Grade Level: Kindergarten

Algebraic Reasoning

Concepts
Patterns and Functions

Enduring Understandings
1.  Objects can be sorted by attributes.
2.  One or more attributes can be sorted by a pattern unit that can be extended.

Skills
1.  Sort and classify objects using attributes.
    a.)        Sort and classify objects by size, shape, color, texture, use, position and orientation and describe the reason.  
2.  Identify a pattern and describe the rule using the physical attributes or position of objects in a sequence.
    a.)        Recognize, copy and extend patterns of sounds, colors, shapes, textures and numbers in a variety of contexts and describe the rule of the pattern.
    b.)       Make comparisons and describe qualitative and quantitative changes of a given pattern (more, less, bigger, smaller, longer, one more, one less.)

Numerical & Proportional Reasoning

Concepts
Numeric Relationships, Ratios, Proportion and Number Sense

Enduring Understandings
1.  Numbers represent quantities.
2.  Quantities can be counted, ordered, and compared using numbers, words, and numerals.

Skills
1.  Use numbers to count, order, compare, label, locate and measure.
   a.)       Use numbers to locate, order, label, and measure.
   b.)       Identify the numerals 1-10, match sets of objects to the numerals.
   c.)       Compare sets using the terms more, less or the same, and order sets from least to greatest.
   d.)       Identify ordinal position of objects, first through fifth, and last.
   e.)       Act out story problems and solve practical problems using objects.
2.   Share equal parts of an object.
   a.)       Use a variety of models to identify a whole and a half of an object.
   b.)       Compare two parts of a whole and describe the parts as closer to a whole, or closer to very little.
   c.)       Recognize that two halves can be put together to make a whole.
3.   Share a set of objects that is divided into groups with equal amount.
   a.)       Share a set of objects considered to be a whole, by forming two smaller sets that have equal amounts.
4.   Count, adding one more to the previous number and group and count by ones and tens.
   a.)       Count to and past 10, to 20, then to 30 and group and count objects by 10.
   b.)       Estimate the amount of objects in a set using ten as a benchmark, and then count to determine if the amount is more or less than ten.
   c.)       Identify sets and numbers which are equal and one more.
   d.)       Recognize and name pennies and dimes; count and trade pennies for objects.

Geometry & Measurement

Concepts
Shapes; Geometric Comparisons; Measurement

Enduring Understandings
1.  Shapes can be identified by common physical characteristics.
2.  Shapes represent our two and three dimensional world.

Skills

1.   Identify and sort shapes and solids by physical characteristics.
   a.)       Sort, order, compare and use comparative language to describe small sets of objects sequenced by size, length, area and volume.
   b.)       Identify, sort and compare two- and three-dimensional shapes and solids in the environment, such as triangles, squares, rectangles, circles, cubes, spheres, cylinders and cones.
   c.)       Use a variety of materials to create geometric shapes and solids and build copies of simple shapes and designs by direct observation and by visual memory.   
2.   Use positional language to describe location, direction, and position of objects.
   a.)       Describe the position, location and direction of objects, or parts of objects, using terms such as inside, outside, top, bottom, close, closer, etc.
3.   Use calendars and clocks to measure and record time.
   a.)       Locate a date on the calendar (yesterday, today, and tomorrow) and sequence events using terms like before and after.
4.   Use nonstandard units to estimate measures of length, area, temperature, weight and capacity.
   a.)       Estimate the number of objects in a handful, and then count to verify.
   b.)       Estimate the amount of objects in a set using benchmarks of 10, and count to determine if the estimate is more or less.
   c.)       Explore, describe, and discuss strategies to estimate length, area, temperature and weight using nonstandard units to compare.
   d.)       Explore using everyday objects as nonstandard units to measure length, area and capacity.
   e.)       Compare the weight of two objects using a balance scale and identify which is heavier.

Working with Data: Probability & Statistics

Concepts
Data Relationships; Prediction; Numeric Communication

Enduring Understandings
1.  Categorical and numerical information represents data.
2.  Data can be collected, organized, and displayed to show similarities and differences.

Skills
1.   Visualize information and make comparisons about information displayed in real and picture graphs.
   a.)       Pose questions about personal information, experiences and environment.
   b.)       Explore ways to record and organize data using tallies and tables.
   c.)       Construct real graphs and picture graphs and describe the data using the terms more, less and same.
   d.)       Organize information through systematic counting, sorting, making lists and graphic organizers.
2.   Extend different types of patterns and make predictions.
   a.)       Identify visual, auditory and physical patterns and extend to make predictions. 
3.   Observe the frequency of real-world events and identify the likelihood of future events.
   a.)       Describe the likelihood of events related to personal experiences.
   b.)       Engage in simple probability activities and discuss the results.