Connecticut State Standards for Mathematics: Grade 6

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. Analyze, describe in writing and extend a variety of patterns to justify predictions and identify trends.

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

1.2.2. Create tables of values and scatterplots from mathematical relationships and equations and vice versa to solve problems.

1.2.3. Examine tables, graphs and equations to determine patterns of change in linear relationships.

1.2.4. Write expressions, formulas, equations or inequalities using symbols or variables to denote a pattern or represent a contextual situation.

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

1.3.5. Evaluate algebraic expressions and formulas using substitution.

1.3.6. Write, model and solve one-step equations using mental math, tables, substitution and concrete models that demonstrate equivalence and justify the solution.

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 and label whole numbers, fractions, decimals and positive and negative integers on number lines, scales, coordinate grids (all four quadrants) and measurement tools.

2.1.2. Compare and order whole numbers, fractions, decimals and positive and negative integers in context using number lines and scales.

2.1.3. Represent and compare whole numbers (to a billion) and decimals (to thousandths) in expanded notation, e.g., 75.654 = (7 x 10) + (5 x 1) + (6 x 0.1) + (5 x 0.01) + (4 x 0.001).

2.1.4. Represent chain multiplication, including powers of 10 in exponential and standard form, e.g., 5 x 5 x 5 = 5^3 = 125.

2.1.5. Factor composite numbers and express them as a product of primes using exponents.

2.1.6. Determine equivalent fraction, decimal, and percent representations and choose among these forms to solve problems.

2.1.7. Use ratios and rates (involving different units) to compare quantities.

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

2.2.8. Understand place value and patterns in place value when multiplying and dividing decimals by powers of 10.

2.2.9. Develop, describe and use strategies for solving, simplifying and estimating multiplication and division problems involving large numbers, decimals and powers of 10, e.g., 4.25 x 100 = 425 and 365,000 / 6,000 = 365 / 6 ; 365 / 6 is approximately equal to 360 / 6 is approximately equal to 60.

2.2.10. Estimate and find percentages of a number in context using benchmarks and number patterns and ratios to 100.

2.2.11. Solve practical problems involving rates, ratios, percentages and proportionality.

2.2.12. Add, subtract, multiply and divide by fractions and decimals in context.

2.2.13. Describe situations in writing that connect multiplying fractions to determining the fractional part of a set.

2.2.14. Examine the relationships between multiplication by a unit fraction and dividing by the fraction's denominator, e.g., 1/2 of $6 is the same as $6 / 2, and use this to solve problems.

2.2.15. Use the inverse relationship between multiplication and division to make sense of procedures for multiplying and dividing fractions.

2.2.16. Understand and defend in writing the magnitude of the result of multiplication or division problems involving fractions or decimals.

2.2.17. Determine when an estimate is sufficient or when an exact answer is needed.

2.2.18. Estimate solutions to problems and justify the reasonableness of estimates in writing.

2.2.19. Write and solve multistep problems in context involving addition, subtraction, multiplication and division with whole numbers, fractions, decimals, money and simple percentages.

2.2.20. Understand and use divisibility rules, factors of composite numbers and powers of 10 to find products and quotients.

2.2.21. Apply the order of operations and algebraic properties; i.e., commutative, associative, distributive, inverse operations, and the additive and multiplicative identities; to compute and solve multistep problems and explain solutions in writing.

2.2.22. Use concrete models to develop strategies to add and subtract integers.

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. Classify sets and subsets of polygons using the relationship of the sides (length, parallel and perpendicular) and angles (types and measure).

3.1.2. Make and test conjectures about polygons and congruence using side and angle relationships and describe the results in writing.

3.1.3. Identify lines of symmetry and reflections, rotations and translations of geometric figures.

3.1.4. Use rectangles as basic shapes to model and develop formulas for finding the area of triangles, parallelograms and trapezoids.

3.1.5. Recognize the relationships among radius, diameter, circumference and area of circles and develop formulas for finding circumference and area based on these relationships.

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

3.2.6. Use and describe concrete strategies for finding the volume of rectangular solids and cylinders.

3.2.7. Use measurements to examine the ratios between corresponding side lengths of scale models and similar figures.

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

3.3.8. Select and use appropriate strategies, tools and units to estimate and solve measurement problems involving length, perimeter, area, volume, capacity, mass and weight.

3.3.9. Use ratios to convert between customary units of length, mass, capacity and time.

3.3.10. Use ratios and powers of ten to convert between metric units.

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. Compare sets of data between two populations, e.g., heights of two classes of students, or within a population, e.g., height vs. arm length of sixth-grade students, using a variety of graphical representations.

4.1.2. Select, create and use appropriate graphical representations of data including, circle graphs, scatter plots, histograms and stem and leaf plots.

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

4.2.3. Describe the shape of numerical data sets using measures of spread (range) and central tendency (mean, median, mode) and outliers.

4.2.4. Determine how the mean, median, mode and range change as a result of changes in the data set and describe in writing.

4.3. Understand and apply basic concepts of probability.

4.3.1. Investigate and describe the relationship between the number of trials in an experiment and the predicted outcomes.

4.3.2. Design and conduct probability experiments to test predictions about outcomes and fairness.

4.3.3. Express probabilities as fractions, ratios, decimals and percentages.

4.3.4. Find all possible outcomes by systematic listing and counting strategies to solve problems.