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Table of Contents
Board of Education & Central Office Administrators
Mathematics Curriculum Committee
Mission
Philosophy
Goals
Ohio Department of Education Mathematics Academic Content Standards.
Standards, Benchmarks and Grade Level Indicators
Mathematics Standards
Assessment
Technology
Interventions
Textbook Programs, Software and Additional Resources
Table of Contents
Curriculum by Grade Level and Course
Kindergarten
Grade One
Grade Two
Grade Three
Grade Four
Grade Five
Grade Six
Secondary Mathematics Course Schedule
Grade Seven
Grade Eight
Algebra I
Geometry
Algebra II
Statistics, Probability & Data Analysis
Advanced Mathematics
Calculus
ST. BERNARD-ELMWOOD PLACE CITY SCHOOLS
BOARD OF EDUCATION
LINDA RADTKE, President
BOB BODE, Vice President
LAURA MOSLEY
MICKI SPEARS
JOE WHEELER
DISTRICT ADMINISTRATORS
Dr. Carroll E. Roberts Superintendent
Michael Mays Treasurer
Bruce Helwagen Director, Business Affairs/Technology
Cynthia K. Leibold Director, Curriculum/Pupil Services
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St. Bernard-Elmwood Place City Schools
Mathematics Course of Study and Textbook Adoption CommitteeSt. Bernard-Elmwood
Place High School
**Sue Brewington
Steve Frisby
Kathy Mears
Sarah Ritz
**Karen Underwood
St. Bernard Elementary Elmwood Place Elementary
*Beth Staggenborg Clare Frentsos
*Wendy Tuell *Kristin McGuire
**Ginny Wood *Mary Kay Powell
*Nancy Franz
Director, Curriculum/Pupil Services
Cynthia K. Leibold
*Investigations Pilot Teacher
** CMP Pilot TeacherSt. Bernard-Elmwood Place City Schools
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MISSION
"Where all students are challenged to learn and inspired to dream"
PHILOSOPHY
The St. Bernard-Elmwood Place City Schools mathematics programs ensure that
students have an opportunity to become mathematically literate, are capable
of extending their learning, have an equal opportunity to learn, and become
informed citizens capable of understanding issues in a technological society.
Knowledge of mathematics is an essential element in the development of the
whole person.Mathematics is more than a collection of concepts and skills
to be memorized and mastered. Mathematics includes problem solving, reasoning,
communicating, and valuing the breadth of its connections. The mathematics
curriculum includes the investigation of the connections, the interplay among
various mathematical topics, and the applications at every grade level.
Students can become mathematically powerful by learning to formulate and
solve problems with a variety of strategies, to verify and interpret results,
and to generalize solutions. An understanding of mathematical concepts can
enable them to identify and generate examples and non-examples in addition
to recognizing the various meanings and interpretations of concepts. Students
can learn to use models, diagrams, and symbols to represent concepts and to
translate from one mode of representation to another. Students can recognize
when a mathematical procedure is appropriate and reliably and efficiently
execute procedures, including appropriate methods of computation. Students
can verify the results of procedures, generate new procedures and extend or
modify familiar ones.
Students will be provided access to the full range of mathematical topics.
Knowledge of patterns, relations, and functions; of geometry and measurement;
of probability and statistics; and of increasingly important topics that collectively
form a necessary foundation for all students. Since students’ interests,
goals, and achievements change as they mature and advance through high school,
the mathematics program is designed to allow options. Recognizing that St.
Bernard-Elmwood Place students will have different career objectives and may
pursue careers as yet undefined, we further recognize that students have the
right to learn significant mathematics and to develop power over mathematical
ideas.
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GOALS
The goals of the St. Bernard-Elmwood Place City Schools mathematics programs
are that all students:
® learn to value mathematics;
® become confident in their ability to do mathematics;
® become mathematical problem-solvers;
® learn to communicate mathematically; and
® learn to reason mathematically.
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Ohio Department of Education Academic
Content Standards K-12 Mathematics
The Ohio State Board of Education unanimously adopted the mathematics academic
content standards in December 2001. This document is available in print and
CD formats in the media centers in each of the three St. Bernard-Elmwood Place
school buildings. It is also available online at the ODE web site www.ode.state.oh.us.ca/ci/
and the St. Bernard-Elmwood Place City Schools web site.These ODE Mathematics
Content Standards are included in their entirety in the St. Bernard-Elmwood
Place City Schools mathematics curriculum adoption. Print copies and CD-ROM
versions have been distributed to teachers and administrators. Mathematics
Toolkits created by the HCESC to support the implementation of the ODE Mathematics
Content Standards by grade levels have also been provided for the mathematics
and special education faculty members.
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Standards, Benchmarks, and Grade-level
Indicators
The six standards that follow represent the mathematics content and processes
students should know and be able to use as they progress through school. The
rigorous, yet realistic standards provide a comprehensive foundation for all
students to think and reason mathematically and use mathematics knowledge
and skills effectively in post-secondary education, the workplace, and daily
life.
Content Standards: Number, Number Sense and Operations
Measurement
Geometry and Spatial Sense
Patterns, Functions and Algebra
Data Analysis and Probability
Process Standard: Mathematical Processes
The following terms and definitions are used in the document:
Standard: An overarching goal or theme in mathematics. The standard statement
describes, in broad terms, what students should know and be able to do as
a result of the K-12 program.
Benchmark: A specific statement of what a student should know and be able
to do at a specific time in his/her schooling. Benchmarks are used to measure
a student’s progress towards meeting the standard. Benchmarks are defined
for grades 2,4,7,10, and 12.
Grade-level A specific statement of the knowledge and/or skills that a student
demonstrates at each grade level.
Indicator: These indicators serve as checkpoints that monitor progress toward
the benchmarks.
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K-12 Mathematics Academic Content
Standards
Number, Number Sense and Operations Standard
Students demonstrate number sense, including an understanding of number systems
and operations and how they relate to one another. Students compute fluently
and make reasonable estimates using paper and pencil, technology-supported
and mental methods.
Measurement Standard
Students estimate and measure to a required degree of accuracy and precision
by selecting and using appropriate units, tools and technologies.
Geometry and Spatial Sense Standard
Students identify, classify, compare and analyze characteristics, properties
and relationships of one-, two- and three-dimensional geometric figures and
objects. Students use spatial reasoning, properties of geometric objects,
and transformations to analyze mathematical situations and solve problems.
Patterns, Functions and Algebra Standard
Students use patterns, relations and functions to model, represent and analyze
problem situations that involve variable quantities. Students analyze, model
and solve problems using various representations such as tables, graphs and
equations.
