Kansas State Standards for Mathematics: Kindergarten

KS.1. Number and Computation: The student uses numerical and computational concepts and procedures in a variety of situations.

1.1. Number Sense - The student demonstrates number sense for whole numbers, fractions, and money using concrete objects in a variety of situations.

1.1.K1. Knowledge Base Indicator: The student establishes a one-to-one correspondence with whole numbers from 0 through 20 using concrete objects and identifies, states, and writes the appropriate cardinal number.

1.1.K2. Knowledge Base Indicator: The student compares and orders whole numbers from 0 through 20 using concrete objects.

1.1.K3. Knowledge Base Indicator: The student recognizes a whole, a half, and parts of a whole using concrete objects, e.g., half a pizza, part of a cookie, or the whole school.

1.1.K4. Knowledge Base Indicator: The student identifies positions as first and last.

1.1.K5. Knowledge Base Indicator: The student identifies pennies and dimes and states the value of the coins using money models.

1.1.A1. Application Indicator: The student solves real-world problems using equivalent representations and concrete objects to compare and order whole numbers from 0 through 10.

1.2. Number Systems and Their Properties - The student demonstrates an understanding of whole numbers with a special emphasis on place value in a variety of situations.

1.2.K1. Knowledge Base Indicator: The student reads and writes whole numbers from 0 through 20 in numerical form.

1.2.K2. Knowledge Base Indicator: The student represents whole numbers from 0 through 20 using place value models, e.g., ten frames, unifix cubes, straws bundled in 10s, or base ten blocks.

1.2.K3a. Knowledge Base Indicator: The student counts whole numbers from 0 through 20.

1.2.K3b. Knowledge Base Indicator: The student counts whole numbers from 10 to 0 backwards.

1.2.K3c. Knowledge Base Indicator: The student counts subsets of whole numbers from 0 through 20.

1.2.K4. Knowledge Base Indicator: The student groups objects by 5s and by 10s.

1.2.K5. Knowledge Base Indicator: The student uses the concept of the zero property of addition (additive identity) with whole numbers from 0 through 20 and demonstrates its meaning using concrete objects, e.g., 4 apples and no (zero) other apples are 4 apples.

1.2.A1. Application Indicator: The student solves real-world problems with whole numbers from 0 through 20 using place value models, e.g., group the class into tens, count by tens; then continue counting by ones to find the total.

1.2.A2. Application Indicator: The student counts forwards and backwards from a specific whole number using a number line from 0 through 10.

1.3. Estimation - The student uses computational estimation with whole numbers in a variety of situations.

1.3.K1. Knowledge Base Indicator: The student determines if a group of 20 concrete objects or less has more, less, or about the same number of concrete objects as a second set of the same kind of objects.

1.3.A1. Application Indicator: The student compares two randomly arranged groups of 10 concrete objects or less and states the comparison using the terms: more, less, about the same.

1.4. Computation - The student models, performs, and explains computation with whole numbers using concrete objects in a variety of situations.

1.4.K1. Knowledge Base Indicator: The student adds and subtracts using whole numbers from 0 through 10 and various mathematical models, e.g., concrete objects, number lines, or unifix cubes.

1.4.K2. Knowledge Base Indicator: The student uses repeated addition (multiplication) with whole numbers to find the sum when given the number of groups (three or less) and given the same number of concrete objects in each group (five or less), e.g., two nests with three eggs in each nest means 3 + 3 = 6 or 2 groups of 3 makes 6.

1.4.K3. Knowledge Base Indicator: The student uses repeated subtraction (division) with whole numbers when given the total number of concrete objects in each group to find the number of groups), e.g., there are 9 pencils. If each student gets 2 pencils, how many students get pencils? 9 - 2 - 2 - 2 - 2 or 9 minus 2 four times means four students get 2 pencils each and there is 1 pencil left over. or There are eight cookies to be shared equally among four people, how many cookies will each person receive?

1.4.A1. Application Indicator: The student solves one-step real-world addition or subtraction problems with whole numbers from 0 through 10 using concrete objects in various groupings and explains reasoning, e.g., seven apples are in a basket and five students each take an apple; how many apples are left in the basket?

