Math - 7th Grade

21^st CENTURY

7^th Grade MATH

CONTENT STANDARDS AND OBJECTIVES FOR WEST VIRGINIA SCHOOLS (2520.2)

Janet Benincosa, TI Specialist

The West Virginia Standards for 21st Century Learning include the following components: 21st Century Content Standards and Objectives and 21st Century Learning Skills and Technology Tools.

All West Virginia teachers are responsible for classroom instruction that integrates learning skills, technology tools and content standards and objectives.

Seventh Grade

Grade 7		Mathematics
Standard 1		Number and Operations
M.S.7.1		Through communication, representation, reasoning and proof, problem solving, and making connections within and beyond the field of mathematics, students will · demonstrate understanding of numbers, ways of representing numbers, and relationships among numbers and number systems, · demonstrate meanings of operations and how they relate to one another, and · compute fluently and make reasonable estimates.
Performance Descriptors (M.PD.7.1)
Distinguished			Above Mastery	Mastery	Partial Mastery	Novice
Seventh grade students at the distinguished level in mathematics compare, order, differentiate among and between rational and irrational numbers; and convert between decimal and fraction representations of rationals (including repeating decimals). They identify a number between any two given numbers and justify their thinking. They model the relationship between perfect squares and square roots and estimate and evaluate square root by estimation and calculation and justify the use of this method. They justify the use of the commutative, associative, distributive, identity, and inverse properties to simplify numeric and algebraic expressions; they explain the connection between simplifying numeric and algebraic expressions. They analyze and solve real-world problems, demonstrate fluency in performing the operations required to solve them; in a clear, concise manner, justify solutions and explain the process used in solving. Using the laws of exponents for expressions with numeric and variable bases, they generalize by expressing the rules algebraically; they solve problems using numbers in scientific notation.			Seventh grade students at the above mastery level in mathematics compare, order, differentiate among and between rational and irrational numbers; and convert between decimal and fraction representations of rationals (including repeating decimals). They model the relationship between perfect squares and square roots and estimate and evaluate square root by estimation and calculation. They justify the use of the commutative, associative, distributive, identity, and inverse properties to simplify numeric and algebraic expressions. They analyze and solve real-world problems, demonstrate fluency in performing the operations required to solve them, justify solutions, and explain the process used in solving. They extend the laws of exponents for expressions with numeric bases to expressions with variable bases; they solve problems using numbers in scientific notation.	Seventh grade students at the mastery level in mathematics compare, order, and differentiate among and between rational and irrational numbers. They model the relationship between perfect squares and square roots and estimate and evaluate square root. They justify the use of the commutative, associative, distributive, identity, and inverse properties to simplify numeric expressions. They analyze and solve real-world problems, demonstrate fluency in performing the operations required to solve them, and justify solutions. They find and justify laws of exponents for expressions with numeric bases; they solve problems using numbers in scientific notation.	Seventh grade students at the partial mastery level in mathematics compare, order, and differentiate among rational numbers. They evaluate square root of perfect squares and identify between which whole numbers the square root of a number from 1-144 is found. They use and identify the commutative, associative, distributive, identity, and inverse properties when appropriate to simplify numeric expressions involving whole numbers. They analyze and solve real-world problems with calculator assistance, but demonstrate fluency in performing the whole number operations required to solve them; justify solutions. They apply laws of positive exponents to expressions with numeric bases. They solve problems using numbers in scientific notation with positive exponents.	Seventh grade students at the novice level in mathematics compare and order integers, terminating decimals, and fractions. They evaluate square root of perfect squares. They use the commutative, associative, distributive, identity, and inverse properties to simplify numeric expressions involving whole numbers. They analyze and solve real-world problems with calculator assistance, and demonstrate fluency in performing the whole number operations required to solve them. They evaluate powers with positive exponents and convert between numbers in scientific notation with positive exponents and standard form.
	Objectives	Students will
	M.O.7.1.1	compare, order, and differentiate among integers, decimals, fractions, and irrational numbers using multiple representations (e.g., symbols, manipulatives, graphing on a number line).
	M.O.7.1.2	model the relationship between perfect squares and square roots using physical representations; estimate square root and evaluate using technology.
	M.O.7.1.3	using simple computation and problem-solving situations, demonstrate fluency and justify solutions in performing operations with rational numbers including negative numbers for · adding · subtracting · multiplying · dividing
	M.O.7.1.4	justify the use of the commutative, associative, distributive, identity and inverse properties to simplify numeric expressions.
	M.O.7.1.5	analyze and solve grade-appropriate real-world problems with whole numbers, integers, decimals, fractions and percents including problems involving · discounts, · interest, · taxes, · tips, · percent increase or decrease, and justify solutions including using estimation and reasonableness.
	M.O.7.1.6	use inductive reasoning to find and justify the laws of exponents with numeric bases
	M.O.7.1.7	solve problems using numbers in scientific notation (positive and negative exponents) with and without technology, and interpret from real life contexts.

