State Standards - AdaptedMind

Created by graduates of Stanford, Berkeley, and Harvard.

State Standards for Arizona - Second Grade

First Grade

Second Grade

Number and Operations

1 Understand and apply numbers, ways of representing numbers, and the relationships among numbers and different number systems.

1.PO 1 Express whole numbers 0 to 1000, in groups of hundreds, tens and ones using and connecting multiple representations.

Place Value Through Hundreds

Place Value and Regrouping

Tens and Ones Places

1.PO 2 Count forward to 1000 and backward from 1000 by 1s, 10s, and 100s using different starting points.

Counting By Twos, Fives and Tens

Patterns and Counting By Twos, Fives and Tens

1.PO 3 Identify numbers which are 100 more or less than a given number to 900.

Comparison and Ordering, to Two Hundred

1.PO 4 Compare and order whole numbers through 1000 by applying the concept of place value.

Comparing Numbers up to One Thousand

Comparison and Ordering, to Two Hundred

1.PO 5 Count money to $1.00.

Nickels and Dimes

Counting Coins Including Quarters

Half Dollars and Dollars

1.PO 6 Sort whole numbers through 1000 into odd and even, and justify the sort.

Even and Odd Numbers

2 Understand and apply numerical operations and their relationship to one another.

2.PO 1 Solve contextual problems using multiple representations involving

2.PO 1.a addition and subtraction with one- and/or two-digit numbers,

Adding Below Twenty

Addition Below One Hundred

Two-Digit Addition

Two-Digit Addition and Subtraction Review

Two-Digit Addition With Carrying

Relating Addition and Subtraction

Addition and Inequalities

Subtraction Below One Hundred

Subtraction Below Fifty With Regrouping

Two-Digit Subtraction

Two-Digit Subtraction With Regrouping

Checking Subtraction With Addition

2.PO 1.b multiplication for 1s, 2s, 5s, and 10s, and

Adding Tens

Basic Multiplication

Counting to Multiply

Multiplying By Two, Five, or Ten

2.PO 1.c adding and subtracting money to $1.00.

2.PO 2 Demonstrate the ability to add and subtract whole numbers (to at least two digits) and decimals (in the context of money)

2.PO 2.a with up to three addends and

Adding Three Two-Digit Numbers

2.PO 2.b to $1.00.

2.PO 3 Demonstrate fluency of addition and subtraction facts.

2.PO 4 Apply and interpret the concept of addition and subtraction as inverse operations to solve problems.

Relating Addition and Subtraction

2.PO 5 Create and solve word problems based on addition and subtraction of two-digit numbers.

2.PO 6 Demonstrate the concept of multiplication for 1s, 2s, 5s, and 10s.

2.PO 7 Describe the effect of operations (addition and subtraction) on the size of whole numbers.

2.PO 8 Apply properties to solve addition/subtraction problems

2.PO 8.a identity property of addition/subtraction,

2.PO 8.b commutative property of addition, and

Properties of Addition

2.PO 8.c associative property of addition.

Properties of Addition

3 Use estimation strategies reasonably and fluently while integrating content from each of the other strands.

3.PO 1 Use estimation to determine if sums of two 2-digit numbers are more or less than 20, more or less than 50, or more or less than 100.

Rounding to the Nearest Ten

Rounding

Rounding and Addition

Rounding and Subtraction

Data Analysis, Probability, and Discrete Mathematics

1 Understand and apply data collection, organization, and representation to analyze and sort data.

1.PO 1 Collect, record, organize, and display data using pictographs, frequency tables, or single bar graphs.

1.PO 2 Formulate and answer questions by interpreting displays of data, including pictographs, frequency tables, or single bar graphs.

2 Understand and apply the basic concepts of probability.

3 Understand and demonstrate the systematic listing and counting of possible outcomes.

3.PO 1 List all possibilities in counting situations.

Counting By Twos, Fives and Tens

Patterns and Counting By Twos, Fives and Tens

3.PO 2 Solve a variety of problems based on the addition principle of counting.

Counting By Twos, Fives and Tens

Patterns and Counting By Twos, Fives and Tens

4 Understand and apply vertex-edge graphs.

4.PO 1 Color simple pictures or maps using the least number of colors and justify the coloring.

4.PO 2 Build vertex-edge graphs using concrete materials and explore simple properties of vertex-edge graphs

4.PO 2.a number of vertices and edges,

4.PO 2.b neighboring vertices, and

4.PO 2.c paths in a graph.

