KINDERGARTEN

EALR 1: The student understands and applies the concepts and procedures of mathematics.

Number and numeration

1.1.1 Understand the concept of number.

·   Count to at least 31.

·   Represent a number to at least 10 in different ways (e.g., numerals, spoken words, pictures, physical models). [CU]

·   Show that the last count word names the quantity of the set (cardinality) (i.e., when counting fingers on a hand “one, two, three, four, five,” the “five” says how many fingers there are). [CU, MC]

·   Identify the base ten digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.

·   Explain how numbers are used and give examples (e.g., to count, to order). [CU]

1.1.2 Understand sequential relationships among whole numbers.

·   Tell what number comes before or after a given number.

·   Use comparative language (e.g., less than, more than, equal to) to compare numbers to at least 20. [CU]

·   Use a known quantity to at least 10 (benchmark) to compare sets (e.g., sets of counters).

·   Identify the ordinal position of objects at least through tenth (e.g., first, second …).

Computation

1.1.5 Understand the meaning of addition.

·   Express stories involving addition (e.g., join) with models, pictures, and symbols. [CU, MC]

·   Use addition in the classroom environment (e.g., tables and chairs in the classroom). [MC]

Attributes, units, and systems

1.2.1 Understand and apply appropriate terminology to compare attributes.

·   Use comparative vocabulary to describe objects (e.g., longer/shorter, heavier/lighter, nearer/further, thicker/thinner, shorter/taller). [CU]

·   Use terms to describe the duration of events (e.g., long time or short time). [CU]

·   Identify and sort objects based on an attribute (e.g., color, shape, texture). [RL]

Procedures, precision, and estimation

1.2.4 Understand and apply procedures to measure with non-standard units.

·   Use non-standard units to measure (e.g., paper strips, cubes, beans, hand widths).

·   Explain how to use a non-standard unit to measure a given length (e.g., length of a table, width of a desk). [CU]

Properties and relationships

1.3.2 Know the characteristics of familiar objects.

·   Describe familiar objects based on characteristics (e.g., big, small, like a box). [CU, MC]

·   Sort objects in their environment by characteristics (e.g., cans, balls, boxes, red, blue). [MC]

·   Describe objects using comparative language (e.g., bigger, taller, shorter, smaller). [CU]

Locations and transformations

1.3.3 Understand the relative position of objects in the environment.

·   Describe the location of an object relative to another (e.g., in, out, over, under, behind, above, below, next to, etc.). [CU]

·   Identify where a three-dimensional object is located relative to another given object (e.g., where the eraser is relative to the desk).

Statistics

1.4.3 Understand how data can be collected and organized.

·   Use physical objects or pictures to build bar graphs. [CU]

·   Organize objects into groups before counting them. [RL]

1.4.5 Understand how a display provides information.

·   Answer questions about graphs (e.g., how many cats? How many dogs?). [CU]

Patterns, functions, and other relations

1.5.1 Know how to recognize patterns.

·   Identify and extend patterns (e.g., ABAB, green-green-blue, counting). [RL]

·   Create an AB pattern.

Symbols and representations

1.5.3 Understand the concepts of equality and inequality.

·   Use physical objects to model language (e.g., same, different, equal, not equal, more, less). [CU]

·   Model/act out story problems to solve whole number equations and inequalities (e.g., there are three kids and two have three crayons, one has two crayons. How can you make it so allkids have the same number of crayons?). [CU, MC]

EALR 2: The student uses mathematics to define and solve problems.

Example: A classroom needs a playground ball for each student in the class. The class has fewer playground balls than are needed.

Understand problems

2.1.1 Understand how to define a problem in a familiar situation with teacher guidance.

·   State information presented in teacher-led discussion to determine if there is a problem that needs an answer (e.g., a classroom activity requires a playground ball for each student. There are some balls available in the classroom).

·   State the problem in own words (e.g., are there enough playground balls? If not, how do we get enough for the class?).

·   Generate questions that would need to be answered in order to solve the problem (e.g., how many balls are in the classroom? How many more do we need?).