Data Analysis and Probability Standard
Students pose questions and collect, organize, represent, interpret and analyze
data to answer those questions. Students develop and evaluate inferences,
predictions and arguments that are based on data.
Mathematical Processes Standard
Students use mathematical processes and knowledge to solve problems. Students
apply problem-solving and decision-making techniques, and communicate mathematical
ideas.
Note: Mathematical processes are used in all content areas and should be incorporated
within instruction and assessment of the content-specific standards, benchmarks
and grade-level indicators.
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ASSESSMENT
Assessment represents a student’s demonstration of understanding. It
provides evidence of what students know and are able to do. A comprehensive
and thoughtful assessment system also provides needed information for instructional
planning and decision-making. Four basic types of assessment, described below
have been incorporated into the K-12 mathematics program
achievement tests;
(a) diagnostic assessments;
(b) classroom assessments;
(c) national and international assessments.
Achievement Tests
Achievement tests provide the broadest picture of student performance. Ohio’s
achievement assessments, including the Ohio Graduation Test (OGT), are administered
at specified grades and are based on the academic content standard benchmarks.
Diagnostic Assessments
Diagnostic assessments are administered annually and are designed to give
teachers and parents detailed information as to the strengths and weaknesses
of individual students. They provide teachers with important performance data
for instructional planning.
Classroom Assessments
Teachers constantly assess student performance on an ongoing basis, using
both informal and formal measures. Samples of classroom assessment employed
by teachers include:
® Projects and investigations
® Portfolios
® Tests, quizzes and short-answer questions
® Extended response and essay questions
® Group tests
® On-demand assessment
® Self-assessment, student reflection
® Teacher observations
A variety of assessments provides a rich picture of student performance, enabling
teachers to evaluate students’ performance and progress.National and
International Assessments
Through participation in national and international assessment opportunities,
student performance can be compared to other states and other nations. The
ACT, SAT, NAEP, TIMSS and AP are examples of this assessment category.
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TECHNOLOGY
Technology, such as calculators and computers, helps students learn mathematics
and support effective mathematics teaching. Rather
than replacing the learning of basic concepts and skills, technology can connect
skills and procedures to deeper mathematical
understanding. For example, geometry software allows experimentation with
families of geometric objects, and graphing utilities
facilitate learning about the characteristics of classes of functions.
INTERVENTION
Intervention services may be implemented to remediate, reinforce or support
student learning relative to the standard benchmarks and grade level indicators.
Intervention must always be aligned with the standards and assessments. Intervention
is a shared responsibility among all individuals who care about student achievement—students,
teachers, parents, and building and district administrators. Intervention
may by activated at three levels: the classroom, within the building, and
throughout the district. The following chart includes suggested resources,
records, and activities that may support intervention initiatives.
INTERVENTION SERVICES LEVEL RESOURCES ACTIVITIES
CLASSROOM
Use of skill grouping
Intraclass Grouping Benchmarks and grade level indicators Modification of
material
Appropriate instructional materials Adjustment of instruction to
Alternative Instruction (including calculators, computers and learning styles
manipulatives) Personalization of instruction
Course of study Use of corrective instruction
BUILDING Use of self-instruction package
Interclass Grouping Student performance data & samples Use of learning
contracts
Documentation of class grouping Use of diagnostic/prescriptive
Course of study teaching
Benchmarks and grade level indicators Conduct student conferences
Appropriate instructional materials Provide time in resource room
Resource/Intervention Documentation of resource/intervention Develop instructional
plan
efforts with student
Course of study Provide independent activities
Appropriate instructional materials coded to specific grade level
indicators and benchmarks
Tutorial Specific skills and indicators not yet Provide skill practice
mastered Use interclass grouping
Provide tutoring:
Intervention Assistance Team Peer tutoring
Volunteer tutoring
DISTRICT Parent tutoring
Summer School Courses of study Cross-age tutoring
Student performance data Cross-grade tutoring
Documentation of intervention Remedial instruction
Appropriate instructional materials Use outside resource personnel
Required Remedial/Intervention Academic Student performance on state assessment
Course Documentation of all previous intervention
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Mathematics Textbook Programs and
Additional Resources
Kindergarten Investigations in Number, Data, and Space
Grade One Investigations in Number, Data, and Space
Grade Two Investigations in Number, Data, and Space
Grade Three Investigations in Number, Data, and Space
Grade Four Investigations in Number, Data, and Space
Grade Five Investigations in Number, Data, and Space
Grade Six Connected Mathematics Program (CMP)
Grade Seven Connected Mathematics Program (CMP)
Grade Eight Connected Mathematics Program (CMP)
Algebra I Algebra 1, Prentice Hall c2001
Cognitive Tutor Algebra
Geometry Geometry for Everyday Life, Holt c2004
Cognitive Tutor Geometry
Algebra II Algebra 2 with Trigonometry, Prentice Hall c2001
Statistics, Data Analysis Elementary Statistics Using Excel, Addison-Wesley
Longman
& Probability
Advanced Mathematics Advanced Mathematical Concepts & Applications,
Glencoe McGraw Hill c2004
Calculus Calculus: Graphical, Numerical, Algebraic,
Prentice Hall c2003
Additional Classroom Resources
www.illuminations.nctm.org/index2.htmlIlluminations — a collection of
Internet resources for improving the teaching and learning of mathematics
using the national standards as a foundation.
www.standards.nctm.orgNCTM’s Principles and Standards for School Mathematics--provides
guidelines for excellence in mathematics education and issues a call for all
students to engage in more challenging mathematics. These guidelines are often
referred to as the national mathematics standards. This document is extended
online through the E-Standards web site through resources, Internet links,
and more.
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CURRICULUM BY GRADE LEVEL AND COURSE
Grade level and course curriculum for the St. Bernard-Elmwood Place City Schools
is strictly aligned to the NCTM and Ohio Department of Education Academic
Standards. The corresponding benchmarks and indicators for the six identified
standards are listed in the appropriate grade level. The outline coding for
this alignment follows:
D The capital letter refers to the benchmark(s) for the designated strand.
3 The number refers to the grade level indicator(s) aligned to the designated
standard and benchmark.
a The lower case letter is a subdivision of the grade level indicator(s).
KINDERGARTEN
NUMBER, NUMBER SENSE AND OPERATIONS STANDARD ACTIVITIES RESOURCES
B1 Compare and order whole numbers up to 10.
