Mathematics Department Scope and Sequence€¦ · Mathematics Department Scope and Sequence Grades...

Mathematics Department Scope and Sequence

Grades Kindergarten through High School

Mathematics Department

Scope and Sequence

for

grades

Kindergarten

through

High School



Common Core Learning Standards – Mathematics Standards Progressions EngageNY

Math Curriculum

Modules

Story of Units Story of Ratios Story of Functions

Grade K 1 2 3 4 5 6 7 8 High School

Do

mai

ns

Counting and

Cardinality

Number and Quantity

Number and Operations in Base Ten Ratios and

Proportional Relationships

Number and Operations -

Fractions The Number System

Operations and Algebraic Thinking

Expressions and Equations Algebra

Functions Functions

Geometry Geometry Geometry

Measurement and Data Statistics and Probability Statistics and

Probability

Common Core

Practices Standards for Mathematical Practice



Grade K Overview MAEKG

K.CC Counting and Cardinality

• Know number names and the count sequence.

• Count to tell the number of objects.

• Compare numbers.

K.OA Operations and Algebraic Thinking

• Understand addition as putting together and adding to, and understand subtraction

as taking apart and taking from.

K.NBT Number and Operations in Base Ten

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

K.MD Measurement and Data

• Describe and compare measurable attributes.

• Classify objects and count the number of objects in categories.

K.G Geometry

• Identify and describe shapes.

• Analyze, compare, create, and compose shapes.

Required Fluency:

K.OA.5 Add and subtract within 5



4

Grade K Checklist

F Fluency Standard * Major Emphases Standard



5

Grade 1 Overview MAE1G

1.OA Operations and Algebraic Thinking

• Represent and solve problems involving addition and subtraction.

• Understand and apply properties of operations and the relationship between

addition and subtraction.

• Add and subtract within 20.

• Work with addition and subtraction equations.

1.NBT Number and Operations in Base Ten

• Extend the counting sequence.

• Understand place value.

• Use place value understanding and properties of operations to add and subtract.

1.MD Measurement and Data

• Measure lengths indirectly and by iterating length units.

• Tell and write time and money.

• Represent and interpret data.

1.G Geometry

• Reason with shapes and their attributes.

Required Fluency:

1.OA.6 Add and subtract within 10



6

Grade 1 Checklist

F Fluency Standard

* Major Emphases Standard



7



• Represent and solve problems involving addition and subtraction.

• Add and subtract within 20.

• Work with equal groups of objects to gain foundations for multiplication.


• Understand place value.

• Use place value understanding and properties of operations to add and subtract.


• Measure and estimate lengths in standard units.

• Relate addition and subtraction to length.

• Work with time and money.


2.G Geometry


Required Fluency:

2.OA.2 Add and subtract within 20

2.NBT.5 Add and subtract within 100



8

Grade 2 Checklist

F Fluency Standard

* Major Emphases Standard



9



• Represent and solve problems involving multiplication and division.

• Understand properties of multiplication and the relationship between

multiplication and division.

• Multiply and divide within 100.

• Solve problems involving the four operations, and identify and explain patterns in

arithmetic.


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

arithmetic.

3. NF Number and Operations—Fractions

• Develop understanding of fractions as numbers.


• Solve problems involving measurement and estimation of intervals of time, liquid

volumes, and masses of objects.


• Geometric measurement: understand concepts of area and relate area to

multiplication and to addition.

• Geometric measurement: recognize perimeter as an attribute of plane figures and

distinguish between linear and area measures.

3.G Geometry


Required Fluency:

3.OA.7 Multiply and divide within 100

3.NBT.2 Add and subtract within 1000



10

Grade 3 Checklist



11



• Use the four operations with whole numbers to solve problems.

• Gain familiarity with factors and multiples.

• Generate and analyze patterns.


• Generalize place value understanding for multidigit whole numbers.

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

arithmetic.

4.NF Number and Operations—Fractions

• 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.


• Solve problems involving measurement and conversion of measurements from a

larger unit to a smaller unit.


• Geometric measurement: understand concepts of angle and measure angles.

4.G Geometry

• Draw and identify lines and angles, and classify shapes by properties of their

lines and angles.

Required Fluency:

4.NBT.4 Add and subtract within 1,000,000



12

Grade 4 Checklist



13



• Write and interpret numerical expressions.

• Analyze patterns and relationships.


• Understand the place value system.

• Perform operations with multi-digit whole numbers and with decimals to

hundredths.

5.NF Number and Operations—Fractions

• 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.


• Convert like measurement units within a given measurement system.


• Geometric measurement: understand concepts of volume and relate volume to

multiplication and to addition.

5.G Geometry

• Graph points on the coordinate plane to solve real-world and mathematical

problems.

• Classify two-dimensional figures into categories based on their properties.

