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Standard #4
Each student will have demonstrated proficiency in mathematics by solving problems requiring number sense, accurate computation, accurate measurement, collection of data and statistics, algebraic methods and geometry.
Kindergarten Mathematics Program
Description
Kindergarten students are introduced to beginning mathematics concepts through hands on learning experiences.
Grade level expectations for each standard indicate what students should know or be able to do as a result of learning that has occurred at this grade in this subject.
Time Allocation:
Approximately 25 minutes during 1/2 day sessions and 50 minutes of full day sessions
Texts/References
Scott Foresman-Addison Wesley, 1999
Assessments
Teacher evaluation of students' skills
Kindergarten Mathematics Expectations
Number Sense and Number Relationships
A. Used objects and pictures to represent whole numbers from 0 to 20 in a variety of ways
B. Used two or more sets of objects to demonstrate which set is equal to, less than, or greater than the other set
C. Used concrete and abstract materials to demonstrate the meaning of wholes and parts (for example, halves)
D. Named pennies, nickels, dimes, quarters, and dollars
E. Read and wrote numerals from 0 to 10 in meaningful contexts
F. Grouped objects into sets of ten
G. Counted from 1 to 50
H. Used one-to-one correspondence to count and compare sets of objects from 0 to 10
I. Started with any whole number less than 50 and counted forward to 50
J. Used ordinal positions for first through tenth
K. Sequenced whole numbers from 0 to 10 (for example, 5 is before 7; 5 is after 4)
L. Described the concept of zero
M. Estimated a reasonable quantity for a given number of objects less than 20
N. Described a relationship between two sets of quantities with more, less, or equal numbers.
Computation and Estimation
A. Added and subtracted whole numbers by combining and separating objects
B. Drew pictures to form sets of up to ten items
Measurement
A. Told time to the nearest hour, using an analog and digital clock
B. Described the units for measuring time
C. Estimated the measurement of length in non-standard units
D. Estimated the measurement of weight by "heavier" and "lighter"
E. Compared objects according to the measurable attributes of length and weight
F. Ordered objects according to the measurable attributes of length and weight
G. Compared the order of various times (for example, morning comes before lunch)
H. Selected the appropriate units of measurement of time and length
I. Measured the lengths of the sides of triangles, squares and rectangles using non-standard units (for example, cubes or paper clips)
Data, Statistics and Probability
A. Read and displayed simple picture and real object graphs
B. Gathered data relating to familiar experiences by counting and tallying
C. Used "more" and "fewer" or "most," "same," and "fewest" to describe sets of manipulatives, pictures, or object graphs
D. Flipped a two-colored counter or coin to generate and tally results
Algebraic Methods
A. Recognized, constructed, and extended patterns in a variety of motions, colors, designs, sounds, rhythms, music, positions, sizes, or quantities
B. Sorted, classified, described and ordered collections of objects in a variety of ways (for example, sorted buttons into groups and explained why they were sorted in a particular way)
C. Recognized when a pattern existed, described the pattern, reproduced that pattern and created a new pattern (for example, red-blue-red-blue = AB,AB pattern)
Geometric Concepts, Properties, and Relationships
A. Placed manipulatives on pictures of shapes congruent to the manipulatives
B. Recognized and identified circles, triangles, squares, rectangles, ovals (ellipses), and diamonds (rhombuses)
C. Used manipulatives (for example, straws or string loops), built circles, triangles, squares, rectangles, ovals (ellipses), and diamonds (rhombuses)
D. Used geometric shapes to solve a problem (for example, created a house)
E. Indicated positions of three or more objects or pictures (for example, left to right, top to bottom, next, last)
F. Combined triangular manipulatives to make a square, and square manipulatives to make a rectangle
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Grade 1 Mathematics Program
Description
Students acquire basic skills and concepts in each area of mathematics.
Grade level expectations for each standard indicate what students should know or be able to do as a result of learning that has occurred at this grade in this subject.
Time Allocation:
Daily - 60 minutes
Texts/References
Scott Foresman-Addison Wesley, 1999
Assessments
Teacher evaluation of students' skills
Scott Foresman-Addison Wesley Assessments
Grades and Performance Levels
Grades are based upon participation, completion of assignments, and work quality. Each student also receives a rating that shows the student's performance level on the appropriate standard. The rating is based upon assessments of the student's attainment of grade level expectations.
