Essential Understandings:

Students will understand that…

Numbers have value.

Essential Questions:

What is a number?

Possible ways to scaffold the question:

• How can you represent the value of a number?
• Why do number values change?

(Answers to this question will evolve and become more sophisticated as instruction progresses.)

Students will know:

Objects in a set can be counted.

Numbers can be compared.

Numbers have names and can be counted.

Adding is putting together and adding to.

Subtraction is taking apart and taking from.

Numbers represent groups of tens and ones.

Students will be able to:

Counting and Cardinality

Count to tell the number of objects.

• Understand the relationship between numbers and quantities; connect counting to cardinality. (K.CC.4)

a. When counting objects, say the number names in the standard order, pairing each object with one and only one number name and each number name with one and only one object.

b. Understand that the last number name said tells the number of objects counted. The number of objects is the same regardless of their arrangement or the order in which they were counted.

c. Understand that each successive number name refers to a quantity that is one larger.

 d. Develop understanding of ordinal numbers (first through tenth) to describe the relative position and magnitude of whole numbers. Justification: this has real-world applications, it bridges a Pre-K standard, and it is present in the NCTM Focal Points.

•Count to answer “how many?” questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 1–20, count out that many objects. (K.CC.5)

Compare numbers.

• Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group, e.g., by using matching and counting strategies. (K.CC.6)

 •Compare two numbers between 1 and 10 presented as written numerals.(K.CC.7)

 Know number names and the count sequence.

 •Count to 100 by ones and by tens.(K.CC.1)

•Count forward beginning from a given number within the known sequence (instead of having to begin at 1). (K.CC.2)

•Write numbers from 0 to 20. Represent a number of objects with a written numeral 0–20 (with 0 representing a count of no objects) (K.CC.3)

 Operations and Algebraic Thinking

Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.

 •Represent addition and subtraction with objects, fingers, mental images, drawings*3, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations. (K.OA.1)

 • Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem. (K.OA.2)

 • Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1). (K.OA.3)

 • For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g., by using objects or drawings, and record the answer with a drawing or equation. (K.OA.4)

 FLUENCY STANDARD  !

•Fluently add and subtract within 5. (K.OA.5)

 *2 Include groups with up to ten objects.

*3 Drawings need not show details, but should show the mathematics in the problem. (This applies wherever drawings are mentioned in the Standards.)

 Number and Operations in Base Ten

Work with numbers 11–19 to gain foundations for place value.

• Compose and decompose numbers from 11 to 19 into ten ones and some further ones, e.g., by using objects or drawings, and record each composition or decomposition by a drawing or equation (e.g., 18 = 10 + 8); understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones. (K.NBT.1)

Color Code Key: Gaps, Major Clusters, Supporting Clusters, Additional Clusters