Curriculum Framework: Math/Problem Solving

SUPPORT SKILLS

Number/Number Sense

Eighth Grade: The student will solidify rational number sense.
-read, write, and order integers, rational numbers, and common irrational numbers (i.e., square root of 2 and pi)
-apply number theory to represent numbers in various ways (primes, factors, and multiples)
-represent numbers in scientific notation
-differentiate between sets of numbers (integers, rationals, whole, etc.)
-use relationships among fractions, decimals, and percents, including ratios and proportions
-use number sense to justify the reasonableness of solutions (rounding and estimating)
-understand the inverse relationships between addition and subtraction and multiplication and division
-use inverse operations to determine unknown quantities in equations
-use the problem solving process (understand, plan, do, check) in a variety of situations
-communicate the mathematical reasoning behind solutions using appropriate mathematical vocabulary
-organize work, label illustrations, and use appropriate techniques to make meaning clear to the audience

Algebra/Patterns

Eighth Grade: The student will use algebraic methods to represent, describe, and analyze patterns and relationships involving numbers, shapes, and data.
-recognize when a pattern exists and describe the pattern
-represent and analyze patterns and relationships using tables, graphs, verbal rules, and standard algebraic notation
-describe patterns using variables, expressions, equations, and inequalities in problem solving situations
-analyze functional relationships to explain how a change in one quantity results in a change in another
-solve simple linear and nonlinear equations using a variety of tools and a variety of methods (informal, formal, and graphical)
-use the problem solving process (understand, plan, do, check) in a variety of situations
-communicate the mathematical reasoning behind solutions using appropriate mathematical vocabulary
-organize work, label illustrations, and use appropriate techniques to make meaning clear to the audience

Data/Probability

Eighth Grade: The student will collect, display, and analyze data using statistical methods and make inferences based on probability models.
-read, construct, compare, and contrast displays of data using the appropriate techniques and technology (i.e., line graphs, circle graphs, scatter plots, box plots, stem and leaf plots)
-determine, describe, and use measures of central tendency (mean, median, and mode) and measures of variability (range and quartiles)
-evaluate arguments based on statistical claims
-gather data, formulate hypotheses, draw conclusions, and make convincing arguments based on data analysis
-determine probability through simulations and experiments
-make predictions by comparing experimental and theoretical probability results
-use counting strategies to determine all the possible outcomes for an experiment
-critique the conclusions and recommendations of others' statistics
-evaluate the effects on reliability of sampling procedures and of missing or incorrect information
-predict the results of a series of trials once the probability for one trial is known
-use the problem solving process (understand, plan, do, check) in a variety of situations
-communicate the mathematical reasoning behind solutions using appropriate mathematical vocabulary
-organize work, label illustrations, and use appropriate techniques to make meaning clear to the audience

Geometry

Eighth Grade: The student will apply geometric concepts, properties, spatial sense, and relationships.
-recognize geometric shapes in the real world
-construct two/three-dimensional geometric models using a variety of materials and tools (rulers, compasses, protractors, nets)
-describe, analyze, and reason informally about the properties of two/three-dimensional figures (congruence, parallelism, and perpendicularly)
-relate geometric ideas to measurement and number sense
-apply the concepts of ratio, proportion, scale, and similarity in problem solving situations
-solve problems using coordinate geometry
-solve problems involving perimeter and area in two dimensions and surface area and volume in three dimensions
-transform geometric figures using reflections, translations, and rotations to explore congruence, tessellations, and symmetry
-reason proportionately in situations with similar figures
-predict what the effects on the overall shape will be if one or more dimensions are changed
-use the problem solving process (understand, plan, do, check) in a variety of situations
-communicate the mathematical reasoning behind solutions using appropriate mathematical vocabulary
-organize work, label illustrations, and use appropriate techniques to make meaning clear to the audience

Measurement

Eighth Grade: The student will use a variety of tools and techniques to measure and apply results.
-select and use appropriate units and tools to measure to the degree of accuracy required in a particular problem solving situation
-estimate, use, and describe measures of distance, perimeter, area, volume, length, weight, time, temperature, money, mass, and angle comparison
-read and interpret various scales including number lines, graphs, and maps
-use and explain the choice of formulas, conversions, and procedures used to solve problems involving measurement
-use the problem solving process (understand, plan, do, check) in a variety of situations
-communicate the mathematical reasoning behind solutions using appropriate mathematical vocabulary
-organize work, label illustrations, and use appropriate techniques to make meaning clear to the audience

Computation

Eighth Grade: The student will estimate and compute with fractions, decimals, and integers.
-compute consistently and accurately with rational numbers, integers, exponents, square roots, and pi
-model and explain the difference between square roots and square numbers
-model, explain, and use mathematical properties (associative, commutative, identity, order of operations, and distributive)
-construct, use, and explain with appropriate mathematics vocabulary (factors, multiples, exponents, scientific notation, etc.) the procedures used to compute and estimate with rational numbers and integers to solve real world problems
-use mental arithmetic, estimation, paper-and-pencil, and calculators to determine whether results are reasonable
-demonstrate automatic recall and maintain proficiency in basic facts
-use mathematical language and representations with appropriate accuracy (including numerical tables and equations, simple algebraic equations and formulas, charts, graphs, tables, and diagrams)
-use the problem solving process (understand, plan, do, check) in a variety of situations
-communicate the mathematical reasoning behind solutions using appropriate mathematical vocabulary,
-organize work, label illustrations, and use appropriate techniques to make meaning clear to the audience