Grade 1 Mathematics Expectations
Number Sense and Number Relationships
A. Used objects and pictures to represent whole numbers from 0 to 100 in a variety of ways.
B. Used objects to demonstrate the meanings of equal, less than, and greater than with the whole numbers 0 to 100
C. Applied equalities using the '=' symbol
D. Used concrete materials to demonstrate the meaning of halves, thirds, and fourths of sets and wholes
E. Demonstrated the value of nickels, dimes, quarters, and dollars in terms of pennies (for example, 25 pennies = 1 quarter)
F. Read and wrote numerals from 0 to 100 in meaningful contexts
G. Read the number words for zero to ten
H. Grouped objects by ones and tens
I. Ordered according to place value (for example, given 9 ones and 2 tens, the student wrote the number 29; given the number 29, the student showed 2 tens and 9 ones)
J. Wrote one- and two- digit whole numbers in expanded form (for example, 29 = 20 + 9)
K. Counted from 0 to 20 by 2's
L. Counted from 0 to 100 by 1's, 5's, and 10's
M. Starting with any whole number less than 100, counted forward to 100
N. Used ordinal positions orally for first through twentieth
O. Sequenced selected whole numbers from 0 to 100
P. Knew the commutative property of addition of whole numbers
Q. Verified the addition and subtraction properties of zero with whole numbers
R. Estimated a reasonable quantity for a given number of objects from 0 to 100
Computation and Estimation
A. Demonstrated the operations of addition and subtraction of whole numbers with materials
B. Used concrete materials or pictures to add and subtract halves and fourths
C. Demonstrated understanding of basic addition sums to 20 and subtraction differences of 10
D. Demonstrated the operations of addition and subtraction of whole numbers with materials
E. Linked the operations of addition and subtraction, and equality with mathematical terms (for example, add, subtract, and equal) and mathematical symbols (for example, +, -, and =)
F. Used paper-and-pencil to demonstrate simple single-digit addition and subtraction
G. Given a real-world problem-solving situation, used the correct operation (addition or subtraction with concrete materials) and appropriate method (mental arithmetic, estimation, paper-and-pencil, calculator, or computer) to solve the problem
Measurement
A. Told time to the nearest hour and half-hour, using an analog and digital clock
B. Named the days of the week in order
C. Estimated and measured the length of objects to the nearest inch, foot, and centimeter
D. Estimated and measured the capacity of a container in cups
E. Estimated and weighed an object on a balance with a non-standard unit
F. Read a variety of thermometers and rounded the temperature to the nearest 5¦F
G. Described the units for measuring time, length, capacity, and temperature
H. Told the number of minutes in an hour, days in a week
I. Compared measurable attributes of objects - length, capacity, weight, and temperature
J. Placed objects in order by length, capacity, weight, and temperature
K. Compared and ordered various times
L. Used familiar objects as reference for measurement (for example, finger length = 2 paperclips)
M. Selected the appropriate units of measurement of time, length, capacity, and temperature
N. Measured the sides of triangles, squares, and rectangles to the nearest inch and centimeter
Data, Statistics and Probability
A. Gathered data about recurring and quantifiable events (for example, daily temperature or attendance)
B. Displayed and explained data from a bar graph or tallies
C. Used a bar graph to interpret data for "more" and "fewer" or "most," "same," and "fewest"
D. Used survey data to make a prediction displayed on a bar graph
E. Used various equipment to find the probability of an event occurring
F. Determined the number of outcomes when flipping a coin
G. Used manipulatives or pictures to determine the possible combinations of matching a set containing one element with a set containing two elements (for example, pants and shirts)
Algebraic Methods
A. Created and extended patterns using concrete materials (for example, used pattern blocks to create a pattern; following another student extended the pattern)
B. Continued the pattern given in a table of data using numbers and/or concrete materials
C. Continued a pattern from a table and verbally described the pattern
D. Used concrete or pictorial patterns to determine how the change in one variable affects the change in another (for example, how changing the number of bicycles changes the number of wheels)
Geometric Concepts, Properties, and Relationships
A. Recognized two-dimensional congruent figures in different positions
B. Created simple designs using concrete materials such as tangrams and pattern blocks
C. Described the number of sides in triangles and quadrilaterals (squares, rectangles)
D. Drew triangles, squares, rectangles, and circles
E. Measured the sides of triangles, squares, rectangles to the nearest inch and centimeter
F. Drew a picture or diagram to solve a problem (for example, used a circle to create a clock face; folded a rectangle to show one half)
G. Manipulated pattern blocks to form a variety of geometric shapes
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Grade 2 Mathematics Program
Description
Students acquire basic skills and concepts in each area of mathematics.
