Connecticut State Standards for Mathematics: Grade 7

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 a variety of patterns (physical phenomena, numeric and geometric patterns, arithmetic sequences) and generalize with algebraic expressions, formulas or equations.

1.1.2. Identify and describe in writing the independent and dependent variables in a mathematical situation, e.g. age vs. height of children.

1.1.3. Determine when mathematical situations are continuous (distance traveled over time) or discrete sets of points, e.g., weekly sales.

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

1.2.4. Write expressions, formulas, equations or inequalities using variables to represent mathematical relationships and solve problems.

1.2.5. Represent and compare the characteristics of linear and nonlinear relationships using verbal descriptions, e.g., linear - ''increases $1 per month'' vs. nonlinear - ''doubles every month,'' tables, graphs, equations or inequalities (when possible).

1.2.6. Examine situations with constant or varying rates of change and know that a constant rate of change describes a linear relationship.

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

1.3.7. Evaluate and simplify algebraic expressions, equations and formulas using algebraic properties (i.e. commutative, associative, distributive, inverse operations, and the additive and multiplicative identities) and the order of operations.

1.3.8. Solve real world problems using a variety of algebraic methods including tables, graphs, equations and inequalities.

1.3.9. Write, model and solve one- and two-step, e.g., 2x + 3 = 11, equations using a variety of methods such as tables, concrete models and the Properties of Equality 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. Compare and order rational numbers, e.g., -2, 3/8, -3.15, 0.8, in context and locate them on number lines, scales and coordinate grids.

2.1.2. Represent rational numbers in equivalent fraction, decimal and percent forms.

2.1.3. Represent fractions as terminating, e.g., 1/2 = 0.5, or repeating, e.g., 1/3 = 0.333... decimals and determine when it is appropriate to round the decimal form in context.

2.1.4. Use patterns to compute with and write whole numbers and fractions as powers of whole numbers and vice versa, e.g., 2^2 = 4, 2^1 = 2, 2^0 = 1, 2^-1 = 1/2, 2^-2 = 1/4.

2.1.5. Understand the relationship between squares and square roots.

2.1.6. Read, write, compare and solve problems with whole numbers in scientific notation and vice versa.

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

2.2.7. Estimate solutions to problems in context or computations with rational numbers and justify the reasonableness of the estimate in writing.

2.2.8. Apply the order of operations and algebraic properties; i.e. commutative, associative, distributive, inverse operations, and the additive and multiplicative identities; to write, simplify, e.g., 4 (3 1/2) = 4 (3) + 4 (1/2) = 12 + 2 = 14, and solve problems, including those with parentheses and exponents.

2.2.9. Apply a variety of strategies to write and solve problems involving addition, subtraction, multiplication and division of positive rational numbers, i.e., whole numbers, fractions and decimals.

2.2.10. Write ratios and proportions to solve problems in context involving rates, scale factors and percentages.

2.2.11. Find and/or estimate a percentage of a number, including percentages that are more than 100 percent and less than 1 percent using a variety of strategies, including:

2.2.11.1. Number patterns - e.g., find 20 percent of 50. Solution: 10 percent of 50 = 5, so 20 percent of 50 = 2 (5) = 10

2.2.11.2. Distributive Property - e.g., find 150 percent of 20. Solution: 150 percent of 20 = 100 percent of 20 + 50 percent of 20. 20 + 10 = 30

2.2.11.3. Proportions - e.g., 75 percent of 48. Solution: 75/100 = x/48; x = 36

2.2.11.4. Multiplication of decimal equivalent - e.g., 0.7 percent of 48. Solution: 0.007 (48) = 0.336

2.2.11.5. Estimation - e.g., 22 percent of $49.95. Estimate 22 percent of $49.95 is approximately equal to 20 percent of 50. 10 percent of 50 = 5, so 20 percent of 50 = 2 (5) = 10, therefore, 22 percent of $49.95 is approximately equal to $10

2.2.12. Solve percent problems in context including what percentage one number is of another, percentage increase and percentage decrease using a variety of strategies, e.g., proportions or equations.

2.2.13. Compare the magnitude of and compute with whole numbers expressed as positive powers of 10.

2.2.14. Develop and describe strategies for estimating and multiplying whole numbers expressed in scientific notation.

2.2.15. Estimate and solve problems containing whole numbers expressed is expanded notation, powers of 10 and scientific notation.

2.2.16. Develop and describe in writing strategies for addition, subtraction, multiplication and division and solve problems with positive and negative integers using models, number lines, coordinate grids and computational strategies.

2.2.17. Develop an understanding of absolute value using a number line while solving problems involving distance.

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 two- and three-dimensional geometric figures based on their properties including relationships of sides and angles and symmetry (line and/or rotational) and apply this information to solve problems.

3.1.2. Identify polygons that have line and/or rotational symmetry.

3.1.3. Draw the result of transformations on polygons on coordinate planes including translations, rotations, reflections and dilations (reductions and enlargements).

3.1.4. Describe the effect of transformations; i.e., position and orientation from the original figure, size; on polygons that have line and/or rotational symmetry.

3.1.5. Compare and describe in writing the relationships (including congruence, equality, scale) between the angles, sides, perimeter and area of congruent and similar geometric shapes.

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

3.2.6. Identify and/or draw two-dimensional representations of three dimensional geometric solids using nets, cross-sections, front, side and top views to solve problems.

3.2.7. Use two-dimensional representations of rectangular prisms, pyramids and cylinders to determine surface area.

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

3.3.8. Use formulas to solve problems involving perimeters and areas of polygons and circles.

3.3.9. Develop and use formulas to determine volumes of geometric solids (rectangular prisms and cylinders).

3.3.10. Use estimation and measurement strategies to solve problems involving area of irregular polygons and volumes of irregular solids and justify solutions in writing.

3.3.11. Write and solve problems in context involving conversions of customary or metric units and units of time.

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. Formulate questions and design studies; e.g., surveys, experiments, research using published sources and the internet; to collect and analyze data.

4.1.2. Organize and display data using appropriate graphical representation such as, tables and charts, line, bar and circle graphs, Venn diagrams, stem and leaf plots, scatter plots, histograms.

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

4.2.3. Make and defend in writing predictions based on patterns and trends from the graphical representations.

4.2.4. Find, use and interpret measures of central tendency and spread, including mean, median, mode, range and outliers.

4.2.5. Compare two sets of data based on their spread and measures of central tendency.

4.3. Understand and apply basic concepts of probability.

4.3.6. Identifying all possible outcomes using models, tree diagrams, tables and/or organized lists to determine theoretical probabilities.

4.3.7. Perform experiments to determine experimental probabilities.

4.3.8. Compare and contrast experimental probability results to theoretical probabilities in writing.

4.3.9. Solve probability problems in familiar contexts including simple events (flipping a coin) and compound events (flipping a coin and rolling a number cube).