1. Develop understanding of addition, subtraction, and strategies for addition and subtraction within 20.
2. Develop understanding of whole number relationships and place value, including grouping in tens and ones.
3. Develop understanding of linear measurement and measuring lengths as iterating length units.
4. Reason about attributes of, and compose and decompose geometric shapes.

Students develop strategies for adding and subtracting whole numbers based on their prior work with small numbers. They use a variety of models, including discrete objects and length-based models (e.g., cubes connected to form lengths), to model add-to, take-from, put-together, take-apart, and compare situations to develop meaning for the operations of addition and subtraction, and to develop strategies to solve arithmetic problems with these operations. Students understand connections between counting and addition and subtraction (e.g., adding two is the same as counting on two). They use properties of addition to add whole numbers and to create and use increasingly sophisticated strategies based on these properties (e.g., “making tens”) to solve addition and subtraction problems within 20. By comparing a variety of solution strategies, children build their understanding of the relationship between addition and subtraction.

(2) Students develop, discuss, and use efficient, accurate, and generalizable methods to add within 100 and subtract multiples of 10. They compare whole numbers (at least to 100) to develop understanding of and solve problems involving their relative sizes. They think of whole numbers between 10 and 100 in terms of tens and ones (especially recognizing the numbers 11 to 19 as composed of a ten and some ones). Through activities that build number sense, they understand the order of the counting numbers and their relative magnitudes.

(3) Students develop an understanding of the meaning and processes of measurement, including underlying concepts such as iterating (the mental activity of building up the length of an object with equal-sized units) and the transitivity principle for indirect measurement.

(4) Students compose and decompose plane or solid figures (e.g., put two triangles together to make a quadrilateral) and build understanding of part-whole relationships as well as the properties of the original and composite shapes. As they combine shapes, they recognize them from different perspectives and orientations, describe their geometric attributes, and determine how they are alike and different, to develop the background for measurement and for initial understandings of properties such as congruence and symmetry.

Grade 1 Math Lessons

Number & Operations in Base Ten

1.NBT.1 Counting

1.NBT.1 Read-Write Numbers

1.NBT.2 Place Value

1.NBT.3 Compare Numbers

1.NBT.4 Add with Regrouping

1.NBT.5 Sums & Differences of Ten

Operations & Algebraic Thinking

1.OA.1 Word Problems

1.OA.3 Properties of Operations

1.OA.4 Subtraction Fact Families

Measurement & Data

1.MD.1 Compare & Order Objects

1.MD.2 Measure Length

1.MD.3 Tell Time

1.MD.4 Graphs & Charts

Geometry

1.G.1 Shapes & Attributes

1.G.2 Combining Shapes

1.G.3 Parts of a Whole

Grade 1 Language Arts Lessons

Language

L.1.1 Adjectives

L.1.2 End Punctuation

L.1.2 Capitalization

L.1.2 Commas

L.1.1 Conjunctions

L.1.1 Noun Usage

L.1.1 Pronoun Usage

L.1.1 Preposition Usage

L.1.1 Subject-Verb Agreement

L.1.1 Verb Tenses

L.1.2 Spelling

Reading

R.1.1 Key Details

R.1.2 Main Idea

R.1.3 Literary Elements

R.1.4 Figurative Language

R.1.3 Compare and Contrast

R.1.6 Point of View

1. extending understanding of base-ten notation
2. building fluency with addition and subtraction
3. using standard units of measure
4. describing and analyzing shapes.

Students understand the relationship among numbers, quantities, and place value in whole numbers up to 100.  They understand that fractions may refer to parts of a set and parts of a whole. Students use their understanding of addition to develop fluency with addition and subtraction within 100.  They model, represent, and interpret number relationships to create and solve problems involving addition and subtraction. Students describe and analyze shapes by examining their sides and investigate, describe, and reason about decomposing and combining shapes to make other shapes.  Students understand how to measure length, temperature, capacity, weight, and time in standard units.  They choose, combine, and apply effective strategies for solving problems in reasonable ways and justifying their reasoning.

