School Administrative District #4

Unity of purpose

CORE CURRICULUM: SCOPE AND SEQUENCE

Department: Mathematics

CONTENT STANDARD: NUMBERS AND NUMBER SENSE

Students will understand and demonstrate a sense of what numbers mean and how they are used. Numbers are used to describe and interpret phenomena. Building a sense of number relationships is essential for developing the ability to deal with any set of numbers. Number sense involves understanding the meaning of numbers, relationships among numbers, relative number magnitudes, and the effects of operations on numbers. Skilled estimation is also an important component of number sense.

 

Performance Indicators: The learner will·

Grade 7

1.        Review and extend prior learning

2.        Use numbers in a variety of equivalent and interchangeable forms in problem solving

á         Integers

á         Exponents

3.        Demonstrate an initial understanding of the concept

á         Absolute value

á         Scientific notation

4.        Apply concepts of ratios, proportions, percents, and number theory (e.g., primes, factors, and multiples) in practical and other mathematical situations

CONTENT STANDARD: COMPUTATION

Students will understand and demonstrate computation skills. Computation involves understanding the fundamental operations of and relationships between and among addition, subtraction, multiplication, and division. Proficiency in computational skills requires that students learn to evaluate the reasonableness of an answer and to obtain accuracy in calculations with ever-increasing ease and confidence, with and without technological tools.

 

Performance Indicators: The learner will·

Grade 7

1.        Review and extend prior learning

2.        Use a variety of materials, strategies, and symbols to manipulate

á         Whole numbers

á         Ratio

á         Proportion

á         Exponents

á         Square roots

á         Scientific notation

3.        Memorize basic facts related to

á         Division up to 144 ü 12

4.        Using correct terminology, compute and model all four operations with

á         Decimals

á         Percents

á         Integers

5.        Apply the order of operations to problems involving

á         Multiple operations

6.        Use a variety of materials, strategies, and symbols to manipulate operations with number systems other than base ten

á         Adding and subtracting

á         Volume

á          Fluid ounces

á          Teaspoons

á          Tablespoons

á         Multiplying and dividing

á         Time

á          Seconds

á          Minutes

á          Hours

á          Days

á          Months

á          Years

á         Distance

á          Inches

á          Feet

á          Yards

á          Miles

á         Volume

á          Cups

á          Pints

á          Quarts

á          Gallons

á          Fluid ounces

á          Teaspoons

á          Tablespoons

á         Mass

á          Ounces

á          Pounds

á          Tons

7.        Solve multi-step, real-life problems involving

á         Division of fractions

8.        Create, solve, and justify the solution to multi-step, real-life problems, using

á         Decimals

á         Percents

CONTENT STANDARD: MEASUREMENT

Students will understand and demonstrate measurement skills. Measurement is valuable as an integrating skill throughout the curriculum and in everyday life. The use of estimation is vital in determining the reasonableness of measurement. Measurement attributes (e.g., length, volume, time), U.S. customary and metric units, and tools enhance the ability to describe and understand the world.

 

Performance Indicators: The learner will·

Grade 7

1.        Review and extend prior learning

2.        Demonstrate an initial understanding of units of measurement

á         Volume

á         Fluid ounces

á         Milliliters

3.        Demonstrate an initial understanding of how to use measurement tools and units appropriately and recognize limitations in the precision of the measurement tools

á         Compass

4.        Read and use the scale of a drawing

á         Find distances and directions on a land map

á         Find the actual dimensions of an object from a scaled drawing

á         Make simple scale drawings

CONTENT STANDARD: PATTERNS, RELATIONS, AND FUNCTIONS

Students will understand that mathematics is the science of patterns, relationships, and functions. Relationships are central to mathematical understanding. A study of patterns often reveals regularity, indicating the presence of a mathematical relationship. Studying relationships allows students to make generalizations and predictions about phenomena and occurrences.

 

Performance Indicators: The learner will·

Grade 7

1.        Review and extend prior learning

2.        Demonstrate an initial understanding of how to find solutions for unknown quantities in linear equations and in simple equations and inequalities

3.        Investigate and describe functional relationships, including the number of sides of a regular polygon and the sum of the measures of the interior angles

CONTENT STANDARD: DISCRETE MATHEMATICS

Students will understand and apply concepts in discrete mathematics. Discrete mathematics studies discrete processes (e.g., all possible bus routes in a school district). This study includes the exploration of diagrams, networks, and flowcharts that students construct to model situations or use for planning, scheduling, and decision making. Three main concerns of discrete mathematics are existence (Is there a solution?), counting (How many solutions are there?), and efficiency (What is the best solution?).

