Math

Counting and Cardinality

Students will

• Demonstrate understanding that number words refer to quantity

• Count with understanding to 20

• Solve problems by matching sets and comparing amounts to 10

Measurement and Data

Students will

• Demonstrate the ability to sort, classify and order objects by size, number, shape and other properties
• Apply vocabulary such as “above”, “below” and “next to” to discuss position of objects
• Identify objects as “the same”,  “different” or “more or less” on the basis of attributes

Counting and Cardinality

Students will

• Count by ones and tens up to 100
• Count forwards and backwards from a given number (other than 1) in a known sequence up to 20
• Understand and demonstrate one to one correspondence
• Identify the number of objects in one group as greater than, less than, or equal to the number of objects in another group within sets of 20

Operations and Algebraic Thinking

Students will

• Fluently add and subtract numbers 5 or less
• Solve addition problems by using words, pictures, and/or numbers with sums of up to 10

Number and Operations in Base Ten

Students will

• Understand that 10 can be thought of as a bundle of ones where the unit equals 10

Measurement and Data

Students will

• Identify and name the value of pennies, nickels, dimes and quarters
• Tell and write time to the hour

Geometry

Students will

• Identify and describe shapes

Operations and Algebraic Thinking

Students will

• Understand addition is commutative and demonstrate with turn-around facts
• Understand the inverse relationship between addition and subtraction
• Apply knowledge of addition and subtraction facts to solve word problems
• Demonstrate fluency in addition and subtraction within 20

Number and Operations in Base Ten

Students will

• Read and write numbers up to 120
• Apply knowledge of counting to 120 by completing any given number sequence
• Use place value to compare and order two-digit numbers

Measurement and Data

Students will

• Represent and interpret data
• Tell and write time in quarter- and half-hours using analog and digital clocks
• Add and subtract coins (quarters, dimes, nickels and pennies)
• Calculate and express the value of a combination of coins (quarters, dimes, nickels and pennies)

Geometry

Students will

• Identify and describe plane and solid figures including circles, triangles, squares, rectangles, spheres, cylinders, rectangular prisms, pyramids, cones and cubes

Operations and Algebraic Thinking

Students will

• Demonstrate fluency in addition and subtraction facts within 20
• Solve problems using words, sentences, pictures and numbers to explain the steps used to solve the problem

Number and Operations in Base Ten

Students will

• Count by 1s, 2s, 5s, 10s, 25s and 100s past 1,000 and back by 1s from any number less than 1,000 with and without number grids, number lines and calculators
• Use place value to compare and order 3-digit numbers
• Read and write numbers up to the 1,000s place
• Compute sums and differences of one- and two-digit numbers using strategies based on place value

Measurement and Data

Students will

• Measure and estimate in standard units to the nearest whole unit
• Represent and interpret data
• Tell and write time from analog and digital clocks to the minute, using a.m. and p.m.
• Solve problems using dollar bills, quarters, dimes, nickels and pennies

Geometry

Students will

• Divide a whole into equal sized parts and describe with appropriate vocabulary
• Recognize shapes and their attributes

Operations and Algebraic Thinking

Students will

• Fluently multiply within 100
• Represent and solve problems involving multiplication and division within 100
• Solve multi-digit arithmetic problems involving the four operations (addition, subtraction, multiplication and division)
• Determine and describe a pattern (sequence) or the unknown number and solve equations that have an unknown number or operation
• Solve open-ended response problems

Number and Operations in Base Ten

Students will

• Read, write, recognize and model numbers and their place values up to 100,000

Number and Operations – Fractions

Students will

• Develop understanding of fractions as numbers

Measurement and Data

Students will

• Solve problems involving measurement
• Represent and interpret data

Geometry

Students will

• Understand and recognize geometric measurement concepts in area and perimeter
• Describe, analyze, compare and classify two- and three-dimensional  shapes by properties

Operations and Algebraic Thinking

Students will

• Use the four operations with whole numbers to solve problems
• Gain familiarity with factors and multiples
• Generate and analyze patterns

