Illustrative Mathematics (2024)

Students begin their work in Grade 4 by revisiting their work with multiplication and division through 100 from Grade 3. They develop an understanding of multiplicative comparisons, distinguishing it from additive comparison. They continue their study of the base-ten system, and compare, order, and round base-ten numbers. They multiply and divide multi-digit numbers, and illustrate and explain calculations using equations, arrays, and area models. They solve word problems involving adding, subtracting, multiplying, and dividing whole numbers.

Next, students deepen their understanding of fraction equivalence and reason about the size of fractions, which leads to comparing and ordering fractions, including decimal fractions. They extend their understanding of multiplication to multiply fractions by whole numbers. They apply their understanding to solve word problems involving multiplication of a fraction by a whole number. Then they extend their understanding of adding and subtracting whole numbers to fractions, including work with decimals. Traditionally, many curricula begin fraction arithmetic by adding and subtracting fractions. This blueprint suggests beginning with multiplication and division because fractions were invented because the quotient of two whole numbers is not always a whole number. Fractions feel at home with multiplication and division; they submit to addition and subtraction more reluctantly.

The standard 4.OA.A.3 is a pinnacle standard for grades K–4, calling on students to use much of what they’ve learned throughout the grade, as well as previous grade’s learning, in order to solve multistep word problems using the four operations. Students represent problems using equations with letters for unknown quantities and assess the reasonableness of answers using mental computation and estimation strategies. This is an opportunity for students to do additional work with unit conversions, applications in measurement, multiplicative comparison. It is in this unit that fluency with addition and subtraction of multi-digit whole numbers is expected.

Students finish the year with a short unit on geometry, where they are introduced to angles. They also classify shapes by their properties and study line symmetry.

Note that this course blueprint is only one of many possible ways of arranging a sequence of topics designed to achieve the standards. It is a continually evolving document and we welcome your comments here.