Connecticut State Standards for Mathematics: Grade 2

CT.1. Algebraic Reasoning: Patterns and Functions: Patterns and functional relationships can be represented and analyzed using a variety of strategies, tools and technologies.

1.1. Understand and describe patterns and functional relationships.

1.1.1. Sort, classify and order objects and numbers in more than one way and by one and two attributes and describe the rule used. Use attributes such as size, shape, color, texture, orientation, position and use; and characteristics such as symmetry and congruence.

1.1.2. Recognize, extend, and create repeating, growing, number; e.g., skip counting, odd/even, counting on by 10; and one and two attribute patterns. Describe the pattern and the rule used to make it.

1.1.3. Replicate the pattern using a different representation, e.g., letters to numbers.

1.1.4. Use patterns and the rules that describe the patterns to identify a missing object, objects with common or different attributes, and the complement of a set of objects.

1.1.5. Analyze and describe observable changes in patterns using language that describes number characteristics and qualitative characteristics such as attributes, orientation and position.

1.2. Represent and analyze quantitative relationships in a variety of ways.

1.2.6. Model real-life situations that represent the addition and subtraction of whole numbers with objects, pictures, symbols and open sentences.

1.3. Use operations, properties and algebraic symbols to determine equivalence and solve problems.

1.3.7. Demonstrate an understanding of equivalence or balance of sets using objects, models, diagrams, numbers whole number relationships (operations) and the equals sign, e.g., 2 + 3 = 5 is the same as 5 = 2 + 3 and the same as 4 + 1 = 5.

CT.2. Numerical and Proportional Reasoning: Quantitative relationships can be expressed numerically in multiple ways in order to make connections and simplify calculations using a variety of strategies, tools and technologies.

2.1. Understand that a variety of numerical representations can be used to describe quantitative relationships.

2.1.1. Locate, label, compare, and order whole numbers up to 1,000 using pictures, place value models, number lines, and benchmarks of 0, 10 and 100, including naming the number that is 10 or 100 more or less than a given number.

2.1.2. Represent whole numbers up to 1,000 by modeling and writing numbers in expanded forms, e.g., 37 = (3 x 10) + (7 x 1), and regrouped forms, e.g., (2 x 10) + (17 x 1) = 37, and use the forms to support computational strategies.

2.1.3. Represent multiplication and division (with factors of 1, 2, 5 and 10 ) using a variety of models and strategies such as arrays, pictures, skip counting, extending number patterns, and repeated addition and subtraction; describe the connection between multiplication and division.

2.1.4. Use a variety of models and familiar objects to compare, order and estimate parts of a whole using the unit fractions 1/2, 1/3, 1/4.

2.1.5. Use a variety of models to represent and describe parts of groups as unit fractions 1/2, through 1/10.

2.1.6. Estimate and determine 1/2, 1/3, 1/4 of a small group of up to 20 objects, such as finding 1/2, 1/3, 1/4 of 12 cookies.

2.1.7. Describe ratios in terms of the linear patterns that develop from the relationships between quantities, e.g., In a pattern of green, green, red blocks there are always two green blocks for one red block.

2.2. Use numbers and their properties to compute flexibly and fluently and to reasonably estimate measures and quantities.

2.2.8. Count whole numbers to 1,000 and beyond.

2.2.9. Count on by tens from a given amount, e.g., 17, 27, 37, etc.

2.2.10. Read and write numerals up to 1,000.

2.2.11. Skip count by twos, fives, tens and hundreds to 1,000 and beyond.

2.2.12. Determine whether a set of objects has an odd or even number of items by pairing objects and creating arrays.

2.2.13. Create word problems and write and solve two- and three-digit number sentences that reflect contextual situations and real-world experiences involving addition and subtraction. Construct and solve open sentences, e.g., __ + 5 = 11. Solve the problems using a variety of methods including models, pictures, pencil and paper, estimation and mental computation, and describe the reasoning or strategies used.

