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Connecticut Math Standards - 8th Grade
MathScore aligns to the Connecticut Math Standards for 8th Grade. The standards appear below along with the MathScore topics that match. If you click on a topic name, you will see sample problems at varying degrees of difficulty that MathScore generated. When students use our program, the difficulty of the problems will automatically adapt based on individual performance, resulting in not only true differentiated instruction, but a challenging game-like experience.
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Patterns and Functions
1.1 Understand and describe patterns and functional relationships.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:
• recursively as "add 3 to the previous number"
• explicitly as 3n + 1 (Patterns: Numbers , Function Tables , Function Tables 2 )
2. Determine whether relationships are linear or nonlinear.
3. Write and solve problems involving proportional relationships (direct variation) using linear equations (y = mx). (Area and Volume Conversions , Area And Volume Proportions , Proportions 1 , Proportions 2 , Distance, Rate, and Time )
4. Examine and make comparisons in writing between linear and non-linear mathematical relationships including y = mx, y = mx2 and y = mx3 using a variety of representations. (Nonlinear Functions )
1.2 Represent and analyze quantitative relationships in a variety of ways.
5. Represent linear and nonlinear mathematical relationships with verbal descriptions, tables, graphs and equations (when possible). (Determining Slope , Graphs to Linear Equations , Graphs to Linear Equations 2 , Graphs to Linear Inequalities , Applied Linear Equations 1 , Applied Linear Equations 2 , Nonlinear Functions )
6. Determine the constant rate of change in a linear relationship and recognize this as the slope of a line. (Determining Slope )
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. (Determining Slope )
8. Compare and contrast the slopes and the graphs of lines to classify lines as parallel, perpendicular or intersecting. (Parallel and Perpendicular Lines )
9. Interpret and describe slope and y-intercepts from contextual situations, graphs and linear equations. (Graphs to Linear Equations )
1.3 Use operations, properties and algebraic symbols to determine equivalence and solve problems.
10. Evaluate and simplify algebraic expressions, equations and formulas including those with powers using algebraic properties and the order of operations. (Order Of Operations , Variable Substitution , Absolute Value 2 , Simplifying Algebraic Expressions , Simplifying Algebraic Expressions 2 , Variable Substitution 2 )
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. (System of Equations Substitution , System of Equations Addition , Age Problems )
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. (Linear Equations , Single Variable Equations 2 , Single Variable Equations 3 , Single Variable Inequalities , Absolute Value Equations , Simplifying Algebraic Expressions )
Numerical and Proportional Reasoning
2.1 Understand that a variety of numerical representations can be used to describe quantitative relationships.1. Compare and order rational and common irrational numbers; e.g., -5, 1/16, -4½, √2, π; and locate them on number lines, scales and coordinate grids. (Compare Mixed Values 2 , Number Line , Compare Integers , Ordered Pairs )
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. (Estimating Square Roots , Perfect Squares )
3. Read and represent whole numbers and those between zero and one in scientific notation (and vice versa) and compare their magnitudes. (Scientific Notation )
4. Represent fractions, mixed numbers, decimals and percentages in equivalent forms. (Fraction Simplification , Fractions to Decimals , Decimals To Fractions , Percentages )
2.2 Use numbers and their properties to compute flexibly and fluently and to reasonably estimate measures and quantities.
5. Compute (using addition, subtraction, multiplication and division) and solve problems with positive and negative rational numbers. (Integer Addition , Integer Subtraction , Integer Multiplication , Integer Division , Integers In Word Problems )
6. Calculate the square roots of positive rational numbers using technology.
7. Develop and use strategies for multiplying and dividing with numbers expressed in scientific notation using the commutative and associative properties. (Scientific Notation 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. (Percentage Change )
9. Use proportional reasoning to write and solve problems in context. (Unit Cost , Proportions 2 , Distance, Rate, and Time , Train Problems , Mixture Word Problems , Work Word Problems )
10. Solve a variety of problems in context involving percents, including the following:
• Percentage 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?
• 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.
• 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?
• 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 percentage increase? (Percentage Change , Percent of Quantity )
11. Use the rules for exponents to multiply and divide with powers of 10 and extend to other bases.
• 102 × 103 = 105 - Add exponents
• 25 ÷ 27 = 2-2 - Subtract exponents (Multiplying and Dividing Exponent Expressions , Exponent Rules For Fractions )
12. Estimate answers to problems in context containing numbers expressed in scientific notation.
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. (Compound Interest )
Geometry and Measurement
3.1 Use properties and characteristics of two- and three- dimensional shapes and geometric theorems to describe relationships, communicate ideas and solve problems.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. (Area And Volume Proportions )
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. (Proportions 2 )
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. (Pythagorean Theorem )
4. Apply side and angle relationships in geometric figures to solve problems including the Pythagorean theorem and similar figures. (Triangle Angles , Quadrilateral Angles , Triangle Angles 2 , Identifying Angles , Pythagorean Theorem , Solving For Angles , Angle Measurements , Angle Measurements 2 , Proportions 2 )
3.2 Use spatial reasoning, location and geometric relationships to solve problems.
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. (Translations and Reflections )
6. Develop and use formulas to determine the surface areas of rectangular prisms, cylinders and pyramids. (Rectangular Solids , Rectangular Solids 2 , Cylinders )
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.
8. Understand and describe in writing that measurement tools, measurements and estimates of measures are not precise and can affect the results of calculations.
9. Use estimation and measurement strategies, including formulas, to solve surface area and volume problems in context.
10. Solve customary or metric measurement problems in context using Dimensional Analysis (the Unit Factor Method) and justify the results in writing.
Probability and Statistics
4.1 Collect, organize and display data using appropriate statistical and graphical methods.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.
2. Use appropriate representations to compare and analyze large data sets.
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. (Stem And Leaf Plots )
4.2 Analyze data sets to form hypotheses and make predictions.
4. Use descriptive statistics, including range, mode, median, mean, quartiles and outliers to describe data and support conclusions in writing. (Mean, Median, Mode , Stem And Leaf Plots )
5. Make predictions from scatter plots by using or estimating a line-of-best-fit.
6. Make observations and inferences and evaluate hypotheses based on collected and/or experimental data.
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.
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.
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).
10. Use tree diagrams, lists or the Counting Principle to determine all possible outcomes in permutations and combinations.
11. Apply permutations and combinations to predict possible outcomes and find probabilities to solve problems in a variety of contexts. (Probability , Probability 2 , Object Picking Probability )
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