4.PO 3 Construct simple vertex-edge graphs from simple pictures or maps.

Patterns, Algebra, and Functions

1 Identify patterns and apply pattern recognition to reason mathematically while integrating content from each of the other strands.

1.PO 1 Recognize, describe, extend, create, and find missing terms in a numerical or symbolic pattern.

1.PO 2 Explain the rule for a given numerical or symbolic pattern and verify that the rule works.

2 Describe and model functions and their relationships.

2.PO 1 Describe a rule that represents a given relationship between two quantities using words or pictures.

3 Represent and analyze mathematical situations and structures using algebraic representations.

3.PO 1 Record equivalent forms of whole numbers to 1000 by constructing models and using numbers.

Place Value Below Ten Thousand

3.PO 2 Compare expressions using spoken words and the symbols =, ""is not equal to"", <, and >.

3.PO 3 Represent a word problem requiring addition or subtraction through 100 using an equation.

3.PO 4 Identify the value of an unknown number in an equation involving an addition or subtraction fact.

Rewriting Addition as Plus Ten

Checking Subtraction With Addition

Geometry and Measurement

1 Analyze the attributes and properties of 2- and 3- dimensional figures and develop mathematical arguments about their relationships.

1.PO 1 Describe and compare the attributes of polygons up to six sides using the terms side, vertex, point, and length.

2 Apply spatial reasoning to create transformations and use symmetry to analyze mathematical situations.

2.PO 1 Identify, with justification, whether a 2-dimensional figure has lines of symmetry.

4 Understand and apply appropriate units of measure, measurement techniques, and formulas to determine measurements.

4.PO 1 Tell time to the nearest minute using analog and digital clocks.

4.PO 2 Apply measurement skills to measure the attributes of an object (length, capacity, weight).

4.PO 3 Read temperatures on a thermometer using Fahrenheit and Celsius.

4.PO 4 Demonstrate unit conversions

4.PO 4.a 1 foot = 12 inches,

Unit Conversion

4.PO 4.b 1 quart = 4 cups,

4.PO 4.c 1 pound = 16 ounces,

4.PO 4.d 1 hour = 60 minutes,

4.PO 4.e 1 day = 24 hours,

4.PO 4.f 1 week = 7 days, and

4.PO 4.g 1 year = 12 months.

Structure and Logic

2 Evaluate situations, select problem-solving strategies, draw logical conclusions, develop and describe solutions, and recognize their applications.

2.PO 1 Identify the question(s) asked and any other questions that need to be answered in order to find a solution.

2.PO 2 Identify the given information that can be used to find a solution.

Comparison and Ordering, to Two Hundred

Relating Addition and Subtraction

Two-Digit Addition

Two-Digit Addition With Carrying

Two-Digit Subtraction

Two-Digit Subtraction With Regrouping

2.PO 3 Select from a variety of problem-solving strategies and use one or more strategies to arrive at a solution.

2.PO 4 Represent a problem situation using any combination of words, numbers, pictures, physical objects, or symbols.

Nickels and Dimes

Counting Coins Including Quarters

Half Dollars and Dollars

Number and Operations

1 Understand and apply numbers, ways of representing numbers, and the relationships among numbers and different number systems.

1.PO 1 Express whole numbers 0 to 1000, in groups of hundreds, tens and ones using and connecting multiple representations.

1.PO 2 Count forward to 1000 and backward from 1000 by 1s, 10s, and 100s using different starting points.

1.PO 3 Identify numbers which are 100 more or less than a given number to 900.

1.PO 4 Compare and order whole numbers through 1000 by applying the concept of place value.

1.PO 5 Count money to $1.00.

1.PO 6 Sort whole numbers through 1000 into odd and even, and justify the sort.

2 Understand and apply numerical operations and their relationship to one another.

2.PO 1 Solve contextual problems using multiple representations involving

2.PO 1.a addition and subtraction with one- and/or two-digit numbers,

2.PO 1.b multiplication for 1s, 2s, 5s, and 10s, and

2.PO 1.c adding and subtracting money to $1.00.

2.PO 2 Demonstrate the ability to add and subtract whole numbers (to at least two digits) and decimals (in the context of money)

2.PO 2.a with up to three addends and

2.PO 2.b to $1.00.

2.PO 3 Demonstrate fluency of addition and subtraction facts.

2.PO 4 Apply and interpret the concept of addition and subtraction as inverse operations to solve problems.

