Students develop an understanding of multi-digit multiplication and division; fraction equivalence and operations with fractions; and classification and analysis of geometric figures and their angles.

## 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, 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 2-digit, 3-digit, and 4-digit by 1-digit, as well as 2-digit by 2-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 problems types in this unit. Unit 3, Multi-Digit Division, similarly relies on place value understanding to introduce students to multi-digit division (including 4-digit, 3-digit, and 2-digit by 1-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 and Ordering students work with fraction equivalence and comparison, developing a general method for generating equivalent fractions and exploring multiple strategies for fraction comparison. This prepares them for Unit 6, Fraction Operations, where they 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, subtraction, and multiplication of fractions. This then extends to Unit 7, 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, add and subtract decimal fractions (including tenths with hundredths, requiring a common denominator), and using decimal notation.

The course ends with Unit 8, 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 is not included in our mathematics units. All students in Grade 4 receive about 45 minutes of practice in those areas during other blocks.

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