School Administrative District #4
Unity of purpose
CORE CURRICULUM:
ESSENTIAL LEARNINGS FOR PROMOTION
Department: Mathematics
Of all the performance indicators listed for a given content standard, some are more critical to future academic success than others. Those that address knowledge and skills needed for students to experience success at the next checkpoint (i.e., specific grade, grade level, or post-graduate experience) are referred to as "essential learn-ings." Such learnings should be assessed at the end of each checkpoint and tied to specific performance standards (e.g., distinguished, advanced, basic, novice). A student who performs at the basic level with respect to these learnings is generally promoted from one grade or level to the next. A student who cannot do so may be (1) promoted with reservations clearly recorded, mailed home to parents, and placed on file or (2) retained, depending upon the severity of that student's deficits with respect to the standards and the promotion-and-retention policy of the district.
Local assessments and performance standards have not yet been established for S.A.D. #4 schools, but teachers are encouraged to consider the benchmarks that follow as they assess their students' readiness for subsequent levels of learning. Students at the kindergarten level have been given one year and high-school students have been given four years to demonstrate the essential learnings delineated beneath Kindergarten and Grades 9-12, respectively. All other students have been given two years to demonstrate the essential learnings.
|
Kindergarten |
Performance Indicators: The learner will·
CONTENT STANDARD: NUMBERS AND NUMBER SENSE
1. Recognize numbers for sets of 20 or more objects
2. Read, write, order, and compare numbers from 0 to 20
CONTENT STANDARD: COMPUTATION
1. Demonstrate an understanding of the processes of addition and subtraction
2. Use a variety of materials, strategies, and symbols to manipulate
á Whole numbers
á Addition of the number 1 or the number 2 to a one-digit positive number
á Subtraction of the number 1 or the number 2 from a one-digit positive number
CONTENT STANDARD: MEASUREMENT
1. Compare two objects, using direct comparisons, according to one or more attributes
á Length (shorter, longer)
á Height (shorter, taller)
á Distance (nearer, farther)
á Mass (heavier, lighter)
á Volume (less, more)
á Time (earlier, later; before, after)
á Temperature (hotter, colder)
CONTENT STANDARD: PATTERNS, RELATIONS, AND FUNCTIONS
1. Sort and classify objects according to similar attributes
2. Recognize and extend a variety of patterns
á Linear, e.g., ABB using Unifix cubes
á Spatial, e.g., pattern block designs
CONTENT STANDARD: DISCRETE MATHEMATICS
1. None
CONTENT STANDARD: MATHEMATICAL REASONING
1. None
CONTENT STANDARD: DATA ANALYSIS AND STATISTICS
1. Gather data relating to familiar experiences by counting and tallying
CONTENT STANDARD: PROBABILITY
1. None
CONTENT STANDARD: ALGEBRA CONCEPTS
1. Use language to express numerical relationships
2. Solve one-step linear word problems by
á Listening to a situation, determining the appropriate operation (addition or subtraction), and solving for an unknown, using manipulatives
CONTENT STANDARD: GEOMETRY
1. Identify and describe representations of plane geometric figures (e.g., circle, triangle, square, rectangle)
2. Compare the size and shape of plane geometric figures
3. Use positional words to describe the proximity of objects in space (e.g., near, far, up, down, beside)
|
Grades 1- 2 |
Performance Indicators: The learner will·
CONTENT STANDARD: NUMBERS AND NUMBER SENSE
1. Read and write three-digit numbers for objects grouped by hundreds, tens, and ones
2. Read, write, order, and compare numbers through 999
3. Count by two's, five's, and ten's
4. Read and write money notation through three digits
á Count a collection of currency and coins through $9.99
5. Recognize even and odd numbers
CONTENT STANDARD: COMPUTATION
1. Use a variety of materials, strategies, and symbols to manipulate
á Whole numbers
á Addition of one-digit positive numbers with sums less than or equal to 18
á Subtraction of one-digit positive numbers with minuends less than or equal to 18
á Addition of two or more one-digit positive numbers
á Addition of two three-digit positive numbers
á Subtraction of two-digit positive numbers
á Multiplication of one-digit positive numbers less than or equal to 5
á Money notation
á Addition, e.g., $1.25 + $2.30 = $3.55
2. Use and apply estimations with
á Quantities
á Computations
CONTENT STANDARD: MEASUREMENT
1. Count and exchange equivalent quantities of money, using
á Pennies
á Nickels
á Dimes
á Quarters
á Half dollars
2. Tell time to the quarter hour, using an analog and a digital clock
3. Find the month, day, and year, using a calendar
CONTENT STANDARD: PATTERNS, RELATIONS, AND FUNCTIONS
1. Sort and classify objects according to one or more attributes, including color, size, shape, and thickness
2. Describe and create a variety of patterns
á Linear
á Spatial
CONTENT STANDARD: DISCRETE MATHEMATICS
1. Create and use an organized list to determine possible outcomes or to solve problems
á Three variations of one attribute, e.g., determine the possible arrangements for a triple ice-cream cone given three flavors of ice cream
á Two variations of two attributes, e.g., determine the possible arrangements for two differing styles of shirts and two differing styles of pants
CONTENT STANDARD: MATHEMATICAL REASONING
1. Draw logical conclusions about mathematics by answering questions such as What do you think the answer is? Why do you think that is a good answer? Why isn't that a good answer?
