## The big ideas in Grade 3 include • multiplication and division of whole numbers; • arrays and area; • building fractions from unit fractions.

This blueprint could start with any of the three units without prerequisites: 3.1 Wrapping up 1,000, 3.2 Polygons and Area, or 3.6 What are Fractions?. We chose the first of these because it provides a natural way for students to bridge from their second grade work on addition and subtraction, but any of the three choices would be reasonable.

In Grade 3 students begin by revisiting their Grade 2 work on addition and subtraction of whole numbers and extend it to addition and subtraction within 1,000. If students start the year with this work, there will be time for them to revisit the ideas as needed throughout the year until they develop fluency with those operations.

Next, students work on understanding the area of a region as the number of square units needed to cover a region without gaps or overlaps. Independently, students are introduced to multiplication of whole numbers as the total number of objects in one or more equal-size groups. Fluency with multiplication and division within 100 builds over an extended period of time, and so work towards fluency begins here. Students work to develop strategies for multiplying using place-value structure, the properties of operations, and the relationship between multiplication and division.

Next, students begin work with fractions. They understand fractions as being built from unit fractions, and represent them on a number line. They compare fractions and begin working on the notion of fraction equivalence. The end of the year culminates in a unit where students can bring together all of the ideas they have studied throughout the year, where they solve word problems involving addition and subtraction of time intervals in minutes, liquid volumes and mass, and perimeters of polygons.

Note that this course blueprint is only one of many possible ways of arranging a sequence of topics designed to achieve the standards. It is a continually evolving document and we welcome your comments here.

## Units

3.1 Wrapping up 1,000

#### Summary

In this unit students

•  round to the nearest 10 and 100;
•  add and subtract within 1,000.

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3.2 Polygons and Area

#### Summary

In this unit students describe and analyze categories of polygons and understand the meaning of area.

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3.3 Multiplication and Division

#### Summary

In this unit students

•  learn the meaning of multiplication and division;
•  learn the relationship between multiplication and division;
•  understand and use the commutative property of multiplication.

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3.4 Multiplying and Dividing

#### Summary

In this unit students use properties of operations and the relationship between multiplication and division to find products and quotients.

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3.5 When and Why to Multiply

#### Summary

In this unit students

•  understand and use the distributive property;
•  solve more complex multiplication problems in context.

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3.6 What are Fractions?

#### Summary

In this unit students

•  understand fractions as built out of unit fractions;
•  compare fractions;
•  work with simple examples of fraction equivalence.

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3.7 Bar Graphs and Line Plots

#### Summary

In this unit students represent and interpret data with an emphasis on using data displays to solve problems.

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3.8 Putting it All Together

#### Summary

In this unit students

•  solve multi-step problems with the four operations on whole numbers;
•  achieve fluency with multiplication and division within 100.

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