Fresno Unified School District

Math

GRADE SEVEN

 

STANDARD 1: NUMBER AND OPERATION Students demonstrate their knowledge of basic skills, conceptual understanding and problem solving in arithmetic and number.

SUPPORTING NCTM STANDARDS, GRADE 5-8

NCTM Standard 5: NUMBER AND NUMBER RELATIONSHIPS

In grade seven, the mathematics curriculum should include the continued development of number and number relationships so that students can:

• Understand, represent, and use numbers in a variety of equivalent forms (integer, fraction, decimal, percent, exponential, and scientific notation) in real-world and mathematical problem situations.
• Develop number sense for whole numbers, fractions, decimals, integers and rational numbers.
• Understand and apply ratios, proportions, and percents in a wide variety of situations.
• Investigate relationships among fractions, decimals, and percents.
• Represent numerical relationships in one-dimensional and two-dimensional graphs.

NCTM Standard 6: NUMBER SYSTEMS AND NUMBER THEORY

In grade seven, the mathematics curriculum should include the study of number systems and number theory so that students can:

• Understand and appreciate the need for numbers beyond the whole numbers.
• Develop and use order relations for whole numbers, fractions, decimals, integers and rational numbers.
• Extend their understanding of whole number operations to fractions, decimals, integers and rational numbers.
• Understand how the basic arithmetic operations are related to one another.
• Develop and apply number theory concepts (e.g., primes, factors, and multiples) in real-world and mathematical problem situations.
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NCTM Standard 7: COMPUTATION AND ESTIMATION

In grade seven, the mathematics curriculum should develop the concepts underlying computation and estimation in various contexts so that students can:

• Compute with whole numbers, fractions, decimals, integers and rational numbers.
• Develop, analyze, and explain procedures for computation and techniques for estimation.
• Develop, analyze, and explain methods for solving proportions.
• Select and use an appropriate method for computing from among mental arithmetic, paper-and-pencil, calculator, and computer methods.
• Use computation, estimation and proportions to solve problems.
• Use estimation to check the reasonableness of result.

CALIFORNIA MATHEMATICS STANDARDS

• Students know the properties of and compute with rational numbers expressed in a variety of forms.
• Students use exponents, powers and roots and use exponents in working with fractions.

Examples of the types of work a student should be able to do to meet the standard:

• Consistently and accurately add, subtract, multiply and divide rational numbers; and raise rational numbers to whole number powers.
• Understand the inverse relationships between addition and subtraction, multiplication and division, and exponentiation and root-extraction, and use the inverse operation to determine unknown quantities in equations.
• Identify and use equivalent fractions, decimals, and percents.
• Compare the size of and order fractions, decimals, and percents.

 

STANDARD 2: GEOMETRY AND MEASUREMENT Students demonstrate their knowledge of basic skills, conceptual understanding, and problem solving in geometry and measurement.

SUPPORTING NCTM STANDARDS, GRADES 5-8

NCTM Standard 12: GEOMETRY

In grade seven, the mathematics curriculum should include the study of the geometry of one, two, and three dimensions in a variety of situations so that students can:

• Identify, describe, compare, and classify geometric figures.
• Explore transformations of geometric figures.
• Represent and solve problems using geometric models.
• Understand and apply geometric properties and relationships.
• Develop an appreciation of geometry as a means of describing the physical.

NCTM Standard 13: MEASUREMENT

In grade seven, the mathematics curriculum should include extensive concrete experiences using measurement so that students can:

• Extend their understanding of the process of measurement.
• Estimate, make, and use measurements to describe and compare phenomena.
• Select appropriate units and tools to measure to the degree of accuracy required in a particular situation.
• Understand the structure and use of systems of measurement.
• Extend their understanding of the concepts of perimeter, area, volume, angle measure, capacity, and weight and mass.
• Develop the concepts of rates and other derived and indirect measurements.
• Develop formulas and procedures for determining measures to solve problems.

CALIFORNIA MATHEMATICS STANDARDS

• Students choose appropriate units of measure and use ratios to convert within and between measurement systems to solve problems.
• Students compute the perimeter, area and volume of common geometric objects and use these to find measures of less common objects: they know how perimeter, area, and volume are affected under changes of scale.
• Students know the Pythagorean Theorem and deepen their understanding of plane and solid geometric shapes by constructing figures that meet given conditions and by identifying attributes of figures.