Grade level expectations for each standard indicate what students should know or be able to do as a result of learning that has occurred at this grade in this subject.
Time Allocation:
Daily - 60 minutes
Texts/References
Scott Foresman-Addison Wesley, 1999
Assessments
Teacher evaluation of students' skills
Scott Foresman-Addison Wesley Assessments
Grades and Performance Levels
Grades are based upon participation, completion of assignments, and work quality. Each student also receives a rating that shows the student's performance level on the appropriate standard. The rating is based upon assessments of the student's attainment of grade level expectations.
Grade 2 Mathematics Expectations
Number, Sense, and Number Relationships
A. Used objects/pictures to represent whole numbers including odds and evens from 0 to 1,000
B. Applied equalities and inequalities with whole numbers from 0 to 1,000 using the symbols =, , <, and >
C. Used concrete materials to demonstrate the meanings of fractions, including halves, thirds, fourths, eighths, and tenths of sets and wholes
D. Demonstrated equivalencies of coins (for example, 5 nickels = 1 quarter)
E. Combined coins up to $1.00 (for example, 20ó = 2 dimes = 1 dime + 2 nickels = 4 nickels)
F. Read and wrote numerals from 0 to 1,000 in meaningful contexts
G. Read the number words from zero to one hundred
H. Grouped objects by ones, tens, and hundreds
I. Ordered by place value (for example, given 9 ones, 5 tens, and 4 hundreds, the student wrote the number 459; given the number 459, the student showed 4 hundreds, 5 tens, and 9 ones)
J. Wrote three-digit numbers in expanded form (for example, 459 = 400 + 50 + 9)
K. Counted by 1's, 2's, 5's and 10's
L. Counted from 1 to 1,000 by 100's
M. Starting with any whole number less than 1,000, counted forward to 1,000
N. Used ordinal positions for first through thirty-first
O. Sequenced selected whole numbers from 0 to 1,000
P. Located and labeled the halfway point between whole numbers on the number line
Q. Verified the commutative and associative properties of addition of whole numbers
R. Verified that subtraction of whole numbers is not commutative
S. Estimated sums and differences first by rounding to the nearest ten prior to performing the operation, and then used the estimate to determine the reasonableness of the solution
Computation and Estimation
A. Used concrete materials to demonstrate and verbally explain addition of whole numbers with regrouping for two-digit numbers
B. Used concrete materials to demonstrate and verbally explain subtraction of whole numbers without regrouping for two digit numbers
C. Used concrete materials or pictures to demonstrate multiplication without regrouping of whole numbers (for example, used arrays or grouping sets of objects)
D. Used concrete materials or pictures to demonstrate division of whole numbers without remainders as partitioning of sets
E. Used concrete materials or pictures to demonstrate the inverse relationship of addition and subtraction of whole numbers
F. Used concrete materials or pictures to demonstrate multiplication of whole numbers as repeated addition
G. Found the total value of coins not to exceed $1.00
H. Demonstrated understanding of basic addition and subtraction facts
I. Demonstrated automatic recall of basic addition facts
J. Used sums on an addition facts table to locate all addends for a particular sum (for example, 7 = 0 + 7, 7 = 1 + 6, ...)
