Subject Area—Mathematics Grade Level --Kindergarten Mission Statement: It is the mission of the Elba Central School District to actualize the phrase “Elba Equals Educational Excellence for Everyone.” We are committed to providing both quality and equity. Every student will have the opportunity to develop to the best of his/her ability.
Elba Standards: In addition to the knowledge and basic skills they need in order to participate in society, graduates of Elba Central School will develop:
1. Empowering skills: decision making, goal setting, creative thinking and problem solving abilities;
2. Communication and social interaction skills;
3. Technological literacy;
4. Total wellness (social, physical, emotional health and self-esteem);
5. The values necessary to participate in society.
As a result of achieving these outcomes, our students will embrace lifelong learning.
New York State Standards: Standard 3---Students will understand mathematics and become mathematically confident by communicating and reasoning mathematically, by applying mathematics in real-world settings, and by solving problems through the integrated study of number systems, geometry, algebra, data analysis, probability, and trigonometry; but also the seven key ideas:
1. Mathematical Reasoning
2. Numbers and Numeration
3. Operations
4. Modeling/Multiple Representation
5. Measurement
6. Uncertainty
7. Patterns/Functions
Standard 6---Interconnectedness: Common Themes. Students will understand the relationships and common themes that connect mathematics, science, and technology and apply the themes to these and other areas of learning.
1. Systems Thinking
2. Models
3. Magnitude and Scale
4. Equilibrium and Stability
5. Patterns of Change
6. Optimization
Performance Indicators: Description of the levels of student achievement pertaining to standard.
Standard 3
Mathematical Reasoning
1A. Use models, facts, and relationships to draw conclusions about
mathematics and explain their reasoning.
1B. Use patterns and relationships to analyze mathematical situations.
1C. Explain their answers and solution processes.
Number and Numeration
2A. Use whole numbers to determine number positions and quantify
groups of objects.
2B. Use concrete materials to model numbers and number relationships
for whole numbers and fractions.
2C. Relate counting to grouping and place value.
2D. Recognize the order of whole numbers.
Operations
3A. Develop strategies for selecting the appropriate computational and
operational methods in problem solving.
3B. Develop readiness for single-digit addition and subtraction facts.
3C. Understand the commutative and associative properties.
Modeling/Multiple Representation
4A. Use concrete materials to model spatial relationships.
4B. Construct charts and graphs to display and analyze real-world
data.
4C. Use multiple representations (manipulative materials, pictures,
diagrams) as tools to explain the operation of everyday procedures.
4D. Use physical materials, pictures, and diagrams to explain
mathematical ideas and processes and to demonstrate geometric
concepts.
Measurement
5A. Select appropriate standard and nonstandard measurement tools
in measurement activities.
5B. Understand the attributes of length, capacity, weight, time, money,
and temperature.
5C. Estimate measures such as length and volume, using both standard
and nonstandard units.
5D. Collect and display data.
5E. Use statistical methods such as graphs and charts to interpret data.
Uncertainty
6A. Recognize situations in which only an estimate is required.
6B. Develop a variety of estimation skills and strategies.
6C. Predict experimental probabilities.
Patterns/ Functions
7A. Recognize, describe, extend, and create a wide variety of
patterns.
7B. Represent and describe mathematical relationships.
7C. Use a variety of manipulative materials to explore patterns.
7D. Interpret graphs.
7E. Explore and develop relationships among two-and three-dimensional
geometric shapes.
7F. Discover patterns in nature, art, music, and literature.
Standard 6
Systems Thinking
1A. Observe and describe interactions among components of simple
systems.
1B. Identify common things that can be considered to be systems
(eg. a plant population, a subway system, human beings).
Models
2A. Analyze, construct, and operate models in order to discover attributes
of the real thing.
2B. Discover that a model of something is different from the real thing
but can be used to study the real thing.
2C. Use different types of models, such as graphs, sketches, diagrams,
and maps, to represent various aspects of the real world.
Magnitude and Scale
3A. Provide examples of natural and manufactured things that belong
to the same category yet have very different sizes, weights, ages,
speeds, and other measurements.
3B. Identify the biggest and the smallest values as well as the average
value of a system when given information about its characteristics
and behavior.
Equilibrium and Stability
4A. Cite examples of systems in which some features stay the same
while other features change
4B. Distinguish between reasons for stability---from lack of changes
to changes that counterbalance one another to changes within cycles.
Patterns of Change
5A. Use simple instruments to measure such quantities as distance, size,
and weight and look for patterns in the data.