Examples of the types of work a student should be able to do to meet the standard:

• Demonstrate the familiarity with assorted two- and three-dimensional objects, including squares, triangles, other polygons, circles, cubes, rectangular prisms, i.e., "boxes," pyramids, spheres, and cylinders.
• Identify similar and congruent shapes and use transformations in the coordinate plane, i.e., translations, rotations, and reflections.
• Identify similarity and rotation and bilateral symmetry in two-and three-dimensional figures.
• Analyze and generalize geometric patterns, such as tessellation's and sequences of shapes.
• Measure length, area, volume, angles, weights, capacities, times, and temperatures.
• Explain the differences between length, area, and volume and the corresponding uses of units, square units, and cubic units of measure using appropriate units.
• Choose appropriate units of measure and convert with ease between units, e.g., inches and miles, within a customary or metric system. (Note that conversions between customary and metric are not required.)
• Demonstrate understanding of proportions by analyzing situations with similar figures.
• Demonstrate understanding of proportions by using measurements to interpret maps and to make smaller and larger scale drawings.
• Model situations geometrically to formulate and solve problems.

STANDARD 3: FUNCTION AND ALGEBRA Students demonstrate their knowledge of basic skills, conceptual understanding, and problem solving in function and algebra.

SUPPORTING NCTM STANDARDS, GRADES 5-8 

NCTM Standard 4: MATHEMATICAL CONNECTIONS

In grade seven, the mathematics curriculum should include the investigation of mathematical connections so that students can:

• See mathematics as an integrated whole.
• Explore problems and describe results, using graphical, numerical, physical, algebraic and verbal mathematical models or representations.
• Use a mathematical idea to further their understanding of other mathematical ideas.
• Apply mathematical thinking and modeling to solve problems that arise in other disciplines, such as art, music, psychology, science, and business.
• Value the role of mathematics in our culture and society.

NCTM Standard 8: PATTERNS AND FUNCTIONS

In grade seven, the mathematics curriculum should include explorations of patterns and functions so that students can:

• Describe, extend, analyze, and create a wide variety of patterns.
• Describe and represent relationships with tables, graphs, and rules.
• Analyze functional relationships to explain how a change in one quantity results in a change in another.
• Use patterns and functions to represent and solve problems.

NCTM Standard 9: ALGEBRA

In grade seven, the mathematics curriculum should include explorations of algebraic concepts and processes so that students can:

• Understand the concepts of variable, expression, and equation.
• Represent simple numerical relationships with tables, graphs, in the coordinate plane and verbal or symbolic rules.
• Analyze tables and graphs to identify properties and relationships.
• Develop confidence in solving linear equations, using concrete, and informal, and formal methods.
• Formulate hypotheses to answer a question and use data to test hypotheses.
• Demonstrate understanding of why two results are equally likely, construct sample spaces, and determine probabilities of events.

CALIFORNIA MATHEMATICS STANDARDS

• Students express quantitative relationships using algebraic terminology, expressions, equations, inequalities and their graphs.
• Students interpret and evaluate expressions involving integer powers and simple roots.
• Students graph and interpret linear and some non-linear functions.
• Students solve simple linear equations and inequalities over the rational numbers.
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Examples of the types of work a student should be able to do to meet the standard:

• Discover, describe, and generalize patterns, including linear exponential, and simple quadratic relationships, i.e., those of the form f(n)=n2 or f(n)=cn2, for constant c.
• Represent relationships with tables, graphs in the coordinate plane, and verbal or symbolic rules.
• Analyze tables and graphs to determine functional relationships.
• Find solutions for unknown quantities in linear equations and in simple equations and inequalities.

STANDARD 4: STATISTICS AND PROBABILITY Students demonstrate their knowledge of basic skills, conceptual understanding, and problem solving in statistics and probability.

SUPPORTING NCTM STANDARDS, GRADES 5-8

NCTM Standard 10: STATISTICS

In grade seven, the mathematics curriculum should include exploration of statistics in real-world situations so that students can:

• Systematically collect, organize, and describe data.
• Construct, read, and interpret tables, charts and graphs.
• Make inferences and convincing arguments based on data analysis.
• Evaluate arguments based on data analysis.
• Develop an appreciation for statistical methods as powerful means for decision making.

NCTM Standard 11: PROBABILITY

In grade seven, the mathematics curriculum should include explorations of probability in real-world situations so that students can:

• Model situations by devising and carrying out experiments or simulations to determine probabilities.
• Model situations by constructing a sample space to determine probabilities.
• Appreciate the power of using a probability model by comparing experimental results with mathematical expectations.
• Make predictions based on experimental or theoretical probabilities.
• Develop an appreciation for the pervasive use of probability in the real world.