Required Fluency:

5.NBT.5 Multi-digit multiplication



14

Grade 5 Checklist



15


6.RP Ratios and Proportional Relationships

• Understand ratio concepts and use ratio reasoning to solve problems.

6.NS The Number System

• 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.

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

numbers.

6.EE Expressions and Equations

• Apply and extend previous understandings of arithmetic to algebraic

expressions.• Reason about and solve one-variable equations and inequalities.

• Represent and analyze quantitative relationships between dependent and

independent variables.

6.G Geometry

• Solve real-world and mathematical problems involving area, surface area, and

volume.

6.SP Statistics and Probability

• Develop understanding of statistical variability.

• Summarize and describe distribution

Required Fluency:

6.NS.2 Multi-digit division

6.NS.3 Multi-digit decimal operations



16

Grade 6 Checklist

F Fluency Standard

* Major Emphases Standard + NYSED May-June Standard



17


7.RP Ratios and Proportional Relationships

• Analyze proportional relationships and use them to solve real-world and

mathematical problems.


• Apply and extend previous understandings of operations with fractions to add,

subtract, multiply, and divide rational numbers.


• Use properties of operations to generate equivalent expressions.

• Solve real-life and mathematical problems using numerical and algebraic

expressions and equations.

7.G Geometry

• Draw, construct and describe geometrical figures and describe the relationships

between them.

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

area, and volume.


• Use random sampling to draw inferences about a population.

• Draw informal comparative inferences about two populations.

• Investigate chance processes and develop, use, and evaluate probability models.

Required Fluency:

7.EE.4 Solve px + q = r and p(x + q) = r



18

Grade 7 Checklist

F Fluency Standard




19



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

rational numbers.


• Work with radicals and integer exponents.

• Understand the connections between proportional relationships, lines, and linear

equations.

• Analyze and solve linear equations and pairs of simultaneous linear equations.

8.F Functions

• Define, evaluate, and compare functions.

• Use functions to model relationships between quantities.

8.G Geometry

• Understand congruence and similarity using physical models, transparencies, or

geometry software.

• Understand and apply the Pythagorean Theorem.

• Solve real-world and mathematical problems involving volume of cylinders,

cones and spheres.


• Investigate patterns of association in bivariate data.

Required Fluency:

8.EE.8b Solve simple 22 systems by inspection



20

Grade 8 Checklist

F Fluency Standard




21

Algebra I Year 1 of 2 Overview AL01GXX1 First part in a TWO-PART SEQUENCE

Number and Quantity

The Real Number System (N-RN)

Quantities (N-Q)

Algebra

Seeing Structure in Expressions (A-SSE)

Interpret the structure of expressions

Arithmetic with Polynomials and Rational Expressions (A-APR)

Perform arithmetic operations on polynomials

Creating Equations (A-CED)

Create equations that describe numbers or relationships

Reasoning with Equations and Inequalities (A-REI)

Understand solving equations as a process of reasoning and explain the reasoning

Solve equations and inequalities in one variable

Represent and solve equations and inequalities graphically

Functions

Interpreting Functions (F-IF)

Understand the concept of a function and use function notation

Interpret functions that arise in applications in terms of the context

Building Functions (F-BF)

Linear, Quadratic, and Exponential Models (F-LE)

Statistics and Probability

Interpreting categorical and quantitative data (S-ID)

Interpret linear models

Modeling

• Specific modeling domains, clusters, and standards, indicated by a star symbol

Fluency Recommendations The PARCC Model Content Frameworks recommend the following fluencies for Algebra I students:

A/G Algebra I students become fluent in solving characteristic problems involving the analytic geometry of lines, such as

writing down the equation of a line given a point and a slope. Such fluency can support them in solving less routine

mathematical problems involving linearity, as well as in modeling linear phenomena (including modeling using

systems of linear inequalities in two variables).

A-APR.A.1 Fluency in adding, subtracting, and multiplying polynomials supports students throughout their work in algebra, as

well as in their symbolic work with functions. Manipulation can be more mindful when it is fluent.

A-SSE.A.1b Fluency in transforming expressions and chunking (seeing parts of an expression as a single object) is essential in

factoring, completing the square, and other mindful algebraic calculations.



22

Algebra I Year 1 of 2 Checklist

F Fluency Recommendations * Major Emphases Standard

Modeling Standards



23

Algebra I Year 2 of 2 Overview AL01RXX2 Second part in a TWO-PART SEQUENCE

Number and Quantity


Quantities (N-Q)

Algebra











Functions









Modeling













24

Algebra I Year 2 of 2 Checklist


Modeling Standards



25

Algebra I Overview AL01R

Number and Quantity


Quantities (N-Q)

Algebra











Functions









Modeling













26

Algebra I Checklist


Modeling Standards



27

Survey of Geometry Overview AG01G

Survey of Geometry combines the study of algebra topics with introductory geometry topics.

