Grade Level: Grade 1

Algebraic Reasoning

Concepts
Patterns and Functions

Enduring Understandings
Objects can be sorted into patterns.
Generalized rules describe patterns.
One or more attributes represent a pattern unit that can be extended.

Skills
Examine attributes of objects and describe the relationships.
   1.)       Sort, classify and order objects and numbers based on one and two attributes and describe the rule used.
   2.)       Recognize, extend, describe and create a variety of patterns, and translate the same pattern from one representation (such as color) to another representation (such as shape).
   3.)       Describe counting patterns and number patterns.
   4.)       Develop and test generalizations based on observations of patterns and relationships.  Represent the result of counting, combining and separating sets of objects using number sentences.
   1.)       Model real-life situations that involve addition and subtraction of whole numbers using objects, pictures and open sentences.  
Identify quantities as equivalent or non-equivalent.
   1.)       Demonstrate balance or equivalence using models.

Numerical & Proportional Reasoning

Concepts
Numeric Relationships, Ratios, Proportion and Number Sense

Enduring Understandings
Numbers represent quantitative relationships.
Number sentences explain part-whole relationships.
Problem solving strategies show various types of reasoning.

Skills
Represent and order two digit numbers as groups of tens and ones in the base ten place value system.
   1.)       Estimate and describe quantity with benchmark amounts such as 0, 10 and 100.
   2.)       Represent 2-digit numbers on number lines and using models.
   3.)       Determine and compare values and trade with sets of pennies and dimes.
   4.)       Identify ordinal position of objects, first through fifth. 
Identify and compare equal parts of a whole.
   1.)       Identify and represent ½, 1/3, and ¼ of a whole and identify portions that are not halves, thirds or fourths.
   2.)       Compare parts of a whole object and estimate whether they are closer to a very little, one half, or one whole.
   3.)       Make a whole of equal sized parts of familiar objects. 
Partition a set of objects into smaller groups with equal amounts.
   1.)       Identify half of a small set of objects considered to be the whole.  
Describe relationships between quantities using ratios.
   1.)       Describe patterns with simple ratios using familiar contexts, such as 1 cat has 4 legs, 2 cats have 8 legs.
Count by groups, add one more to the grouping and compare values of groups.
   1.)       Count whole numbers to 100.
   2.)       Identify, read and write numerals to 100 and beyond.
   3.)       Group and skip count by 2s, 5s, and 10s.
   4.)       Count on from a given amount, orally and with models and count back from ten.
   5.)       Identify 1 more and 1 less and explore 10 more and 10 less.  
Add by counting and combining and subtract by separating, comparing or counting on.
   1.)       Write number sentences and use objects and pictures to model and solve addition and subtraction story problems.
   2.)       Develop, describe and use a variety of strategies to add and subtract 1-digit numbers.
   3.)       Explore finding the sum of two 2-digit numbers using models and counting strategies.
   4.)       Identify reasonable answers to problems that reflect real-world experiences.

Geometry & Measurement

Concepts
Shapes; Geometric Comparisons; Measurement

Enduring Understandings
Lines of symmetry divide an object into identical parts.
Areas of shapes can be compared by using non-standard and standard units of measure.

Skills
Classify shapes and solids by common characteristics.
   1.)       Sort, build, name and draw two- and three-dimensional objects.
   2.)       Use a variety of materials to create two- and three-dimensional designs and copy them from visual memory.
   3.)       Create and explore shapes and designs with a line of symmetry.  
Describe, name and interpret direction and position of objects.
   1.)       Indicate relative position, direction and location with terms such as inside, outside, top, bottom, left and right.   
Plan and sequence events.
   1.)       Estimate and compare the length of time needed to complete tasks using terms such as longer or shorter.
   2.)       Use the calendar to identify dates, days, weeks, months and to plan and sequence events.
   3.)       Tell time to the hour with analog and digital clocks.  
Estimate length, area, volume, weight and temperature using nonstandard units.
   1.)       Use physical referents to make estimates, and to determine and describe the reasonableness of answers to measurement problems.
   2.)       Use estimation, physical referents and nonstandard units to sort and compare objects.
Use standard units of measure to communicate measurement in a universal manner.
   1.)       Explore using the standard units of inch and centimeter to estimate and measure length.

Working with Data: Probability & Statistics

Concepts
Data Relationships; Prediction; Numeric Communication

Enduring Understandings
Data can be collected, organized, and displayed by using a variety of formats (graphs, charts, etc.)
Data can be analyzed to make predictions and solve real-life problems.
Sets of data can be compared and analyzed using data tables and bar graphs.

Skills
Collect, organize, record and describe data.
   1.)       Pose questions and collect, organize, record and describe data using tallies, tables, real graphs, picture graphs, glyphs (code pictures) and bar graphs.  
Organize data in tables and graphs and make comparisons of the data.
   1.)       Use various methods to organize information including lists, systematic counting, sorting, graphic organizers, and tables.
   2.)       Use comparative language to describe the data in tables and graphs.  
Determine the likelihood of certain events through simple experiments and observations of games.
   1.)       Observe, record, graph, and describe the results of simple probability activities and games.
   2.)       Describe and explain the likelihood of various events in the students’ world.