F2 Explain rules of counting, such as each object should be counted once and
that order
does not change the number.
F3 Count to twenty; e.g., in play situations or while reading number books.
F4 Determine "how many" in sets (groups) of 10 or fewer objects.
A5 Relate, read and write numerals for single-digit numbers (0-9).
I6 Construct multiple sets of objects each containing the same number of objects.
B7 Compare the number of objects in two or more sets when one has one or two
more,
or one or two fewer objects.
KHG8 Represent and use whole numbers in flexible ways, including relating,
composing
and decomposing numbers; e.g., 5 marbles can be 2 red and 3 green or 1 red
and 4 green.
D9 Identify and state the value of a penny, nickel and dime.
HG10 Model and represent addition as combining sets and counting on, and subtraction
as
take-away and comparison. For example:
a. Combine and separate small sets of objects in contextual situations: e.g.,
add or subtract one, two, or another small amount.
b. Count on (forward) and count back (backward) on a number line between 0
and 10.
I11 Demonstrate joining multiple groups of objects, each containing the same
number of objects; e.g.,
combining 3 bags of candy, each containing 2 pieces.
J12 Partition or share a small set of objects into groups of equal size; e.g.,
sharing 6 stickers equally
among 3 children.
B13 Recognize the number or quantity of sets up to 5 without counting; e.g.,
recognize without counting
the dot arrangement on a domino as 5.
KINDERGARTEN
MEASUREMENT STANDARD ACTIVITIES RESOURCES
CB1 Identify units of time (day, week, month, year) and compare calendar elements;
e.g., weeks are longer than days.
C2 Compare and order objects of different lengths, areas, weights and capacities;
and use
relative terms, such as longer, shorter, bigger, smaller, heavier, lighter,
more and less.
D3 Measure length and volume (capacity) using uniform objects in the environment.
For example, find:
a. how many paper clips long is a pencil;
b. how many small containers it takes to fill one big container using sand,
rice, beans.
C4 Order events based on time. For example:
a. activities that take a long or short time;
b. review what we do first, next, last;
c. recall what we did or plan to do yesterday, today, tomorrow.
KINDERGARTEN
GEOMETRY AND SPACIAL SENSE STANDARD ACTIVITIES RESOURCES
ABC1 Identify and sort two-dimensional shapes and three-dimensional objects.
For example:
a. Identify and describe two-dimensional figures and three-dimensional objects
from the environment using the child’s own vocabulary.
b. Sort shapes and objects into groups based on student-defined categories.
c. Select all shapes or objects of one type from a group.
d. Build two-dimensional figures using paper shapes or tangrams; build
simple three-dimensional objects using blocks.
F2 Name and demonstrate the relative position of objects as follows:
a. place objects over, under, inside, outside, on, beside, between, above,
below,
on top of, upside-down, behind, in back of, in front of;
b. describe placement of objects with terms, such as on, inside, outside,
above,
below, over, under, beside, between, in front of, behind.
KINDERGARTEN
PATTERNS, FUNCTIONS AND ALGEBRA STANDARD ACTIVITIES RESOURCES
A1 Sort, classify and order objects by size, number and other properties.
For example:
a. Identify how objects are alike and different.
b. Order three events or objects according to a given attribute, such as time
or size.
c. Recognize and explain how objects can be classified in more than one way.
d. Identify what attribute was used to sort groups of objects that have already
been
sorted.
B2 Identify, create, extend and copy sequences of sounds (such as musical
notes),
shapes (such as buttons, leaves or blocks), motions (such as hops or skips),
and numbers from 1 to 10.
C3 Describe orally the pattern of a given sequence.
D4 Model a problem situation using physical materials.
KINDERGARTEN
DATA ANALYSIS AND PROBABILITY STANDARD ACITIVITIES RESOURCES
A1 Gather and sort data in response to questions posed by teacher and students;
e.g., how many sisters and brothers, what color shoes.
B2 Arrange objects in a floor or table graph according to attributes, such
as use,
size, color or shape.
B3 Select the category or categories that have the most or fewest objects
in a floor
or table graph.
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FIRST GRADE
NUMBER, NUMBER SENSE AND OPERATIONS STANDARD ACTIVITIES RESOURCES
B1 Use ordinal numbers to order objects; e.g., first, second, third.
B2 Recognize and generate equivalent forms for the same number using physical
models, words and number expressions; e.g., concept of ten is described by
"10 blocks," full tens frame, numeral 10, 5+5, 15-1, one less than
11, my brother’s age.
A3 Read and write the numerals for numbers to 100.
BF4 Count forward to 100, count backwards from 100, and count forward to backward
starting at any number between 1 and 100.
A5 Use place value concepts to represent whole numbers using numerals, words,
expanded notation and physical models with ones and tens. For example:
a. Develop a system to group and count by twos, fives and tens.
b. Identify patterns and grouping in a 100’s chart and relate to place
value concepts.
c. Recognize the first digit of a two-digit number as the most important to
indicate size of a number and the nearness to 10 or 100.
D6 Identify and state the value of a penny, nickel, dime, quarter and dollar.
D7 Determine the value of a small collection of coins (with a total value
up to one dollar)
using 1 or 2 different type coins, including pennies, nickels, dimes, and
quarters.
E8 Show different combinations of coins that have the same value.
C9 Represent commonly used fractions using words and physical models for halves,
thirds and fourths, recognizing fractions are represented by equal size parts
of a whole
and of a set of objects.
FIRST GRADE
NUMBER, NUMBER SENSE AND OPERATIONS STANDARD ACTIVITIES RESOURCES
G10 Model, represent and explain addition as combining sets (part+part=whole)
and
Counting on. For example:
a. Model and explain addition using physical materials in contextual situations.
b. Draw pictures to model addition.
c. Write number sentences to represent addition.
d. Explain that adding two whole numbers yields a larger whole number.
H11 Model, represent and explain subtraction as take-away and comparison.
For example:
a. Model and explain subtraction using physical materials in contextual situations.
b. Draw pictures to model subtraction.
c. Write number sentences to represent subtraction.
d. Explain that subtraction of whole numbers yields an answer smaller than
the
original number.
GH12 Use conventional symbols to represent the operations of addition and
subtraction.
I13 Model and represent multiplication as repeated addition and rectangular
arrays in
contextual situations; e.g., Four people will be at my party and if I want
to give
3 balloons to each person, how many balloons will I need to buy?
J14 Model and represent division as sharing equally in contextual situations;
e.g.,
sharing cookies.
B15 Demonstrate that equal means "the same as" using visual representations.
