Connecticut State Standards for Mathematics: Grade 8

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. Generalize the relationships in patterns in a variety of ways including recursive and explicit descriptions; e.g., the pattern 1, 4, 7, 10... is represented as follows:

1.1.1.1. Recursively as ''add 3 to the previous number''

1.1.1.2. Explicitly as 3n + 1

1.1.2. Determine whether relationships are linear or nonlinear.

1.1.3. Write and solve problems involving proportional relationships (direct variation) using linear equations (y = mx).

1.1.4. Examine and make comparisons in writing between linear and non-linear mathematical relationships including y = mx, y = mx^2 and y = mx^3 using a variety of representations.

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

1.2.5. Represent linear and nonlinear mathematical relationships with verbal descriptions, tables, graphs and equations (when possible).

1.2.6. Determine the constant rate of change in a linear relationship and recognize this as the slope of a line.

1.2.7. Compare and contrast the slopes and the graphs of lines that have a positive slope, negative slope, zero slope, undefined slope, slopes greater than one and slopes between zero and one.

1.2.8. Compare and contrast the slopes and the graphs of lines to classify lines as parallel, perpendicular or intersecting.

1.2.9. Interpret and describe slope and y-intercepts from contextual situations, graphs and linear equations.

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

1.3.10. Evaluate and simplify algebraic expressions, equations and formulas including those with powers using algebraic properties and the order of operations.

1.3.11. Examine systems of two linear equations in context that have a common solution, i.e. point of intersection, using tables, graphs and substitution and interpret the solution.

1.3.12. Write and solve multistep equations using various algebraic methods including the distributive property, e.g., 3 (x + 2) =10, combining like terms, e.g., 3x + 2x = 15, and properties of equality and justify the solutions.

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 and common irrational numbers; e.g., -5, 1/16, -4 1/2, pi^2, pi; and locate them on number lines, scales and coordinate grids.

2.1.2. Identify perfect squares and their square roots; e.g., squares 1, 4, 9, 16...to corresponding roots 1, 2, 3, 4 ...; and use these relationships to estimate other square roots.

2.1.3. Read and represent whole numbers and those between zero and one in scientific notation (and vice versa) and compare their magnitudes.

2.1.4. Represent fractions, mixed numbers, decimals and percentages in equivalent forms.

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

2.2.5. Compute (using addition, subtraction, multiplication and division) and solve problems with positive and negative rational numbers.

2.2.6. Calculate the square roots of positive rational numbers using technology.

2.2.7. Develop and use strategies for multiplying and dividing with numbers expressed in scientific notation using the commutative and associative property.

2.2.8. Estimate reasonable answers and solve problems in context involving rational and common irrational numbers, ratios and percentages (including percentage of increase and decrease) and justify solutions in writing.

2.2.9. Use proportional reasoning to write and solve problems in context.

2.2.10. Solve a variety of problems in context involving percents, including the following:

2.2.10.1. Percent of a number, e.g., If 65 percent of the 250 applicants will be accepted to the Arts Magnet School, how many students will be accepted?

2.2.10.2. The percentage one number is of another number, e.g., Find the percent of students who play soccer if 39 students play soccer out of a total of 387 students.

2.2.10.3. The percentage of a missing amount, e.g., 5 percent of the money from a fundraiser will be donated to a charity. If $25 is donated to the charity, how much money was made from the fundraiser?

2.2.10.4. Percentage increase/decrease, e.g., The number of music downloads have increased from 1,345 per minute to 1,567 per minute. What is the percent increase?

2.2.11. Use the rules for exponents to multiply and divide with powers of 10 and extend to other bases.

2.2.11.1. 10^2 x 10^3 = 10^5 - Add exponents

2.2.11.2. 2^5 / 2^7 = 2^-2 = 1/2^2 = 1/4 - Subtract exponents

2.2.12. Estimate answers to problems in context containing numbers expressed in scientific notation.

2.2.13. Solve problems in context that involve repetitive multiplication; e.g., compound interest, depreciation; using tables, spreadsheets and calculators to develop an understanding of exponential growth and decay.

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. Determine the effect of scale factors (resulting in similar figures) on the perimeters and areas of two-dimensional shapes and the surface areas and volumes of three-dimensional solids.

3.1.2. Make and test conjectures about the angle and side relationships to determine that similar figures have congruent angles and corresponding sides proportional and congruent figures have congruent angles and sides.

3.1.3. Construct and/or examine right triangles and make and test conjectures about the relationships of the angles and sides and develop the Pythagorean theorem.

3.1.4. Apply side and angle relationships in geometric figures to solve problems including the Pythagorean theorem and similar figures.

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

3.2.5. Use a coordinate plane to make and test conjectures about changes in the coordinates of the vertices of polygons as a result of a transformation (translation and/ or reflection) and describe the results in writing.

3.2.6. Develop and use formulas to determine the surface areas of rectangular prisms, cylinders and pyramids.

3.2.7. Develop formulas using measurement strategies and concrete models; and use formulas to determine the volumes of pyramids, cones and spheres.

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

3.3.8. Understand and describe in writing that measurement tools, measurements and estimates of measures are not precise and can affect the results of calculations.

3.3.9. Use estimation and measurement strategies, including formulas, to solve surface area and volume problems in context.

3.3.10. Solve customary or metric measurement problems in context using Dimensional Analysis (the Unit Factor Method) and justify the results 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. Collect, organize and display data using an appropriate representation (including box-and-whisker plots, stem and leaf plots, scatter plots, histograms) based on the size and type of data set and purpose for its use.

4.1.2. Use appropriate representations to compare and analyze large data sets.

4.1.3. Identify where measures of central tendency and spread are found in graphical displays including box-and-whisker plots, stem and leaf plots, scatter plots and histograms.

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

4.2.4. Use descriptive statistics, including range, mode, median, mean, quartiles and outliers to describe data and support conclusions in writing.

4.2.5. Make predictions from scatter plots by using or estimating a line-of-best-fit.

4.2.6. Make observations and inferences and evaluate hypotheses based on collected and/or experimental data.

4.2.7. Describe in writing the accuracy of statistical claims, e.g., 4 out of 5 dentists prefer Brand x toothpaste, by recognizing when a sample is biased or when data is misrepresented.

4.2.8. Explain the effects of sample size and sampling techniques (convenience sampling, voluntary response sampling, systematic sampling and random sampling) on statistical claims.

4.3. Understand and apply basic concepts of probability.

4.3.9. Determine when a situation is a permutation (changing the order results in a different outcome) or a combination (changing the order does not result in a different outcome.)

4.3.10. Use tree diagrams, lists, or the Counting Principle to determine all possible outcomes in permutations and combinations.

4.3.11. Apply permutations and combinations to predict possible outcomes and find probabilities to solve problems in a variety of contexts.