Standards - Mathematics

Interpret and write equations for multiplicative comparisons.

Solve word problems involving multiplicative comparison using drawings and write equations to represent the problem, using a symbol for the unknown number.

Determine and justify solutions for multi-step word problems, including problems where remainders must be interpreted.

Write equations to show solutions for multi-step word problems with a letter standing for the unknown quantity.

Determine reasonableness of answers for multi-step word problems, using mental computation and estimation strategies including rounding.

For whole numbers in the range 1 to 100, find all factor pairs, identifying a number as a multiple of each of its factors.

Determine whether a whole number in the range 1 to 100 is a multiple of a given one-digit number.

Determine whether a whole number in the range 1 to 100 is prime or composite.

Generate and analyze a number or shape pattern that follows a given rule.

Using models and quantitative reasoning, explain that in a multi-digit whole number, a digit in any place represents ten times what it represents in the place to its right.

Read and write multi-digit whole numbers using standard form, word form, and expanded form.

Use place value understanding to compare two multi-digit numbers using >, =, and < symbols.

Round multi-digit whole numbers to any place using place value understanding.

Use place value strategies to fluently add and subtract multi-digit whole numbers and connect strategies to the standard algorithm.

Find the product of two factors (up to four digits by a one-digit number and two two-digit numbers), using strategies based on place value and the properties of operations.

Illustrate and explain the product of two factors using equations, rectangular arrays, and area models.

Use strategies based on place value, properties of operations, and/or the relationship between multiplication and division to find whole-number quotients and remainders with one-digit divisors and up to four-digit dividends.

Illustrate and/or explain quotients using equations, rectangular arrays, and/or area models.

Using area and length fraction models, explain why one fraction is equivalent to another, taking into account that the number and size of the parts differ even though the two fractions themselves are the same size.

Apply principles of fraction equivalence to recognize and generate equivalent fractions.

Compare two fractions with different numerators and different denominators using concrete models, benchmarks (0, $\frac{1}{2}$, 1), common denominators, and/or common numerators, recording the comparisons with symbols >, =, or <, and justifying the conclusions.

Explain that comparison of two fractions is valid only when the two fractions refer to the same whole.

Model and justify decompositions of fractions and explain addition and subtraction of fractions as joining or separating parts referring to the same whole.

Decompose a fraction as a sum of unit fractions and as a sum of fractions with the same denominator in more than one way using area models, length models, and equations.

Add and subtract fractions and mixed numbers with like denominators using fraction equivalence, properties of operations, and the relationship between addition and subtraction.

Solve word problems involving addition and subtraction of fractions and mixed numbers having like denominators, using drawings, visual fraction models, and equations to represent the problem.

Apply and extend previous understandings of multiplication to multiply a whole number times a fraction.

Model and explain how a non-unit fraction can be represented by a whole number times the unit fraction.

Extend previous understanding of multiplication to multiply a whole number times any fraction less than one.

Solve word problems involving multiplying a whole number times a fraction using visual fraction models and equations to represent the problem.

Express, model, and explain the equivalence between fractions with denominators of 10 and 100.

Use fraction equivalency to add two fractions with denominators of 10 and 100.

Use models and decimal notation to represent fractions with denominators of 10 and 100.

Use visual models and reasoning to compare two decimals to hundredths (referring to the same whole), recording comparisons using symbols >, =, or <, and justifying the conclusions.

Interpret data in graphs (picture, bar, and line plots) to solve problems using numbers and operations.