FIRST GRADE
NUMBER, NUMBER SENSE AND OPERATIONS STANDARD ACTIVITIES RESOURCES
KL16 Develop strategies for basic addition facts, such as:
a. counting all;
b. counting on;
c. one more, two more;
d. doubles;
e. doubles plus or minus one;
f. make ten;
g. using tens frames;
h. identify property (adding zero).
KL17 Develop strategies for basic subtraction facts such as;
a. relating to addition (for example, think of 7-3=? as "3 plus ? equals
7");
b. one less, two less;
c. all but one (for example, 8-7, 5-4);
d. using tens frames;
e. missing addends.
FIRST GRADE
MEASUREMENT STANDARD ACTIVITIES RESOURCES
A1 Recognize and explain the need for fixed units and tools for measuring
length and
weight; e.g. rulers and balanced scales.
C2 Tell time to the hour and half-hour on digital and analog (dial) timepieces.
C3 Order a sequence of events with respect to time; e.g., summer, fall, winter
and spring;
morning, afternoon and night.
D4 Estimate and measure weight using non-standard units; e.g., blocks of uniform
size.
D5 Estimate and measure length using non-standard and standard units; i.e.,
centimeters,
inches, and feet.
FIRST GRADE
GEOMETRY AND SPATIAL SENSE STANDARD ACTIVITIES RESOURCES
ACE1 Identify, compare and sort two-dimensional shapes; i.e., square, circle
ellipse, triangle, rectangle, rhombus, trapezoid, parallelogram, pentagon
and hexagon. For example:
a. Recognize and identify triangles and rhombuses independent of position,
shape or size;
b. Describe two-dimensional shapes using attributes such as number of sides
and number of vertices (corners or angles).
A2 Create new shapes by combining or cutting apart existing shapes.
ABE3 Identify the shapes of the faces of three-dimensional objects.
F4 Extend the use of location words to include distance (near, far, close
to) and
directional words (left, right).
ADEG5
Copy figures and draw simple two-dimensional shapes from memory.
FIRST GRADE
PATTERNS, FUNCTIONS AND ALGEBRA STANDARD ACTIVITIES RESOURCES
A1 Sort, classify and order objects by two or more attributes, such as color
and shape,
and explain how objects were sorted.
B2 Extend sequences of sounds, shapes or simple number patterns, and create
and
record similar patterns. For example:
a. Analyze and describe patterns with multiple attributes using numbers and
shapes; e.g., AA, B, a, b, AA, B, a, b…
b. Continue repeating and growing patterns with materials, pictures and
geometric items; e.g., XO, XOO, XOOO, XOOOO.
C3 Describe orally the basic unit or general plan of a repeating or growing
pattern.
E4 Solve open sentences by representing an expression in more than one way
using the
commutative property; e.g., 4+5=5+4 or the number of blue balls plus red balls
is the same as the number of red balls plus blue balls (R+B=B+R).
D5 Describe orally and model a problem situation using words, objects or number
phrase
or sentence.
FIRST GRADE
DATA ANALYSIS AND PROBABILITY STANDARD ACTIVITIES RESOURCES
B1 Identify multiple categories for sorting data.
B2 Collect and organize data into charts using tally marks.
C3 Display data in picture graphs with units of 1 and bar graphs with intervals
of 1.
C4 Read and interpret charts, picture graphs and bar graphs as sources of
information to identify main ideas, draw conclusions, and make predictions.
A5 Construct a question that can be answered by using information from a graph.
B6 Arrange five objects by an attribute, such as size or weight, and identify
the
ordinal position of each object.
B7 Answer questions about the number of objects represented in a picture graph,
bar graph or table graph; e.g., category with most, how many more in a
category compared to another, how many altogether in two categories.
D8 Describe the likelihood of simple events as possible/impossible and more
likely/less likely; e.g., when using spinners or number cubes in classroom
activities.
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SECOND GRADE
NUMBER, NUMBER SENSE,AND OPERATIONS STANDARD ACTIVITIES RESOURCES
AB1 Use place value concepts to represent, compare and order whole numbers
using
Physical models, numerals and words, with ones, tens and hundreds. For example:
a. Recognize 10 can mean "10 ones" or a single entity (1 ten) through
physical
models and trading games.
b. Read and write 3-digit numerals (e.g., 243 as two hundred forty three,
24 tens and
3 ones, or 2 hundreds and 43 ones, etc.) and construct models to represent
each.
B2 Recognize and classify numbers as even or odd.
E3 Count money and make change using coins and a dollar bill.
D4 Represent and write the value of money using the cent sign and in decimal
form when
using the $ sign.
C5 Represent fractions (halves, thirds, fourths, sixths and eighths), using
words,
numerals and physical models. For example:
a. Recognize that a fractional part can mean different amounts depending on
the
original quantity.
b. Recognize that a fractional part of a rectangle does not have to be shaded
with
contiguous parts.
c. Identify and illustrate parts of a whole and parts of sets of objects.
d. Compare and order physical models of halves, thirds and fourths in relation
to 0 and 1.
H6 Model, represent and explain subtraction as comparison, take-away and part-to-whole;
e.g., solve missing addend problems by counting up or subtracting, such as
"I had six
baseball cards, my sister gave me more, and I now have ten. How many did she
give
me?" can be represented as 6+?=10 or 10-6=?.
SECOND GRADE
NUMBER, NUMBER SENSE AND OPERATIONS STANDARD ACTIVITIES RESOURCES
I7 Model, represent and explain multiplication as repeated addition, rectangular
arrays
and skip counting.
J8 Model, represent and explain division as sharing equally and repeated subtraction.
KM9 Model and use the commutative property for addition.
K10 Demonstrate fluency in addition facts with addends through 9 and corresponding
subtractions; e.g., 9+9=18, 18-9=9.
L11 Add and subtract multiples of 10.
M12 Demonstrate multiple strategies for adding and subtracting 2- or 3-digit
whole numbers, such as:
a. compatible numbers;
b. compensatory numbers;
c. informal use of commutative and associative properties of addition.
13* Estimate the results of whole number addition and subtraction problems
using front-end
estimation, and judge the reasonableness of the answers.
*This grade-level indicator does not correlate with a K-2 Benchmark.
SECOND GRADE
MEASUREMENT STANDARD ACTIVITIES RESOURCES
B1 Identify and select appropriate units of measure for:
a. length – centimeters, meters, inches, feet or yards;
b. volume (capacity) – liters, cups, pints, or quarts;
c. weight – grams, ounces or pounds;
d. time – hours, half-hours, quarter-hours or minutes and time designations,
a.m. or p.m.