Grade 2 Math Lessons

Number & Operations in Base Ten

2.NBT.1 Place Value

2.NBT.2 Skip Counting

2.NBT.3 Read-Write Numbers

2.NBT.4 Compare Numbers

2.NBT.5 Add-Subtract to 100

2.NBT.7 Add-Subtract to 1,000

2.NBT.8 Add-Subtract 10 & 100

2.NBT.9 Properties of Addition

Operations & Algebraic Thinking

2.OA.1 Word Problems

2.OA.2 Add-Subtract to 20

2.OA.3 Odds and Evens

2.OA.4 Arrays

Measurement & Data

2.MD.1 Measure Length

2.MD.3 Estimate Length

2.MD.4 Measure Difference

2.MD.7 Tell Time

2.MD.8 Money

Geometry

2.G.1 Shapes

2.G.2 Introduction to Area

2.G.3 Parts of a Whole

Grade 2 Language Arts Lessons

Language

L.2.1 Adjectives &Adverbs

L.2.1 Irregular Verbs

L.2.1 Noun Usage

L.2.1 Pronoun Usage

L.2.1 Sentence Structure

L.2.2 Capitalization

L.2.2 Spelling

L.2.4 Affixes

L.2.4 Words in Context

Reading

R.2.1 Key Details

R.2.2 Main Idea

R.2.3 Characterization

R.2.4 Poetic Structure

R.2.5 Story Structure

R.2.7 Author’s Purpose

1. Develop understanding of multiplication and division and strategies for multiplication and division within 100
2. Develop understanding of fractions, especially unit fractions
3. Develop understanding of the structure of rectangular arrays and of area
4. Describe and analyze two-dimensional shapes

Students understand the relationships among numbers, quantities, and place value in whole numbers up to 1,000.  They understand the relationship among whole numbers, simple fractions, and decimals.  Students solve problems involving addition and subtraction and develop an understanding of the meanings of multiplication and division of whole numbers through activities and problems involving equal-sized groups, arrays, and area models.  They solve simple problems involving multiplication and division.  Students select appropriate symbols, operations, and properties to represent, describe, simplify, and solve simple number and functional relationships. Students describe, analyze, and compare properties of two-dimensional shapes. They compare and classify shapes by their sides and angles, and connect these with definitions of shapes.  Students choose and use appropriate units and measurement tools for length, capacity, weight, temperature, time and money.  They choose, combine, and apply effective strategies for solving problems in reasonable ways, justifying their reasoning, and determine when a solution is complete and reasonable and move beyond a particular problem by generalizing to other situations.

Grade 3 Math Lessons

Number & Operations in Base Ten

3.NBT.1 Estimation & Rounding

3.NBT.2 Add and Subtract

3.NBT.3 Multiply by Tens

Number and Operations-Fractions

3.NF.1 Represent Fractions

3.NF.2 Number Line

3.NF.3 Compare & Order Fractions

3.NF.3 Equivalent Fractions

Operations & Algebraic Thinking

3.OA.3 Model Multiplication-Division

3.OA.4 Number Sentences

3.OA.8 Represent Word Problems

3.OA.8 Solve Word Problems

3.OA.9 Patterns

Measurement & Data

3.MD.1 Elapsed Time

3.MD.2 Weight & Capacity

3.MD.3 Graphs and Charts

3.MD.4 Line Plots

3.MD.5 Area and Perimeter

Geometry

3.G.1 Classify Shapes

3.G.2 Parts of a Whole

Grade 3 Language Arts Lessons

Language

L.3.1 Adjectives &Adverbs

L.3.1 Conjunctions

L.3.1 Noun Usage

L.3.1 Pronoun Usage

L.3.1 Sentence Structure

L.3.1 Verb Tenses

L.3.2 Capitalization

L.3.2 Punctuation

L.3.2 Spelling

Reading

R.3.1 Key Details

R.3.2 Main Idea

R.3.3 Sequence

R.3.4 Figurative Language

R.3.4 Words In Context

R.3.6 Point of View

R.3.9 Compare and Contrast

1. Develop understanding and fluency with multi-digit multiplication, and develop understanding of dividing to find quotients involving multi-digit dividends
2. Develop an understanding of fraction equivalence, addition and subtraction of fractions with like denominators, and multiplication of fractions by whole numbers
3. Understand that geometric figures can be analyzed and classified based on their properties, such as having parallel sides, perpendicular sides, particular angle measures, and symmetry.

