Standard Number

Count forward by ones beginning from any number less than 100.

Read numbers from 0 – 20 and represent a number of objects 0 – 20 with a written numeral.

Understand the relationship between number and quantity. Connect counting to cardinality by demonstrating an understanding that: a. the last number said tells the number of objects in the set (cardinality); b. the number of objects is the same regardless of their arrangement or the order in which they are counted (conservation of number); c. each successive number name refers to a quantity that is one more and each previous number name refers to a quantity that is one less.

Count a given number of objects from 1 – 20 and connect this sequence in a one-to one manner.

Extend the number sequence to: a. count forward by ones to 120 starting at any number; b. count by fives and tens to 100, starting at any number;

read, write and represent numbers to 100 using concrete models, standard form, and equations in expanded form;

Add through 99 using concrete models, drawings, and strategies based on place value to: a. add a two-digit number and a one-digit number, understanding that sometimes it is necessary to compose a ten (regroup); b. add a two-digit number and a multiple of 10.

Demonstrate: a. addition and subtraction through 20; b. fluency with addition and related subtraction facts through 10.

Count by tens and hundreds to 1,000 starting with any number.

Read, write and represent numbers through 999 using concrete models, standard form, and equations in expanded form.

Add and subtract fluently through 99 using knowledge of place value and properties of operations.

Demonstrate fluency with addition and related subtraction facts through 20.

Add and subtract whole numbers fluently to 1,000 using knowledge of place value and properties of operations.

Solve real-world problems involving equal groups, area/array, and number line models using basic multiplication and related division facts. Represent the problem situation using an equation with a symbol for the unknown.

Demonstrate fluency with basic multiplication and related division facts of products and dividends through 100.

Fluently add and subtract multi-digit whole numbers using strategies to include a standard algorithm.

Multiply up to a four-digit number by a one-digit number and multiply a two-digit number by a two-digit number using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using rectangular arrays, area models and/or equations.

Divide up to a four-digit dividend by a one-digit divisor using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division.

Read and write decimals in standard and expanded form. Compare two decimal numbers to the thousandths using the symbols >, =, or <.

Fluently multiply multi-digit whole numbers using strategies to include a standard algorithm.

Divide up to a four-digit dividend by a two-digit divisor, using strategies based on place value, the properties of operations, and the relationship between multiplication

Understand that, in a multi-digit whole number, a digit in one place represents 10 times what the same digit represents in the place to its right, and represents 1/10 times what the same digit represents in the place to its left.

Understand that the positive and negative representations of a number are opposites indirection and value. Use integers to represent quantities in real-world situations and explain the meaning of zero in each situation.

Investigate and translate among multiple representations of rational numbers (fractions, decimal numbers, percentages). Fractions should be limited to those with denominators of 2, 3, 4, 5, 8, 10, and 100.

Write and solve one-step linear equations in one variable involving non negative rational numbers for real-world and mathematical situations.

Extend prior knowledge of operations with positive rational numbers to add and to subtract all rational numbers and represent the sum or difference on a number line. e. Apply mathematical properties (e.g., commutative, associative, distributive, or the properties of identity and inverse elements) to add and subtract rational numbers.

Extend prior knowledge of operations with positive rational numbers to multiply and to divide all rational numbers. b. Understand sign rules for multiplying rational numbers. .c. Extend prior knowledge of operations with positive rational numbers to multiply and to divide all rational numbers. c. Understand sign rules for dividing rational numbers and that a quotient of integers (with a non-zero divisor) is a rational number.

Apply the concepts of linear equations and inequalities in one variable to real-world and mathematical situations. b. Write and solve multi-step linear equations that include the use of the distributive property and combining like terms. Exclude equations that contain variables on both sides.

Extend prior knowledge to translate among multiple representations of rational numbers (fractions, decimal numbers, percentages). Include the conversion of repeating decimal numbers to fractions.

Explore the concept of functions. c. Translate among the multiple representations of a function, including mappings, tables, graphs, equations, and verbal descriptions.

Explore the concept of functions.e. Graph a function from a table of values. Understand that the graph and table both represent a set of ordered pairs of that function

Extend concepts of linear equations and inequalities in one variable to more complex multi-step equations and inequalities in real-world and mathematical situations. a. Solve linear equations and inequalities with rational number coefficients that include the use of the distributive property, combining like terms, and variables on both sides.