Rogers Public Schools 1 of 6 | Revised 5-15-13

R.P.S. Common Core Math Curriculum Overview Kindergarten

Summary of the Year In Kindergarten, instructional time should focus on two critical areas:

1. Representing, relating, and operating on whole numbers, initially with sets of objects 2. Describing shapes and space

More learning time in Kindergarten should be devoted to number than to other topics. CCSSM, p.9 - Kindergarten Overview

Required Fluency: K.OA.5 Add and subtract within 5.

Quarterly Sequence 1st Quarter: Using Numbers to Represent Quantities; Identifying and Describing Shapes Students begin to use numbers (including written numerals) to represent quantities. They begin to count objects in a set and pair each object with one number name. They begin to explore the concept that the number of objects is the same regardless of their arrangement or the order in which they are counted. They also begin to model simple joining and separating situations using objects, fingers, mental images, drawings, sounds, acting out situations and verbal explanations. Students also learn to identify and describe 2-dimensional and 3-dimensional shapes.

2nd Quarter: Exploring and Representing Quantities; Describing and Comparing Measurable Attributes Students continue to build their understanding of numbers and how they are used to represent quantities and solve problems. They will continue to model simple joining and separating situations using objects, fingers, mental images, drawings, sounds, acting out situations and verbal explanations. Students will begin to explore the numbers 11-19 by representing these numbers with objects or drawings. Students will explore measurable attributes of an object and classify objects based on similarities and differences. They will explore direct comparisons of two objects. Comparison begins with developing the meaning of the word “than” in the context of “taller than,” “shorter than,” “heavier than,” “longer than,” etc. This understanding will lead into the more abstract idea of comparing numbers with the terms “more than” and “less than”.

3rd Quarter: Composing and Decomposing Numbers; Deepening Understanding of Addition and Subtraction Students will deepen their understanding of numbers and how they are used to represent quantities and solve problems. They will also deepen their work with simple joining and separating situations and work to strengthen their fluency within 5. Students will build upon their understanding of the numbers 11-19 through composing and decomposing these numbers into ten ones and some further ones, thus developing the idea that the number 10 is special. (It will eventually become the “ten” unit in the place value system in 1st Grade.)

4th Quarter: Solidifying Foundational Understandings; Analyzing, Comparing, Creating, and Composing Shapes Students will solidify their understanding of how we use numbers to represent quantities and to model simple joining and separating situations. Students continue to compose and decompose the numbers 11-19 into ten ones and some further ones, gaining a solid foundation for place value. Students will demonstrate fluency of addition and subtraction within 5. Students will also build on their understanding of shapes. They will analyze and compare 2-D and 3-D shapes, create shapes, and discover that shapes can be composed of smaller shapes.

Kindergarten Major Emphasis Clusters

Counting and Cardinality

Know number names and count sequence

Count to tell the number of objects

Compare numbers Operations and Algebraic Thinking

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

Number and Operations in Base Ten

Work with numbers 11-19 to gain foundations for place value

Rogers Public Schools 2 of 6 | Revised 5-15-13

R.P.S. Common Core Math Curriculum Overview Kindergarten

1. Make sense of problems and persevere in solving them.

•I can find ways to solve the problem and ask "Does this make sense?".

2. Reason abstractly and quantitatively.

•I can use numbers and words to help me make sense of problems.

3. Construct viable arguments and critique the reasoning of others.

•I can explain my thinking and consider the mathematical thinking of others.

4. Model with mathematics.

•I can recognize math in everyday life and use math I know to solve problems.

5. Use appropriate tools strategically.

•I can use math tools and know when to use them.

6. Attend to precision.

•I can work carefully, check my work, and be clear when I share my ideas.

7. Look for and make use of structure.

•I can see and understand how numbers and shapes are organized and put together as parts and wholes.

8. Look for and express regularity in repeated reasoning.

•I can notice when calculations are repeated. Then, I can find more efficient ways to solve the problem.

Standards for Mathematical Practice

The Standards for Mathematical Practice describe ways that students should engage with the content standards. These practices are essential to understanding and implementing the mathematical subject material. Content standards that begin with the word “understand” are often especially good opportunities to connect the practices to content. (CCSSM p.6-8) Below you will find the Mathematical Practice Standards and a related student friendly “I can” statement.

Mathematically Proficient Students…

The practices have been arranged in pairs to show which may

naturally appear together when students are engaged in certain types of tasks or with certain mathematics content. SMP 1 & 6

are overarching in the sense that if students are truly engaged in ‘solving’ tasks that are ‘problems’ to them, they will need to make sense of problems and have perseverance, and refine

their thinking and their ability to communicate about the mathematics, which is part of attending to precision.

Visit the Mathematical Practices Resources Page for additional classroom resources, explanations, examples, and videos of the practices in action.

Rogers Public Schools 3 of 6 | Revised 5-15-13

R.P.S. Common Core Math Curriculum Overview Kindergarten

Content Emphases by Cluster

The content emphases in the standards at the cluster level are provided because curriculum, instruction, and assessment at each grade must reflect the focus and emphasis of the standards.

Not all of the content in a given grade is emphasized equally in the standards.

The list of content standards for each grade is not a flat, one-dimensional checklist.

Some clusters require greater emphasis than the others based on the depth of the ideas, the time that they take to master, and/or their importance to future mathematics or the demands of college and career readiness.