2. Distinguish between "important" and "unimportant" mathematical information
CONTENT STANDARD: DATA ANALYSIS AND STATISTICS
1. Interpret information displayed in an object or picture graph, using the vocabulary more, less, fewer, greater than, less than.
CONTENT STANDARD: PROBABILITY
1. Use data from an experiment to predict which of two events is more likely to occur if the experiment is repeated
CONTENT STANDARD: ALGEBRA CONCEPTS
1. Use symbols to express numerical relationships
2. Recognize and use algebraic properties
á Zero property/identity property
á Addition
á Subtraction
á Commutative property for
á Addition
3. Solve problems by completing a numerical sequence involving basic addition and subtraction facts (e.g., 3 + __ = 7 or 7 - __ = 3)
4. Solve one-step linear word problems by
á Listening to a situation, determining the appropriate operation (addition or subtraction), and solving for an unknown, using an equation
á Reading about a situation, determining the appropriate operation (addition or subtraction), and solving for an unknown, using an equation
CONTENT STANDARD: GEOMETRY
1. Identify, describe, and draw representations of plane geometric shapes according to the number of sides, corners, and square corners
2. Identify and describe objects in his/her environment that depict geometric figures
|
Grades 3-4 |
Performance Indicators: The learner will·
1. Read, write, order, compare, and explain numbers through six digits
2. Read and write money notation through four digits
3. Recognize and use ordinal numbers through fortieth
4. Read, write, order, compare, and explain simple fractions through tenths
5. Read, write, and explain decimals through hundredths
6. Demonstrate knowledge of the meaning and use of whole numbers, fractions, and decimals
CONTENT STANDARD: COMPUTATION
1. Use a variety of materials, strategies, and symbols to manipulate
á Whole numbers
á Addition of three or more two-digit positive numbers
á Addition of two four-digit positive numbers
á Subtraction of four-digit positive numbers
á Multiplication of one-digit positive numbers
á Division with quotients and divisors less than or equal to 9 with or without remainders
á Multiplication of three-or-more-digit positive numbers by two-digit positive numbers
á Fractions
á Addition with like denominators
á Subtraction with like denominators
á Money notation
á Subtraction, e.g., $3.55 - $2.30 = $1.25
2. Memorize basic facts related to
á Addition up to 9 + 9
á Subtraction up to 18 - 9
á Multiplication up to 5 x 10
3. Round numbers to the nearest
á Ten
á Hundred
4. Demonstrate and explain computations
á Defending the reasonableness of a result/answer
5. Use estimation to determine the reasonableness of a result/answer
6. Solve real-life problems involving
á Addition of whole numbers
á Subtraction of whole numbers
á Multiplication of whole numbers
á Division of whole numbers
CONTENT STANDARD: MEASUREMENT
1. Count and exchange equivalent quantities of money
2. Estimate and measure
á Length
á Mass
á Volume
á Time
á Temperature
3. Identify equivalent periods of time (e.g., seven days equal one week, sixty minutes equal one hour)
4. Tell time to the nearest minute, using an analog and a digital clock
CONTENT STANDARD: PATTERNS, RELATIONS, AND FUNCTIONS
1. Recognize, describe, and extend a variety of relationships using variables (e.g., if John earns two cents per day, how many days will it take to earn sixteen cents?)
2. Recognize and describe the relationship between
á Addition and subtraction
á Addition and multiplication
á Multiplication and division
3. Use the patterns of numbers, geometry, and/or graphs to solve a problem
CONTENT STANDARD: DISCRETE MATHEMATICS
1. Create and use
á Organized lists
á Tree diagrams
á Venn diagrams
á Networks (e.g., routes, pathways, etc.)