2.2.14. Solve problems using addition and subtraction facts involving sums and differences to 20 with flexibility and fluency

2.2.15. Add two-digit numbers with and without regrouping. Subtract two-digit numbers without regrouping and with regrouping using models.

2.2.16. Determine when an estimate for a problem involving two- and three-digit numbers is appropriate or when an exact answer is needed.

2.2.17. Use a variety of strategies to estimate solutions and to determine if a solution to a computation or word problem reflecting real-world experiences involving addition and subtraction of two- and three-digit whole numbers is reasonable.

2.2.18. Determine and compare the value of pennies, nickels, dimes, quarters and half dollars.

2.2.19. Count, compare and trade sets of pennies, dimes and dollars up to $10.00

CT.3. Geometry and Measurement: Shapes and structures can be analyzed, visualized, measured and transformed using a variety of strategies, tools and technologies.

3.1. Use properties and characteristics of two- and three-dimensional shapes and geometric theorems to describe relationships, communicate ideas and solve problems.

3.1.1. Identify, describe and draw polygons (triangles, quadrilaterals including trapezoids and rhombuses, pentagons and hexagons), solids, and other familiar two- and three- dimensional objects in the environment.

3.1.2. Compare and sort familiar polygons, solids, and other two- and three- dimensional objects in the environment.

3.1.3. Construct polygons, solids and other two- and three-dimensional objects using a variety of materials and create two-dimensional shapes and designs with one or more lines of reflective symmetry (lines that divide the shape or design into two congruent parts).

3.2. Use spatial reasoning, location and geometric relationships to solve problems.

3.2.4. Investigate and predict the result of putting together and taking apart two- and three-dimensional shapes in the environment, e.g. use objects to find other shapes that can be made from three triangles or a rectangle and a triangle.

3.3. Develop and apply units, systems, formulas and appropriate tools to estimate and measure.

3.3.5. Know the months of the year in order and locate dates, days, weeks and months on a calendar. Use the information to write and solve problems involving calendars.

3.3.6. Solve problems involving telling time, including estimating and measuring the length of time needed to complete a task, to the half-hour using analog and digital clocks.

3.3.7. Use measurement tools such as thermometers to measure temperature, basic rulers to measure length to the nearest half-inch or centimeter, and balance scales to measure weight /mass in grams.

3.3.8. Use nonstandard referents and standard benchmarks to estimate and measure the following:

3.3.8.1. Length(to the nearest inch, half-inch, foot, yard, centimeter or meter);

3.3.8.2. Area (in square inches);

3.3.8.3. Capacity (in liters and cups);

3.3.8.4. Weight (in grams);

3.3.8.5. Temperature; and

3.3.8.6. Volume (using water or sand).

3.3.9. Describe the strategy used to determine an estimate and determine if the estimate is reasonable.

3.3.10. Describe the relationships between and centimeter and meter among inch, foot and yard.

CT.4. Working with Data: Probability and Statistics: Data can be analyzed to make informed decisions using a variety of strategies, tools and technologies.

4.1. Collect, organize and display data using appropriate statistical and graphical methods.

4.1.1. Pose questions that can be used to guide data collection, organization and representation.

4.1.2. Collect and systematically organize and represent the data that answer the questions using lists, charts and tables, tallies, glyphs (coded pictures), picture graphs and bar graphs.

4.2. Analyze data sets to form hypotheses and make predictions.

4.2.3. Describe data that have been organized and make comparisons using terms such as largest, smallest, most often or least often.

4.2.4. Determine patterns and make predictions from data displayed in tables and graphs.

4.3. Understand and apply basic concepts of probability.

4.3.5. Describe and explain the likelihood of the occurrence of various events. State possibilities, make predictions and test the predictions in practical situations.

4.3.6. Conduct simple probability investigations involving activities of chance and games with number cubes and spinners; record, graph and describe the results of the investigations.