### 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, and Addition and Subtraction, students rely on their substantial work on place value in Grade 2 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 toward 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, and 9. Students are also introduced to multiplication and division word problems involving equal groups and arrays, and solve two-step word problems involving all four operations.

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 they use their fluency with addition to find the area of composite two-dimensional shapes. As a step toward 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, 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.

In Unit 6, 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 they use those measurements to solve one-step word problems in all four operations with liquid volumes and masses.

In Unit 7, Data, students represent and interpret data on scaled picture and bar graphs, as well as line plots with fractional units. All of these types of data representations further rely on their work with number lines throughout the year.

The course ends with Unit 8, Shapes and their Perimeter, in which students start by exploring two-dimensional shapes in different categories, seeing that shapes in those categories share attributes. They then explore the specific attribute of perimeter and come to differentiate between perimeter and area as different measurements.

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 are not included in our mathematics units. All scholars in Grade 3 receive about 45 minutes of practice in those areas during other blocks.

### Course Map

#### Unit 1 14 Lessons

Place Value, Rounding, and Addition and Subtraction

#### Unit 2 Coming 5/18

Multiplication and Division, Part 1

#### Unit 3 Coming 5/18

Multiplication and Division, Part 2

Area

Fractions

Measurement

Data

#### Unit 8 Coming 6/18

Shapes and their Perimeter

### Mathematics at Match

The goals of Match Education’s math program are intrinsically tied to our school’s mission of providing our students with the skills and knowledge they will need to succeed in college and beyond. At Match, we seek to inspire our scholars to pursue advanced math courses, and we provide them with the foundations they will need to be successful in these courses.

Our math curriculum is designed around several core beliefs about how to best achieve our ambitious goals. These beliefs drive the decisions we make about what to teach and how to teach it.

1. Content-rich Tasks: We believe that students learn best when asked to solve problems that spark their curiosity, require them to make novel connections between concepts, and may offer more than one avenue to the solution.
2. Practice and Feedback: We believe that practice and feedback are essential to developing students’ conceptual understanding and fluency.
3. Productive Struggle: We believe that students develop essential strategies for tackling complex problems, and build non-cognitive skills such as grit and resilience, through productive struggle.
4. Procedural Fluency Combined with Conceptual Understanding: We believe that knowing “how” to solve a problem is not enough; students must also know “why” mathematical procedures and concepts exist.
5. Communicating Mathematical Understanding: We believe that the process of communicating their mathematical thinking helps students solidify their learning and helps teachers assess student understanding.