Connecticut State Standards for Mathematics: Grade 4

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. Extend and compare numerical and geometric sequences and classify patterns as growing or repeating, e.g. 2, 4, 8, _, _, grows and visual sequence.

1.1.2. Develop and test generalizations based on observable patterns and relationships and describe the rules for number patterns using equations, e.g., in this sequence 1, 6, 16, 36 ..., to get the next number the current number can be doubled and four added to the product.

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

1.2.3. Describe mathematical relationships and situations, involving ratios and computation of whole numbers, in all four operations with using symbols, number sentences and equations. If one trapezoid = three triangles, then three trapezoids = __.

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

1.3.4. Represent possible values by using symbols, e.g., variables, to represent quantities in expressions and number sentences. Use number sentences (equations) to model and solve word problems.

1.3.5. Solve problems and demonstrate an understanding of equivalence in mathematical situations that reflect the commutative and associative properties of addition and multiplication of whole numbers and the distributive property.

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

2.1.2. Extend number patterns to determine 1,000 and 10,000 more and less than a given number in practical situations.

2.1.3. Round whole numbers up to 100,000 using number patterns, number lines, diagrams and place value models.

2.1.4. Write and describe equivalent representations of four- and five-digit whole numbers up to 100,000 and beyond, in expanded and regrouped forms. Use the forms to support computational strategies.

2.1.5. Relate multiplication and division to number patterns and models of groups and rectangular arrays.

2.1.6. Identify and define prime and composite numbers through the use of models including rectangular arrays, place value models and pictures.

2.1.7. Construct and use number lines, pictures and models, including rulers, to determine and identify equivalent ratios and fractions.

2.1.8. Locate, label and estimate (round) fractions with like and unlike denominators of 2, 3, 4, 5, 6, 8 and 10 by constructing and using models, pictures and number lines.

2.1.9. Construct and use models, pictures and number lines, including rulers to compare and order fractional parts of a whole and mixed numbers with like and unlike denominators of 2, 3, 4, 5, 6 and 8 and 10.

2.1.10. Construct and use models, pictures and number lines, including rulers, to identify wholes and parts of a whole (including a part of a group or groups) as simple fractions and mixed numbers.

2.1.11. Use models to represent tenths and hundredths and record the representations using equivalent ratio, fraction and decimal notation (1/10, 0.1)

2.1.12. Express a ratio or division problem as a fraction and describe the relationship between the divisor and the remainder written as a fraction. For example: When determining the number of groups of 3 in 14, we say 14 / 3 = 4 with a remainder of 2 or 4 2/3).

2.1.13. Solve practical problems involving simple ratios and proportions, e.g., determining distance on maps, by using models, pictures and number patterns

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

2.2.14. Develop and use a variety of computation strategies including place value concepts, number lines and the commutative and associative properties to add and subtract three- and four-digit numbers and money amounts up to $1,000.00.

2.2.15. Solve contextual problems involving addition and subtraction of whole numbers using a variety of methods, including writing appropriate number sentences (equations) and explaining the strategies used.

2.2.16. Create story problems to match a given number sentence (equation).

2.2.17. Recall the multiplication and division facts 1 through 10.

2.2.18. Write multiplication and division story problems involving basic facts and two- and three-digit by one-digit numbers to match a given number sentence and vice versa; solve the problems using strategies that include models and arrays and justify the solutions.

2.2.19. Determine and explain in writing when an estimate is appropriate and whether a particular estimation strategy is reasonable or will result in an overestimate or underestimate involving computation with three- and four- digit numbers and money amounts up to $1,000.

2.2.20. Use models and pictures to add and subtract fractions with like and unlike denominators of 2, 3, 4, 5, 6, 8 and 10 and match number sentences or equations to the problems.

2.2.21. Identify or write number sentences to solve simple problems involving fractions with like denominators, decimals (tenths) and mixed numbers.

2.2.22. Write contextual problems involving the addition and subtraction of fractions with like denominators, decimals (tenths) and mixed numbers; solve the problems and justify the solutions.

2.2.23. Estimate a reasonable answer to simple problems involving fractions, mixed numbers and decimals (tenths).

2.2.24. Write and solve multistep contextual problems, including problems with extraneous information and explain orally and in writing how the answers were determined.

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. Describe and represent polygons, solids, and other familiar two- and three-dimensional objects.

3.1.2. Compare and classify polygons based on relationships such as parallel or perpendicular lines, symmetry and congruence.

3.1.3. Make and test conjectures about polygons using geometric relationships such as symmetry and congruence.

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

3.2.4. Draw and interpret simple maps with ordered pairs of numbers and/or letters in quadrant one of an x, y coordinate system and find possible paths between two points.

3.2.5. Analyze geometric reflections (flips), rotations (turns), and translations (slides) of plane figures and describe the relationship to the original figure.

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

3.3.6. Use calendars and clocks to solve problems and schedule events involving elapsed time.

3.3.7. Write and solve problems involving the conversion of simple measures of time, e.g., minutes to hours, hours to days and days to weeks and months.

3.3.8. Use customary and metric tools and units and non-standard units to estimate, measure and solve problems involving length and perimeter to the nearest quarter-inch or half-centimeter, area, capacity, weight, temperature and volume.

3.3.9. Use estimation strategies to predict reasonable answers to measurement problems and explain the reasoning used orally and in writing.

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 and develop a plan to collect data using observations, surveys and experiments to answer the questions.

4.1.2. Collect, organize and represent the data that answer the questions using simple circle graphs and broken line graphs.

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

4.2.3. Discuss, make predictions and write about patterns and trends in categorical and numerical data that have been represented in a variety of ways.

4.2.4. Determine the range, median, mode and mean of a set of data and describe characteristics of the data set as typical or average based on those determinations.

4.3. Understand and apply basic concepts of probability.

4.3.5. Conduct probability experiments and express the probability based on possible outcomes, e.g., 8 out of 10 tiles chosen were red.

4.3.6. Determine and describe possible combinations, where order does not matter, e.g., when there is a choice of vanilla (V), chocolate (C) or strawberry (S) ice cream for a two-scoop cone and two different scoops are desired, the possible combinations are CV, CS, or VS.