C2 Establish personal or common referents for units of measure to make estimates
and
comparisons; e.g., the width of a finger is a centimeter, a large bottle of
soda pop
is 2 liters, a small paper clip weighs about 1 gram.
E3 Describe and compare the relationships among the units of measure, such
as
centimeters and meters; inches, feet and yards; cups, pints and quarts; ounces
and
pounds; and hours, half-hours and quarter-hours; e.g., how many inches in
a foot?
C4 Tell time to the nearest minutes interval on digital and to the nearest
5 minute interval
on analog (dial) timepieces.
D5 Estimate and measure the length and weight of common objects, using metric
and
U.S. customary units, accurate to the nearest unit.
D6 Select and use appropriate measurement tools; e.g., a ruler to draw a segment
3 inches long, a measuring cup to place 2 cups of rice in a bowl, a scale
to weigh
50 grams of candy.
E7 Make and test predictions about measurements, using different units to
measure the same
length or volume.
SECOND GRADE
GEOMETRY AND SPACIAL SENSE STANDARD ACTIVITIES RESOURCES
ABC1 Identify, describe, compare and sort three-dimensional objects (i.e.,
cubes,
spheres, prisms, cones, cylinders and pyramids) according to the shape of
the
faces or the number of faces, edges or vertices.
A2 Predict what new shapes will be formed by combining or cutting apart existing
shapes.
E3 Recognize two-dimensional shapes and three-dimensional objects from different
positions.
D4 Identify and determine whether two-dimensional shapes are congruent (same
shape
and size) or similar (same shape different size) by copying or using superposition
(lay one thing on top of another).
G5 Create and identify two-dimensional figures with line symmetry; e.g., what
letter shapes, logos, polygons are symmetrical?
SECOND GRADE
PATTERNS, FUNCTIONS AND ALGEBRA STANDARD ACTIVITIES RESOURCES
1 Extend simple number patterns (both repeating and growing patterns),
and create similar patterns using different objects, such as using physical
materials
or shapes to represent numerical patterns.
BC2 Use patterns to make generalizations and predictions; e.g., determine
a missing element
in a pattern.
C3 Create new patterns with consistent rules or plans, and describe the rule
or general
plan of existing patterns.
D4 Use objects, picture, numbers and other symbols to represent a problem
situation.
E5 Understand equivalence and extend the concept to situations involving symbols;
e.g.,
4+5=9 and 9=4+5, and 4+5=3+6=D + o …
F6 Use symbols to represent unknown quantities and identify values for symbols
in an
expression or equation using addition and subtraction; e.g. o + O =10, D -2=4.
G7 Describe qualitative and quantitative changes, especially those involving
addition and
subtraction; e.g., a students growing taller versus a student growing two
inches
in one year.
SECOND GRADE
DATA ANALYSIS AND PROBABILITY STANDARD ACTIVITIES RESOURCES
AB1 Pose questions, use observations, interviews and surveys to collect data,
and organize data in charts, picture graphs and bar graphs.
C2 Read, interpret and make comparisons and predictions from data
represented in charts, line plots, picture graphs and bar graphs.
C3 Read and construct simple timelines to sequence events.
B4 Write a few sentences to describe and compare categories of data represented
in a chart or graph, and make statements about the data as a whole.
C5 Identify untrue or inappropriate statements about a given set of data.
A6 Recognize that data may vary from one population to another; e.g.,
favorite TV shows of students and of parents.
D7 List some of the possible outcomes of a simple experiment, and predict
whether given outcomes are more, less or equally likely to occur.
D8 Use physical models and pictures to represent possible arrangements of
2 or 3 objects.
Top
THIRD GRADE
NUMBER, NUMBER SENSE AND OPERATIONS STANDARD ACTIVITIES RESOURCES
B1 Identify and generate equivalent forms of whole numbers; e.g.,
36, 30+6, 9x4, 46-10, number of inches in a yard.
A2 Use place value concepts to represent whole numbers and decimals using
numerals, words, expanded notation and physical models. For example:
a. Recognize 100 means "10 tens" as well as a single entity (1 hundred)
through
physical models and trading games.
b. Describe the multiplicative nature of the number system; e.g., the structure
of 3205 as 3x1000 plus 2x100 plus 5x1.
c. Model the size of 1000 in multiple ways; e.g., packaging 1000 objects into
10
boxes of 100, modeling a meter with centimeter and decimeter strips, or
gathering 1000 pop-can tabs.
d. Explain the concept of tenths and hundredths using physical models, such
as
metric pieces, base ten blocks, decimal squares or money.
AD3 Use mathematical language and symbols to compare and order; e.g., less
than,
greater than, at most, at least, < , > ,=, £, Ž .
F4 Count money and make change using coins and paper bills to ten dollars.
C5 Represent fractions and mixed numbers using words, numerals and physical
models.
D6 Compare and order commonly used fractions and mixed numbers using number
lines,
models (such as fraction circles or bars), points of reference (such as more
or less
than 1/2), and equivalent forms using physical or visual models.
B7 Recognize and use decimal and fraction concepts and notations as related
ways of
representing parts of a whole or set; e.g., 3 of 10 marbles are red can also
be
described as 3/10 and 3 tenths are red.
THIRD GRADE
NUMBER, NUMBER SENSE AND OPERATIONS STANDARD ACTIVITIES RESOURCES
L8 Model, represent and explain multiplication; e.g., repeated addition, skip
counting,
rectangular arrays and area model. For example:
a. Use conventional mathematical symbols to write equations for word problems
involving multiplication.
b. Understand that, unlike addition and subtraction, the factors in multiplication
and division may have different units; e.g., 3 boxes of 5 cookies each.
L9 Model, represent and explain division; e.g., sharing equally, repeated
subtraction,
rectangular arrays and area model. For example:
a. Translate contextual situations involving division into conventional
mathematical symbols.
b. Explain how a remainder may impact an answer in a real-world situation;
e.g.,
14 cookies being shared by 4 children.
H10 Explain and use relationships between operations, such as:
a. relate addition and subtraction as inverse operations;
b. relate multiplication and division as inverse operations;
c. relate addition to multiplication (repeated addition);
d. relate subtraction to division (repeated subtraction).
G11 Model and use the commutative and associative properties for addition
and multiplication.
K12 Add and subtract whole numbers with and without regrouping.
IJ13 Demonstrate fluency in multiplication facts through 10 and corresponding
division facts.