2.PO 5 Create and solve word problems based on addition and subtraction of two-digit numbers.

2.PO 6 Demonstrate the concept of multiplication for 1s, 2s, 5s, and 10s.

2.PO 7 Describe the effect of operations (addition and subtraction) on the size of whole numbers.

2.PO 8 Apply properties to solve addition/subtraction problems

2.PO 8.a identity property of addition/subtraction,

2.PO 8.b commutative property of addition, and

2.PO 8.c associative property of addition.

3 Use estimation strategies reasonably and fluently while integrating content from each of the other strands.

3.PO 1 Use estimation to determine if sums of two 2-digit numbers are more or less than 20, more or less than 50, or more or less than 100.

Data Analysis, Probability, and Discrete Mathematics

1 Understand and apply data collection, organization, and representation to analyze and sort data.

1.PO 1 Collect, record, organize, and display data using pictographs, frequency tables, or single bar graphs.

1.PO 2 Formulate and answer questions by interpreting displays of data, including pictographs, frequency tables, or single bar graphs.

2 Understand and apply the basic concepts of probability.

3 Understand and demonstrate the systematic listing and counting of possible outcomes.

3.PO 1 List all possibilities in counting situations.

3.PO 2 Solve a variety of problems based on the addition principle of counting.

4 Understand and apply vertex-edge graphs.

4.PO 1 Color simple pictures or maps using the least number of colors and justify the coloring.

4.PO 2 Build vertex-edge graphs using concrete materials and explore simple properties of vertex-edge graphs

4.PO 2.a number of vertices and edges,

4.PO 2.b neighboring vertices, and

4.PO 2.c paths in a graph.

4.PO 3 Construct simple vertex-edge graphs from simple pictures or maps.

Patterns, Algebra, and Functions

1 Identify patterns and apply pattern recognition to reason mathematically while integrating content from each of the other strands.

1.PO 1 Recognize, describe, extend, create, and find missing terms in a numerical or symbolic pattern.

1.PO 2 Explain the rule for a given numerical or symbolic pattern and verify that the rule works.

2 Describe and model functions and their relationships.

2.PO 1 Describe a rule that represents a given relationship between two quantities using words or pictures.

3 Represent and analyze mathematical situations and structures using algebraic representations.

3.PO 1 Record equivalent forms of whole numbers to 1000 by constructing models and using numbers.

3.PO 2 Compare expressions using spoken words and the symbols =, ""is not equal to"", <, and >.

3.PO 3 Represent a word problem requiring addition or subtraction through 100 using an equation.

3.PO 4 Identify the value of an unknown number in an equation involving an addition or subtraction fact.

Geometry and Measurement

1 Analyze the attributes and properties of 2- and 3- dimensional figures and develop mathematical arguments about their relationships.

1.PO 1 Describe and compare the attributes of polygons up to six sides using the terms side, vertex, point, and length.

2 Apply spatial reasoning to create transformations and use symmetry to analyze mathematical situations.

2.PO 1 Identify, with justification, whether a 2-dimensional figure has lines of symmetry.

4 Understand and apply appropriate units of measure, measurement techniques, and formulas to determine measurements.

4.PO 1 Tell time to the nearest minute using analog and digital clocks.

4.PO 2 Apply measurement skills to measure the attributes of an object (length, capacity, weight).

4.PO 3 Read temperatures on a thermometer using Fahrenheit and Celsius.

4.PO 4 Demonstrate unit conversions

4.PO 4.a 1 foot = 12 inches,

4.PO 4.b 1 quart = 4 cups,

4.PO 4.c 1 pound = 16 ounces,

4.PO 4.d 1 hour = 60 minutes,

4.PO 4.e 1 day = 24 hours,

4.PO 4.f 1 week = 7 days, and

4.PO 4.g 1 year = 12 months.

Structure and Logic

2 Evaluate situations, select problem-solving strategies, draw logical conclusions, develop and describe solutions, and recognize their applications.

2.PO 1 Identify the question(s) asked and any other questions that need to be answered in order to find a solution.

2.PO 2 Identify the given information that can be used to find a solution.

2.PO 3 Select from a variety of problem-solving strategies and use one or more strategies to arrive at a solution.

2.PO 4 Represent a problem situation using any combination of words, numbers, pictures, physical objects, or symbols.

2.PO 5 Explain and clarify mathematical thinking.

2.PO 6 Determine whether a solution is reasonable.