### Course Summary

Grade 4 focuses on three key advancements from previous years: (1) developing understanding with multi-digit multiplication and division; (2) developing an understanding of fraction equivalence and certain cases of fraction addition, subtraction, and multiplication; and (3) understanding that geometric figures can be analyzed and classified based on their properties, including their angle measure and symmetry.

How did we order the units?
Unit 1, Place Value, Rounding, and Addition and Subtraction, begins the year with the foundational content on which much of the remaining units are based—place value. Students start to see the structure of the place-value system in the context of multiplicative comparison (e.g., 1 thousand is 10 times as much as 1 hundred). They then use that place-value understanding to compare, round, add, and subtract numbers up to 1,000,000. They also solve multi-step word problems involving addition and subtraction, using rounding to assess the reasonableness of their answers.

In Unit 2, Multi-Digit Multiplication, students use this place-value understanding to start to develop an understanding of multi-digit multiplication (including two-digit, three-digit, four-digit by one-digit, and two-digit by two-digit multiplication). While students were introduced to the idea of multiplicative comparison in Unit 1 in the context of the structure of our place-value system, they more deeply delve into these story problem types in this unit. Unit 3, Multi-Digit Division, similarly relies on place-value understanding to introduce students to multi-digit division (including four-digit, three-digit, and two-digit by one-digit division). Students continue their work with multi-step word problems by working with remainders, interpreting them in the context of the problem.

In Unit 4, Angles, students get a formal introduction to angles after many years of informally categorizing shapes according to their angles. Students measure angles and find unknown angle measures, then use this deeper understanding to classify shapes and explore reflectional symmetry.

In Unit 5, Fraction Equivalence, Ordering, and Operations, students work with fraction equivalence and comparison, and start to explore operations with fractions (namely addition, subtraction, and multiplication by a whole number). Students also start to solve word problems involving the addition and subtraction of fractions. This then extends to Unit 6, Decimal Fractions, in which students explore decimal fractions, which are particularly important since they are an extension of the place-value system. They find equivalent decimal fractions, adding and subtracting decimal fractions (including tenths with hundredths, requiring a common denominator), and using decimal notation.

The course ends with Unit 7, Unit Conversion, in which students apply much of their understanding of the four operations, as well as fractions and decimals, to solve word problems involving the conversion from a larger unit to a smaller unit within the same system.

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 4 receive about 45 minutes of practice in those areas during other blocks.

### Course Map

#### Unit 1 22 Lessons

Place Value and Addition and Subtraction

#### Unit 2 Coming 12/17

Multi-Digit Multiplication

#### Unit 3 Coming 1/18

Multi-Digit Division

#### Unit 4 Coming 1/18

Shapes and Angles

Fractions

#### Unit 6 Coming 4/18

Decimal Fractions

Unit Conversions

### 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.