## The big ideas in Grade 1 include •  understanding addition, subtraction, and strategies for addition and subtraction within 20; •  understanding whole number relationships and place value; •  understanding linear measurement.

This course blueprint could start with either of the the two units that have no prerequisites: 1.1 Length and Number Lines and 1.5 Polygons and Circles. We have chosen the first of these so that the number line is available right away.

Students begin the year developing the concepts of length and the number line. Even though the standards don't explicitly call for first graders to work with the number line, it can still be used as an instructional tool in first grade.

Next, students begin their work on addition and subtraction, returning to and extending the work they did in Kindergarten. Students’ work with addition and subtraction throughout the year balances conceptual understanding, procedural fluency, and applications. By the end of first grade, students should be fluent with adding and subtracting within 10. Since fluency develops over time, work towards fluency starts at the beginning of the year. Students use drawings, number lines, and equations to connect concrete representations with more abstract mathematical symbols.

The units are structured so that students build their understanding of place value in order to add and subtract larger numbers. Students begin by focusing on "making a ten." They build on that idea by adding ones to a ten in order to compose the numbers 11–19. Students also work on counting, making progress towards counting to 120, and reading and writing numerals. Once students have a solid understanding of 10 as a bundle of ten ones, they focus on addition and subtraction within 20.

Students' work in geometry in Grade 1 is relatively modest. The placement of the geometry unit (1.E) in this course blueprint is intended to provide an interlude in the major work of the grade, allowing students to process the work they did in the first four units. However, this unit can come at any time, as it has no prerequisites. Much of the work in geometry that students do in Grade 1 foreshadows important ideas that come to fruition in later grades, such as the notion of a defining attribute and the implications of composing and decomposing geometric figures and how this relates to geometric measurement. Students' Grade 1 work in geometry is selected to support their understanding of numbers and operations.

As students' understanding of and skill with addition and subtraction deepens, they begin to work with two-digit numbers. They find the sum of a two-digit number and a one-digit number, and of a two-digit number and a multiple of 10. Students' work in Grade 1 culminates in a unit where they can put all of their acquired knowledge and skill to use, capitalizing on their fluency with adding and subtracting within 10.

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

1.1 Length and the Number Line

#### Summary

In this unit students •  measure lengths by iterating length units; •  use an understanding of length to introduce the number line.

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1.2 Adding and Subtracting within 10

#### Summary

In this unit students build on their work in Kindergarten on addition and subtraction within 10 to include new types of addition and subtraction contexts.

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1.3 Making Ten

#### Summary

In this unit students •  find all decompositions of 10 and write them using equations; •  represent a number between 11 and 19 as a bundle of ten and some ones; •  take a first pass at adding one-digit numbers whose sum is greater than 10.

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1.4 Adding and Subtracting within 20

#### Summary

In this unit students •  solve problems in all adding and subtracting contexts within 20; •  make adding and subtracting strategies within 20 explicit.

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1.5 Polygons and Circles

#### Summary

In this unit students •  build and draw shapes based on attributes; •  create composite shapes from two- and three-dimensional shapes; •  partition circles and rectangles into equal shares.

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1.6 Multiples of ten

#### Summary

In this unit students •  count by tens; •  represent multiples of ten on the number line; •  count on by ones from any multiple of ten; •  count on and back by tens from any multiple of ten; •  compare two-digit numbers; •  count forward and backward by ones and tens starting from a number that is not a multiple of ten.

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1.7 Adding and Subtracting within 100

#### Summary

In this unit students •  add and subtract multiples of ten; •  add and subtract a two-digit number and a one-digit number, or a two-digit number and multiple of ten; •  make adding and subtracting strategies explicit; •  write addition and subtraction equations.

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1.8 Telling Time

#### Summary

In this unit students tell and write time in hours and half-hours.

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1.9 Putting it All Together

#### Summary

In this unit students use fluent addition and subtraction within 10 and understanding of adding and subtracting within 100 to represent, solve, and communicate about problems involving addition and subtraction.

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