K. Used estimation techniques such as rounding and compatible numbers (numbers whose sum is 10) before performing operations
L. Added two-digit whole numbers with regrouping (paper-pencil)
M. Subtracted two-digit whole numbers with regrouping (paper-pencil)
N. Given a real-world problem-solving situation, used the correct operation (addition or subtraction) and appropriate method (mental arithmetic, estimation, paper-and-pencil, calculator, or computer) to solve the problem
Measurement
A. Told time to the nearest five minutes, using an analog and digital clock
B. Used A.M. and P.M.
C. Estimated and measured objects to the nearest half inch, foot, yard, centimeter, and meter
D. Estimated and measured the perimeter of a figure using non-standard and standard units
E. Estimated and measured the capacity of a container in cups, pints, quarts, and gallons
F. Estimated and weighed an object on a balance with a non-standard unit and used a scale to measure an object to the nearest pound
G. Measured temperatures to the nearest 2¦ and 10¦F
H. Described the units for measuring time, length, capacity, weight, and temperature
I. Knew the number of hours in a day, months in a year, inches in a foot, feet in a yard, and cups in a pint
J. Compared objects by measurable attributes of length, capacity, weight, and temperature
K. Placed objects in order by measurable attributes of length, capacity, weight, and temperature
L. Compared and placed in order various times
M. Used familiar objects as referents for measurement (for example, second grader is taller than a meter)
N. Selected the appropriate units of measurement of time, length, capacity, and temperature
O. Measured the lengths of the sides of triangles, squares, and rectangles to the nearest half
inch and centimeter
P. Measured the perimeter of triangles, squares, and rectangles using non-standard and
standard units
Data, Statistics, and Probability
A. Designed a survey and collected data
B. Displayed data using tallies, bar graphs, pictographs, or tables
C. Transferred the same set of data to different displays (for example, from a table to a bar graph)
D. Interpreted and compared data from displays, using the terms "least often", "most often", and "how much more", or "how much less"
E. Used survey data to make predictions about a larger similar population (for example, from a class survey made a prediction about all second graders in the school)
F. Rolled a number cube to generate and record results
G. Analyzed the results (including likely, more likely, less likely, and unlikely outcomes) of spinning a spinner, recognized if different spinners are fair or unfair, and determined the number of outcomes when spinning a spinner
H. Used manipulatives or pictures to determine the possible combinations of matching a set containing two elements with a different set containing two elements
Algebraic Methods
A. Verbally described patterns
B. Created and extended patterns using symbols, such as words and numbers
C. Found missing elements of a repeating pattern (for example, 1, 3, ___, 7)
D. Verbally described the relationship between a graph and a table
Geometric Concepts, Properties, and Relationships
A. Identified congruent figures from a selection of similar figures
B. Slid, flipped, and turned concrete materials, such as tangrams and pattern blocks, to create and reproduce simple designs
C. Described symmetry
D. Identified lines of symmetry of squares and rectangles
E. Described the attributes of circles, triangles, and quadrilaterals (for example, squares and rectangles)
F. Recognized three-dimensional figures: cubes, spheres, cylinders, cones, and pyramids
G. Drew a picture or diagram to solve a problem (for example, drew a map of the room to show how to get from a desk to the reading area; drew a map of the neighborhood)
H. Investigated and predicted the pattern block shapes that can be used to form pattern block triangles
I. Investigated and predicted the geometric shapes that result from cutting along a line of symmetry
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Grade 3 Mathematics Program
Description
Students continue acquisition of basic skills and concepts in each area of mathematics and expand their problem solving skills.
Grade level expectations for each standard indicate what students should know or be able to do as a result of learning that has occurred at this grade in this subject.
Time Allocation:
Daily - 60 minutes
Texts/References
Scott Foresman-Addison Wesley, 1999
Assessments
Teacher evaluation of students' skills
Scott Foresman-Addison Wesley Assessments
STAR Math (beginning and end of year)
Grades and Performance Levels
Grades are based upon participation, completion of assignments, and work quality. Each student also receives a rating that shows the student's performance level on each standard. The rating is based upon assessments of the student's attainment of grade level expectations and a rating received from the Colorado Student Assessment Program (CSAP).