Students generalize their understanding of place value to 1,000,000, understanding the relative sizes of numbers in each place. They understand decimals to two decimal places and how whole number and decimals relate to simple fractions. Students solve problems involving addition, subtraction, multiplication, and division of whole numbers, as well as solve simple fraction and decimal problems. They use and interpret variables, mathematical symbols, and properties to write and simplify numerical expressions and sentences. Students describe, analyze, compare, and classify two-dimensional shapes. Through building, drawing, and analyzing two-dimensional shapes, students deepen their understanding of properties of two-dimensional objects and the use of them to solve problems involving symmetry. Students understand perimeter and area, as well as measuring volume, capacity, time, and money. They represent data on a number line and in frequency tables, interpret data graphs to answer questions, and show outcomes for simple probability situations.

Grade 4 Math Lessons

Number & Operations in Base Ten

4.NBT.1 Place Value

4.NBT.2 Compare & Order

4.NBT.2 Read-Write Numbers

4.NBT.3 Estimation & Rounding

4.NBT.4 Add-Subtract Multi-Digits

4.NBT.5 Multiply Multi-Digits

4.NBT.6 Divide Multi-Digits

Number and Operations-Fractions

4.NF.1 Equivalent Fractions

4.NF.2 Compare Fractions

4.NF.3 Add-Subtract Fractions

4.NF.4 Multiply Fractions

Operations & Algebraic Thinking

4.OA.1 Number Sentences

4.OA.2 Word Problems

4.OA.3 Estimation & Rounding

4.OA.4 Factor Pairs

4.OA.5 Patterns

Measurement & Data

4.MD.1 Conversions

4.MD.2 Elapsed Time

4.MD.2 Money

4.MD.2 Volume & Mass

4.MD.3 Area & Perimeter

4.MD.4 Line Plots

4.MD.5 Angles

Geometry

4.G.1 2D Lines & Angles

4.G.2 Classify Shapes

4.G.3 Symmetry

Grade 4 Language Arts Lessons

Language

L.4.1 Adjectives

L.4.1 Pronoun Usage

L.4.1 Sentence Structure

L.4.1 Verb Tenses

L.4.2 Conjunctions

L.4.2 Capitalization

L.4.2 Punctuation

L.4.2 Spelling

Reading

R.4.1 Inferences

R.4.1 Key Details

R.4.2 Main Idea

R.4.2 Summarization

R.4.3 Literary Elements

R.4.6 Point of View

R.4.8 Supporting Details

1. Develop fluency with addition and subtraction of fractions, and developing understanding of the multiplication of fractions and of division of fractions in limited cases (unit fractions divided by whole numbers and whole numbers divided by unit fractions)
2. Extend division to 2-digit divisors, integrating decimal fractions into the place value system and develop understanding of operations with decimals to hundredths, and develop fluency with whole number and decimal operations
3. Develop understanding of volume.

Students solve problems involving multiplication and division of whole numbers and solve problems involving addition, subtraction, and simple multiplication and division of fractions and decimals. They understand the relationship among decimals, fractions, and percents and they understand the relative magnitudes of numbers. Students use variables in simple expressions, compute the value of an expression for specific values of the variable, and plot and interpret the results. They use two-dimensional coordinate grids to represent points and graph lines. Students identify, describe, and classify the properties of plane and solid geometric shapes and the relationship between them. They recognize volume as an attribute of three-dimensional space, aw well as measure weight, temperature, time and money. Students collect, display, analyze, compare and interpret data sets. Students choose, combine, and apply effective strategies for solving problems in reasonable ways and justifying their reasoning. They determine when a solution is complete and reasonable and move beyond a particular problem by generalizing to other situations.