Grade 7		Mathematics
Standard 2		Algebra
M.S.7.2		Through communication, representation, reasoning and proof, problem solving, and making connections within and beyond the field of mathematics, students will demonstrate understanding of patterns, relations and functions, represent and analyze mathematical situations and structures using algebraic symbols, use mathematical models to represent and understand quantitative relationships, and analyze change in various contents.
Performance Descriptors (M.PD.7.2)
Distinguished			Above Mastery	Mastery	Partial Mastery	Novice
Seventh grade students at the distinguished level in mathematics express a rule algebraically and extend the sequence in arithmetic and geometric sequence. They plot lines on a coordinate plane, determine the slope, and solve problems algebraically, in a clear, concise manner, justify solution, and explain the process used in solving. They simplify and evaluate algebraic expressions with whole numbers, fractions, integers, absolute value, and exponents, using order of operations. They create input/output function tables to predict values in problem solving situations and express the rule algebraically. They distinguish between proportional and non-proportional situations, write and solve a proportion for a proportional situation, and justify the solution. They solve multi-step linear equations containing rational numbers and solve and graph multi-step inequalities.			Seventh grade students at the above mastery level in mathematics create a rule and extend the sequence in arithmetic and geometric sequences. They plot lines on a coordinate plane, determine the slope, and solve problems algebraically, justifying solutions, and explain the process used in solving. They evaluate algebraic expressions with whole numbers, fractions, integers, absolute value, and exponents, using order of operations. They create input/output function tables to predict values in problem solving situations and state the rule. They write and solve a proportion for a proportional situation and justify the solution. They solve one-step linear equations containing rational numbers and solve and graphs basic inequalities.	Seventh grade students at the mastery level in mathematics find missing elements in arithmetic and geometric sequences. They plot lines on a coordinate plane, determine the slope, and solve problems algebraically justifying solutions. They evaluate algebraic expressions with whole numbers, integers, absolute value, and exponents, using order of operations. They create input/output function tables to predict values in problem solving situations. They solve problems involving proportional situations. They solve one-step linear equations containing rational numbers and solve basic inequalities.	Seventh grade students at the partial mastery level in mathematics identify which operation is used to create a sequence and identify it as an arithmetic or geometric sequence. They plot lines on a coordinate plane, determine the slope, and solve problems algebraically. They evaluate algebraic expressions with whole numbers, and integers using order of operations. They solve one-step linear equations involving integers. They complete input/output function tables to predict values in problem solving situations. They recognize that two equal ratios form a proportion and solve one-step equations and inequalities involving whole numbers.	Seventh grade students at the novice level in mathematics identify which operation is used to create a sequence. They plot lines on a coordinate plane and identify the slope as being positive or negative. They evaluate algebraic expressions using whole numbers and the order of operations. They solve one-step linear equations involving whole numbers. They complete input/output function tables. They solve proportions. They solve one-step equations involving whole numbers.
	Objectives	Students will
	M.O.7.2.1	use inductive reasoning to find missing elements in a variety of arithmetic and geometric patterns including algebraic sequences and series.
	M.O.7.2.2	evaluate algebraic expressions with whole numbers, integers, absolute value and exponents using the order of operations.
	M.O.7.2.3	solve problems by creating an input/output function table(including, but not limited to, spreadsheets) to predict future values, given a real-world situation involving rational numbers.
	M.O.7.2.4	analyze proportional relationships in real-world situations, select an appropriate method to determine the solution and justify reasoning for choice of method to solve.
	M.O.7.2.5	solve one-step linear equations and inequalities using a variety of strategies containing rational numbers with integer solutions; graph solutions, and justify the selection of the strategy and the reasonableness of the solution.
	M.O.7.2.6	plot lines within the Cartesian coordinate plane from a table of values to solve mathematical real-world problems.
	M.O.7.2.7	determine the slope of a line from its graphical representation.
	M.O.7.2.8	represent algebraically and solve real-world application problems and justify solutions.
	M.O.7.2.9	identify a real life problem involving proportionality; make a hypothesis as to the outcome; develop, justify, and implement a method to collect, organize, and analyze data; generalize the results to make a conclusion; compare the hypothesis and the conclusion; present the project using words, graphs, drawings, models, or tables.