Grade 3 Mathematics Expectations
Number Sense and Number Relationships
A. Identified whether a given number is odd or even
B. Identified the fractional part of a drawing or a set (restricted to halves, thirds, fourths)
C. Used concrete materials or pictures, identifying combinations of coins up to $0.99
D. Read, wrote, and ordered numerals 0-9, 999
E. Read the number words for selected numbers from zero to nine thousand, nine hundred ninety-nine
F. Identified place value through ten-thousands (for example, in 86,243, ' 6' is in the thousands place)
G. Generated equivalent representations for the same number up to a 4 digit number (for example: 25 = 20 + 5 or 10 + 15 or 2 tens and 5 ones)
H. Compared whole numbers as greater than, less than, or equal to one another using words or symbols
I. Located, labeled, or counted forward from any even number by 2's and from any number by 10's and 100's up to 999
J. Located and labeled 1/2's between whole numbers on the number line
K. Used the multiplication properties of zero and one with whole numbers
L. Solved addition and subtraction problems using commutative and associative properties (for example, 2+3+6 = 6+3+2)
M. Used estimation strategies to determine the reasonableness of solutions to problems
Computation and Estimation
A. Used pictures, diagrams, numbers, or words to demonstrate addition and subtraction of whole numbers with 2-digit numbers
B. Used pictures to demonstrate addition and subtraction of proper fractions with common denominators of four or less
C. Used money notation to add and subtract commonly used decimals in which sums and differences should not exceed $10.00
D. Demonstrated understanding of basic multiplication facts of 1's, 2's, 3's, 5's, and 10's
E. Demonstrated proficiency with basic addition and subtraction facts
F. Used estimation strategies with whole numbers prior to performing the operations of addition and subtraction (for example, front-end estimation, estimation by rounding, friendly numbers, flexible rounding, clustering)
G. Demonstrated three basic operations of whole numbers (for example, addition and subtraction of three digits, and multiplication of multiples of ten by 1,2,3,5)
H. Given a real world problem-solving situation, used addition, subtraction, or multiplication to solve the problem
I. Determined from real-world problems, whether an estimated or exact sum, difference, or product was acceptable
Measurement
A. Used an analog and digital clock to tell time to the nearest 5 minutes
B. Read and interpreted pictorial representations of measurements of length, weight, temperature or time
C. Chose the appropriate tools to measure familiar objects/situations containing length, weight, temperature or time
D. Compared objects according to the measurable attributes of length, capacity, weight, or temperature
E. Measured the length of objects including the sides of rectangles and squares to the nearest inch and centimeter
F. Approximated the measurement of familiar objects using standard units
Data, Statistics, and Probability
A. Organized and displayed data using tallies, bar graphs, pictographs, or tables
B. Determined the mode from a given set of numbers
C. Used various displays of data to interpret and draw conclusions
D. Determined which outcomes are the most likely, least likely, or equally likely when using a chance device (for example, a spinner)
E. Given pictures, determined all the possible combinations of matching a set containing two elements with a set containing three elements
Algebraic Methods
A. Reproduced, extended, and created patterns, using pictures or geometric shapes
B. Used a pattern to find missing elements (for example, multiples of 2, 3, 4, 5, 10)
C. Identified a rule using addition or subtraction patterns and solved a new problem using the rule
D. Given numbers in a table, extended the table
E. Using whole numbers, determined how the change in one quantity affects the change in the other by addition or subtraction (for example, one bicycle has 2 wheels, 2 bicycles have 4 wheels, and 3 bicycles have 6 wheels. How many wheels do 4 bicycles have?)
Geometric Concepts, Properties, and Relationships
A. Identified figures which are congruent
B. Identified a line of symmetry for regular polygons and other familiar objects
C. Created a figure with at least one line of symmetry
D. Identified the characteristics of two-dimensional figures (for example, number of sides or vertices, contains a right angle, contains parallel)
E. Identified points, lines, and line segments
F. Identified three dimensional figures (for example, cubes, spheres, cylinders, cones and pyramids)
G. Identified right angles
H. Created and identified the results of combining or subdividing given geometric shapes (for example, pattern blocks, tan grams)
I. Found the perimeter of a polygon
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Grade 4 Mathematics Program
Description
Students expand their basic skills and apply these skills to solve problems.
Grade level expectations for each standard indicate what students should know or be able to do as a result of learning that has occurred at this grade in this subject.
