1 st Standard #2: Number Sense and number relationships to solve a Standard #1: Algebraic Reasoning Patterns and Relationships: The student will use algebraic methods to describe patterns, simplify and write algebraic expressions and equations, and solve simple equations in a variety of contexts. Standard #5 Data Analysis The student will use data analysis, probability, and statistics to interpret data in a variety of contexts. Number Sense and Convert, compare, and order fractions, decimals and percents using <, >, or = symbols.* Add, subtract, multiply, and divide decimals with one or two digit multipliers or divisors.* Estimate solutions to problems using whole numbers, fractions, decimals, and percents to various place values. * Evaluate numerical expressions and solve equations using exponents that are whole numbers.* Simplify numerical operations with exponents and parentheses using the order of operations.* Algebraic Reasoning Use the algebraic properties (associative, commutative, distributive, identity of addition and multiplication) to solve problems. * Write algebraic expressions and simple equations containing up to three different variables.* Substitute values for variables in algebraic expressions when given the value.* Write and solve equations using variables, the properties of operations, and the properties of equality.* Extend number patterns and sequences involving whole numbers, fractions, integers, * Data Analysis Solve for measures of central tendency, including mean, median, mode, and range with and without Vocabulary: algebraic expression, base number, convert, evaluate, exponent, median, mode, non-terminating decimal, numerical expression, order of operations, substitution, terminating decimal Develop and test strategies to solve problems. Formulate problems and generalize solutions and strategies to new situations. Evaluate results to determine reasonableness. problems. Model and discuss mathematical situations through various modalities. Reflect and justify reasoning in problem solving. Use appropriate terminology when discussing mathematical concepts. various types of problems. Connect one area of mathematics to another.
1 st outliers.* Use a specific measure of central tendency to determine the most useful method of analyzing data.* Collect and organize data to use in surveys and samples and create graphs to represent the data.* : STAR tests 2 nd Standard #5 Data Analysis The student will use data analysis, probability, and statistics to interpret data in a variety of contexts. Standard #2 Number Sense and Data Analysis Organize, construct displays, and interpret data to solve problems.* Create charts, graphs, diagrams based on experiments with data.* Use the fundamental counting principle on sets with up to five items to determine the number of possible combinations (permutations and combinations/probability).* Solve for measures of central tendency--mean, median, mode and range with and without outliers.* Vocabulary factorization, prime factor, reciprocal, sequences, simplify Use technology to generate and analyze data to solve problems. problems with emphasis on multi-step and non-routine problems. Use various oral, written, concrete, pictorial, graphical, and/or algebraic
2 nd number relationships to solve a Standard #1 Algebraic Reasoning Patterns and Relationships: The student will use algebraic methods to describe patterns, simplify, and write algebraic expressions and equations, and solve simple equations in a variety of contexts. Create and analyze bar graphs, circle graphs, histograms, frequency tables, line plots, stem and leaf plots, box & whisker graphs, and misleading graphs.* Number Sense and s Solve and analyze the prime factorization of whole numbers with 4 digits or less.* Evaluate the greatest common factor and least common multiple of sets of numbers.* Add, subtract, multiply, and divide fractions with like and unlike denominators.* Add, subtract, multiply, and divide fractions and mixed numbers to solve problems using a variety of methods.* Algebraic Reasoning Generalize and extend patterns and functions using tables, graphs, and number properties (e.g. number sequences, prime and composite numbers, recursive patterns, Fibonacci numbers).* Identify and analyze prime and composite numbers.* Write and solve equations with variables, decimals, and fractions using number sense, the properties of operations, and the properties of equality.* Solve using order of operations with variables, exponents, square roots.* methods to model mathematical situations. Identify and extend patterns and use experiences and observations to make suppositions. Select and use various types of reasoning: recursive, inductive, deductive, spatial, and proportional. problems that arise from other disciplines in the real world. Connect one area or idea of mathematics to another. Develop a variety of mathematical representations that can be used flexibly and appropriately. model and solve physical, social, and mathematical problems. : STAR tests
