Number Sense and Operations Students will… - Understand numbers, ways of representing numbers, relationships among numbers, and number systems.
- Understand meanings of operations and how they relate to one another.
- Compute fluently and make reasonable estimates.
They will… - Compare, order, estimate, and translate among integer, fractions and mixed numbers (i.e., rational numbers), decimals and percents.
- Continue to investigate and describe the relationship among fractions, decimals, and percents
- Use estimation to solve problems involving money, length, area, perimeter and volume
- Define, compare, order, and apply frequently used irrational numbers, such as √2 and π.
- Master computations with fractions and real numbers.
- Master operations involving fractions, decimals, integers, rational and irrational numbers.
- Master the types of numbers (whole and real numbers, integers, rational, and irrational numbers).
- Use ratios and proportions in the solution of problems, in particular, problems involving unit rates, scale factors, and rate of change.
- Understand and apply ratio and proportion to probability and geometry to solve numerical problems.
- Represent numbers in scientific notation, and use them in calculations and problem situations.
- Relate place value to computation, metric system, exponential form and scientific notation.
- Apply number theory concepts, including prime factorization and relatively prime numbers, to the solution of problems.
- Master the use of primes and properties of numbers such as, GCF and LCM to compute and/or approximate powers and roots.
- Demonstrate an understanding of absolute value, e.g., I –3I =I3I = 3.
- Apply the rules of powers and roots to the solution of problems. Extend the Order of Operations to include positive integer exponents and square roots.
- Master the laws of exponents(integer and rational)
- Demonstrate an understanding of the properties of arithmetic operations on rational numbers.
- Use the associative, commutative, and distributive properties; properties of the identity and inverse elements (e.g., -7+7 = 0; ¾ x 4/3 = 1); and the notion of closure of a subset of the rational numbers under an operation (e.g., the set of odd integers is closed under multiplication but not under addition).
- Master equivalent representation of procedures(i.e .demonstrate and describe the relationship of addition for whole numbers, fractions, decimals)
- Use the inverse relationships of addition and subtraction, multiplication and division, and squaring and finding square roots to simplify computations and solve problems, e.g., multiplying by ½ or 0.5 is the same as dividing by 2.
- Estimate and compute with fractions (including simplification of fractions), integers, decimals, and percents (including those greater than 100 and less than 1).
- Use concrete and abstract models to understand and describe the mathematical processes underlying the operations of addition, subtraction, multiplication and division(and their relationship with one another) on fractions, decimals, and integers.
- Create and solve problems that require the use of numbers other than whole numbers in the context of geometry, probability and statistics.
- Determine when an estimate rather than an exact answer is appropriate and apply in problem situations.
- Use estimation techniques and inverse operations to confirm results.
- Select and use appropriate operations – addition, subtraction, multiplication, division, and positive integer exponents – to solve problems with rational numbers (including negatives).
Patterns, Relations and Algebra Students will… - Understand patterns, relations and functions.
- Represent and analyze mathematical situations and structures using algebraic symbols.
- Use mathematical models to represent and understand quantitative relationships.
- Analyze change in various contexts.
They will… - Extend, represent, analyze, and generalize a variety of patterns with tables, graphs, words, and when possible, symbolic expressions. Include arithmetic and geometric progressions, e.g., compounding.
- Explore number patterns: generate rules for number sequences
- Evaluate simple algebraic expressions for given variable values, e.g., 3a2- b for a=3 and b=7.
- Continue to develop and apply key concepts such as variable, equivalence, order and inverse in the context of number, algebra, and geometry.
- Demonstrate an understanding of the identity (-x)(-y)=xy. Use this identity to simplify algebraic expressions, e.g., (-2)(-x+2 )= 2x – 4.
- Create and use symbolic expressions and relate them to verbal, tabular, and graphic representations.
- Use graphing calculator to express the data in tabular, symbolic and graphic form.
- Continue to describe and represent patterns using models, tables, graphs, simple rules, and manipulatives
- Continue to use the graphing calculator to generate tables and graphs and identify algebraic relationships
- Continue to use tables and graphs to identify and describe properties and relationships
- Construct, interpret, and evaluate formulas and expressions drawn from real-life and other academic domains.
- Identify the slope of a line as a measure of its steepness and as a constant rate of change from its table of values, equation, or graph. Apply the concept of slope to the solution of problems.
- Identify the roles of variables within an equation, e.g., y=mx+b, expressing y as a function of x with parameters m and b.