Time Allocation:
Daily - 60 minutes
Texts/References
Scott Foresman-Addison Wesley, 1999
Assessments
Teacher evaluation of students' skills
Scott Foresman-Addison Wesley Assessments
STAR Math (beginning and end of year)
Grades and Performance Levels
Grades are based upon participation, completion of assignments, and work quality. Each student also receives a rating that shows the student's performance level on each standard. The rating is based upon assessments of the student's attainment of grade level expectations and rating received from the Colorado Student Assessment Program (CSAP).
Grade 4 Mathematics Expectations
Number Sense and Number Relationships
A. Used concrete materials and visual representations to compare, order, and represent decimal fractions of tenths, hundredths, and commonly used fractions with like and unlike denominators such as: halves, fourths, and tenths (for example, may use base-ten blocks, pictures, fraction strips, fraction circles)
B. Recognized different combinations of currency and coins for a set amount up to $10.00
C. Read, wrote, and ordered numerals and number words from zero to 999
D. Identified place value through 99,999
E. Generated equivalent representations for whole numbers up to 99,999 (for example: 87,459 = 80,000 + 7,000 + 400 + 50 + 9 or 36 = 30 + 6 or 2 tens + 16 ones)
F. Using a number line, a hundreds chart, or other number charts, located, labeled or counted from any number by 2s, 3s, 5s, 10s, or 100s
G. Located and labeled halves, and multiples of fourths, and thirds, between whole numbers on a number line
H. Showed division of whole numbers is not commutative (one digit into 2 digits)
I. Used number properties with any of the four basic operations (commutative, associative, properties of zero and one)
J. Used estimation strategies to determine the reasonableness of solutions involving the four basic operations
K. Used estimation to round to the nearest dollar in context and determined reasonableness
Computation and Estimation
A. Demonstrated the conceptual meaning (using pictures, words, diagrams or numbers) of addition, subtraction, multiplication, and division
B. Used pictures to demonstrate addition and subtraction of commonly used fractions with the same denominators where sums/differences are equal or less than a whole (1/2, 1/3, 1/4, 1/8, 1/10)
C. Using money notation, add and subtract decimals in which sums and differences should not exceed $100.00
D. Demonstrated proficiency of basic multiplication and division facts
E. Continued to demonstrate proficiency of basic addition and subtraction facts
F. Used a multiplication facts table to locate all the factors for a particular product (for example, for a product of six; 1, 6, 2, and 3 are all factors)
G. Used reasonable estimation techniques before performing basic math operations (for example, front-end estimation, estimation by rounding, friendly numbers, compatible numbers, flexible rounding, clustering)
H. Used paper and pencil to demonstrate the four basic operations of whole numbers including: addition; subtraction; multiplication of 2 or 3-digit numbers by a 1-digit number; division of a 2-digit number by a 1-digit divisor
I. Given a real-world problem solving situation, used an appropriate operation (any four basic math operation) and an appropriate method (paper-pencil, mental math, estimation, calculator, computer) to solve the problem
J. Determined from a real-world problem whether an estimated or exact sum, difference, product, or quotient is acceptable
Measurement
A. Told time in hours and minutes, including a.m. and p.m. using both analog and digital displays
B. Chose the appropriate tool to measure familiar objects in situations that contained length, weight, capacity, time and temperature
C. Compared objects according to measurable attributes of length, area, volume, capacity, weight, and/or temperature in U.S. customary and/or metric units
D. Measured and determined perimeter of polygons to the nearest half inch or centimeter
E. Determined the areas of squares and rectangles on a grid
F. Related units of measurement of length, area, volume, capacity, weight, and/or temperature in U.S. customary and/or metric units to every day objects or situations
G. Chose appropriate units of measure for length, area, volume, capacity, weight, temperature, and/or time to solve problems
Data, Statistics, and Probability
A. Organized, constructed, read and interpreted a table, line plot, bar graph and/or pictograph from given data
B. Drew conclusions from a given data display
C. Found the median, the mode, the smallest and the largest element in a set of data
D. Predicted the outcomes of flipping a coin, spinning a spinner with four congruent sectors, and/or rolling a number cube
E. Determined and supported which outcomes are most likely, least likely or equally likely when using a chance device
F. Given pictures, described all possible combinations of matching the elements of two sets
Algebraic Methods
A. Reproduced, extended, created, or described patterns, using pictures, geometric shapes, or numbers
B. Determined a missing element in a pattern using pictures, geometric shapes, or numbers
C. Displayed numbers in tables or graphs to show patterns
D. Described patterns given in tables and graphs
E. Identified a rule using addition, subtraction, or multiplication and solved a problem using the rule
F. Using whole numbers, determined how a change in one quantity affects a change in another by addition, subtraction, or multiplication (for example, Maria is making ladybugs. For 1 ladybug she needs 6 black dots, for 2 ladybugs she needs 12 dots. How many black dots will she need for 4 lady bugs?)