K14 Multiply and divide 2- and 3-digit numbers by a single-digit number,
without remainders for division.
J15 Evaluate the reasonableness of computations based upon operations and
the numbers
involved; e.g., considering relative size, place value and estimates.
THIRD GRADE
MEASUREMENT STANDARD ACTIVITIES RESOURCES
A1 Identify and select appropriate units for measuring:
a. length – miles, kilometers and other units of measure as appropriate;
b. volume (capacity) – gallons;
c. weight – ounces, pounds, grams, or kilograms;
d. temperature – degrees (Fahrenheit or Celsius).
C2 Establish personal or common referents to include additional units, e.g.,
a gallon
container of milk; a postage stamp is about a square inch.
E3 Tell time to the nearest minute and find elapsed time using a calendar
or a clock.
AD4 Read thermometers in both Fahrenheit and Celsius scales.
CD5 Estimate and measure length, weight and volume (capacity), using metric
and
U.S. customary units, accurate to the nearest 1/2 or 1/4 unit as appropriate.0
6* Use appropriate measurement tools and techniques to construct a figure
or
approximate an amount of specified length, weight or volume (capacity); e.g.,
constructs a rectangle with length 2 1/2 inches and width 3 inches, fill a
measuring
cup to the 3/4 cup mark.
D7 Make estimates for perimeter, area and volume using links, tiles, cubes
and
other models.
*The grade-level indicator does not correlate with a 3-4 Benchmark.
THIRD GRADE
GEOMETRY AND SPATIAL SENSE STANDARD ACTIVITIES RESOURCES
AE1 Analyze and describe properties of two-dimensional shapes and three-dimensional
objects using terms such as vertex, edge, angle, side and face.
D2 Identify and describe the relative size of angles with respect to right
angles as
follows:
a. Use physical models, like straws, to make different sized angles by opening
And closing the sides, not by changing the side lengths.
b. Identify, classify and draw right, acute, obtuse and straight angles.
G3 Find and name locations on a labeled grid or coordinate system; e.g., a
map or graph.
H4 Draw lines of symmetry to verify symmetrical two-dimensional shapes.
E5 Build a three-dimensional model of an object composed of cubes; e.g., construct
a
model based on an illustration or actual object.
THIRD GRADE
PATTERNS, FUNCTIONS AND ALGEBRA STANDARD ACTIVITIES RESOURCES
A1 Extend multiplicative and growing patterns, and describe the pattern or
rule in words.
A2 Analyze and replicate arithmetic sequences with and without a calculator.
B3 Use patterns to make predictions, identify relationships, and solve problems.
E4 Model problem situations using objects, pictures, tables, numbers letters
and
other symbols.
C5 Write, solve, and explain simple mathematical statements, such as 7 + o
>8 or
D + 8 = 10.
C6 Express mathematical relationships as equations and inequalities.
F7 Create tables to record, organize and analyze data to discover patterns
and rules.
G8 Identify and describe quantitative changes, especially those involving
addition and
subtraction; e.g., the height of water in a glass becoming 1 centimeter lower
each
week due to evaporation.
THIRD GRADE
DATA ANALYSIS AND PROBABILITY STANDARD ACTIVITIES RESOURCES
A1 Collect and organize data from an experiment, such as recording and classifying
observations or measurements, in response to a question posed.
D2 Draw and interpret picture graphs in which a symbol or picture represents
more
than one object.
D3 Read, interpret and construct bar graphs with intervals greater than one.
B4 Support a conclusion or prediction orally and in writing, using information
in a table
or graph.
B5 Match a set of data with a graphical representation of the data.
C6 Translate information freely among charts, tables, line plots, picture
graphs and bar
graphs; e.g., create a bar graph from the information in a chart.
B7 Analyze and interpret information represented on a timeline.
E8 Identify the mode of a data set and describe the information it gives about
a data set.
F9 Conduct a simple experiment or simulation of a simple event, record the
results in a
chart, table or graph, and use the results to draw conclusions about the likelihood
of
possible outcomes.
G10 Use physical models, pictures, diagrams and lists to solve problems involving
possible
arrangements or combinations of two to four objects.
Top
FOURTH GRADE
NUMBER, NUMBER SENSE AND OPERATIONS STANDARD ACTIVITIES RESOURCES
B1 Identify and generate equivalent forms of fractions and decimals. For example:
a. Connect physical, verbal and symbolic representations of fractions, decimals
and
whole numbers; e.g., 1/2, 5/10, "five tenths," 0.5, shaded rectangles
with
half, and five tenths.
b. Understand and explain that ten tenths is the same as one whole in both
fraction and decimal form.
A2 Use place value structure of the base-ten number system to read, write,
represent
and compare whole numbers through millions and decimals through thousandths.
A3 Round whole numbers to a given place value.
E4 Identify and represent factors and multiples of whole numbers through 100,
and
classify numbers as prime or composite.
D5 Use models and points of reference to compare commonly used fractions.
K6 Use associative and distributive properties to simplify and perform computations;
e.g., use left to right multiplication and the distributive property to find
an exact answer
without paper and pencil, such as 5x47=5x40+5x7=200+35=235.
K7 Recognize that division may be used to solve different types of problem
situations and
interpret the meaning of remainders; e.g. situations involving measurement,
money.
FK8 Solve problems involving counting money and making change, using both
coins and
paper bills.
JM9 Estimate the results of computations involving whole numbers, fractions
and decimals,
using a variety of strategies.
M10 Use physical models, visual representations, and paper and pencil to add
and subtract
decimals and commonly used fractions with like denominators.
L11 Develop and explain strategies for performing computations mentally.
FOURTH GRADE
NUMBER, NUMBER SENSE AND OPERATIONS STANDARD ACTIVITIES RESOURCES
K12 Analyze and solve multi-step problems involving addition, subtraction,
multiplication
and division using an organized approach, and verify and interpret results
with respect
to the original problem.
L13 Use a variety of methods and appropriate tools for computing with whole
numbers;
e.g., mental math, paper and pencil, and calculator.
IL14 Demonstrate fluency in adding and subtracting whole numbers and in multiplying
and
dividing whole numbers by 1- and 2-digit numbers and multiples of ten.
FOURTH GRADE
MEASUREMENT STANDARD ACTIVITIES RESOURCES
B1 Relate the number of units to the size of the units used to measure an
object;
e.g., compare the number of cups to fill a pitcher to the number of quarts
to fill the
same pitcher.
D2 Demonstrate and describe perimeter as surrounding and area as covering
a two-
dimensional shape, and volume as filling a three-dimensional object.
