Grade Level: Grade 2

Algebraic Reasoning

Concepts
Patterns and Functions

Enduring Understandings
The organization of data determines the resulting pattern.
Functional relationships are discovered using visual representations.

Skills
Recognize, reproduce, extend, describe and create patterns.
   1.)       Describe and classify data and objects based on more than one attribute.
   2.)       Use patterns and the rules that describe them to identify a missing object, objects with common or different attributes, and the complement of a set of objects.
   3.)       Explore a variety of ways to describe and write rules for patterns.
   4.)       Replicate the pattern using a different representation.
Analyze and describe change in terms of quantity and quality using patterns.
   1.)       Explore and describe number patterns including odd and even numbers, counting by 2s, 5s, 10s, 100s and counting on by 10.  
   2.)       Make comparisons of data and analyze observable changes using qualitative and quantitative descriptions.  
Represent real-life situations using number sentences.  
   1.)       Model situations involving addition and subtraction of whole numbers using objects, pictures, symbols and open sentences.  
Show equivalence or balance of whole number relationships and fractional amounts.  
   1.)       Demonstrate understanding of the = sign as an equality symbol.
   2.)       Use objects, diagrams or numbers to show equivalence.

Numerical & Proportional Reasoning

Concepts
Numeric Relationships, Ratios, Proportion and Number Sense

Enduring Understandings
Place value determines the magnitude of a number.
Fractions model proportional quantities.
The reasonableness of a number depends on the context.
Location on a number line represents relationships among numbers.

Skills
Represent three digit numbers as groups of hundreds, tens and ones in the base ten place value system.
   1.)       Use place value models and pictures to represent 2- and 3-digit numbers and write numbers in expanded and regrouped forms.
   2.)       Locate, label and order 2- and 3-digit numbers using place value models, pictures and number lines.
   3.)       Use place value models, pictures and number lines, to identify 10 more and 10 less and 100 more and 100 less.
   4.)       Count with, determine and compare values and trade pennies, dimes and dollars.  
   5.)       Count whole numbers up to 1,000 and beyond.
Represent fractions by sharing portions of equal size as parts of a whole or parts of a set.
   1.)       Model and describe equal parts of a whole as unit fractions 1/2 through 1/10.
   2.)       Use models and familiar objects to estimate, compare and order unit fractions (1/2, 1/3, 1/4) of a whole.
   3.)       Estimate and use counting and grouping of objects to find equal parts of a small set of counting objects, such as 1/2, 1/3, 1/4 of 12 cookies.
   4.)       Explore equivalent fractions using models.  
Recognize that the denominator of a fraction tells how many equal parts an object or a set has been divided into, and the numerator indicates how many of the parts are being considered.
   1.)       Identify and build models of fractional parts of a whole (such as 3/4), other than unit fractions.
   2.)       Explore and describe addition with like denominators and write matching fraction sentences using models.  
Describe relationships between quantities using ratios.
   1.)       Describe simple ratios in patterns using models and pictures such as in a pattern of green, green, red blocks, there are always two green blocks for each red block. 
Develop fact families of basic facts using the inverse relationship of addition and subtraction.
   1.)       Recall basic addition and subtraction facts to 18.
   2.)       Identify reasonable answers and solve addition and subtraction problems involving real-world experiences using a variety of methods including models, pictures, pencil and paper, estimation and mental computation.
Explore the relationship of multiplication and division through a variety of methods.
   1.)       Explore multiplication with factors of 2, 5, and 10 by extending number patterns, skip counting, combining repeated addends, building models of groups the same size and using arrays and pictures.
   2.)       Explore the connection between multiplication and division using models and pictures of groups and arrays.   
Identify and use equivalent representations of numbers to estimate and compute.
   1.)       Compare and round numbers to the nearest ten using place value models and number lines.
   2.)       Explore and describe strategies for representing, estimating, adding and subtracting two 2-digit numbers with and without regrouping.
   3.)       Recognize when an estimate is appropriate and use estimation strategies that result in identifying a reasonable answer to a problem.
   4.)       Add and subtract 3-digit numbers without regrouping.

Geometry & Measurement

Concepts
Shapes; Geometric Comparisons; Measurement

Enduring Understandings
Standard units provide consistent measurement.
Two and three dimensional shapes can be classified, compared and analyzed using various attributes.

Skills
Identify shapes as the same when there are changes in position.
   1.)       Explore translations (slides), reflections (flips) and rotations (turns) of simple polygons using manipulative materials.
   2.)       Build and identify shapes that have one or more lines of reflective symmetry or that can be divided into two congruent parts.
   3.)       Explore filling a two-dimensional region with different shapes.  
Recognize and use geometric relationships to solve problems.
   1.)       Explore combining and subdividing polygons and solids with manipulative materials and reconstruct them from visual memory.
   2.)       Build, describe, draw and identify polygons, solids and other two- and three-dimensional objects found in the environment.  
Estimate and measure the length of time to complete activities and tasks.
   1.)       Locate dates, days, weeks and months on a calendar.
   2.)       Use the calendar to write and solve problems involving time.
   3.)       Tell time to the half-hour, and explore time to the quarter-hour (analog and digital.)
Measure through direct comparison and through repetition of units.
   1.)       Develop and use nonstandard referents and standard benchmarks to estimate and measure length, area, weight, capacity and volume.
   2.)       Identify reasonable estimates and describe the strategies used to determine the estimates.
   3.)       Explore using measurement tools such as thermometers, basic rulers and balance scales to measure temperature, length and weight.
   4.)       Describe relationship between centimeter and meter, inch, foot and yard.

Working with Data: Probability & Statistics

Concepts
Data Relationships; Prediction; Numeric Communication

Enduring Understandings
Data can be organized and interpreted to make predictions and solve problems.
Predictions can be formulated and tested based on data relationships.

Skills
Construct graphs from data then make comparisons and draw conclusions.
   1.)       Pose questions and systematically collect, sort, organize, record and analyze data using tables, charts, picture and bar graphs.
   2.)       Use comparative terms to describe data.  
Determine patterns and make predictions from data displayed in tables and graphs.
   1.)       Investigate combinations using models.  
Analyze data gathered from experiments and identify the likelihood of future events.
   1.)       Discuss the likelihood of various events, state possibilities, make predictions and test them in practical situations.
   2.)       Conduct probability experiments and record the results in tables and graphs.