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

Comparing The Standards Comparing The Standards Across Grade LevelsAcross Grade Levels

K – High SchoolK – High School

High School Number and High School Number and QuantityQuantity

Numbers and Number Numbers and Number SystemsSystems

It’s about extending the students It’s about extending the students conception of number. conception of number.

Number for K - 5Number for K - 5

Counting and Counting and CardinalityCardinality

Numbers and Numbers and Operations in Base Operations in Base TenTen

K 1 2 3 4 5 6 7 8

Geometry

Measurement and Data Statistics and Probability

Number and Operations in Base Ten

The Number System

Operations and Algebraic Thinking

Expressions and Equations

Counting and

Cardinality

Number and

Operations---

Fractions

Ratios and Proportional Relationships

Functions

KindergartenKindergarten

Counting and Cardinality Counting and Cardinality

Kindergarten K.CCKindergarten K.CC Know number names Know number names

and the count and the count sequence. sequence.

Count to tell the number Count to tell the number of objects. of objects.

Compare numbers. Compare numbers.

Number and Operations Number and Operations in Base Tenin Base Ten

Kindergarten Kindergarten K.NBTK.NBT

Work with numbers 11--19 Work with numbers 11--19 to gain foundations for to gain foundations for place value.place value.

First GradeFirst Grade

Numbers and Operations in Base Ten Numbers and Operations in Base Ten 1.NBT1.NBT

Extend the counting sequence. Extend the counting sequence. Understand place value.Understand place value.Use place value understanding and Use place value understanding and

properties of operations to add and properties of operations to add and subtract.subtract.

Second GradeSecond Grade

Numbers and Operations in Base Ten Numbers and Operations in Base Ten 2.NBT2.NBT

Understand place value.Understand place value.Use place value understanding and Use place value understanding and

properties of operations to add and properties of operations to add and subtract.subtract.

Third GradeThird Grade

Numbers and Operations Numbers and Operations in Base Ten 3.NBTin Base Ten 3.NBT

Use place value Use place value understanding and understanding and properties of properties of operations to operations to perform multi-digit perform multi-digit arithmetic.arithmetic.

Number and Number and Operations---Fractions Operations---Fractions 3.NF 3.NF

Develop Develop understanding of understanding of fractions as fractions as numbers.numbers.

Fourth GradeFourth Grade

Numbers and Operations Numbers and Operations in Base Ten in Base Ten

4.NBT 4.NBT

Generalize place value Generalize place value understanding for multi-understanding for multi-digit whole numbers. digit whole numbers.

Use place value Use place value understanding and understanding and properties of operations properties of operations to perform multi-digit to perform multi-digit arithmetic. arithmetic.

Number and Number and Operations---Fractions Operations---Fractions

4.NF 4.NF

Extend understanding Extend understanding of fraction equivalence of fraction equivalence and ordering. and ordering.

Build fractions from unit Build fractions from unit fractions by applying fractions by applying and extending previous and extending previous understandings of understandings of operations on whole operations on whole numbers. numbers.

Understand decimal Understand decimal notation for fractions, notation for fractions, and compare decimal and compare decimal fractions.fractions.

Fifth GradeFifth Grade

Numbers and Operations Numbers and Operations in Base Ten in Base Ten 5.NBT5.NBT

Understand the place Understand the place value system.value system.

Perform operations with Perform operations with multi-digit whole multi-digit whole numbers and with numbers and with decimals to hundredths.decimals to hundredths.

Number and Number and Operations---Fractions Operations---Fractions 5.NF 5.NF

Use equivalent fractions Use equivalent fractions as a strategy to add as a strategy to add and subtract fractions.and subtract fractions.

Apply and extend Apply and extend previous previous understandings of understandings of multiplication and multiplication and division to multiply and division to multiply and divide fractions. divide fractions.

Number for 6 - 8Number for 6 - 8

The Number The Number SystemSystem

K 1 2 3 4 5 6 7 8

Geometry


Number and Operations in Base Ten The Number System

Operations and Algebraic Thinking Expressions and Equations

Counting and

Cardinality

Number and

Operations---Fractions


Functions

Sixth GradeSixth Grade

The Number System 6.NSThe Number System 6.NS

Apply and extend previous understandings Apply and extend previous understandings of multiplication and division to divide of multiplication and division to divide fractions by fractions.fractions by fractions.

Compute fluently with multi-digit numbers Compute fluently with multi-digit numbers and find common factors and multiples.and find common factors and multiples.

Apply and extend previous understandings Apply and extend previous understandings of numbers to the system of rational of numbers to the system of rational numbers.numbers.