CALIFORNIA ACADEMIC STANDARDS

• Students collect, organize and represent data sets that have one or more variables and identify relationships among variables within a data set both manually and by using an electronic spreadsheet program.

Examples of the types of work a student should be able to do to meet the standard:

• Organize data on charts and graphs, including scatter plots, bar, line, and circle graphs, and VENN diagrams.
• Collect and organize data and display data with appropriate tables, charts, and graphs.
• Analyze data with respect to frequency and distribution, including mode and range.
• Analyze appropriately central tendencies of data with mean and median.
• Make conclusions and recommendations based on data analysis.
• Critique the conclusions and recommendations derived from others' statistics.

STANDARD 5: PROBLEM SOLVING AND MATHEMATICAL REASONING Students solve problems that make significant demands in one or more of these aspects of the solution process: problem formulation, problem implementation, and problem conclusion.

SUPPORTING NCTM STANDARDS, GRADES 5-8

NCTM Standard 1: MATHEMATICS AS PROBLEM SOLVING

In grade seven, the mathematics curriculum should include numerous and varied experiences with problem solving as a method of inquiry and application so that students can:

• Use problem-solving approaches to investigate and understand mathematical content.
• Formulate problems from situations within and outside mathematics.
• Develop and apply a variety of strategies to solve problems, with emphasis on multi-step and nonroutine problems.
• Verify and interpret results with respect to the original problem situation.
• Generalize solutions and strategies to new problems situations.
• Acquire confidence in using mathematics meaningfully.

NCTM Standard 3: MATHEMATICS AS REASONING

In grade seven, reasoning should permeate the mathematics curriculum so that students can:

• Recognize and apply deductive and inductive reasoning.
• Understand and apply reasoning processes, with special attention being given to spatial reasoning and reasoning with proportions and graphs.
• Make and evaluate mathematical conjectures and arguments.
• Validate their own thinking.
• Appreciate the pervasive use and power of reasoning as a part of mathematics.

CALIFORNIA MATHEMATICS STANDARDS

• Students make decisions about how to approach problems.
• Students use strategies, skills, and concepts in finding solutions.
• Students determine a solution is complete and move beyond a particular by generalizing to other situations.

Examples of the types of work a student should be able to do to meet the standard:

• Problem Formulation
• Formulate and solve a variety of meaningful problems.
• Extract pertinent information from situations and figures and identify what additional information is needed.
• Formulate conjectures and argue, short of formal proof, why they must be or seem to be true.
• Problem Implementation
• Use and invent a variety of approaches and understand and evaluate the of others.
• Invoke problem solving strategies, such as illustrating with sketches to clarify situations or organizing information in a table.
• Explain, where helpful, how to break a problem into simpler parts.
• Solve for unknown or undecided quantities using algebra, graphing, sound reasoning, and other strategies.
• Integrate concepts and techniques from different areas of mathematics.
• Make sensible, reasonable estimates.
• Make justified, logical statements.
• Problem Conclusions
• Verify and interpret results of a problem
• Generalized solutions and strategies to new problems.

STANDARD 6: MATHEMATICAL COMMUNICATION Students communicate their knowledge of basic skills, conceptual understanding, and problem solving and demonstrate their understanding of the mathematical communication of other.

 

SUPPORTING NCTM STANDARDS, GRADES 5-8

NCTM Standard 2: MATHEMATICS AS COMMUNICATION

In grade seven, the study of mathematics should include opportunities to communicate so that students can:

• Model situations, using oral, written, concrete, pictorial, graphical, and algebraic methods.
• Reflect on and clarify their own thinking about mathematical ideas and situations.
• Develop common understandings of mathematical ideas, including the role of definitions.
• Use the skills of reading, listening, and viewing to interpret and evaluate mathematical ideas.
• Discuss mathematical ideas and make conjectures and convincing arguments.
• Appreciate the value of mathematical notation and its role in the development of mathematical ideas.

CALIFORNIA MATHEMATICS STANDARDS

• None

Examples of the types of work a student should be able to do to meet the standard:

• Use mathematical language and representation with appropriate accuracy, including numerical tables and equations, simple algebraic equations, formulas, charts, graphs, and diagrams.
• Organize work, explain facets of solution orally and in writing, label drawings, and use other techniques to make meaning clear to the audience.
• Use mathematical language to explain complex situations.
• Exhibit developing reasoning abilities by justifying statements and defending work.
• Demonstrate understanding of concepts by explaining ideas not only to teachers but to fellow students or younger children.
• Demonstrate comprehension of mathematics from reading assignments and from other sources.