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·
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Grade 6 |
1. Review and extend prior learning
2. Read, write, order, compare, and explain numbers through twelve digits
3. Analyze algorithms
4. Use numbers in a variety of equivalent and interchangeable forms
á Fractions
á Decimals
á Percents
5. Read, write, and use Roman numerals involving combinations of
á D
á M
6. Recognize and use
á Prime numbers
á Composite numbers
7. Demonstrate an initial understanding of the concept
á Integers
á Ratio
á Proportion
á Exponents
á Square roots
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 6 |
1. Review and extend prior learning
2. Use a variety of materials, strategies, and symbols to manipulate
á Whole numbers
á Division by three-or-more-digit positive numbers
á Fractions
á Addition with unlike denominators
á Subtraction with unlike denominators
á Division
3. Memorize basic facts related to
á Multiplication up to 12 x 12
á Division up to 100 ü 10
4. Round decimal numbers to the nearest thousandth
5. Apply the order of operations to problems involving
á Multiple parentheses
6. Solve multi-step, real-life problems involving
á Addition and subtraction of simple fractions with unlike denominators
7. Recognize when a solution to a problem needs to be simplified and simplify it
8. Use a variety of materials, strategies, and symbols to manipulate operations with number systems other than base ten
á Adding and subtracting
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 Mass
á Ounces
á Pounds
á Tons
9. Create, solve, and justify the solution to multi-step, real-life problems, using
á Fractions
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 6 |
1. Review and extend prior learning
2. Recognize, understand, and use equivalent measures within both U.S. customary units and the metric system, e.g., how many cups in a quart or milliliters in a liter
3. Demonstrate an initial understanding of reading and using the scale of a drawing
á Make simple scale drawings
4. Estimate and measure angles using a protractor
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 6 |
1. Review and extend prior learning
2. Demonstrate an understanding of the interrelationships between and among addition, subtraction, multiplication, and division as operations
3. Investigate, describe, and extend numerical and geometric patterns (e.g., triangular numbers, perfect squares, patterns formed by powers of 10, and arithmetic sequences)
4. Create a variety of relationships, using variables and expressions
5. Demonstrate an initial understanding of 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 6 |
1. Review and extend prior learning
2. Create and use networks to explain practical situations or to solve problems
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 6 |
1. Review and extend prior learning
2. Follow logical arguments
á Demonstrate an initial understanding of deductive and inductive reasoning
á Demonstrate and justify that multiple paths to a conclusion may exist
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 6 |
1. Review and extend prior learning
2. Collect, organize, display, and interpret data in a variety of graphical forms
á Circle graph (halves, fourths, and eighths)
á Stem-and-leaf plot
3. Find the mean, median, mode, and range of 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 6 |
1. Review and extend prior learning
2. Determine and interpret the probability of an event occurring from a given sample space
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 6 |
1. Review and extend prior learning
2. Recognize and use algebraic properties
á Associative property for
á Addition
á Multiplication
3. Solve two-step linear word problems by
á Reading about a situation, determining the appropriate operations (addition, subtraction, multiplication or division), and solving for an unknown, using an equation
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 6 |
1. Review and extend prior learning
2. Identify and classify angles as
á Complementary
á Supplementary
3. Identify, classify, describe, and draw polygons (e.g., pentagon, hexagon, heptagon, octagon, nonagon, and decagon)
4. Determine congruence or noncongruence of segments, angles, and polygons by direct comparison, given their attributes
5. Sketch, construct models, and classify rectangular prisms, cones, cylinders, and pyramids
6. Investigate circles by
á Identifying points and lines related to circles
á Center point
á Radius
á Diameter
7. Find the area of a circle, given the diameter or the radius
8. Investigate, create, and solve problems requiring him/her to find
á Perimeter/circumference
á Area
9. Investigate triangles by
á Classifying triangles according to their angle measure
á Acute
á Right
á Obtuse
á Isosceles
á Equilateral
á Scalene
10. Verify the Pythagorean Theorem by measuring and then applying the Pythagorean Theorem to find the missing length of a side of a right triangle when the lengths of the other two sides are given
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Developed 07/17/97 Revised 07/08/98 |
curr-math-scope-6.doc |