Geometric Concepts, Properties, and Relationships
A. Identified and gave examples of congruency
B. Identified one line of symmetry for a give shape
C. Identified, classified, and compared 2 dimensional shapes and use of vocabulary to describe attributes (for example, number of sides, vertices, angles, parallel sides)
D. Identified parallel, and intersecting lines and right angles
E. Identified 2- and 3- dimensional figures; such as trapezoid, parallelograms, rhombuses and other polygons
F. Recognized common attributes of squares and rectangles
G. Solved for perimeter and area of rectangles and squares using a drawing on a grid
H. Located objects on a coordinate grid (1st quadrant only) and labeled ordered pairs
I. Recognized geometry in their world
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Grade 5 Mathematics Program
Description
Students expand their basic skills and apply these skills to solve problems.
Grade level expectations for each standard indicate what students should know or be able to do as a result of learning that has occurred at this grade in this subject.
Time Allocation:
Daily - 60 minutes
Texts/References
Scott Foresman-Addison Wesley, 1999
Maths Mate
Assessments
Teacher evaluation of students' skills
Scott Foresman-Addison Wesley Assessments
CSAP
STAR Math (beginning and end of year)
Grades and Performance Levels
Grades are based upon participation, completion of assignments, and work quality. Each student also receives a rating that shows the student's performance level on each standard. The rating is based upon assessments of the student's attainment of grade level expectations and ratings received from the Colorado Student Assessment Program (CSAP).
Grade 5 Mathematics Expectations
Number Sense and Number Relationships
A. Located commonly used positive rational numbers including terminating decimals through hundredths, fractions (halves, thirds, fourths, eighths, and tenths), mixed numbers, and percents on a number line
B. Using concrete materials, demonstrated the equivalence of commonly-used fractions, terminating decimals, and percents (for example, 7/10 = 0.7 = 70 %)
C. Demonstrated the meaning of square numbers using pictorial or concrete materials
D. Read, wrote, and ordered positive rational numbers, including commonly-used fractions and terminating decimals through hundredths
E. Compared commonly-used proper fractions and terminating decimals
F. Identified factors, multiples, and prime/composite numbers
G. Recognized equivalent representations for the same number and generate them by decomposing and composing numbers (for example, 36 can be represented as 30 + 6, 20 + 16, 9 x 4, 40 - 4, three dozen and/or the square of 6)
H. Described numbers by their characteristics (for example, even, odd, prime, square)
I. Demonstrated the equivalent relationships among commonly used fractions, decimals, and percents using pictorial or concrete materials
J. Developed, tested, and explained conjectures about properties of whole numbers and commonly-used fractions and decimals
K. Used number properties (commutative, associative, identity) to evaluate numeric expressions and solve equations
L. Used number sense to estimate sums and differences of fractions and decimals using benchmarks (for example, 5/6 + 7/8 must be equal to an amount less than 2, since each fraction is less than 1)
M. Used appropriate techniques to estimate, determine, and then justify the reasonableness of solutions to problems involving whole numbers
Computation and Estimation
A. Used concrete materials or pictures to determine commonly-used percentages (for example, 25%, 50%) in problem-solving situations
B. Demonstrated the conceptual meaning of the four basic arithmetic operations (addition, subtraction, multiplication, and division)
C. Used and explained strategies to add, subtract, multiply and divide whole numbers in problem-solving situations
D. Demonstrated proficiency of addition, subtraction, multiplication, and division of whole numbers in problem-solving situations
E. Used and explained strategies to add and subtract commonly-used fractions with like denominators in problem-solving situations
F. Used and explained strategies to add and subtract commonly-used decimals in problem-solving situations
G. Determined from real-world problems whether an estimated or exact answer is acceptable
H. Used and explained a variety of estimation techniques to solve problems
I. Determined whether information given in a problem-solving situation is sufficient, insufficient, or extraneous
