Kindergarten
The big ideas in Kindergarten include • counting objects in a set; • comparing sets or numerals; •  using numbers to represent quantities and solve problems; • modeling simple joining and separating situations with sets of objects.
Kindergarten is the start of a formal education for some students, and students enter Kindergarten with varying levels of mathematical understanding and skill. This course blueprint calls for students to begin working with whole numbers to five so that they can begin to develop an understanding of the relationship between numbers and quantities.
Next, they are introduced to the ideas of putting together and taking apart as a foundation for understanding addition and subtraction. Students then expand their work with numbers to ten, first connecting the number names and count sequence to counting and cardinality, and then expanding their work with addition and subtraction. Foundational ideas underlying place-value are implicitly built into this work as students work on "making a ten." Students then expand their work to 20, where work with the numbers 11-19 prepares them for working with place-value in later grades.
Students have an opportunity to practice and apply most of the skills and strategies they have learned throughout the course of the year in a unit titled Putting it All Together. Students solve word problems involving addition and subtraction to 10 using objects, drawings, and/or equations. Students use multiple representations to demonstrate their conceptual understanding of addition and subtraction. Additional work with composing and decomposing numbers supports the expectation that all Kindergartners demonstrate fluency with adding and subtracting within 5.
In kindergarten, students also begin to name and describe shapes in their environment and to name and compare measurable attributes of objects. This course blueprint has students' geometric work interspersed with their work with number, although these topics are independent of each other and can be ordered in other ways.
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
K.1
Numbers to 5
Summary
In this unit students • learn the count sequence to 5, counting by ones; • connect counting to cardinality by pairing objects with a number name; • answer “how many?” questions; • count objects in sets; • compare numbers of objects; • write numbers.
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K.2
Introducing Addition and Subtraction
Summary
In this unit students • understand addition as putting together or adding to, and subtraction as taking apart or taking from; • represent addition and subtraction with objects; • compose and decompose 5 or less; • begin working towards fluency within 5.
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K.3
Shapes Around Us
Summary
In this unit students • identify and describe shapes in the environment using shape names and relative position of the objects; • classify objects into given categories and compose shapes to model real-world objects; • describe measurable attributes of objects (e.g. length or weight) and compare objects based on those attributes.
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K.4
Numbers within 10
Summary
In this unit students • count by ones; • pair objects with a number name; • further their understanding of the relationship between number and quantity; • answer “how many?” questions about objects in varied arrangements (lines, arrays, circles, scattered); • count objects in sets and compare sets of objects using greater than, less than, or equal to; • write numbers.
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K.5
Addition and Subtraction to 10
Summary
In this unit students • represent addition and subtraction with objects; • solve word problems; • compose and decompose 10 or less into pairs in more than one way; • introduce expressions in relation to addition and subtraction situations; • develop fluency with addition and subtraction within 5.
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K.6
Numbers to 20
Summary
In this unit students • count by ones and tens; • compare sets of objects; • count forward from a number other than one; • write numbers; • answer “how many?” questions about objects in varied arrangements.
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K.7
Ten Ones + More Ones
Summary
In this unit students • compose and decompose numbers 11–19 into ten ones and more ones, recording with an equation (e.g., 18 = 10 + 8); • write and identify numbers to 20.
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K.8
Putting it All Together
Summary
In this unit students
• count by ones and tens to 100;
• practice writing numbers;
• understand cardinality;
• solve addition and subtraction word problems;
• represent addition and subtraction in multiple ways;
• compose and decompose numbers;
• compare numbers to 10 written as numerals;
• achieve fluency in addition and subtraction within 5.
K.9
A Closer Look at Shapes
Summary
In this unit students • classify, analyze, and compare two- and three-dimensional shapes; • use simple shapes to compose more complex shapes.
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