Count aloud to one hundred, read and write any numeral from 0 to 100, and count a set of up to twenty objects with one-to-one correspondence.

Count by ones, fives, and tens to one hundred, and by twos to twenty.

Recall sums and differences within five without counting on fingers.

Compare two sets or two numerals and state which is greater, which is less, or whether they are equal.

Name six plane shapes, identify and value the penny, nickel, dime, and quarter, tell time to the hour, and extend a repeating pattern.

Add and subtract multi-digit numbers with regrouping, using the standard written algorithm.

Recall all multiplication and division facts through 12 × 12 automatically.

Divide a four-digit number by a one-digit divisor, interpreting the remainder correctly for the context.

Identify equivalent fractions, reduce to lowest terms, compare fractions, and add and subtract fractions with like denominators.

Read, write, and compare decimals to hundredths, relate them to fractions, and state place value through the millions.

Calculate perimeter and area of rectangles and composite rectilinear figures, labeling units correctly.

Solve two-step word problems involving any of the four operations, showing the work for each step.

Add, subtract, multiply, and divide fractions with unlike denominators, mixed numbers, and decimals.

Write and solve ratios and proportions and convert fluently among fractions, decimals, and percents, including percent increase and decrease.

Divide multi-digit numbers by two-digit divisors, including decimal quotients.

Apply the order of operations to expressions with parentheses and exponents, and add, subtract, multiply, and divide positive and negative integers.

Solve one- and two-step linear equations in one variable and check the solution by substitution.

Calculate area of triangles, parallelograms, and circles; circumference of circles; and volume and surface area of rectangular prisms.

Compute mean, median, mode, and range for a data set, and construct and interpret bar graphs, line graphs, and circle graphs.

Score at or above the publisher's placement threshold for a first-year algebra course.