- Set up and solve linear equations and inequalities with one or two variables, using algebraic methods, models, and/or graphs.
- • Set up and solve everyday problems involving linear equations and inequalities with one or two variables, using algebraic methods, models, and/or graphs.
- Continue to use calculators, computers, concrete manipulatives(i.e. Algebra Lab Gear) and real life situations to explore and describe linear relationships and to solve linear equations,
- Master the attributes of linear equations and inequalities, absolute value and quadratic equations.
- Represent real life situations to solve linear and square functions
- Develop and apply the concept of function through the linear and quadratic levels.
- Explain and analyze __both quantitatively and qualitatively, using pictures, graphs, charts, or equations how a change in one variable results in a change in another variable in functional relationships, e.g., C=π d, A=π r2 (As a function of r), Arectangle =lw (Arectangle as a function of l and w).
- Use linear equations to model and analyze problems involving proportional relationships. Use technology as appropriate.
- Use tables and graphs to represent and compare linear growth patterns. In particular, compare rates of change and x- and y-intercepts of different linear patterns.
Geometry Students will… - Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships.
- Specify locations and describe spatial relationships using coordinate geometry and other representational systems.
- Apply transformations and use symmetry to analyze mathematical situations.
- Use visualization, spatial reasoning, and geometric modeling to solve problems.
They will… - Classify figures in terms of congruence and similarity, and apply these relationships to the solution of problems.
- Demonstrate an understanding of the relationships of angles formed by intersecting lines, including parallel lines cut by a transversal.
- Demonstrate an understanding of the Pythagorean theorem. Apply the theorem to the solution of problems.
- Use the Pythagorean theorem to identify the distance between two points on a coordinate plane.
- Master the use of sine, cosine, tangent ratios to solve everyday problems involving right triangles.
- Use the properties of special right triangles to solve everyday problems.
- Use a straightedge, compass, or other tools to formulate and test conjectures, and to draw geometric figures.
- Predict the results of transformations on unmarked or coordinate planes and draw the transformed figure, e.g., predict how tessellations transform under translations, reflections, and rotations.
- Use in combination the transformation of translation, reflection, rotations and dilation.
- Define similarity and congruence in terms of transformation
Measurement Students will… - Understand measurable attributes of objects and the units, systems, and processes of measurement.
- Apply appropriate techniques, tools, and formulas to determine measurements.
They will… - Select, convert (within the same system of measurement), and use appropriate units of measurement or scale.
- Master the reading and interpretation of scales and the degree of accuracy that is appropriate.
- Given the formulas, convert from one system of measurement to another. Use technology as appropriate.
- Demonstrate an understanding of the concepts and apply formulas and procedures for determining measures, including those of area and perimeter/circumference of parallelograms, trapezoids, and circles. Given the formulas, determine the surface area and volume of rectangular prisms, cylinders, and spheres. Use technology as appropriate.
- Use models, graphs, and formulas to solve simple problems involving rates, e.g., velocity and density.
Data Analysis, Statistics and Probability Students will… - Formulate questions that can be answered with data and collect, organize and display relevant data to answer them.
- Select and use appropriate statistical methods to analyze data.
- Develop and evaluate inferences and predictions that are based on data.
- Understand and apply basic concepts of probability.
They will… - Describe the characteristics and limitations of a data sample. Identify different ways of selecting a sample, e.g., convenience sampling, responses to a survey, random sampling.
- Select, create, interpret, and utilize various tabular and graphical representations of data, e.g., circle graphs, Venn diagrams, scatterplots, stem-and-leaf plots, box-and-whisker plots, histograms, tables, and charts.
- Design and use data collection sheets; access information from reference sources; where appropriate, use graphing calculators to create frequency tables.
- Design a questionnaire or an experiment to capture needed to follow lines of inquiry and to test hypothesis.
- Find, describe, and interpret appropriate measures of central tendency (mean, median, and mode) and spread (range) that represent a set of data. Use these notions to compare different sets of data.
- Read and interpret statistical data to make predictions, inferences, and decisions.
- Investigate the benefits of simple circuits and networks.
- Create simple algorithms to solve problems.
- Use counting techniques, tree diagrams, permutations, and combination techniques.
- Use logic and inductive reasoning to make predictions related to a series of statements.
Discussion, Presentation, Composition - Students will be able to…
- Use agreed upon rules to participate in discussions in large and small groups.
- Express ideas in an organized way.
- Explain their mathematical thinking in writing.
- Maintain a system for collecting, referring to, and sharing their work.
|
