interpret the value of each place-value position as 10 times the position to the right and as one-tenth of the value of the place to its left

represent the value of the digit in whole numbers through 1,000,000,000 and decimals to the hundredths using expanded notation and numerals

compare and order whole numbers to 1,000,000,000 and represent comparisons using the symbols >, <, or =

round whole numbers to a given place value through the hundred thousands place

represent decimals, including tenths and hundredths, using concrete and visual models and money

compare and order decimals using concrete and visual models to the hundredths

relate decimals to fractions that name tenths and hundredths

determine the corresponding decimal to the tenths or hundredths place of a specified point on a number line

represent a fraction a/b as a sum of fractions 1/b, where a and b are whole numbers and b > 0, including when a > b

decompose a fraction in more than one way into a sum of fractions with the same denominator using concrete and pictorial models and recording results with symbolic representations

determine if two given fractions are equivalent using a variety of methods

compare two fractions with different numerators and different denominators and represent the comparison using the symbols >, =, or <

represent and solve addition and subtraction of fractions with equal denominators using objects and pictorial models that build to the number line and properties of operations

evaluate the reasonableness of sums and differences of fractions using benchmark fractions 0, 1/4, 1/2, 3/4, and 1, referring to the same whole

represent fractions and decimals to the tenths or hundredths as distances from zero on a number line

add and subtract whole numbers and decimals to the hundredths place using the standard algorithm

determine products of a number and 10 or 100 using properties of operations and place value understandings

represent the product of 2 two-digit numbers using arrays, area models, or equations, including perfect squares through 15 by 15

use strategies and algorithms, including the standard algorithm, to multiply up to a four-digit number by a one-digit number and to multiply a two-digit number by a two-digit number. Strategies may include mental math, partial products, and the commutative, associative, and distributive properties

represent the quotient of up to a four-digit whole number divided by a one-digit whole number using arrays, area models, or equations

use strategies and algorithms, including the standard algorithm, to divide up to a four-digit dividend by a one-digit divisor

round to the nearest 10, 100, or 1,000 or use compatible numbers to estimate solutions involving whole numbers

solve with fluency one- and two-step problems involving multiplication and division, including interpreting remainders

represent multi-step problems involving the four operations with whole numbers using strip diagrams and equations with a letter standing for the unknown quantity

represent problems using an input-output table and numerical expressions to generate a number pattern that follows a given rule representing the relationship of the values in the resulting sequence and their position in the sequence

solve problems related to perimeter and area of rectangles where dimensions are whole numbers

identify points, lines, line segments, rays, angles, and perpendicular and parallel lines

identify and draw one or more lines of symmetry, if they exist, for a two-dimensional figure

apply knowledge of right angles to identify acute, right, and obtuse triangles

classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines or the presence or absence of angles of a specified size

determine the approximate measures of angles in degrees to the nearest whole number using a protractor

draw an angle with a given measure

determine the measure of an unknown angle formed by two non-overlapping adjacent angles given one or both angle measures

identify relative sizes of measurement units within the customary and metric systems

convert measurements within the same measurement system, customary or metric, from a smaller unit into a larger unit or a larger unit into a smaller unit when given other equivalent measures represented in a table

solve problems that deal with measurements of length, intervals of time, liquid volumes, mass, and money using addition, subtraction, multiplication, or division as appropriate

represent data on a frequency table, dot plot, or stem-and-leaf plot marked with whole numbers and fractions

solve one- and two-step problems using data in whole number, decimal, and fraction form in a frequency table, dot plot, or stem-and-leaf plot

distinguish between fixed and variable expenses

calculate profit in a given situation

describe the basic purpose of financial institutions, including keeping money safe, borrowing money, and lending