Comparing The Standards Across Grade Levels K – High School High School Number and Quantity

Numbers and Number Systems It’s about extending the students conception of number. It’s about extending the students conception of number.

Number for K - 5 Counting and Cardinality Counting and Cardinality Numbers and Operations in Base Ten Numbers and Operations in Base Ten K Geometry Measurement and DataStatistics and Probability Number and Operations in Base TenThe Number System Operations and Algebraic ThinkingExpressions and Equations Counting and Cardinality Number and Operations--- Fractions Ratios and Proportional Relationships Functions

Kindergarten Counting and Cardinality Kindergarten K.CC Know number names and the count sequence. Know number names and the count sequence. Count to tell the number of objects. Count to tell the number of objects. Compare numbers. Compare numbers. Number and Operations in Base Ten Kindergarten K.NBT Work with numbers to gain foundations for place value. Work with numbers to gain foundations for place value.

First Grade Numbers and Operations in Base Ten 1.NBT Extend the counting sequence. Extend the counting sequence. Understand place value. Understand place value. Use place value understanding and properties of operations to add and subtract. Use place value understanding and properties of operations to add and subtract.

Second Grade Numbers and Operations in Base Ten 2.NBT Understand place value. Understand place value. Use place value understanding and properties of operations to add and subtract. Use place value understanding and properties of operations to add and subtract.

Third Grade Numbers and Operations in Base Ten 3.NBT Use place value understanding and properties of operations to perform multi-digit arithmetic. Use place value understanding and properties of operations to perform multi-digit arithmetic. Number and Operations--- Fractions 3.NF Develop understanding of fractions as numbers.

Fourth Grade Numbers and Operations in Base Ten 4.NBT Generalize place value understanding for multi- digit whole numbers. Generalize place value understanding for multi- digit whole numbers. Use place value understanding and properties of operations to perform multi-digit arithmetic. Use place value understanding and properties of operations to perform multi-digit arithmetic. Number and Operations--- Fractions 4.NF Extend understanding of fraction equivalence and ordering. Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers. Understand decimal notation for fractions, and compare decimal fractions.

Fifth Grade Numbers and Operations in Base Ten 5.NBT Understand the place value system. Understand the place value system. Perform operations with multi-digit whole numbers and with decimals to hundredths. Perform operations with multi-digit whole numbers and with decimals to hundredths. Number and Operations--- Fractions 5.NF Use equivalent fractions as a strategy to add and subtract fractions. Apply and extend previous understandings of multiplication and division to multiply and divide fractions.

Number for The Number System The Number System K Geometry Measurement and DataStatistics and Probability Number and Operations in Base TenThe Number System Operations and Algebraic ThinkingExpressions and Equations Counting and Cardinality Number and Operations--- Fractions Ratios and Proportional Relationships Functions

Sixth Grade The Number System 6.NS Apply and extend previous understandings of multiplication and division to divide fractions by fractions. Apply and extend previous understandings of multiplication and division to divide fractions by fractions. Compute fluently with multi-digit numbers and find common factors and multiples. Compute fluently with multi-digit numbers and find common factors and multiples. Apply and extend previous understandings of numbers to the system of rational numbers. Apply and extend previous understandings of numbers to the system of rational numbers.

Seventh Grade The Number System 7.NS Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers. Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.

Eighth Grade The Number System 8.NS Know that there are numbers that are not rational, and approximate them by rational numbers. Know that there are numbers that are not rational, and approximate them by rational numbers.

High School The Real Number System N-RN Extend the properties of exponents to rational exponents. Extend the properties of exponents to rational exponents. Use properties of rational and irrational numbers. Use properties of rational and irrational numbers.

High School Complex Numbers N-CN Perform arithmetic operations with complex numbers. Perform arithmetic operations with complex numbers. Represent complex numbers and their operations on the complex plane. Represent complex numbers and their operations on the complex plane. Use complex numbers in polynomial identities and equations. Use complex numbers in polynomial identities and equations. Vector and Matrix Quantities N-VM Represent and model with vector quantities. Perform operations on vectors. Perform operations on matrices and use matrices in applications.

What did I learn about “Number”? At first, “number” means “counting number”: 1, 2, 3, … At first, “number” means “counting number”: 1, 2, 3, … Soon after that, 0 is used to represent “none” and the whole numbers are formed by the counting numbers together with zero. Soon after that, 0 is used to represent “none” and the whole numbers are formed by the counting numbers together with zero. The next extension is fractions. At first, fractions are barely numbers and tied strongly to pictorial representations. The next extension is fractions. At first, fractions are barely numbers and tied strongly to pictorial representations. The concept of fractions as numbers is used to connect them to their decimal representations, with the base-ten system used to represent the whole numbers. The concept of fractions as numbers is used to connect them to their decimal representations, with the base-ten system used to represent the whole numbers.

During middle school, fractions are augmented by negative fractions to form the rational numbers. During middle school, fractions are augmented by negative fractions to form the rational numbers. In Grade 8, students extend this system by, augmenting the rational numbers with the irrational numbers to form the real numbers. In Grade 8, students extend this system by, augmenting the rational numbers with the irrational numbers to form the real numbers. Finally, in high school, students are exposed to another extension of number, when the real numbers are augmented by the imaginary numbers to form the complex numbers. Finally, in high school, students are exposed to another extension of number, when the real numbers are augmented by the imaginary numbers to form the complex numbers.

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Quantity When applying mathematics to real world problems, the answers are usually not numbers but quantities: numbers with units, which involves measurement. When applying mathematics to real world problems, the answers are usually not numbers but quantities: numbers with units, which involves measurement.

Quantity for PK - 5 Measurement and Data Measurement and Data

Kindergarten Measurement and Data K.MD Describe and compare measurable attributes.

First Grade Measurement and Data 1.MD Measure lengths indirectly and by iterating length units.

Second Grade Measurement and Data 2.MD Measure and estimate lengths in standard units.

Third Grade Measurement and Data 3.MD Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects.

Fourth Grade Measurement and Data 4.MD Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit.

Fifth Grade Measurement and Data 5.MD Convert like measurement units within a given measurement system.

Quantity for Geometry Geometry K Geometry Measurement and DataStatistics and Probability Number and Operations in Base TenThe Number System Operations and Algebraic ThinkingExpressions and Equations Counting and Cardinality Number and Operations--- Fractions Ratios and Proportional Relationships Functions

Sixth Grade Geometry 6.G Solve real-world and mathematical problems involving area, surface area, and volume.

Seventh Grade Geometry 7.G Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.

Eighth Grade Geometry 8.G Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.

High School Quantities N-Q Reason quantitatively and use units to solve problems. Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays. Define appropriate quantities for the purpose of descriptive modeling. Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.

What did I learn about “Quantity”? Quantity is about the real world problems. Quantity is about the real world problems. The answers are usually not numbers but quantities: numbers with units, which involves measurement. The answers are usually not numbers but quantities: numbers with units, which involves measurement. In their work in measurement up through Grade 8, students primarily measure commonly used attributes such as length, area, and volume. In their work in measurement up through Grade 8, students primarily measure commonly used attributes such as length, area, and volume. In high school, students encounter a wider variety of units in modeling, e.g. acceleration, currency conversions, social science rates such as per-capita income, and rates in everyday life such as points scored per game or batting averages. In high school, students encounter a wider variety of units in modeling, e.g. acceleration, currency conversions, social science rates such as per-capita income, and rates in everyday life such as points scored per game or batting averages.

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