Seventh GradeSeventh Grade

The Number System The Number System 7.NS7.NS

Apply and extend previous Apply and extend previous understandings of operations with understandings of operations with fractions to add, subtract, multiply, and fractions to add, subtract, multiply, and divide rational numbers.divide rational numbers.

Eighth GradeEighth Grade

The Number System The Number System 8.NS8.NS

Know that there are numbers that are Know that there are numbers that are not rational, and approximate them by not rational, and approximate them by rational numbers.rational numbers.

High SchoolHigh School

The Real Number System N-The Real Number System N-RNRN

Extend the properties of exponents to Extend the properties of exponents to rational exponents.rational exponents.

Use properties of rational and irrational Use properties of rational and irrational numbers. numbers.

High SchoolHigh SchoolComplex Numbers N-CNComplex Numbers N-CN

Perform arithmetic Perform arithmetic operations with operations with complex numbers. complex numbers.

Represent complex Represent complex numbers and their numbers and their operations on the operations on the complex plane.complex plane.

Use complex numbers Use complex numbers in polynomial identities in polynomial identities and equations.and equations.

Vector and Matrix Quantities Vector and Matrix Quantities N-VMN-VM

Represent and model Represent and model with vector quantities.with vector quantities.

Perform operations on Perform operations on vectors.vectors.

Perform operations on Perform operations on matrices and use matrices and use matrices in applications.matrices in applications.

What did I learn about What did I learn about “Number”?“Number”?

At first, “number” means “counting number”: 1, 2, At first, “number” means “counting number”: 1, 2, 3, … 3, …

Soon after that, 0 is used to represent “none” and Soon after that, 0 is used to represent “none” and the whole numbers are formed by the counting the whole numbers are formed by the counting numbers together with zero. numbers together with zero.

The next extension is fractions. At first, fractions The next extension is fractions. At first, fractions are barely numbers and tied strongly to pictorial are barely numbers and tied strongly to pictorial representations. representations.

The concept of fractions as numbers is used to The concept of fractions as numbers is used to connect them to their decimal representations, connect them to their decimal representations, with the base-ten system used to represent the with the base-ten system used to represent the whole numbers.whole numbers.

During middle school, fractions are During middle school, fractions are augmented by negative fractions to form augmented by negative fractions to form the rational numbers. the rational numbers.

In Grade 8, students extend this system In Grade 8, students extend this system by, augmenting the rational numbers with by, augmenting the rational numbers with the irrational numbers to form the real the irrational numbers to form the real numbers. numbers.

Finally, in high school, students are Finally, in high school, students are exposed to another extension of number, exposed to another extension of number, when the real numbers are augmented by when the real numbers are augmented by the imaginary numbers to form the the imaginary numbers to form the complex numbers.complex numbers.

The End for “Number”The End for “Number”

QuantityQuantity

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

Quantity for PK - 5Quantity for PK - 5

Measurement and Measurement and DataData

KindergartenKindergarten

Measurement and Data K.MD

Describe and compare measurable attributes.

First GradeFirst Grade

Measurement and Data 1.MD

Measure lengths indirectly and by iterating length units.

Second GradeSecond Grade


Measure and estimate lengths in standard units.

Third GradeThird Grade


Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects.

Fourth GradeFourth Grade


Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit.

Fifth GradeFifth Grade


Convert like measurement units within a given measurement system.

Quantity for 6 - 8Quantity for 6 - 8

GeometryGeometry K 1 2 3 4 5 6 7 8

Geometry


Number and Operations in Base Ten The Number System

Operations and Algebraic Thinking Expressions and Equations

Counting and

Cardinality

Number and

Operations---Fractions


Functions

Sixth GradeSixth Grade

Geometry 6.G

Solve real-world and mathematical problems involving area, surface area, and volume.

Seventh GradeSeventh Grade

Geometry 7.G

Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.

Eighth GradeEighth Grade

Geometry 8.G

Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.

High SchoolHigh SchoolQuantities N-QReason 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 What did I learn about “Quantity”?“Quantity”?

Quantity is about the real world problems.Quantity is about the real world problems. The answers are usually not numbers but The answers are usually not numbers but

quantities: numbers with units, which involves quantities: numbers with units, which involves measurement. measurement.

In their work in measurement up through Grade 8, In their work in measurement up through Grade 8, students primarily measure commonly used students primarily measure commonly used attributes such as length, area, and volume. attributes such as length, area, and volume.

In high school, students encounter a wider variety In high school, students encounter a wider variety of units in modeling, e.g. acceleration, currency of units in modeling, e.g. acceleration, currency conversions, social science rates such as per-conversions, social science rates such as per-capita income, and rates in everyday life such as capita income, and rates in everyday life such as points scored per game or batting averages. points scored per game or batting averages.

The EndThe End

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