3 rd Standard #3 Geometry The student will use geometric properties and relationships to recognize, describe, and analyze shapes and representations in a variety of contexts. Standard # 4 Measurement The student will use measurements within the metric and the customary systems to solve problems in a variety of contexts. Standard #2 Number Sense and Geometry Compare and contrast the basic characteristics of three-dimensional figures: pyramids, prisms, cones, cylinders.* Identify and compare the characteristics of threedimensional figures: bases, vertices, edges.* Compare and contrast congruent and similar plane and three-dimensional figures.* Identify the characteristics of the rectangular coordinate system and use them to locate positive and negative points and ordered pairs.* Describe shapes drawn in all four quadrants of the coordinate plane.* Measure and compare angles: acute, obtuse, right.* Measure and compare angles: supplementary, complementary, line, vertical, corresponding, and adjacent.* Name, draw, and classify polygons: all types of triangles, quadrilaterals, pentagons, hexagons, Academic Vocabulary: circumference, complement, congruent, coordinate plane, diameter, pi, plane figure, quadrilateral, radius, similarity, square units, supplement problems (restate the problem, look for patterns, diagrams, solve simpler problem, work backwards, trial and error) with emphasis on multi-step and non-routine problems. Use oral, written, concrete, pictorial, graphical, and/or algebraic methods to model mathematical situations. Use counter examples to disprove suppositions (all squares are rectangles, but are all rectangles
number relationships to solve a octagons, decagons, and n-gons.* Name, draw, and classify all types of quadrilaterals and circles.* Measurement Use formulas to find the circumference and area of circles in terms of pi.* Convert, add, or subtract measurements within the same system to solve problems (e.g. 9'8" + 3'6", 150 minutes= hours and minutes, 6 square inches = square feet).* squares?). Select and use various types of reasoning: recursive, inductive, deductive, spatial, and proportional. problems that arise from other disciplines in the real world. Connect one area or idea of mathematics to another. 3 rd Number Sense and s Use the number line to determine the value of integers.* Use the basic operations on integers to solve problems.* Use representations to promote the communication of mathematical ideas (e.g. number lines, rectangular coordinate systems, scales to illustrate the balance of equations.) Develop a variety of mathematical representations that can be used flexibly and appropriately. model and solve physical, social, and mathematical problems. : STAR tests
4 th Standard #2 Number Sense and number relationships to solve a Standard # 4 Measurement The student will use measurements within the metric and the customary systems to solve problems in a variety of contexts. Standard #1 Algebraic Reasoning Patterns and Relationships: The student will use algebraic methods to describe patterns, simplify, and write algebraic expressions and equations, and solve simple equations in a variety of contexts. Number Sense and s Use the basic operations on integers to solve problems.* Evaluate the absolute value of an integer.* Identify and order rational numbers on a number line.* Compare and order rational numbers using <, >, and = symbols.* Follow the order of operations to solve problems with integers.* Measurement Use formulas to find the circumference and area of circles in terms of pi.* Convert, add, or subtract measurements within the same system to solve problems (e.g. 9'8" + 3'6", 150 minutes= hours and minutes, 6 square inches = square feet).* Evaluate the volume of solid figures: cylinders, prisms, and pyramids.* Evaluate the surface area of a rectangular prism.* Algebraic Reasoning Solve, write, and analyze algebraic proportions, ratios, and rates.* Use proportions and similar figures to find Vocabulary: corresponding, proportions, ratio, scale drawings, surface area, volume problems (restate the problem, look for patterns, diagrams, solve simpler problem, work backwards, trial and error) with emphasis on multi-step and non-routine problems. Use oral, written, concrete, pictorial, graphical, and/or algebraic methods to model mathematical situations. Use counter examples to disprove suppositions (all squares are rectangles, but are all rectangles squares?). Select and use various types of reasoning: recursive, inductive, deductive, spatial, and proportional. problems that arise from other disciplines in the real world.
unknown measures (indirect measurement).* Create scale drawings, read and analyze maps and scales.* Connect one area or idea of mathematics to another. 4 th Use representations to promote the communication of mathematical ideas (e.g. number lines, rectangular coordinate systems, scales to illustrate the balance of equations.) Develop a variety of mathematical representations that can be used flexibly and appropriately. model and solve physical, social, and mathematical problems. : STAR tests