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 5 |
1. Review and extend prior learning
2. Read, write, order, compare, and explain numbers through nine digits
3. Read, write, and use Roman numerals involving combinations of
á L
á C
4. Read, write, compare, order, and explain decimals through thousandths
5. Recognize and use
á Factors
á Multiples
6. Demonstrate an initial understanding of the concept
á Percent
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 5 |
1. Review and extend prior learning
2. Use a variety of materials, strategies, and symbols to manipulate
á Fractions
á Multiplication
3. Memorize basic facts related to
á Multiplication up to 10 x 10
á Division up to 50 ü 5
4. Round numbers to the nearest
á Thousand
á Million
5. Apply the order of operations to problem solving
á Parentheses
6. Solve multi-step, real-life problems involving
á Addition and subtraction of simple fractions with like denominators
á Multiplication of fractions
7. Create, solve, and justify the solution to multi-step, real-life word problems, using
á Whole numbers
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 5 |
1. Review and extend prior learning
2. Estimate the conversion of a metric measure to a U.S. customary measure
3. Demonstrate an initial understanding of reading and using the scale of a drawing
á Find the actual dimensions of an object from a scaled drawing
4. Select and use the appropriate measurement tool to solve problems involving
á Length
á Weight/mass
á Area
á Volume
á Time
á Temperature (Fahrenheit/Celsius)
5. Demonstrate an initial understanding of how to use measurement tools and units appropriately and recognize limitations in the precision of the measurement tools
á Protractor
6. Determine the amount of lapsed time in hours, minutes, and seconds
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 5 |
1. Review and extend prior learning
2. Analyze relationships to explain how a change in one quantity can result in a change in another
3. Use patterns and multiple representations to solve problems
4. Recognize and describe the relationship between
á Subtraction and division
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 5 |
1. Review and extend prior learning
2. Identify patterns in the world and express these patterns as rules, e.g., the date one week from any given day
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 5 |
1. Review and extend prior learning
2. Follow logical arguments
á Use models, known facts, properties, and relationships to explain his/her thinking
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 5 |
1. Review and extend prior learning
2. Collect, organize, display, and interpret data in a variety of graphical forms
á Double bar graph
á Double line graph
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 5 |
1. Review and extend prior learning
2. Create a problem statement involving probability based on information from a given problem situation (he/she may or may not be able to solve the problem)
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 5 |
1. Review and extend prior learning
2. Create and solve a problem situation based upon a given expression, using a single variable
3. Recognize and use algebraic properties
á Distributive property
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 5 |
1. Review and extend prior learning
2. Identify lines which illustrate intersection, parallelism, and perpendicularity
3. Distinguish between and use the appropriate symbols for
á Angles
á Acute
á Obtuse
á Straight
á Planes
á Second dimension
á Third dimension
4. Identify and classify angles as
á Acute
á Right
á Obtuse
á Straight
5. Measure and draw right, acute, obtuse, and straight angles and triangles, using appropriate tools
6. Construct the perpendicular bisector of a line segment and an angle bisector, using a compass and straightedge
7. Demonstrate an initial understanding of how to determine congruence or noncongruence of segments, angles, and polygons by direct comparison, given their attributes
8. Find the area of polygons, given the lengths of sides
á Triangles
á Squares
á Rectangles
9. Find the diameter, radius, and circumference of a circle, given a center point
10. Differentiate between area and perimeter and know when to apply the concepts of perimeter and area to given situations
11. Investigate and predict the results of combining, dividing, and changing two-dimensional shapes
12. Investigate triangles by
á Identifying corresponding parts of congruent triangles
13. Investigate quadrilaterals by
á Identifying corresponding parts of congruent quadrilaterals
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Developed 07/17/97 Revised 07/08/98 |
curr-math-scope-5.doc |