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**PA CORE STANDARDS
OVERVIEW – MATH**

__Content Standards__

**Kindergarten**

Counting and Cardinality

- Know number names and write and recite the count sequence
- Apply one-to-one correspondence to count the number of objects
- Apply the concept of magnitude to compare numbers and quantities

Numbers & Operations in Base Ten

- Use place value to compose an decompose numbers within 19

Operations and Algebraic Thinking

- Extend the concepts of putting together and taking apart to add and subtract within 10

Geometry

- Identify and describe 2- and 3- dimensional shapes
- Analyze, compare, create, and compose 2- and 3- dimensional shapes

Measurement and Data

- Describe and compare attributes of length, area, weight, and capacity of everyday objects
- Classify objects and count the number of objects in each category

**Grade 1**

Numbers & Operations in Base Ten

- Extend the counting sequence to read and write numerals to represent objects
- Use place-value concepts to represent amounts of tens and ones and to compare 2-digit numbers
- Use place-value concepts and properties of operations to add and subtract within 100

Operations and Algebraic Thinking

- Represent and solve problems involving addition and subtraction within 20
- Understand and apply properties and the relationship between addition and subtraction

Geometry

- Compose and distinguish between 2- and 3- dimensional shapes based on their attributes
- Use the understanding of fractions to partition shapes into halves and quarters

Measurement and Data

- Order lengths and measure them both indirectly and by repeating length units
- Tell and write time to the nearest half hour using both analog and digital clocks
- Represent and interpret data using tables/charts

**Grade 2**

Numbers & Operations in Base Ten

- Use place-value concepts to represent amounts of tens and ones and to compare three digit numbers
- Use place-value concepts to read, write, and skip count to 1000
- Use place-value understanding and properties of operations to add and subtract within 1000

Operations and Algebraic Thinking

- Represent and solve problems involving addition and subtraction within 100
- Understand and apply properties of operations and the relationship between addition and subtraction

Geometry

- Analyze and draw 2- and 3- dimensional shapes having specified attributes
- Use the understanding of fractions to partition shapes into halves, quarters, and thirds

Measurements and Data

- Measure and estimate lengths in standard units using appropriate tools
- Tell and write time to the nearest five minutes using both analog and digital clocks
- Solve problems and make change using coins and paper currency with appropriate symbols
- Represent and interpret data using line plots, picture graphs, and bar graphs
- Extend the concepts of addition and subtraction to problems involving length

**Grade 3**

Numbers & Operations in Base Ten

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

Number & Operations – Fractions

- Explore and develop an understanding of fractions as numbers

Operations and Algebraic Thinking

- Represent and solve problems involving multiplication and division
- Understand properties of multiplication and the relationship between multiplication and division
- Demonstrate multiplication and division fluency
- Solve problems involving the four operations, and identify and explain patterns in arithmetic

Geometry

- Identify, compare, and classify shapes and their attributes
- Use the understanding of fractions to partition shapes into parts with equal areas and express the area of each part as a unit fraction of the whole

Measurement and Data

- Solve problems involving measurement and estimation of temperature, liquid volume, mass, and length
- Tell and write time to the nearest minute and solve problems by calculating time intervals
- Solve problems and make change involving money using a combination of coins and bills
- Represent and interpret data using tally charts, tables, pictographs, line plots, and bar graphs
- Determine the area of a rectangle and apply the concept to multiplication and to addition
- Solve problems involving perimeters of polygons and distinguish between linear and area measures

**Grade 4**

Numbers & Operations in Base Ten

- Apply place-value concepts to show an understanding of multi-digit whole numbers
- Use place-value understanding and properties of operations to perform multi-digit arithmetic

Numbers & Operations – Fractions

- Extend the understanding of fractions to show equivalence and ordering
- Build fractions from unit fractions by applying and extending previous understanding of operations of whole numbers
- Connect decimal notation to fractions, and compare decimal fractions9base 10 denominator, e.g., 19/100)

Operations and Algebraic Thinking

- Represent and solve problems involving the four operations
- Develop and/or apply number theory concepts to find factors and multiples
- Generate and analyze patterns using one rule

Geometry

- Draw lines and angles and identify these in 2-dimensional figures
- Classify 2-dimensional figures by properties of their lines and angles
- Recognize symmetric shapes and draw lines of symmetry

Measurement and Data

- Solve problems involving measurement and conversions from a larger unit to a smaller unit
- Translate information from one type of data display to another
- Represent and interpret data involving fractions using information provided in a line plot
- Measure angles and use properties of adjacent angles to solve problems

- Make sense of problems and persevere in solving them
- Reason abstractly and quantitatively
- Construct viable arguments and critique the reasoning of others
- Model with mathematics
- Use appropriate tools strategically
- Attend to precision
- Look for and make use of structure
- Look for and express regularity in repeated reasoning

- Habits of Mind of a Productive Mathematical Thinker - # 1 and #6 (These are overarching goals that include the other six practices.)
- Reasoning and Explaining - #2 and #3
- Modeling and Using Tools - #4 and #5
- Seeing Structure and Generalizing #7 and #8

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