In this common-core-aligned course, third graders develop an understanding of and fluency with multiplication and division within 100, fractions, area, and properties of two-dimensional shapes.

## Course Summary

Grade 3 focuses on four key advancements from previous years: (1) developing understanding of and fluency with multiplication and division within 100; (2) developing understanding of fractions, especially unit fractions; (3) developing understanding of rectangular arrays and of area; and (4) describing and analyzing two-dimensional shapes.

How did we order the units?

In Unit 1, Place Value, Rounding, Addition, and Subtraction, students rely on their substantial work in Grade 2 on place value to develop an understanding of rounding. They then develop fluency with addition and subtraction within 1,000. Finally, they use both aforementioned skills to solve one-and two-step word problems involving addition and subtraction, using rounding to assess the reasonableness of their answers. While the content taught in this unit is not major work of Grade 3 as determined by the Common Core State Standards, it serves as a foundation for later work, such as assessing the reasonableness of all types of two-step word problems and multiplying one-digit numbers by multiples of ten. Thus, it serves as an introduction to the course.

In Units 2 & 3, Multiplication and Division Parts I & II, students are introduced to the other two major operations, multiplication and division. They come to understand multiplication as finding the total number of objects in a certain number of equal-sized groups, and division as finding either the size of the group or the number of groups. Students work towards fluency of all multiplication and division facts within 100, relying on the properties and patterns to help in particular with the difficult facts of 6, 7, 8, 9. Students solve one-step multiplication and division word problems involving equal groups and arrays, and solve two-step word problems involving all four operations. They also explore myriad connections to multiplication and division, including exploring patterns, including patterns in the skip-counting sequence, and scaled picture and bar graphs.

In Unit 4, Area, students define area to be the number of square units needed to cover a two-dimensional space. They initially find the area of rectangles by counting unit squares or skip-counting by rows and columns. Then, seeing the connection between skip-counting and multiplication that was built in the prior two units, students apply their recently acquired fluency with multiplication to calculate the area of a rectangle, and use their fluency with addition to find the area of composite two-dimensional shapes. As a step towards mastery of all word problem types expected of Grade 3 students, they are introduced to one-step word problems involving area in this unit, as well.

In Unit 5, Shapes and their Perimeter, students start by exploring the specific attribute of perimeter, and come to differentiate between perimeter and area as different measurements. They then explore two-dimensional shapes in different categories, seeing that shapes in those categories share attributes.

In Unit 6, Fractions, students build on their work partitioning circles and rectangles in Grade 2 to study fractions. They build more complex fractions from unit fractions, and start to understand fractions as numbers, rather than portions of shapes. To do so, students do extensive work with placing fractions on a number line, a helpful representation for comparing and finding equivalent fractions. Students also explore line plots with fractional measurements, a key advancement from Grade 2 work with line plots that connects to their work with fractions.

In Unit 7, Measurement, students study time as well as liquid volumes and masses. Students learn to read time to the nearest minute and use their work with number lines in Unit 1 (with rounding) and Unit 5 (with fractions) to solve problems involving elapsed time. They also rely on their work with number lines to read measurement scales, and use those measurements to solve one-step word problems in all four operations with liquid volumes and masses.

This course follows the 2017 Massachusetts Curriculum Frameworks, which incorporate the 2010 Common Core State Standards. Further, we believe that daily fluency and application practice are an important part of elementary mathematics instruction, but is not included in our mathematics units. All students in Grade 3 receive about 45 minutes of practice in those areas during other blocks.