Grade 7		Mathematics
Standard 3		Geometry
M.S.7.3		Through communication, representation, reasoning and proof, problem solving, and making connections within and beyond the field of mathematics, 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, and · solve problems using visualization, spatial reasoning, and geometric modeling.
Performance Descriptors (M.PD.7.3)
Distinguished			Above Mastery	Mastery	Partial Mastery	Novice
Seventh grade students at the distinguished level in mathematics identify and construct angle-pairs, congruent segments and angles, perpendicular bisectors of segments, and angle-bisectors. They find the missing measure in an angle-pair, identify corresponding, alternate-interior and alternate-exterior angles given a measure. They apply line, rotational symmetry and transformations. They solve real-world problems involving scale by writing proportions and creating scale models and use compound geometric figures.			Seventh grade students at the above mastery level in mathematics identify and construct angle-pairs, congruent segments and angles, perpendicular bisectors of segments, and angle-bisectors. They find the missing measure in an angle-pair given a measure. They apply line symmetry and transformations and recognize rotational symmetry. They solve real-world problems involving scale by writing proportion and use compound geometric figures.	Seventh grade students at the mastery level in mathematics identify and construct angle-pairs, congruent segments and angles, perpendicular bisectors of segments, and angle-bisectors. They apply line symmetry and transformations. They solve real-world problems involving scale and use compound geometric figures.	Seventh grade students at the partial mastery level in mathematics identify and construct angle-pairs, angles, congruent segments and bisectors of segments. They identify line symmetry and transformations. They solve ratio and proportion and real-world problems involving geometric figures.	Seventh grade students at the novice level in mathematics identify angle-pairs, congruent segments and angles. They recognize line symmetry and transformations. They solve simple ratio and proportion problems with simple geometric figures.
	Objectives	Students will
	M.O.7.3.1	identify and construct angle-pairs adjacent, complementary, supplementary, vertical congruent segments and angles perpendicular bisectors of segments angle-bisectors
	M.O.7.3.2	apply line symmetry to classify plane figures.
	M.O.7.3.3	apply rotations, reflections, translations to plane figures and determine the coordinates of its transformation.
	M.O.7.3.4	pose and solve ratio and proportion problems including scale drawings and similar polygons.
	M.O.7.3.5	solve problems and explain the relationships among scale factor and area and volume including square of a scale factor cube of a scale factor
	M.O.7.3.6	solve mathematical real-world problems using compound geometric figures.