Performance Indicators: The learner will·

Grade 7

1.        Review and extend prior learning

2.        Analyze and solve problems, including

á         Communication networks

á         Tournament matchings

CONTENT STANDARD: MATHEMATICAL REASONING

Students will understand and apply concepts of mathematical reasoning. Reasoning is fundamental to the knowing and doing of mathematics. To give more students access to mathematics as a powerful way of making sense of the world, it is essential that an emphasis on reasoning pervade all mathematics. Students need a great deal of time and many experiences to develop their ability to construct and evaluate valid arguments in problem settings and to evaluate the arguments of others.

Performance Indicators: The learner will·

Grade 7

1.        Review and extend prior learning

2.        Recognize and apply deductive and inductive reasoning

3.        Understand and apply reasoning processes, with special attention to spatial reasoning and reasoning with proportions and graphs

4.        Follow logical arguments

á         Make and evaluate mathematical conjectures and arguments

CONTENT STANDARD: DATA ANALYSIS AND STATISTICS

Students will understand and apply concepts of data analysis. Individuals are faced with massive quantities of information which must be selected, sorted, and analyzed to reach conclusions. Sound decision making requires the ability to collect data effectively, organize data, discover patterns, summarize trends, make inferences, draw conclusions, and make predictions. The ethical use of statistics is a paramount concern in the Information Age.

 

Performance Indicators: The learner will·

Grade 7

1.        Review and extend prior learning

2.        Collect, organize, display, and interpret data in a variety of graphical forms

á         Frequency distribution

á         Box-and-whisker plot

á         Line plot

á         Scatter plot

3.        Describe the mean, median, and mode as measures of central tendency and determine their meaning for a set of data

CONTENT STANDARD: PROBABILITY

Students will understand and apply concepts of probability. Probability is the study of uncertainty. Informed consumers of information understand the basic principles of probability. People need to understand the uncertainties and limitations involved when drawing conclusions from data.

 

Performance Indicators: The learner will·

Grade 7

1.        Review and extend prior learning

2.        Investigate and describe the difference between the probability of an event found through simulation versus the theoretical probability of that same event

3.        Determine the probability of a given simple event and express that probability as a ratio, decimal, or percent

CONTENT STANDARD: ALGEBRA CONCEPTS

Students will understand and apply algebraic concepts. Algebra and analytic thinking are fundamental tools for working in and thinking about mathematics. These tools provide ways to generalize and predict problem solutions when not all information is known. Taught within the context of mathematical and practical applications, the concept of functions is a unifying theme for algebraic concepts.

 

Performance Indicators: The learner will·

Grade 7

1.      Review and extend prior learning

2.      Investigate and describe concepts of exponents, perfect squares, and square roots

3.      Write verbal expressions/sentences as algebraic expressions/equations

4.      Recognize and use algebraic properties

á         Multiplicative inverse property

á         Inverse property of addition

5.      Use algebraic terms appropriately

á         Equation

á         Inequality

á         Variable

á         Expression

á         Domain

á         Range

6.        Create and translate a pattern into a two-step linear equation that can be verified

7.        Compute with integers, using

á         Number line

á         Additive inverse

8.        Identify and graph ordered pairs in the four quadrants of a coordinate plane

CONTENT STANDARD: GEOMETRY

Students will understand and apply concepts from geometry. Geometry is the study of the spatial world and its symmetries. The ideas of geometry are used to describe, interpret, represent, and change the spatial world in which people live. The understanding and development of spatial and visual skills strengthens problem-solving abilities.

 

Performance Indicators: The learner will·

Grade 7

1.        Review and extend prior learning

2.        Identify and classify angles as

á         Adjacent

á         Vertical

3.        Use inductive and deductive reasoning to compare and contrast quadrilaterals (e.g., parallelogram, rectangle, square, rhombus, trapezoid)

4.        Determine if geometric figures (triangles and quadrilaterals) are similar and write proportions to express the relationships between corresponding parts of similar figures

5.        Construct a three-dimensional model, using cubes, given the top, side, and/or bottom views; and determine the volume and surface area of the model

6.        Inscribe equilateral triangles, squares, and hexagons in circles, using a compass and a straightedge

7.        Given appropriate dimensions, estimate and find the area of a polygon by sub-dividing that polygon into rectangles and right triangles

8.        Investigate, create, and solve problems involving the volume and surface area of

á         Rectangular prisms

á         Cylinders

9.      Find the volume and surface area of rectangular prisms and cylinders, given the appropriate dimensions

Developed 07/17/97

Revised 07/08/98

curr-math-scope-7.doc