Grade 5 Math Lessons

Number & Operations in Base Ten

5.NBT.1 Place Value

5.NBT.2 Exponents

5.NBT.3 Compare Decimals

5.NBT.3 Expanded Form

5.NBT.3 Read-Write Decimals

5.NBT.5 Multiply Multi-Digits

5.NBT.6 Divide Multi-Digits

5.NBT.7 Model Decimals

Number and Operations-Fractions

5.NF.1 Add-Subtract Fractions

5.NF.2 Model Fractions

5.NF.3 Divide Fractions

5.NF.4 Multiply Fractions

Operations & Algebraic Thinking

5.OA.1 Substitution

5.OA.2 Expressions

5.OA.3 Patterns

Measurement & Data

5.MD.1 Conversions

5.MD.2 Line Plots

5.MD.4 Volume

Geometry

5.G.1 Coordinate Geometry

5.G.3 2D Figures

Grade 5 Language Arts Lessons

Language

L.5.1 Conjunctions

L.5.1 Verb Tenses

L.5.2 Punctuation

L.5.2 Spelling

L.5.3 Sentence Structure

L.5.4 Affixes

Reading

R.5.1 Inferences

R.5.2 Main Idea

R.5.2 Summarization

R.5.3 Compare & Contrast

R.5.4 Figurative Language

R.5.6 Point of View

R.5.8 Supporting Details

1. Connecting ratio and rate to whole number multiplication and division and using concepts of ratio and rate to solve problems
2. Completing understanding of division of fractions and extending the notion of number to the system of rational numbers, which includes negative numbers
3. Writing, interpreting, and using expressions and equations
4. Developing understanding of statistical thinking

Students perform operations on positive and negative integers, decimals, fractions, and mixed numbers. They find multiples and factors and solve problems involving ratios, proportions, and percentages. They construct and evaluate algebraic expressions, solve simple linear equations, and graph and interpret their result.  They identify, describe, and classify the properties of plane and solid geometric shapes and the relationships between them, and investigate geometric relationships algebraically.  Students extend their knowledge of plane and solid shapes to measurement and use this understanding to solve problems.  They solve problems involving time and money and choose appropriate units in other areas. Students analyze data sets statistically and determine theoretical and experimental probabilities, using these probabilities to make predictions. Throughout the course, students use strategies, skill and concepts in finding and communicating solutions to problems and move beyond a particular problem by generalizing to other situations.

Grade 6 Math Lessons

The Number System

6.NS.1 Divide Fractions

6.NS.2 Divide Multi-Digits

6.NS.3 Add-Subtract Decimals

6.NS.3 Multiply-Divide Decimals

6.NS.4 Greatest Common Factors

6.NS.6 Number Lines

Ratios & Proportional Relationships

6.RP.1 Ratios

6.RP.2 Unit Rates

6.RP.3 Graph Rates

6.RP.3 Measurement Ratios

6.RP.3 Rates and Percents

Expressions & Equations

6.EE.1 Order of Operations

6.EE.2a Write Expressions

6.EE.2b Terms of Expressions

6.EE.2c Evaluate Expressions

6.EE.3 Properties of Operations

6.EE.4 Simplify Expressions

Geometry

6.G.1 Area of Composite Figures

6.G.2 Volume Fractional Edges

6.G.3 Polygons on Grids

6.G.4 Surface Area of Nets

Statistics and Probability

6.SP.1 Statistical Questions

6.SP.2 Box Plots

6.SP.3 Mean Absolute Deviation

6.SP.3 Measures of Center

6.SP.4 Histograms

6.SP.4 Line Plots

Grade 6 Language Arts Lessons

Language

L.6.1 Pronoun Forms

L.6.2 Capitalization

L.6.2 Parentheses and Dashes

L.6.2 SpellingL.6.4 Affixes

L.6.4 Words in Context

Reading

R.6.1 Inferences

R.6.1 Supporting Details

R.6.2 Main Idea

R.6.2 Summarization

R.6.3 Plot

R.6.4 Figurative Language

R.6.6 Author’s Purpose

1. Develop understanding of and apply proportional relationships;
2. Develop understanding of operations with rational numbers and work with expressions and linear equations;
3. Solve problems involving scale drawings and informal geometric constructions, and work with two- and three-dimensional shapes to solve problems involving area, surface area, and volume; and
4. Draw inferences about populations based on samples.

Students solve problems involving integers, fractions, decimals, ratios, percentages, scientific notation and square roots, converting between each of these forms as appropriate. They express quantitative relationships algebraically, using correct terminology, expressions, equations, inequalities, and graphs. They manipulate plane and solid geometric shapes and use similarity and congruence to solve problems. They analyze and compute measures of common geometric objects (including perimeter, area, and volume) and use these results to find measures of irregular objects. Students generate and analyze data sets, identifying relationships among variables within a data set.  They determine probabilities and use them to make predictions. Throughout the course, students use strategies, skill and concepts in finding and communicating solutions to problems and move beyond a particular problem by generalizing to other situations.