A3 Identify and select appropriate units to measure:
a. perimeter – string or links (inches or centimeters).
b. area – tiles (square inches or square centimeters).
c. volume – cubes (cubic inches or cubic centimeters).
D4 Develop and use strategies to find perimeter using string or links, area
using tiles or a
grid, and volume using cubes; e.g., count squares to find area of regular
or irregular
shapes on a grid, layer cubes in a box to find its volume.
5* Make simple unit conversions within a measurement system; e.g., inches
to feet,
kilograms to grams, quarts to gallons.
6* Write, solve and verify solutions to multi-step problems involving measurement.
*This grade-level indicator does not correlate with a 3-4 Benchmark.
FOURTH GRADE
GEOMETRY AND SPATIAL SENSE STANDARD ACTIVITIES RESOURCES
C1 Identify, describe and model intersecting, parallel and perpendicular lines
and line
segments; e.g., use straws or other material to model lines.
AEF2 Describe, classify, compare and model two- and three-dimensional objects
using their
attributes.
AF3 Identify similarities and differences of quadrilaterals; e.g., squares,
rectangles,
parallelograms and trapezoids.
B5 Describe points, lines and planes, and identify models in the environment.
G6 Specify locations and plot ordered pairs on a coordinate plane, using first
quadrant
points.
I7 Identify, describe and use reflections (flips), rotations (turns), and
translations (slides)
in solving geometric problems; e.g., use transformations to determine if 2
shapes are congruent.
J8 Use geometric models to solve problems in other areas of mathematics, such
as
number (multiplication/division) and measurement (area, perimeter, border).
FOURTH GRADE
PATTERNS, FUNCTIONS AND ALGEBRA STANDARD ACTIVITIES RESOURCES
B1 Use models and words to describe, extend and make generalizations of patterns
and
relationships occurring in computation, numerical patterns, geometry, graphs
and
other applications.
AD2 Represent and analyze patterns and functions using words, tables and graphs.
F3 Construct a table of values to solve problems associated with a mathematical
relationship.
E4 Use rules and variable to describe patterns and other relationships.
C5 Represent mathematical relationship with equations or inequalities.
G6 Describe how a change in one variable affects the value of a related variable;
e.g., as one increases the other increases or as one increases the other decreases.
FOURTH GRADE
DATA ANALYSIS AND PROBABILITY STANDARD ACTIVITIES RESOURCES
A1 Create a plan for collecting data for a specific purpose.
BC2 Represent and interpret data using tables, bar graphs, line plots and
line graphs.
C3 Interpret and construct Venn diagrams to sort and describe data.
C4 Compare different representations of the same data to evaluate how well
each
representation shows important aspects of the data, and identify appropriate
ways to
display the data.
B5 Propose and explain interpretations and predictions based on data displayed
in tables,
charts and graphs.
E6 Describe the characteristics of a set of data based on a graphical representation,
such
as range of the data, clumps of data, and holes in the data.
E7 Identify the median of a set of data and describe what it indicates about
the data.
E8 Use range, median and mode to make comparisons among related sets of data.
F9 Conduct simple probability experiments and draw conclusions from the results;
e.g.,
rolling number cubes or drawing marbles from a bag.
FH10 Represent the likelihood of possible outcomes for chance situations;
e.g., probability
of selecting a red marble from a bag containing 3 red and 5 white marbles.
FH11 Relate the concepts of impossible and certain-to-happen events to the
numerical values
of 0 (impossible) and 1 (certain).
F12 Place events in order to likelihood and use a diagram or appropriate language
to
compare the chance of each event occurring; e.g., impossible, unlikely, equal,
likely,
certain.
G13 List and count all possible combinations using one member from each of
several sets,
each containing 2 or 3 members; e.g., the number of possible outfits from
3 shirts,
shorts and 2 pairs of shoes.
Top
FIFTH GRADE
NUMBER, NUMBER SENSE AND OPERATIONS STANDARD ACTIVITIES RESOURCES
BD1 Use models and visual representation to develop the concept of ratio as
part-to-part
and part-to-whole, and the concept of percent as part-to-whole.
B2 Use various forms of "one" to demonstrate the equivalence of
fractions;
e.g., 18/24=9/12x2/2=3/4x6/6.
B3 Identify and generate equivalent forms of fractions, decimals and percents.
I4 Round decimals to a given place value and round fractions (including mixed
numbers)
to the nearest half.
G5 Recognize and identify perfect squares and their roots.
A6 Represent and compare numbers less than 0 by extending the number line
and using
familiar applications; e.g., temperature, owing money.
F7 Use commutative, associative, distributive, identity and inverse properties
to simplify
and perform computations.
E8 Identify and use relationships between operations to solve problems.
E9 Use order of operations, including use of parentheses, to simplify numerical
expressions.
H10 Justify why fractions need common denominators to be added or subtracted.
H11 Explain how place value is related to addition and subtraction of decimals;
e.g., 0.2+0.14; the two tenths is added to the one tenth because they are
both tenths.
I12 Use physical models, points of reference, and equivalent forms to add
and subtract
commonly used fractions with like and unlike denominators and decimals
I13 Estimate the results of computations involving whole numbers, fractions
and decimals,
using a variety of strategies.
FIFTH GRADE
MEASUREMENT STANDARD ACTIVITIES RESOURCES
A1 Identify and select appropriate units to measure angles; i.e., degrees.
E2 Identify paths between points on a grid or coordinate plane and compare
the lengths
of the paths; e.g. shortest path, paths of equal length.
FG3 Demonstrate and describe the differences between covering the faces (surface
area)
and filling the interior (volume) of three-dimensional objects.
FG4 Demonstrate understanding of the differences among linear units, square
units and
cubic units.
B5 Make conversions within the same measurement system while performing
computations.
CE6 Use strategies to develop formulas for determining perimeter and area
of triangles,
rectangles and parallelograms, and volume of rectangular prisms.
C7 Use benchmark angles (e.g., 45, 90, 120) to estimate the measure of angles,
and
use a tool to measure and draw angles.
FIFTH GRADE
GEOMETRY AND SPATIAL SENSE STANDARD ACTIVITIES RESOURCES
B1 Draw circles, and identify and determine relationships among the radius,
diameter,
center and circumferences; e.g., radius is half of the diameter, the ratio
of the
circumference of a circle to its diameter is an approximation of p.
AD2 Use standard language to describe line, segment, ray angle, skew, parallel
and
perpendicular.
A3 Label vertex, rays, interior and exterior for an angle.