J. Given a real-world problem, used an appropriate method (mental arithmetic, estimation, paper-and-pencil, calculator) to correctly solve the problem
K. Given a math sentence, using any of one of the four operations with whole numbers, created and illustrated a real-world problem
L. In a problem-solving situation, determined whether the results are reasonable and justified those results with correct computations
Measurement
A. Determined the appropriate unit of measure (metric and US customary) when estimating distance, capacity, and weight
B. Estimated the length of common objects
C. Estimated the perimeter of polygons
D. Estimated the measures of angles (for example, 90o, less than 90o, more than 90o)
E. Described angles as acute, obtuse and right
F. Read and interpreted scales on number lines, graphs, and maps
G. Selected the appropriate scale for a given problem (for example, using the appropriate scale when setting up a graph)
H. Found the perimeter and area of rectangles and squares, using appropriate units
I. Demonstrated how changing one of the dimensions of a rectangle affects its perimeter (using concrete materials or graph paper)
J. Demonstrated how changing one of the dimensions of a rectangle affects its area (using concrete materials or graph paper)
K. Selected and used the appropriate unit and tool to measure to the degree of accuracy required in a particular problem
L. Measured the sides of rectangles, squares, and triangles to the nearest + inch and nearest centimeter
Data, Statistics, and Probability
A. Differentiated between categorical and numerical data
B. Organized, constructed, and interpreted displays of data including tables, charts, pictographs, line plots, bar graphs, and line graphs
C. Read, interpreted, and drew conclusions from various displays of data
D. From a given scenario, chose the correct graph from possible graph representations
E. Distinguished between the median and mode of a data set
F. Determined the range of a set of data
G. Analyzed data and drew conclusions based on data displays such as tables, charts, line graphs, bar graphs, pictographs, and line plots
H. Described how data collection methods affect the nature of the data set
I. Made convincing arguments based on data analysis
J. Described events such as likely or unlikely and explain the degree of likelihood using words, such as certain, equally likely, and impossible
K. Used zero to represent the probability of an impossible event and one to represent the probability of a certain event
L. Used common fractions to represent the probability of events that are neither certain nor impossible
M. Using one chance device, such as a number cube or a spinner, designed a fair game and an unfair game, and explained why they are fair and unfair
N. Made predictions based on data obtained from simple probability experiments
O. Solved problems using strategies for making combinations
Algebraic Methods
A. Represented, described, and analyzed geometric and numeric patterns (whole numbers)
B. Recognized that a variable is used to represent an unknown quantity
C. Identified such properties as commutativity, associativity, and distributivity and used them to compute with whole numbers
D. Solved problems by representing and analyzing patterns using words, tables, and graphs
E. Described how a change in one quantity results in a change in another quantity
F. Matched a description of a situation with its continuous graph
G. Used tables, charts, concrete objects, or pictures to solve problems involving linear relationships with whole numbers
Geometric Concepts, Properties, and Relationships
A. Represented a three-dimensional shape in two dimensions (for example, recognizing a three-dimensional figure from its net)
B. Identified, compared, and analyzed the attributes of two- and three-dimensional shapes and developed vocabulary to describe the attributes (for example, acute, obtuse, right angle, parallel lines, perpendicular lines, intersecting lines, and line segments)
C. Made and tested conjectures about geometric relationships and developed logical arguments to justify conclusions
D. Given a coordinate graph, read coordinate pairs in quadrant one
E. Chose the coordinate graph, which represented a given data set
F. Used maps and grids to locate points, created paths and measured distances within a coordinate system
G. Solved problems involving the perimeter of polygons
H. Solved problems involving the area of rectangles and squares
I. Predicted and described the results of flipping, sliding, or turning a two-dimensional shape
J. Showed lines of symmetry for geometrical shapes
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