## The big ideas in Grade 4 include • developing understanding with multi-digit multiplication and division; • understanding fraction equivalence; • adding and subtracting fractions with like denominators; • multiplication of fractions and whole numbers.

This blueprint could start with any of the four units without prerequisites: 4.1 Factors and Multiples, 4.3 Base Ten Structure, 4.5 Comparing Fractions, and 4.9 Points, Lines, and Angles. We chose the first of these because it provides a natural way for students to bridge from their third grade work on multiplication and division, but any of the four choices is reasonable.

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.

## Units

4.1 Factors and Multiples

#### Summary

In this unit students

•  define factors and multiples;
•  convert units and see the connection to factors and multiples;
•  look for and explain patterns in tables that have multiples.

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4.2 Multiplicative Comparison

#### Summary

In this unit students understand, represent, and solve multiplicative comparison problems.

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4.3 Base Ten Structure

#### Summary

In this unit students

•  understand base-ten structure for whole numbers;
•  multiply and divide multi digit numbers;
•  look for and explain patterns in tables in terms of base-ten structure.

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4.4 Measurement Applications

#### Summary

In this unit students

•  use measurement contexts to work on adding, subtracting, multiplying, and dividing whole numbers;
•  solve problems involving area and perimeter;
•  work towards adding and subtracting with fluency.

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4.5 Comparing Fractions

#### Summary

In this unit students

•  compare equal and unequal fractions;
•  understand fraction equivalence;
•  work with decimal fractions for tenths and hundredths.

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4.6 Multiplying Fractions

#### Summary

In this unit students extend their understanding of multiplication of whole numbers to multiplying whole numbers and fractions.

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#### Summary

In this unit students

•  extend understanding of addition and subtraction of whole numbers to addition and subtraction of fractions with the same denominator;
•  use fraction equivalence in the special case of decimals.

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4.8 Operations with Whole Numbers

#### Summary

In this unit students

•  solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including applications in measurement, unit conversions and problems involving multiplicative comparison;
•  achieve fluency with addition and subtraction of whole numbers.

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4.9 Points, Lines, and Angles

#### Summary

In this unit students

•  draw and identify points, lines, segments, rays, angles, perpendicular and parallel lines, triangles, and line symmetry;
•  practice the four operations in length, area, and angle measure contexts.

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