Grade 7		Mathematics
Standard 4		Measurement
M.S.7.4		Through communication, representation, reasoning and proof, problem solving, and making connections within and beyond the field of mathematics, students will: demonstrate understanding of measurable attributes of objects and the units, systems, and processes of measurements, and apply appropriate techniques, tools and formulas to determine measurements.
Performance Descriptors (M.PD.7.4)
Distinguished			Above Mastery	Mastery	Partial Mastery	Novice
Seventh grade students at the distinguished level in mathematics solve real-world problems (including those that have missing measures) involving perimeter, circumference, area, surface area, distance and temperature and volume of prisms and cylinders and develop formulas; they convert units of measure. They create and solve problems involving the Pythagorean Theorem and indirect measurement in right triangles.			Seventh grade students at the above mastery level in mathematics solve real-world problems involving perimeter, circumference, area, surface area, distance and temperature and volume of prisms and cylinders and develop formulas; they convert units of measure. They use the Pythagorean Theorem, indirect measure, and definitions to solve right-triangle application problems.	Seventh grade students at the mastery level in mathematics solve real-world problems involving perimeter, circumference, area, surface area, distance and temperature and volume of prisms and cylinders they convert units of measure. They use the Pythagorean Theorem to find the length of any side of a right triangle.	Seventh grade students at the below mastery level in mathematics solve problems involving perimeter, circumference, area, surface area, distance and temperature; they convert units of measure. They use the Pythagorean Theorem to find the length of the hypotenuse of a right triangle.	Seventh grade students at the novice level in mathematics solve problems involving perimeter, circumference, area and, surface area; they convert units of measure. They state the Pythagorean Theorem.
	Objectives	Students will
	M.O.7.4.1	select and apply an appropriate method to solve (including, but not limited to, formulas) justify the method and the reasonableness of the solution, given a real-world problem solving situation involving perimeter circumference area surface area of prisms (rectangular and triangular) volume of prisms and cylinders distance and temperature (Celsius, Fahrenheit )
	M.O.7.4.2	use the Pythagorean Theorem to find the length of any side of a right triangle and apply to problem solving situations.
	M.O.7.4.3	convert units of measurement, linear, area and volume, within customary and metric systems.

Grade 7		Mathematics
Standard 5		Data Analysis and Probability
M.S.7.5		Through communication, representation, reasoning and proof, problem solving, and making connections within and beyond the field of mathematics, students will: formulate questions that can be addressed 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 models, and apply and demonstrate an understanding of basic concepts of probability
Performance Descriptors (M.PD.7.5)
Distinguished			Above Mastery	Mastery	Partial Mastery	Novice
Seventh grade students at the distinguished level in mathematics determine theoretical probability of compound, independent events, make and test predictions, and explain their thinking. They create and solve problems involving combinations and permutations. They collect, organize, graphically represent, analyze, and interpret data displays; solve problems using measures of central tendency to interpret the data; and solve problems using measures of central tendency that involve missing data.			Seventh grade students at the above mastery level in mathematics determine theoretical probability of compound, independent events, and make and test predictions. They use appropriate technology to solve application problems involving combinations and permutations. They collect, organize, graphically represent, analyze, and interpret data displays; and solve problems using measures of central tendency to interpret the data.	Seventh grade students at the mastery level in mathematics determine theoretical probability to make, test predictions. They determine combinations and permutations by constructing sample spaces. They collect, organize, graphically represent, analyze, and interpret data displays and solve problems using measures of central tendency.	Seventh grade students at the partial mastery level in mathematics predict the outcome of an event given its probability and test their prediction and identify the theoretical and experimental probability. They list combinations and permutations of three items. They collect, organize, graphically represent data displays and solve problems using measures of central tendency.	Seventh grade students at the novice level in mathematics predict the outcome of an event given its probability and test their prediction. They recognize a situation involving a combination and a permutation. They collect and organize data and determine measures of central tendency.
	Objectives	Students will
	M.O.7.5.1	determine theoretical probability of an event, make and test predictions through experimentation.
	M.O.7.5.2	determine combinations and permutations by constructing sample spaces (e.g., listing, tree diagrams, frequency distribution tables).
	M.O.7.5.3	collect, organize, graphically represent, and interpret data displays including frequency distributions, line-plots, scatter plots, box and whiskers, and multiple-line graphs.
	M.O.7.5.4	analyze and solve application problems involving measures of central tendency (mean, median, mode) and dispersion (range) from data, graphs, tables, and experiments using appropriate technology to compare two sets of data.