5B. Analyze data by making tables and graphs and looking for patterns
of change
Optimization
6A. Determine the criteria and constraints of a simple decision making
problem
6B. Use simple quantitative methods, such as ratios, to compare costs to
benefits of a decision problem.
National Standards: Instructional programs from prekindergarten through grade 12 should enable all students to—
Number and Operations
Number and Operations Understand numbers, ways of representing numbers, relationships among numbers, and number systems
Understand meanings of operations and how they relate to one another
Compute fluently and make reasonable estimates
Algebra
Algebra Understand patterns, relations, and functions
Represent and analyze mathematical situations and structures using algebraic symbols
Use mathematical models to represent and understand quantitative relationships
Analyze change in various contexts
Geometry
Geometry Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships
Specify locations and describe spatial relationships using coordinate geometry and other representational systems
Apply transformations and use symmetry to analyze mathematical situations
Use visualization, spatial reasoning, and geometric modeling to solve problems
Measurement
Measurement Understand measurable attributes of objects and the units, systems, and processes of measurement
Apply appropriate techniques, tools, and formulas to determine measurements
Data Analysis and Probability
Data Analysis and Probability Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them
Select and use appropriate statistical methods to analyze data
Develop and evaluate inferences and predictions that are based on data
Understand and apply basic concepts of probability
Problem Solving
Problem Solving * build new mathematical knowledge through problem solving;
* solve problems that arise in mathematics and in other contexts;
* apply and adapt a variety of appropriate strategies to solve problems;
* monitor and reflect on the process of mathematical problem solving.
Reasoning and Proof
Reasoning and Proof * recognize reasoning and proof as fundamental aspects of mathematics;
* make and investigate mathematical conjectures;
* develop and evaluate mathematical arguments and proofs;
* select and use various types of reasoning and methods of proof.
Communication
Communication * organize and consolidate their mathematical thinking through communication;
* communicate their mathematical thinking coherently and clearly to peers, teachers, and others;
* analyze and evaluate the mathematical thinking and strategies of others;
* use the language of mathematics to express mathematical ideas precisely.
Connections * recognize and use connections among mathematical ideas;
* understand how mathematical ideas interconnect and build on one another to produce a coherent whole;
* recognize and apply mathematics in contexts outside of mathematics.
Representation * create and use representations to organize, record, and communicate mathematical ideas;
* select, apply, and translate among mathematical representations to solve problems;
* use representations to model and interpret physical, social, and mathematical phenomena.
Assessment
:
Acceptable Performance Level
A measure of student progress on performance indicators.
Based on pre-established criteria.
(any kind of test you are giving that is testing the performance indicator - formal or informal)
Scope:
Sorting and Classifying
Geometry/Patterns
Number Readiness and Graphing
Counting/One to One Correspondence/Numeral Recognition
Spatial Relationships and Position
Money and Time
Comparing and Measuring
Exploring Addition and Subtraction
Sequence:
Fall
Sorting and Classifying (ex. color, size, shape etc.,)
Identify geometric shapes (circle, square, triangle)
Recognize an A,B pattern
Recognize equality and inequality
Verbalize comparisons using data on a graph
Count by l’s to 10
Recognize numerals 0-5
Demonstrate one to one correspondence to 5
Identify and describe positional words (Ex. Inside, outside, top, middle, bottom, left, right)
Recognize a penny and nickel
Identify days of the week
Explore the Fall months
Explore the concept of size
Winter
Winter
Sort by size
Identify geometric shape (rectangle,oval)
Identify and create patterns
Copy and extend an existing pattern
Identify groups of more and less
Make and interpret a graph
Count by 1’s to 20
Count by 10’s to 100
Recognize numerals 0-10
Demonstrate one to one correspondence to 10
Identify and describe positional words (before, after, between, first ,next, last)
Recognize a dime and quarter
Explore the Winter months
Read a clock and say time to the hour
Compare daily temperatures
Compare weight of objects
Measure length in arbitrary units
Measure capacity of containers
Writing numerals 0-10
Introduce concept words (Horizontal, vertical, diagonal)
Spring
Spring
Identify geometric shape (diamond, cone)
Recognize numerals 0-20
Demonstrate one to one correspondence to 20
Order groups of objects from least to greatest
Identify ordinal positions to fifth
Use a graph to solve a problem
Recognize and extend a number pattern
Identify the value of penny, nickel, dime
Introduce the value of a group of coins
Explore the Spring months
Read a clock and say time to the half hour
Write numerals 0-20
Identify whole and half
Introduce concept of addition and subtraction under 10