Last updated: 8/15/2021

## Grade K - Counting and Cardinality, Operations and Algebraic Thinking

 Subject: Mathematics (NYS P-12 Common Core)
 Unit Title: Grade K - Counting and Cardinality, Operations and Algebraic Thinking
 Approx. Number of Weeks: Whole year

#### Unit Summary:

Whole numbers can be represented, have relationships to one another and can be operated on.

Sets can be joined and separated.

Numbers will be used to represent quantities and solve quantitative problems.

(count objects in a set, create sets for given numerals, compare and order sets and numerals using cardinal and ordinal meaning, model simple joining and separating situations/objects, use written numerals,  eventually use equations such as 5+2=7, 7-2=5)

Multiple Representations will be used (standard and non-standard) including: manipulatives, verbal language, acting out, modeling a situation, drawing pictures to organize, record and communicate mathematical ideas, see equations but writing not required.

Effective Strategies for answering quantitative questions will be chosen, combined and applied.(quickly recognize the number in a small set, count and produce sets of given sizes, count the numbers in combined sets, count the # of objects that remain in a set after some are taken away.)

 Collaboration & Communication Creativity & Innovation Critical Thinking & Problem Solving Research & Information Fluency Social & Emotional Intelligence

### 1. What will students know and be able to do?

#### Standards:

 K.CC.1 - Count to 100 by ones and by tens. K.CC.2 - Count forward beginning from a given number within the known sequence (instead of having to begin at 1). K.CC.3 - 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.4 - Understand the relationship between numbers and quantities; connect counting to cardinality. K.CC.5 - 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.6 - 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.7 - Compare two numbers between 1 and 10 presented as written numerals. K.OA.1 - Represent addition and subtraction with objects, fingers, mental images, drawings, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations. K.OA.2 - 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.3 - 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.4 - 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.5 - Fluently add and subtract within 5. K.NBT.1 - 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.

#### 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.

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

### 3. What learning activities will students participate in?

#### Discipline Specific Considerations:

Vocabulary – Specialized and High Frequency

Numbers, quantities, numerals, joining and separating, putting together, adding to, taking apart, taking from, set, how many, altogether, manipulatives, equations, number names, sequence, order, count objects, count-on, count-back, more than, less than, equal, greater than, addition, subtraction, number line, compare, pattern, sort, tens, onse

Reversing written numerals is developmental!

Rote skill does not demonstrate conceptual understanding!

Common Core State Standards:  Standards for Mathematical Practice

Standard 1:    Make sense of problems and persevere in solving them

Standard 2:    Reason abstractly and quantitatively

Standard 3:    Construct viable arguments and critique the reasoning of others

Standard 4:    Model with Mathematics

Standard 5:    Use appropriate tools strategically

Standard 6:   Attend to precision

Standard 7:  Look for and make use of structure

Standard 8:  Look for and express regularity in repeated reasoning