Use place value concepts to represent amounts of tens and ones and to compare three digit numbers.


When grade appropriate instruction pertaining to an eligible content should begin

Use place value concepts to represent amounts of tens and ones and to compare three digit numbers.


When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content

Demonstrate that when a whole or set is partitioned into y equal parts, the fraction 1/y represents 1 part of the whole and/or the fraction x/y represents x equal parts of the whole (limit denominators to 2, 3, 4, 6, and 8; limit numerators to whole numbers less than the denominator; and no simplification necessary).


When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content

Represent fractions on a number line (limit denominators to 2, 3, 4, 6, and 8; limit numerators to whole numbers less than the denominator; and no simplification necessary).


When grade appropriate instruction pertaining to an eligible content should begin

Represent fractions on a number line (limit denominators to 2, 3, 4, 6, and 8; limit numerators to whole numbers less than the denominator; and no simplification necessary).


When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content

Recognize and generate simple equivalent fractions (limit the denominators to 1, 2, 3, 4, 6, and 8 and limit numerators to whole numbers less than the denominator). Example 1: 1/2 = 2/4 Example 2: 4/6 = 2/3


When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content

Express whole numbers as fractions, and/or generate fractions that are equivalent to whole numbers (limit denominators to 1, 2, 3, 4, 6, and 8). Example 1: Express 3 in the form 3 = 3/1. Example 2: Recognize that 6/1 = 6.


When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content

Recognize and generate equivalent fractions.


When grade appropriate instruction pertaining to an eligible content should begin

Recognize and generate equivalent fractions.


When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content

Decompose a fraction or a mixed number into a sum of fractions with the same denominator (denominators limited to 2, 3, 4, 5, 6, 8, 10, 12, and 100), recording the decomposition by an equation. Justify decompositions (e.g., by using a visual fraction model). Example 1: 3/8 = 1/8 + 1/8 + 1/8 OR 3/8 = 1/8 + 2/8 Example 2: 2 1/12 = 1 + 1 + 1/12 = 12/12 + 12/12 + 1/12


When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content

Use decimal notation for fractions with denominators 10 or 100. Example: Rewrite 0.62 as 62/100 and vice versa.


When grade appropriate instruction pertaining to an eligible content should begin

Use decimal notation for fractions with denominators 10 or 100. Example: Rewrite 0.62 as 62/100 and vice versa.


When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content

Read and write whole numbers in expanded, standard, and word form through 1,000,000.


When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content

Read and write decimals to thousandths using base-ten numerals, word form, and expanded form. Example: 347.392 = 300 + 40 + 7 + 0.3 + 0.09 + 0.002 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (0.1) + 9 × (0.01) + 2 × (0.001)


When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content

Represent quantities in real-world contexts using positive and negative numbers, explaining the meaning of 0 in each situation (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge).


When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content

Locate and plot integers and other rational numbers on a horizontal or vertical number line; locate and plot pairs of integers and other rational numbers on a coordinate plane.


When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content

Represent addition and subtraction on a horizontal or vertical number line.


When grade appropriate instruction pertaining to an eligible content should begin

Represent addition and subtraction on a horizontal or vertical number line.


When grade appropriate instruction pertaining to an eligible content should begin

Represent addition and subtraction on a horizontal or vertical number line.


When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content

Use ratio language and notation (such as 3 to 4, 3:4, 3/4) to describe a ratio relationship between two quantities. Example 1: “The ratio of girls to boys in a math class is 2:3 because for every 2 girls there are 3 boys.” Example 2: “For every five votes candidate A received, candidate B received four votes.”


When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content

Construct tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and/or plot the pairs of values on the coordinate plane. Use tables to compare ratios.


When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content

Determine whether two quantities are proportionally related (e.g., by testing for equivalent ratios in a table, graphing on a coordinate plane and observing whether the graph is a straight line through the origin).


When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content

Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.


When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content

Represent proportional relationships by equations. Example: If total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn.


When grade appropriate instruction pertaining to an eligible content should begin

Represent proportional relationships by equations. Example: If total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn.


When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content

Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r), where r is the unit rate.


When grade appropriate instruction pertaining to an eligible content should begin

Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r), where r is the unit rate.


When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content

Convert a terminating or repeating decimal to a rational number (limit repeating decimals to thousandths).


When grade appropriate instruction pertaining to an eligible content should begin

Convert a terminating or repeating decimal to a rational number (limit repeating decimals to thousandths).


When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content

Locate/identify rational and irrational numbers at their approximate locations on a number line.


When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content