KS.2. Algebra: The student uses algebraic concepts and procedures in a variety of situations.

2.1. Patterns - The student recognizes, describes, extends, develops, and explains relationships in patterns using concrete objects in a variety of situations.

2.1.K1a. Knowledge Base Indicator: The student uses concrete objects, drawings, and other representations to work with types of patterns: repeating patterns.

2.1.K1b. Knowledge Base Indicator: The student uses concrete objects, drawings, and other representations to work with types of patterns: growing (extending) patterns, e.g., 5, 6, 7, ... is an example of a pattern that adds one to the previous number to continue the pattern.

2.1.K2a. Knowledge Base Indicator: The student uses whole numbers to generate patterns, e.g., 2, 4, 6, ...

2.1.K2b. Knowledge Base Indicator: The student uses geometric shapes with one attribute change to generate patterns.

2.1.K2c. Knowledge Base Indicator: The student uses things related to daily life to generate patterns, e.g., breakfast, lunch, and dinner.

2.1.K3. Knowledge Base Indicator: The student identifies and continues a pattern presented in various formats including numeric (list or table), visual (picture, table, or graph), verbal (oral description), and kinesthetic (action).

2.1.K4a. Knowledge Base Indicator: The student generates repeating patterns for the AB pattern, the ABC pattern, and the AAB pattern.

2.1.K4b. Knowledge Base Indicator: The student generates growing (extending) patterns that add 1, 2, or 10 to continue the pattern.

2.1.K5. Knowledge Base Indicator: The student classifies and sorts concrete objects by similar attributes.

2.1.A1a. Application Indicator: The student generalizes the following patterns using pictorial, and/or oral descriptions including the use of concrete objects: repeating patterns for the AB pattern, the ABC pattern, and the AAB pattern.

2.1.A1b. Application Indicator: The student generalizes the following patterns using pictorial, and/or oral descriptions including the use of concrete objects: patterns using geometric shapes with one attribute change.

2.1.A2. Application Indicator: The student recognizes multiple representations of the AB pattern, e.g., big- little, big-little, big-little, ... and 1-2, 1-2, 1-2, ..., or AB, AB, AB, ....

2.1.A3a. Application Indicator: The student uses concrete objects to model a whole number pattern: counting by ones.

2.1.A3b. Application Indicator: The student uses concrete objects to model a whole number pattern: counting by twos.

2.1.A3c. Application Indicator: The student uses concrete objects to model a whole number pattern: counting by tens.

2.2. Variables, Equations, and Inequalities - The student solves addition equations using concrete objects in a variety of situations.

2.2.K1. Knowledge Base Indicator: The student finds the unknown sum using the basic facts with sums through 10 using concrete objects and pictures.

2.2.A1. Application Indicator: The student describes real-world problems using concrete objects and pictures and the basic facts with sums through 10, e.g., given some marbles, Sue says: There are 3 red marbles and 3 blue marbles. Altogether, there are 6 marbles.

2.3. Functions - The student recognizes and describes whole number relationships using concrete objects in a variety of situations.

2.3.K1. Knowledge Base Indicator: The student locates whole numbers from 0 through 20 on a number line.

2.3.A1. Application Indicator: The student represents and describes mathematical relationships for whole numbers from 0 through 10 using concrete objects, pictures, and oral descriptions.

2.4. Models - The student uses mathematical models including concrete objects to represent, show, and communicate mathematical relationships in a variety of situations.

2.4.K1a. Knowledge Base Indicator: The student knows, explains, and uses mathematical models to represent mathematical concepts, procedures, and relationships. Mathematical models include process models (concrete objects, pictures, number lines, unifix cubes, measurement tools, or calendars) to model computational procedures and mathematical relationships, to compare and order numerical quantities, and to represent fractional parts.

2.4.K1b. Knowledge Base Indicator: The student knows, explains, and uses mathematical models to represent mathematical concepts, procedures, and relationships. Mathematical models include place value models (ten frames, unifix cubes, bundles of straws, or base ten blocks) to represent numerical quantities.

2.4.K1c. Knowledge Base Indicator: The student knows, explains, and uses mathematical models to represent mathematical concepts, procedures, and relationships. Mathematical models include fraction models (fraction strips or pattern blocks) to represent numerical quantities.

