## Grade overview

### What is included in the year?

Grade 3 LearnZillion Math Companion Curriculum consists of 15 units and a total of 158 lessons. Each lesson is designed to be completed in one 45-55 minute class period. Each unit includes a summative Unit Assessment designed to be completed in one class period, this assessment day is not included in the number of days allotted to lessons. The organization of the units, and lessons within each unit, creates a coherent sequence based on the progressions of the standards. As shown in the figure below, the majority of lessons are focused on the major work of Grade 3. The remaining lessons focus on supporting or additional clusters, often in the service of the major work. In third grade, 71% of lessons (112 lessons) are devoted to the major work of the grade. Many lessons dedicated to major work standards are enhanced and deepened by simultaneously engaging students in standards from supporting or additional clusters. In some instances when appropriate, students work only with supporting or additional work clusters.

### Grade 3 lesson focus across major, supporting, and additional clusters

### Grade 3 units across the year

Unit | Title | Major clusters | Supporting clusters | Additional clusters |
---|---|---|---|---|

1 | Exploring equal groups as a foundation for multiplication & division | 3.OA.A, 3.OA.C | ||

2 | Developing conceptual understanding of area | 3.MD.C, 3.OA.B | ||

3 | Developing strategies for addition and subtraction | 3.NBT.A, 3.MD.D | ||

4 | Understanding unit fractions | 3.NF.A | 3.G.A | |

5 | Using fractions in measurement & data | 3.NF.A | 3.MD.B | |

6 | Solving addition & subtraction problems involving measurement | 3.MD.A | ||

7 | Understanding the relationship between multiplication and division | 3.OA.A | ||

8 | Investigating patterns in number and operations | 3.OA.D | 3.MD.B | 3.NBT.A |

9 | Developing strategies for multiplication and division | 3.MD.C, 3.OA.B | ||

10 | Understanding equivalent fractions | 3.NF.A | ||

11 | Comparing fractions | 3.NF.A | ||

12 | Solving problems involving area | 3.MD.C, 3.OA.A, 3.OA.B | ||

13 | Solving problems involving shapes | 3.G.A | 3.MD.D | |

14 | Using multiplication & division to solve measurement problems | 3.MD.A, 3.OA.A | ||

15 | Demonstrating computational fluency in fluency problem solving | 3.OA.C, 3.OA.D | 3.NBT.A |

### Overview of Grade 3 Major, Supporting, and Additional Work

#### Major work of the year

In third grade the major work focuses on the development of multiplicative reasoning. Students develop an understanding of the properties of multiplication and division, and the relationship between multiplication and division as they engage in explorations involving arrays, equal-sized groups, and area models. They develop strategies for solving multiplication and division problems within 100 and understand multiplication as finding an unknown product and division as finding an unknown factor. Third grade students become fluent with all the single digit combinations and also develop efficient strategies for calculating the products of whole numbers.

The major work with geometric measurement is connected to the development of multiplicative concepts. Third grade students are able to recognize area as an attribute of two-dimensional regions. They use the structure of a rectangular array to find the total number of same sized units, which will cover a specified shape. Building on the work of second grade with rectangular arrays and equal addends, third grade students now are able to connect multiplication to a rectangular array. They use the square to tile and justify that the area of a rectangle is the same as would be found by multiplying the side lengths. As students decompose and compose shapes, they begin to use area models to build ideas about the distributive property. Students also relate area to the operations of multiplication and addition.

Developing an understanding of fractions as numbers is a critical area in third grade that is foundational to ongoing major work in fourth and fifth grade. Students develop meaning for the unit fraction and can describe fractions as being built out of unit fractions. In first and second grade, students work with fractions as area models and that work is expanded in third grade as students compare fractions and use fractions to represent numbers equal to, less than, and greater than one. Representing fractions as a number and on a number line is introduced and students use the number line representation to justify equivalence and ordering of fractions. Students are able to compare fractions with the same numerator or same denominator by reasoning about the size of their size and by relating to the unit fraction. They also recognize that comparisons are only valid when the two fractions originate from the same sized wholes.

Third grade students solve a variety of problems involving the four operations and notice and explain arithmetic patterns. Students apply their understanding of the four operations and apply computation and reasoning strategies as they estimate and then solve measurement problems related to intervals of time, liquid volumes, and masses of objects.

#### Supporting work

The supporting work in third grade is central to the development of multiplicative ideas and the geometric measurement work. Students describe, compare, and analyze the properties of two-dimensional shapes. They use their understanding of the properties of shapes to classify shapes by their sides and angles. This angle work will support the upcoming related fourth grade standards. Throughout this work with shapes, third grade students can relate their fraction work to geometry by expressing the area of parts of shapes as a unit fraction of the whole.

Students further deepen their understanding of the operations as they represent and interpret data. As students use rulers to generate measurement data, they are applying major work concepts. They solve one and two step problems and represent their data finding with scaled graphs and line plots. Both of these representations of data support the work of multiplication and fractions.

#### Additional work

The additional work of third grade is closely related to the major work standards. Students again work with the concept of geometric measurement as they solve problems about the perimeter of a plane shape. Students recognize perimeter as an attribute of plane figures and are able to differentiate between linear and area measures. Through a variety of experiences, such as measuring the perimeter of their classroom or desks and through solving real world problems such as constructing a pen for a classroom pet, students develop an understanding of the connections between perimeter and area; rectangles with the same perimeter can have different areas and rectangles with the same area can have different perimeters.

In third grade, students extend the meaning of the base ten structure as they explore what happens to a number when multiplied by a multiple of ten. They use place value understandings to round numbers to the nearest ten or hundred and then apply those strategies as an estimation method when solving problems. Students also reach fluency within 1000 when solving addition and subtraction problems. They develop efficient and generalizable methods using a range of strategies and algorithms for solving addition and subtraction problems.

The lesson plans in LearnZillion's full math curriculum, by LearnZillion, Inc. are licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

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