using ratio reasoning given conversion factors.
• MAT-10.GM.36 Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; scaling a model).
• MAT-09.NO.03 Choose and interpret the scale and the origin in graphs and data displays.
• MAT-09.NO.04 Define appropriate quantities and units for the purpose of descriptive modeling.
• MAT-09.NO.05 Choose a level of accuracy or precision appropriate to limitations on measurement when reporting quantities.
• MAT-12.NO.04 Use units to understand problems and to guide the solution of multi-step problems (e.g., unit analysis). Choose and interpret units consistently in formulas. Choose and interpret the scale and the units in graphs and data displays.
• MAT-12.NO.05 Choose a level of accuracy or precision appropriate to limitations on measurement when reporting quantities.

Displaying Data

• MAT-01.DPS.D.01 Collect, organize and represent data with up to three categories using picture and bar graphs.
• MAT-02.DPS.D.01 Formulate questions and collect, organize, and represent data, with up to four categories using single unit scaled pictures and bar graphs.
• MAT-03.DPS.D.01 Formulate questions to collect, organize, and represent data with more than four categories using scaled pictures and bar graphs.
• MAT-04.DPS.D.01 Formulate questions to collect, organize, and represent data to reason with math and across disciplines.
• MAT-02.DPS.D.02 Generate data and create line plots marked in whole number units.
• MAT-03.DPS.D.02 Generate data and create line plots marked in whole numbers, halves, and fourths of a unit.
• MAT-04.DPS.D.02 Generate data and create line plots to display a data set of fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots.
• MAT-05.DPS.D.01 Generate data and create line plots to display a data set of fractions of a unit (1/2, 1/4, 1/8). Use grade-level operations for fractions to solve problems involving information presented in line plots.
• MAT-06.DPS.DA.04 Display numerical data in plots on a number line, including dot plots and histograms. Describe any overall patterns in data, such as gaps, clusters, and skews.
• MAT-09.NO.03 Choose and interpret the scale and the units in graphs and data displays.
• MAT-09.NO.05 Choose a level of accuracy or precision appropriate to limitations on measurement when reporting quantities.
• MAT-10.DPS.01 Represent data with plots on the real number line (dot plots, histograms, and box plots).
• MAT-10.DPS.03 Represent data on two quantitative variables on a scatter plot and describe how the variables are related.
• MAT-10.DPS.10 Construct and interpret two-way frequency tables of data for two categorical variables. Use the two-way table as a sample space to decide if events are independent and approximate conditional probabilities.
• MAT-12.NO.04 Use units as a way to understand problems and to guide the solution of multi-step problems (e.g., unit analysis). Choose and interpret units consistently in formulas. Choose and interpret the scale and the units in graphs and data displays.
• MAT-12.DPS.04 Represent data on a scatter plot for two quantitative variables and describe how the variables are related.