Grade 7 Math Lessons

The Number System

7.NS.1 Add-Subtract Signed Numbers

7.NS.2 Multiply-Divide Signed Numbers

7.NS.2a Fractions-Multiply

7.NS.2b Fractions-Divide

7.NS.2d Fraction-Decimal Conversions

7.NS.3 Operations-Real World

Ratios and Proportions

7.RP.1 Compute Unit Rate

7.RP.2b Identify Unit Rate

7.RP.2d Graph Rates

7.RP.3 Percent Increase

7.RP.3 Solving Proportions

Expressions & Equations

7.EE.1 Simplify Expressions

7.EE.2 Rewriting Expressions

7.EE.3 Real-Life Problems

7.EE.4 Solve-Graph Inequalities

Geometry

7.G.1 Scale Drawings

7.G.3 Plane Sections of 3D Figures

7.G.4 Circle Measurements

7.G.5 Complementary Angles

7.G.5 Transversals

7.G.6 Area-Volume Dimensions

Statistics and Probability

7.SP.1 Random Samples

7.SP.2 Multiple Random Samples

7.SP.3 Comparing Variabilities

7.SP.4 Comparing Box Plots

7.SP.4 Comparing Box Plots

7.SP.8 Compound Probability

Grade 7 Language Lessons

Language

L.7.1 Misplaced Modifiers

L.7.2 Capitalization

L.7.2 Spelling

L.7.3 Fragments and Run-Ons

L.7.4 Affixes

Reading Lessons

R.7.1 Supporting Details

R.7.2 Summarization

R.7.3 Literary Elements

R.7.3 Plot

R.7.4 Figurative Language

R.7.6 Author’s Purpose

R.7.8 Reasoning & Validity

1. Formulate and reason about expressions and equations, including modeling an association in bivariate data with a linear equation, and solving linear equations and systems of linear equations
2. Grasp the concept of a function and using functions to describe quantitative relationships
3. Analyze two- and three-dimensional space and figures using distance, angle, similarity, and congruence, and understand and apply the Pythagorean Theorem

Students extend their knowledge of number sense to rational and irrational numbers and use and understand exponents, powers, and roots. They solve problems and make computations involving rational numbers, as well as problems involving ratios, proportions, and percentages. They solve linear equations and inequalities, and extend their previous knowledge of linear expressions to interpret and evaluate expressions with integer powers. They graph and interpret functions, understanding the concepts of slope and rate of change. They deepen their understanding of plane and solid geometric shapes and properties by construction shapes that meet given conditions, by identifying attributes of shapes, and by applying geometric concepts to solve problems. They apply scale factors to shapes and measurement of shapes, and use this understanding to solve problems.  Students generate and analyze data sets, identifying relationships among variables within a data set.  They determine probabilities and use them to make predictions. Throughout the course, students use strategies, skill and concepts in finding and communicating solutions to problems and move beyond a particular problem by generalizing to other situations.

Grade 8 Math Lessons

The Number System

8.NS.1 Compare and Order

8.NS.1 Rational-Irrational Numbers

8.NS.2 Compare Irrational Numbers

Functions

8.F.1 Functions and Relations

8.F.3 Linear-Nonlinear Graphs

8.F.4 Constructing Functions

Expressions & Equations

8.EE.1 Integer Exponents

8.EE.2 Square Roots

8.EE.3 Scientific Notation

8.EE.4 Scientific Notation Operations

8.EE.5 Graph Proportional Relationships

8.EE.6 Slope-Intercept Formula

Geometry

8.G.3 Dilations on Grids

8.G.2 Transformations on Grids

8.G.5 Transversals

8.G.7 Pythagorean Theorem

8.G.8 Pythagorean-Coordinates

8.G.9 Volumes

Statistics and Probability

8.SP.1 Patterns of Association

8.SP.3 Bivariate Data

8.SP.4 Two-Way Tables

Grade 8 Language Arts Lessons

Language

L.8.1 Active and Passive Voice

L.8.1 Verb Moods

L.8.2 Capitalization

L.8.2 Spelling

L.8.4 Affixes

Reading

R.8.1 Supporting Details

R.8.2 Main Idea

R.8.2 Summarization

R.8.3 Cause & Effect

R.8.3 Compare & Contrast

R.8.4 Figurative Language

R.8.8 Reasoning & Validity