2. Give examples of infinite and finite solutions
CONTENT STANDARD: MATHEMATICAL REASONING
1. Follow logical arguments
á Justify his/her answers and solution processes
CONTENT STANDARD: DATA ANALYSIS AND STATISTICS
1. Make generalizations and draw conclusions using various types of graphs, charts, and tables
2. Collect, organize, display, and interpret data in a variety of graphical forms
á Bar graph
á Line graph
CONTENT STANDARD: PROBABILITY
1. Determine the probability of a given simple event, using manipulatives
2. Solve problems involving probability of a single event by using tree diagrams or by constructing a sample space representing all possible results
CONTENT STANDARD: ALGEBRA CONCEPTS
1. Recognize and use algebraic properties
á Identity property for
á Multiplication
á Division
á Zero property for
á Multiplication
á Division
á Commutative property for
á Multiplication
2. Identify and locate missing whole numbers on a given number line
3. Solve one-step linear word problems by
á Reading about a situation, determining the appropriate operation (addition, subtraction, multiplication or division), and solving for an unknown, using an equation
CONTENT STANDARD: GEOMETRY
1. Analyze plane geometric figures and identify relevant properties, including the number of angles, square angles, and segments
2. Analyze solid geometric figures and identify relevant properties, including the number of faces, vertices, and edges
3. Identify and draw representations of
á Points
á Lines
á Line segments
á Rays
á Angles
4. Use the properties of shapes and figures to describe the physical world
5. Find the perimeter of polygons, given the lengths of sides
á Triangles
á Squares
á Rectangles
|
Grades 5-6 |
Performance Indicators: The learner will·
CONTENT STANDARD: NUMBERS AND NUMBER SENSE
1. Read, write, order, compare, and explain numbers through nine digits
2. Read, write, compare, order, and explain decimals through thousandths
3. Use numbers in a variety of equivalent and interchangeable forms
á Fractions
á Decimals
á Percents
4. Recognize and use
á Factors
á Multiples
á Prime numbers
á Composite numbers
CONTENT STANDARD: COMPUTATION
1. Use a variety of materials, strategies, and symbols to manipulate
á Fractions
á Division
á Addition with unlike denominators
á Subtraction with unlike denominators
2. Memorize basic facts related to
á Multiplication up to 12 x 12
á Division up to 100 ü 10
3. Round numbers to the nearest
á Thousand
á Million
á Thousandths
4. Apply estimation to real life situations
5. Apply the order of operations to problem solving
á Parentheses
á Multiple parentheses
6. 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
7. Solve multi-step, real-life problems involving
á Addition and subtraction of simple fractions
8. Create, solve, and justify the solution to multi-step, real-life word problems, using
á Whole numbers
á Fractions
CONTENT STANDARD: MEASUREMENT
1. Recognize,
understand, and use equivalent measures within both
2. 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)
3. Use corresponding units of measure to label length, area, and volume (e.g. in, in2, in3)
4. Estimate and measure angles using a protractor
5. Determine the amount of lapsed time in hours and minutes
CONTENT STANDARD: PATTERNS, RELATIONS, AND FUNCTIONS
1. Demonstrate an understanding of the interrelationships between and among addition, subtraction, multiplication, and division as operations
2. Analyze relationships to explain how a change in one quantity can result in a change in another
CONTENT STANDARD: DISCRETE MATHEMATICS
1. 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
1. Follow logical arguments
á Use models, known facts, properties, and relationships to explain his/her thinking
á Demonstrate and justify that multiple paths to a conclusion may exist
CONTENT STANDARD: DATA ANALYSIS AND STATISTICS
1. Collect, organize, display, and interpret data in a variety of graphical forms
á Table
á Chart
á Double bar graph
á Double line graph
á Circle graph (halves, fourths, and eighths)
2. Find the mean, median, mode, and range of a set of data
CONTENT STANDARD: PROBABILITY
1. None
CONTENT STANDARD: ALGEBRA CONCEPTS
1. Create and solve a problem situation based upon a given open sentence, using a single variable
2. Recognize and use algebraic properties
á Distributive property
á Associative property for
á Addition
á Multiplication
CONTENT STANDARD: GEOMETRY
1. Distinguish between and use the appropriate symbols for
á Angles
á Acute
á Obtuse
á Straight
2. Identify lines which illustrate intersection, parallelism, and perpendicularity
3. Identify and classify angles as
á Acute
á Right
á Obtuse
á Straight
á Complementary
á Supplementary
4. Measure and draw right, acute, obtuse, and straight angles and triangles, using appropriate tools
5. Identify, classify, describe, and draw polygons (e.g., pentagon, hexagon, heptagon, octagon, nonagon, and decagon - two dimensional shapes)
6. Find the area of polygons, given the lengths of sides
á Triangles
á Squares
á Rectangles
7. Determine congruence or noncongruence of segments, angles, and polygons by direct comparison, given their attributes
8. Investigate circles by
á Identifying points and lines related to circles
á Center point
á Radius
á Diameter
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. Find the area of a circle, given the diameter or the radius