·   Identify known and unknown information with teacher guidance (e.g., known ─ the number of students in the class, and the number of balls needed; unknown ─ the number of additional playground balls needed).  [1.1.5]

2.2.1 Understand how to create a plan to solve a problem with teacher guidance.

·   Gather and organize categorical data (e.g., in a teacher-led activity, create a two-column chart ─ one column for student names and tally marks in the other to represent which students are assigned a ball). [1.4.3]

2.2.2 Apply mathematical tools to solve the problem with teacher guidance.  W

·   Use appropriate tools to find a solution (e.g., draw pictures, use chart to count how many empty spaces there are for the playground balls). [1.1.1, 1.1.5]

·   Recognize when an approach is unproductive and try a new approach.

EALR 3: The student uses mathematical reasoning.

Example: A classroom needs a playground ball for each student in the class. The class has fewer playground balls than are needed.

3.1.1 Understand how to compare information presented in familiar situations with teacher guidance.

·   Restate understanding of the situation (e.g., each student requires a playground ball; there are not enough in the classroom).

3.2.1 Understand how to make a reasonable prediction based on the information given in a familiar situation.

·   Predict a numerical solution for a problem (e.g., guess how many more playground balls are needed).

3.3.1 Understand how to justify results using evidence.

·   Use tools (e.g., tally marks, physical models, words) to check for reasonableness of an answer (e.g., line up students; pass out the playground balls to students to see how many students do not receive one).

·   Check reasonableness of an estimation by acting it out, using pictures, or physical models.

EALR 4: The student communicates knowledge and understanding in both everyday and mathematical language.

4.2.1 Understand how to organize information to communicate to a given audience with teacher guidance.

·   Use a two-column chart to organize data (e.g., one column for student names and tally marks in the other to represent which students are assigned a ball) for the classroom with teacher guidance.

·   Use physical objects or pictures to build bar graphs to answer a question generated by the class (e.g., how many of each kind of pet do we own?).

4.2.2 Understand how to communicate or represent ideas or information using mathematical language or notation.

·   Explain or represent ideas using mathematical language from:

o       Number sense (e.g., numbers 1 to 10) [1.1.1];

o       Measurement (e.g., compare objects to describe relative size) [1.2.1];

o       Geometric sense (e.g., name objects based on their characteristics ─ I have four equal sides, what am I?) [1.3.1];

o       Algebraic sense (e.g., create a pattern such as AB). [1.5.1]

EALR 5: The student understands how mathematical ideas connect within mathematics, to other subject areas, and to real-life situations.

5.1.1 Understand how to use concepts and procedures from any two of the content components from EALR 1 in a given problem or situation.

·   Organize data collections (e.g., bar graph, sorted groups) and compare data using comparative language. [1.1.2, 1.4.3]

·   Sort objects based on chosen attribute and create a simple AB pattern using the sorted objects. [1.3.2, 1.5.1]

5.1.2 Understand how to recognize and create equivalent mathematical models and representations in familiar situations.

·   Identify different representations of a number to 20 (e.g., numerals, pictures, physical models). [1.1.1]

·   Express stories involving addition (e.g., join) with models, pictures, and symbols. [1.1.5]

5.2.1 Apply and analyze the use of mathematical patterns and ideas in familiar situations in other disciplines.

·   Describe how math is used in science when a number of objects are needed for an experiment or measurement is used to illustrate change.

·   Identify patterns in a piece of artwork.

Component 5.3:  Relate mathematical concepts and procedures to real-world situations.

5.3.1 Understand how mathematics is used in everyday life.

·   Generate examples of mathematics in everyday life:

o       counting (e.g., the number of people ahead of us in a line);

o       sorting things (e.g., grouping socks by color in order to match them up);

o       comparing things (e.g., who has the biggest piece of cake for dessert, or who is tallest/shortest in the family);

o       pointing out patterns (e.g., in clothing, fence posts, designs on buildings).

·   Identify objects based on a description of their geometric attributes (e.g., buildings have sides; some windows are shaped like a rectangle).

·   Describe the location of objects relative to each other (e.g., in, out, over, under, school bus stops next to each other).