The first semester includes principle Algebra topics that will prepare students to retake the

Algebra I examination, and the second semester includes elemental geometry topics that will

prepare students for Geometry next year.

Geometry (7.G)

• Draw, construct and describe geometrical figures and describe the relationships

between them.

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

area, and volume.

Geometry (8.G)

• Understand congruence and similarity using physical models, transparencies, or

geometry software.

• Understand and apply the Pythagorean Theorem.

• Solve real-world and mathematical problems involving volume of cylinders,

cones and spheres.



28

Survey of Geometry Checklist




29

Geometry Overview GE01R

Geometry

Congruence (G-CO)

Understand congruence in terms of rigid motions

Prove geometric theorems

Similarity, Right Triangles, and Trigonometry (G-SRT)

Understand similarity in terms of similarity transformations

Prove theorems using similarity

Define trigonometric ratios and solve problems involving right triangles

Circles (G-C)

Expressing Geometric Properties with Equations (G-GPE)

Use coordinates to prove simple geometric theorems algebraically

Geometric Measurement and Dimensions (G-GMD)

Modeling with Geometry (G-GMD)

Apply geometric concepts in modeling situations

Modeling


Recommended Fluencies for Geometry

Triangle congruence and similarity criteria.

Using coordinates to establish geometric results.

Calculating length and angle measures.

Using geometric representations as a modeling tool.

Using construction tools, physical and computational to draft models of geometric

phenomenon.



30

Geometry Checklist

* Major Emphases Cluster

ff Additional Fluency Suggestion Modeling Standards



31

Algebra II Overview AT02R

Number and Quantity

• The Real Number System (N-RN)

Extend the properties of exponents to rational exponents

• Quantities (N-Q)

• The Complex Number System (N-CN)

Algebra

• Seeing Structure in Expressions (A-SSE)


Write expressions in equivalent forms to solve problems

• Arithmetic with Polynomials and Rational Expressions (A-APR)

Understand the relationship between zeros and factors of polynomials

• Creating Equations (A-CED)

• Reasoning with Equations and Inequalities (A-REI)



• Expressing Geometric Properties with Equations (G-GPE) *

Functions

• Interpreting Functions (F-IF)


• Building Functions (F-BF)

Build a function that models a relationship between two quantities

• Linear, Quadratic, and Exponential Models (F-LE)

• Trigonometric Functions (F-TF)


• Interpreting categorical and quantitative data (S-ID)

• Making Inferences and Justifying Conclusions (S-IC)

Make inferences and justify conclusions from sample surveys, experiments and

observational studies

• Conditional Probability and the Rules of Probability (S-CP)

Recommended Fluencies for Algebra II

Divide polynomials with remainder by inspection in simple cases.

See structure in expressions and use this structure to rewrite expressions (e.g., factoring, grouping).

Translate between recursive definitions and closed forms for problems involving sequences and series.



32

Algebra II Checklist

Checklist continued on next page



33

Algebra II Checklist Continued

* Major Emphases Cluster

ff Additional Fluency Suggestion Modeling Standards



34

PreCalculus & Advanced Topics Overview PC03G Number and Quantity

The Complex Number System (N-CN)

Perform arithmetic operations with complex numbers.

Represent complex numbers and their operations on the complex plane.

Use complex numbers in polynomial identities and equations.

Vector Quantities and Matrices (N-VM)

Represent and model with vector quantities.

Perform operations on vectors.

Perform operations on matrices and use matrices in applications.

Algebra


Use polynomial identities to solve problems.

Rewrite rational expressions.


Solve systems of equations.

Functions


Analyze functions using different representations.


Build a function that models a relationship between two quantities.

Build new functions from existing functions.

Trigonometric Functions (F-TF)

Extend the domain of trigonometric functions using the unit circle.

Model periodic phenomena with trigonometric functions.

Prove and apply trigonometric identities.

Geometry

Congruence (G-CO)

Experiment with transformations in the plane.

Understand and apply theorems about circles.

Expressing Geometric Properties with Equations (G-GPE)

Translate between the geometric description and the equation for a conic section.

Geometric Measurement and Dimension (G-GMD)

Explain volume formulas and use them to solve problems.

Similarity, Right Triangles, and Trigonometry (G-SRT)

Apply trigonometry to general triangles.


Conditional Probability and the Rules of Probability (S-CP)

Use the rules of probability to compute probabilities of compound events in a uniform

probability model.

Using Probability to Make Decisions (S-MD)

Calculate expected values and use them to solve problems.

Use probability to evaluate outcomes of decisions.



35

PreCalculus & Advanced Topics Checklist

Checklist continued on next page



36

PreCalculus & Advanced Topics Checklist Continued

Mathematics Department Scope and Sequence€¦ · Mathematics Department Scope and Sequence Grades...

Documents

Transcript of Mathematics Department Scope and Sequence€¦ · Mathematics Department Scope and Sequence Grades...