Number and Operations in Base Ten

Students will

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

Number and Operations – Fractions

Students will

• Extend understanding of fraction equivalence and ordering
• Build fractions from unit fractions by applying and extending previous understanding of operations on whole numbers
• Understand decimal notation for fractions and compare fractions and decimals

Measurement and Data

Students will

• Solve problems involving measurement and conversions of measurement

• Represent and interpret data
• Classify events/describe chances of events using words or numbers

Geometry

Students will

• Understand, draw and identify concepts of angles and measure angles
• Classify shapes by properties of lines and angles

Operations and Algebraic Thinking

Students will

• Write and interpret numerical expressions
• Analyze patterns and relationships
• Solve for the unknown in an equation with a single operation
• Choose an appropriate strategy to solve a problem
• Write an explanation using mathematical and strategic knowledge

Number and Operations in Base Ten

Students will

• Understand the place value system
• Perform operations with multi-digit whole numbers and with decimals to hundredths

Number and Operations – Fractions

Students will

• Use equivalent fractions as a strategy to add and subtract fractions
• Apply and extend previous understanding of addition, subtraction, multiplication and division to add, subtract, multiply and divide fractions

Measurement and Data

Students will

• Convert like measurement units within a given measurement system
• Represent and interpret data
• Understand concepts of volume and relate volume to multiplication and addition

Geometry

Students will

• Graph points on the coordinate plane to solve real-world and mathematical problems
• Classify two-dimensional figures into categories based on their properties

Ratios and Proportional Relationships

Students will

• Understand ratio concepts and use ratio reasoning to solve problems

The Number System

Students will

• Convert and compare fractions (including improper fractions and mixed numbers), decimals and percents within 100%

• Solve problems and number sentences with integers
• Use ordered pairs of numbers to name, locate and plot points in all four quadrants of a coordinate grid

Expressions and Equations

Students will

• Determine a rule of a pattern or table and represent it using a variable expression
• Write and solve one variable equation
• Write and graph inequalities
• Justify and explain the steps used to solve a problem

Geometry

Students will

• Determine perimeter, area and volume
• Identify properties of single figures and determine the relationship between and among multiple figures

Statistics and Probability

Students will

• Read and interpret data in multiple representations
• Determine and apply the probabilities of events

Ratios and Proportional Relationships

Students will

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

The Number System

Students will

• Apply and extend previous understanding of numerical operations to adding, subtracting, multiplying and dividing rational numbers

Expressions and Equations

Students will

• Use properties of operations to generate equivalent expressions
• Solve real-life and mathematical problems using numerical and algebraic expressions, linear equations and linear inequalities
• Justify and explain the steps used to solve a problem

Geometry

Students will

• Draw and describe geometrical figures and describe the relationships between them including coordinate geometry
• Solve real-life and mathematical problems involving angle measures, perimeter, area, surface area and volume

Statistics and Probability

Students will

• Create, read, interpret and make predictions from data represented in graphs

Expressions and Equations

Students will

• Fluently compute with real numbers
• Solve linear equations and inequalities
• Use and apply proportional reasoning
• Compute and evaluate expressions
• Solve systems linear equations
• Perform operations with polynomials
• Solve and factor polynomials
• Solve and perform operations with radical expressions and equations
• Solve and perform operations with rational expressions and equations
• Apply exponent properties
• Justify and explain the steps used to solve a problem

Functions

Students will

• Graph and write linear equations and inequalities

Geometry

Students will

• Solve real-life and mathematical problems involving angle measure, area, surface area and volume
• Understand and apply formulas and theorems

Mathematical Practice

Students will

• Apply the concept of deductive and inductive reasoning
• Recognize and/or apply properties of polygons
• Recognize and apply relationships within and among geometric figures

Congruence

Students will

• Recognize and/or apply properties of triangles and their congruencies

Expressing Geometric Properties with Equations

Students will

• Determine the perimeter, area, surface area and volume of two-dimensional and three-dimensional figures

Similarity, Right Triangles and Trigonometry

Students will

• Apply the properties of similarity
• Determine unknown lengths or angle measures in right triangles

Circles

Students will

• Apply the definition and properties of circles

Modeling with Geometry

Students will

• Apply probability to geometric situations