2.4.K1d. Knowledge Base Indicator: The student knows, explains, and uses mathematical models to represent mathematical concepts, procedures, and relationships. Mathematical models include money models (base ten blocks or coins) to represent numerical quantities.

2.4.K1e. Knowledge Base Indicator: The student knows, explains, and uses mathematical models to represent mathematical concepts, procedures, and relationships. Mathematical models include two-dimensional geometric models (geoboards, dot paper, or attribute blocks), three-dimensional geometric models (solids), and real-world objects to compare size and to model attributes of geometric shapes.

2.4.K1f. Knowledge Base Indicator: The student knows, explains, and uses mathematical models to represent mathematical concepts, procedures, and relationships. Mathematical models include two-dimensional geometric models (spinners), three-dimensional geometric models (number cubes), and concrete objects to model probability.

2.4.K1g. Knowledge Base Indicator: The student knows, explains, and uses mathematical models to represent mathematical concepts, procedures, and relationships. Mathematical models include graphs using concrete objects, pictographs, and frequency tables to organize and display data.

2.4.K2. Knowledge Base Indicator: The student uses concrete objects, pictures, drawings, diagrams, or dramatizations to show the relationship between two or more things.

2.4.A1a. Application Indicator: The student recognizes that various mathematical models can be used to represent the same problem situation. Mathematical models include process models (concrete objects, pictures, number lines, unifix cubes, measurement tools, or calendars) to model computational procedures and mathematical relationships, to compare and order numerical quantities, and to model problem situations.

2.4.A1b. Application Indicator: The student recognizes that various mathematical models can be used to represent the same problem situation. Mathematical models include place value models (ten frames, unifix cubes, bundles of straws, or base ten blocks) to represent numerical quantities.

2.4.A1c. Application Indicator: The student recognizes that various mathematical models can be used to represent the same problem situation. Mathematical models include two-dimensional geometric models (geoboards, dot paper, or attribute blocks), three-dimensional geometric models (solids), and real-world objects to compare size and to model attributes of geometric shapes.

2.4.A1d. Application Indicator: The student recognizes that various mathematical models can be used to represent the same problem situation. Mathematical models include two-dimensional geometric models (spinners), three-dimensional geometric models (number cubes), and concrete objects to model probability.

2.4.A1e. Application Indicator: The student recognizes that various mathematical models can be used to represent the same problem situation. Mathematical models include graphs using concrete objects, pictographs, and frequency tables to organize and display data.

KS.3. Geometry: The student uses geometric concepts and procedures in a variety of situations.

3.1. Geometric Figures and Their Properties - The student recognizes geometric shapes and their attributes using concrete objects in a variety of situations.

3.1.K1. Knowledge Base Indicator: The student recognizes circles, squares, rectangles, triangles, and ellipses (ovals) (plane figures/ two-dimensional figures).

3.1.K2. Knowledge Base Indicator: The student recognizes and investigates attributes of circles, squares, rectangles, triangles, and ellipses using concrete objects, drawings, and/or appropriate technology.

3.1.K3. Knowledge Base Indicator: The student sorts cubes, rectangular prisms, cylinders, cones, and spheres (solids/three-dimensional figures) by their attributes using concrete objects.

3.1.A1. Application Indicator: The student demonstrates how several plane figures (circles, squares, rectangles, triangles, ellipses) can be combined to make a new shape.

3.1.A2. Application Indicator: The student sorts by one attribute real-world geometric shapes that are representations of the solids (cubes, rectangular prisms, cylinders, cones, spheres), e.g., boxes can be sorted as rectangular prisms, cans can be sorted as cylinders, some ice cream cones can be sorted as cones, and some balls can be sorted as spheres.

3.1.A3a. Application Indicator: The student recognizes circles, squares, rectangles, triangles, and ellipses (plane figures) within a picture.

3.1.A3b. Application Indicator: The student recognizes cubes, rectangular prisms, cylinders, cones, and spheres (solids) within a picture.

3.2. Measurement and Estimation - The student estimates and measures using standard and nonstandard units of measure with concrete objects in a variety of situations.

