Connecticut State Standards for Mathematics: Grade 3

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 a group of objects and numbers in more than one way and explain the reason or describe the rule used.

1.1.2. Create and construct numerical and spatial patterns and sequences that repeat and grow.

1.1.3. Analyze, describe and extend repeating and growing patterns and sequences, including those found in real-world contexts, by constructing and using tables, graphs and charts.

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

1.2.4. Describe mathematical relationships and situations involving computation of whole numbers (addition, subtraction, multiplication and division) using words, symbols, open number sentences and equations, e.g., 56 + __ = 100 and 3 x 5 = 9 + 6.

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

1.3.5. .Demonstrate understanding of equivalence as a balanced relationship of quantities by using the equals sign to relate two quantities that are equivalent and the inequality symbols, < and >, to relate two quantities that are not equivalent. (23 x 5 > 23 x 2)

1.3.6. Solve problems and demonstrate an understanding of equivalence using the equals sign in number sentences that reflect the commutative and associative properties of addition and multiplication of whole numbers, e.g. 3 x 5 = 5 x 3.

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 10,000 using place value models, number lines and number patterns (including multiples of 100 and 1,000).

2.1.2. Identify the number that is 100 and 1,000 more or less than a given number up to 10,000 using place value models, pictures and number lines.

2.1.3. Round three- and four-digit numbers to the nearest hundred and thousand using place value models, number lines and number patterns.

2.1.4. Represent three- and four-digit numbers up to 10,000 in expanded forms, e.g., 5,472 = (5 x 1,000) + (4 x 100) + (7 x 10) + (2 x 1), and regrouped forms, e.g., 5,472 = (4 x 1,000) + (14 x 100) + (6 x 10) + (12 x 1). Use the forms to support computational strategies.

2.1.5. Represent fractions with like and unlike denominators of 2, 3, 4, 5, 6 and 8 using a variety of materials; label the fractional parts using words and fraction symbols.

2.1.6. Locate, label and estimate fractions with like and unlike denominators of 2, 3, 4, 5, 6 and 8 by constructing and using models, pictures and number lines.

2.1.7. Determine equivalence, compare and order fractions through the construction and use of models, pictures and number lines with like and unlike denominators of 2, 3, 4, 5, 6 and 8, including identifying a whole object or a whole set of objects as a fraction with the same numerator and denominator.

2.1.8. .Use models, number patterns and counting and grouping of objects, to find equal parts of a set of objects and identify amounts such as 2/3 of 12 is 8.

2.1.9. Describe quantitative relationships using ratios and identify patterns with equivalent ratios such as 3 out of 6 crayons are red or 4 out of 8 crayons are red and are the same as 1 out of 2 crayons is red.

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

2.2.10. Recall the multiplication and division facts for 1, 2, 3, 4, 5 and 10.

2.2.11. Write multiplication and division story problems to match a given multiplication or division number sentence and vice versa; solve the problems and justify the solution.

2.2.12. Solve problems involving addition and subtraction of two- and three-digit whole numbers and money amounts up to $100.00 with and without regrouping, using a variety of strategies, including models.

2.2.13. Create and solve addition and subtraction word problems by using place value patterns and algebraic properties (commutative and associative for addition).

2.2.14. Solve problems involving the multiplication and division of two- and three-digit numbers by one digit (2, 3, 4, 5 or 10) with models, arrays and pictures of sets.

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

2.2.16. Use a variety of estimation strategies to determine and justify the reasonableness of an answer to a computation or word problem involving addition and subtraction of two- and three-digit whole numbers and money amounts up to $100.00.

2.2.17. Determine when a strategy will result in an overestimate or an underestimate in problems involving two- and three-digit numbers.

2.2.18. Determine and compare the value of sets of coins and write the values using decimal notation, e.g., two quarters = 50 cents or $0.50 (50 of 100 cents in a dollar) and is less than two quarters, two dimes and a nickel or $0.75.

2.2.19. Determine, compare and write the value of money amounts up to $100.00 and identify equivalent ways to represent a given amount of money, including combinations of pennies, nickels, dimes, quarters and half dollars, e.g., $0.25 can be five nickels, two dimes and one nickel or one quarter.

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, construct and draw two- dimensional shapes such as quadrilaterals (including parallelograms), pentagons and hexagons.

3.1.2. Identify, describe, construct and represent three-dimensional figures such as cubes, spheres, cylinders, cones, pyramids, prisms.

3.1.3. Compare and classify polygons and solids and determine congruence by using attributes such as the number and length of sides, faces and edges, and the number and kinds of angles (acute, right and obtuse).

3.1.4. Create two-dimensional figures with one or more lines of reflective symmetry.

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

3.2.5. Draw and interpret simple maps using shapes or pictures on a coordinate grid.

3.2.6. Investigate ways to tile or tessellate a shape or region using a variety of polygons.

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

3.3.7. Use calendar and clocks to plan and sequence events and identify events and times as occurring in the a.m. and p.m.

3.3.8. Solve problems involving telling time to the nearest quarter hour, five minutes and minute using analog and digital clocks.

3.3.9. Develop an understanding and describe the relationships between appropriate units of measure through concrete experiences (ounces and pounds; gram and kilograms; inches, feet and yards; meters and kilometers; cups, pints and quarts; and milliliters and liters).

3.3.10. Estimate and measure using nonstandard units and appropriate customary and metric tools and units:

3.3.10.1. Length and perimeter to the nearest 1/4 inch or 1/2 centimeter;

3.3.10.2. Area in square inches or square centimeters;

3.3.10.3. Capacity in cups, pints, quarts, milliliters or liters,

3.3.10.4. Weight in ounces, pounds and grams (mass is weighed in grams);

3.3.10.5. Temperature to the nearest degree; and

3.3.10.6. Volume using inch cubes and centimeter cubes.

3.3.11. Describe and use estimation strategies that can identify a reasonable answer to a measurement problem when an estimate is appropriate.

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 organize the data that answer the questions using diagrams, charts, tables, lists, pictographs, bar graphs and line plots

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

4.2.3. Analyze data that have been collected and organized, to draw and defend conclusions based on the data.

4.2.4. Describe an event or element as typical based upon the range, median and mode of a set of data.

4.3. Understand and apply basic concepts of probability.

4.3.5. Experiment to test predictions and determine probability in practical situations such as investigating the fairness of games using a variety of spinners and dice.

4.3.6. Describe the probability of an outcome as __ out of __, e.g., 3 out of 5.

4.3.7. Investigate combinations using models.