12. Investigate triangles by
á Classifying triangles according to their angle measure
á Acute
á Right
á Obtuse
á Isosceles
á Equilateral
á Scalene
|
Grades 7-8 |
Performance Indicators: The learner will·
CONTENT STANDARD: NUMBERS AND NUMBER SENSE
1. Use numbers in a variety of equivalent and interchangeable forms
á Integers
á Exponents
á Scientific notation
CONTENT STANDARD: COMPUTATION
1. Use a variety of materials, strategies, and symbols to manipulate and communicate
á Whole numbers
á Ratio
á Proportion
á Scientific notation
2. Memorize basic facts related to
á Division up to 144 ü 12
3. Using correct terminology, compute and model all four operations with
á Decimals
á Percents
á Integers
á Real numbers
á Scientific notation
4. Apply the order of operations to problems involving
á Multiple operations
á Exponents
á Square roots
á Absolute value
5. 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
6. Create, solve, and justify the solution to multi-step, real-life problems, using
á Decimals
á Percents
1. Verify by measuring and describe the relationships between vertical angles and angles that are supplementary and complementary
2. 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
á Design and construct a model to scale
CONTENT STANDARD: PATTERNS, RELATIONS, AND FUNCTIONS
1. Investigate and describe functional relationships including the number of sides of a regular polygon, the sum of the measures of the interior angles, and the maximum number of possible diagonals, expressing the algebraic concept of the number of diagonals of the nth-sided polygon
CONTENT STANDARD: DISCRETE MATHEMATICS
1. Analyze and solve problems, including
á Communication networks
á Tournament matchings
á Production schedules
á Consumer applications
2. Investigate sets and relations
á Union
á Intersection
á Empty or null set
CONTENT STANDARD: MATHEMATICAL REASONING
1. None
CONTENT STANDARD: DATA ANALYSIS AND STATISTICS
1. 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
á Spreadsheet
2. Use information displayed in various graphical forms to make comparisons, predictions, and inferences
CONTENT STANDARD: PROBABILITY
1. Determine the probability of a given simple event and express that probability as a ratio, fraction, decimal, or percent
2. Use knowledge of probability to analyze problem situations
CONTENT STANDARD: ALGEBRA CONCEPTS
1. Write verbal expressions/sentences as algebraic expressions/equations
2. Recognize and use algebraic properties
á Multiplicative inverse property
á Inverse property of addition
á Addition property of equality
á Multiplication property of equality
3. Use algebraic terms appropriately
á Equation
á Inequality
á Variable
á Expression
4. Compute with integers, using
á Number line
á Additive inverse
5. Manipulate algebraic expressions by
á Adding
á Subtracting
á Multiplying
á Dividing
6. Identify and graph ordered pairs in the four quadrants of a coordinate plane
7. Graph a linear equation in two variables on the coordinate plane, using a table of ordered pairs
8. Create and solve problems using proportions, formulas, and functions
CONTENT STANDARD: GEOMETRY
1. Identify and classify angles as
á Adjacent
á Vertical
2. Compare, classify and draw three dimensional shapes
3. Find the volume and surface area of rectangular prisms, cylinders, cones, and pyramids given the appropriate dimensions
|
Grades 9-12 |
Performance Indicators: The learner will·
CONTENT STANDARD: NUMBERS AND NUMBER SENSE
1. Describe the structure of the real number system and identify its appropriate applications and limitations
2. Use numbers in a variety of equivalent and interchangeable forms in problem solving
á Integers
á Fractions
á Decimals
á Percents
á Exponents
á Scientific notation
á Irrational numbers
3. Explain what complex numbers (real and imaginary) mean and describe some of their many uses
CONTENT STANDARD: COMPUTATION
1. Use a variety of materials, strategies, and symbols to manipulate
á Real numbers
2. Create, solve, and justify the solution to multi-step, real-life problems, using
á Inverse proportion
3. Use various techniques to approximate solutions to real-life and abstract problems, determine the reasonableness of answers to those problems, and justify the results
CONTENT STANDARD: MEASUREMENT
1. Convert from one measurement system to another, using unit multipliers
á Metric
to
á
2. Use measurement tools and units appropriately and recognize limitations in the precision of the measurement tools
á Protractor
á Compass
á Graphing calculator
CONTENT STANDARD: PATTERNS, RELATIONS, AND FUNCTIONS
1. Create a graph to explain a real-life situation and draw inferences from it
2. Translate and solve a real-life problem using symbolic language
3. Apply techniques to fit functions (model) to collected data and make predictions from the function of best fit
á Median-fit line
4. Identify and use the different types of functions and their descriptions
á Constant
á Linear
á Quadratic
á Polynomial
5. Find the area of non-right triangles when the height is not given
6. Solve right triangles
á 30-60-90o
á 45-45-90o
á Other right triangles
7. Identify angles of rotation
á Degree measure
á Radian measure
8. Convert radians to degrees and degrees to radians
9. Manipulate with functions
á Evaluate
á Add
á Subtract
á Multiply
á Divide
á Graph
á