3.2.K1. Knowledge Base Indicator: The student uses whole number approximations (estimations) for length using nonstandard units of measure, e.g., the classroom door is about two kindergartners high or this paper is about two pencils long.

3.2.K2a. Knowledge Base Indicator: The student compares two measurements using these attributes: longer, shorter (length).

3.2.K2b. Knowledge Base Indicator: The student compares two measurements using these attributes: taller, shorter (height).

3.2.K2c. Knowledge Base Indicator: The student compares two measurements using these attributes: heavier, lighter (weight).

3.2.K2d. Knowledge Base Indicator: The student compares two measurements using these attributes: hotter, colder (temperature).

3.2.K3. Knowledge Base Indicator: The student reads and tells time at the hour using analog and digital clocks.

3.2.A1. Application Indicator: The student compares and orders concrete objects by length or weight.

3.2.A2. Application Indicator: The student locates and names concrete objects that are about the same length or weight as a given concrete object.

3.3. Transformational Geometry - The student develops the foundation for spatial sense using concrete objects in a variety of situations.

3.3.K1. Knowledge Base Indicator: The student describes the spatial relationship between two concrete objects using appropriate vocabulary, e.g., behind, above, below, on, or under.

3.3.K2. Knowledge Base Indicator: The student identifies two like objects or shapes from a set of four objects or shapes.

3.3.A1. Application Indicator: The student shows two concrete objects or shapes are congruent by physically fitting one object or shape on top of the other.

3.3.A2. Application Indicator: The student follows directions to move concrete objects from one location to another using appropriate vocabulary.

3.4. Geometry From An Algebraic Perspective - The student identifies one or more points on a number line in a variety of situations.

3.4.K1. Knowledge Base Indicator: The student locates and plots whole numbers from 0 through 20 on a horizontal number line.

3.4.K2. Knowledge Base Indicator: The student counts forwards and backwards from a given whole number from 0 through 10 on a number line.

3.4.A1. Application Indicator: The student solves real-world problems involving counting whole numbers from 0 through 20 using a number line, e.g., if Bill has 8 pieces of candy and his dad gives him 4 more pieces, how many pieces of candy does he have now?

KS.4. Data: The student uses concepts and procedures of data analysis in a variety of situations.

4.1. Probability - The student applies the concepts of probability using concrete objects in a variety of situations.

4.1.K1. Knowledge Base Indicator: The student recognizes whether an event is impossible or possible, e.g., the possibility of a person having ten heads is impossible, while the possibility of a person having red hair is possible.

4.1.K2. Knowledge Base Indicator: The student recognizes and states whether a simple event in an experiment or simulation including the use of concrete objects can have more than one outcome.

4.1.A1. Application Indicator: The student conducts an experiment or simulation with a simple event and records the results in a graph using concrete objects or frequency tables (tally marks).

4.2. Statistics - The student collects, records, and explains numerical (whole numbers) and non-numerical data sets including the use of concrete objects in a variety of situations.

4.2.K1a. Knowledge Base Indicator: The student records numerical (quantitative) and non-numerical (qualitative) data including concrete objects, graphs, and tables using these data displays: graphs using concrete objects.

4.2.K1b. Knowledge Base Indicator: The student records numerical (quantitative) and non-numerical (qualitative) data including concrete objects, graphs, and tables using these data displays: pictographs with a whole symbol or picture representing one (no partial symbols or pictures).

4.2.K1c. Knowledge Base Indicator: The student records numerical (quantitative) and non-numerical (qualitative) data including concrete objects, graphs, and tables using these data displays: frequency tables (tally marks).

4.2.K2. Knowledge Base Indicator: The student collects data related to familiar everyday experiences by counting and tallying.

4.2.K3. Knowledge Base Indicator: The student determines the mode (most) after sorting by one attribute, e.g., color, shape, or size.

4.2.A1. Application Indicator: The student communicates the results of data collection from graphs using concrete objects and frequency tables, e.g., there are sixteen kindergartners. Using themselves as concrete objects, the six students wearing tennis shoes line up in a row. The ten students wearing sandals line up in a row. The kindergartners become the bar graph. Then someone says: There are less kids wearing tennis shoes than kids wearing sandals.