Intense focus on the most critical material at each grade allows depth in learning, which is carried out through the Standards for Mathematical Practice.

Assessments will strongly focus where the standards strongly focus.

Therefore, to make the emphases in the standards more transparent and useful, the clusters have been designated as Major, Supporting and Additional. Some clusters that are not major emphases in themselves are designed to support and strengthen areas of major emphasis, while other clusters that may not connect tightly or explicitly to the major work of the grade are called additional.

PARCC Model Content Frameworks for Mathematics p.13-14

Major Clusters Areas of intensive focus, where students need fluent understanding and application of the core concepts

(approximately 70% of instructional time)

Supporting Clusters Rethinking and linking; areas where material is being

covered, but in a way that applies to core understandings

(approximately 20% of instructional time)

Additional Clusters Expose students to other subjects, though at a distinct

level of depth and intensity

(approximately 10% of instructional time) Counting and Cardinality

Know number names and count sequence.

Count to tell the number of objects.

Compare numbers. Operations and Algebraic Thinking

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

Number and Operations in Base Ten

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

Geometry

Identify and describe shapes.

Analyze, compare, create, and compose shapes.

Measurement and Data

Describe and compare measurable attributes.

Classify objects in categories.

For further information regarding the content emphases by cluster visit: www.engageny.org/resource/math-content-emphases/

Rogers Public Schools 4 of 6 | Revised 5-15-13

R.P.S. Common Core Math Curriculum Overview Kindergarten

Year Long Pacing of the Common Core State Standards (p. 1of 3) Shading indicates standards for instruction each quarter Approximate Instructional time distribution: 70% to Major Clusters 20 % to Supporting Clusters 10% to Additional Clusters

1st

Quarter 2nd

Quarter 3rd

Quarter 4th

Quarter

Counting and Cardinality Know number names and the count sequence

K.CC.1. Count to 100 by ones and by tens. Rote count by

1's to 20

Rote count by 1's and 10's to

50

Rote count by 1's to 75;

by 10's to 100

Rote count by 1's and 10's to

100

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). Write

numbers to 5 Write

numbers to 10 Write

numbers to 15 Write

numbers to 20

Count to tell the number of objects.

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

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.

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.

With as many as 5 objects

With as many as 10 objects

With as many as 15 objects

With as many as 20 objects

Compare numbers

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. [Include groups with up to ten objects.]

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

Rogers Public Schools 5 of 6 | Revised 5-15-13

R.P.S. Common Core Math Curriculum Overview Kindergarten

Year Long Pacing of the Common Core State Standards (p. 2 of 3) Shading indicates standards for instruction each quarter Approximate Instructional time distribution: 70% to Major Clusters 20 % to Supporting Clusters 10% to Additional Clusters

1st Quarter

2nd Quarter

3rd Quarter

4th Quarter

Operations and Algebraic Thinking

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

K.OA.1. Represent addition and subtraction with objects, fingers, mental images, drawings [Drawings need not

show details, but should show the mathematics in the problem. (This applies wherever drawings are mentioned in the Standards.)], 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). With numbers

up to 5 With numbers

up to 10 With numbers

up to 10 With numbers

up to 10

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. Not formally

reported

K.OA.5. Fluently add and subtract within 5. Not formally

reported Not formally

reported

Number and Operations in Base Ten Work with numbers 11–19 to gain foundations for place value.

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.

Represent numbers 11 to 19

Rogers Public Schools 6 of 6 | Revised 5-15-13

R.P.S. Common Core Math Curriculum Overview Kindergarten

Year Long Pacing of the Common Core State Standards (p. 3 of 3) Shading indicates standards for instruction each quarter Approximate Instructional time distribution: 70% to Major Clusters 20 % to Supporting Clusters 10% to Additional Clusters

1st Quarter

2nd Quarter

3rd Quarter

4th Quarter

Measurement and Data Describe and compare measurable attributes K.MD.1. Describe measurable attributes of objects, such as length or weight. Describe several measurable attributes

of a single object.

K.MD.2. Directly compare two objects with a measurable attribute in common, to see which object has “more

of”/“less of” the attribute, and describe the difference. For example, directly compare the heights of two children and describe one child as taller/shorter.

Classify objects and count the number of objects in each category K.MD.3. Classify objects into given categories; count the numbers of objects in each category and sort the categories

by count. [Limit category counts to be less than or equal to 10.]

Geometry

Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres).

K.G.1. Describe objects in the environment using names of shapes, and describe the relative positions of these

objects using terms such as above, below, beside, in front of, behind, and next to.

K.G.2. Correctly name shapes regardless of their orientations or overall size.

K.G.3. Identify shapes as two-dimensional (lying in a plane, “flat”) or three-dimensional (“solid”).

Analyze, compare, create, and compose shapes

K.G.4. Analyze and compare two- and three-dimensional shapes, in different sizes and orientations, using informal

language to describe their similarities, differences, parts (e.g., number of sides and vertices/“corners”) and other attributes (e.g., having sides of equal length).

K.G.5. Model shapes in the world by building shapes from components (e.g., sticks and clay balls) and drawing

shapes.

K.G.6. Compose simple shapes to form larger shapes. For example, “Can you join these two triangles with full sides

touching to make a rectangle?”

Standards per Quarter 14 16 13 16