FJ4 Describe and use properties of congruent figures to solve problems.
G5 Use physical models to determine the sum of the interior angles of triangles
and
quadrilaterals.
C6 Extend understanding of coordinate system to include points whose x or
y values may be negative numbers.
D7 Understand that the measure of an angle is determined by the degree of
rotation of
an angle side rather than the length of either side.
I8 Predict what three-dimensional object will result from folding a two-dimensional
net,
then confirm the prediction by folding the net.
FIFTH GRADE
PATTERNS, FUNCTIONS AND ALGEBRA STANDARD ACTIVITIES RESOURCES
A1 Justify a general rule for a pattern or a function by using physical materials,
visual
representations, words, tables or graphs.
A2 Use calculators or computers to develop patterns, and generalize them using
tables
and graphs.
BEG3 Use variables as unknown quantities in general rules when describing
patterns and
other relationships.
C4 Create and interpret the meaning of equations and inequalities representing
problem
situations.
F5 Model problems with physical materials and visual representations, and
use models,
graphs and tables to draw conclusions and make predictions.
D6 Describe how the quantitative change in a variable affects the value of
a related
variable; e.g., describe how the rate of growth varies over time, based upon
data in a
table or graph.
FIFTH GRADE
DATA ANALYSIS AND PROBABILITY STANDARD ACTIVITIES RESOURCES
A1 Read, construct and interpret frequency tables, circle graphs and line
graphs.
E2 Select and use a graph that is appropriate for the type of data to be displayed;
e.g.,
numerical vs. categorical data, discrete vs. continuous data.
D3 Read and interpret increasingly complex displays of data, such as double
bar graphs.
E4 Determine appropriate data to be collected to answer questions posed by
students or
teacher, collect and display data, and clearly communicate findings.
C5 Modify initial conclusions, propose and justify new interpretations and
predictions as
additional data are collected.
F6 Determine and use the range, mean, median and mode, and explain what each
does
and does not indicate about the set of data.
H7 List and explain all possible outcomes in a given situation.
I8 Identify the probability of events within a simple experiment, such as
three chances
out of eight.
I9 Use, 0,1 and ratios between 0 and 1 to represent the probability of outcomes
for an
event, and associate the ratio with the likelihood of the outcome.
J10 Compare what should happen (theoretical/expected results) with what did
happen
(experimental/actual results) in a simple experiment.
K11 Make predictions based on experimental and theoretical probabilities.
Top
SIXTH GRADE
NUMBER, NUMBER SENSE AND OPERATIONS STANDARD ACTIVITIES RESOURCES
G1 Decompose and recompose whole numbers using factors and exponents (e.g.,
32=2x2x2x2x2=25), and explain why "squared" means "second power"
and
"cubed" means "third power."
G2 Find and use the prime factorization of composite numbers. For example:
a. Use the prime factorization to recognize the greatest common factor (GCF).
b. Use the prime factorization to recognize the least common multiple (LCM).
c. Apply the prime factorization to solve problems and explain solutions.
D3 Explain why a number is referred to as being "rational," and
recognize that the
expression a/b can mean a parts of size 1/b each, a divided by b, or the ratio
of
a to b.
C4 Describe what it means to find a specific percent of a number, using real-life
examples.
CD5 Use models and pictures to relate concepts of ratio, proportion and percent,
including percents less than 1 and greater than 100.
E6 Use the order of operations, including the use of exponents, decimals and
rational
numbers, to simplify numerical expressions.
I7 Use simple expressions involving integers to represent and solve problems;
e.g., if a
running back loses 15 yards on the first carry but gains 8 yards on the second
carry,
what is the net gain/loss?
H8 Represent multiplication and division situations involving fractions and
decimals with
models and visual representations; e.g., show with pattern blocks what it
means to
take 2 2/3Þ1/6.
D9 Give examples of how ratios are used to represent comparisons; e.g., part-to-part,
part-to-whole, whole-to-part.
SIXTH GRADE
NUMBER, NUMBER SENSE AND OPERATIONS STANDARD ACTIVITIES RESOURCES
10* Recognize that a quotient may be larger than the dividend when the divisor
is a
fraction; e.g., 6Þ 1/2 = 12.
I11 Perform fraction and decimal computations and justify their solutions;
e.g., using
manipulative, diagrams, mathematical reasoning.
H12 Develop and analyze algorithms for computing with fractions and decimals,
and
demonstrate fluency in their use.
I13 Estimate reasonable solutions to problem situations involving fractions
and decimals;
7/8+12/13ª2 and 4.23x5.8ª25.
I14 Use proportional reasoning, ratios and percents to represent problem situations
and
determine the reasonableness of solutions.
I15 Determine the percent of a number and solve related problems; e.g., find
the percent
markdown if the original price was $140, and the sale price is $100.
*This grade-level indicator does not correlate with a 5-7 Benchmark.
SIXTH GRADE
MEASUREMENT STANDARD ACTIVITIES RESOURCES
G1 Understand and describe the difference between surface area and volume.
C2 Use strategies to develop formulas for finding circumference and area of
circles, and
to determine the area of sectors; e.g., 1/2 circle, 2/3 circle, 1/3 circle,
1/4 circle.
C3 Estimate perimeter or circumference and area for circles, triangles, and
quadrilaterals, and surface area and volume for prisms and cylinders by:
a. Estimating lengths using string or links, areas using tiles or grid, and
volumes using cubes;
b. Measuring attributes (diameter, side lengths, or heights) and using established
formulas for circles, triangles, rectangles, parallelograms and rectangular
prisms.
AE4 Determine which measure (perimeter, area, surface area, volume) matches
the
context for a problem situation; e.g., perimeter is the context for fencing
a garden,
surface area is the context for painting a room.
G5 Understand the difference between perimeter and area, and demonstrate that
two
shapes may have the same perimeter, but different areas may have the same
area,
but different perimeters.
F6 Describe what happens to the perimeter and area of a two-dimensional shape
when
the measurements of the shape are changed; e.g., length of sides are doubled.
SIXTH GRADE
GEOMETRY AND SPATIAL SENSE STANDARD ACTIVITIES RESOURCES
D1 Classify and describe two-dimensional and three-dimensional geometric
figures and objects by using their properties; e.g., interior angle measures,
perpendicular/parallel sides, congruent angles/sides.
D2 Use standard language to define geometric vocabulary: vertex, face, altitude,
diagonal, isosceles, equilateral, acute, obtuse and other vocabulary as appropriate.
DG3 Use multiple classification criteria to classify triangles; e.g., right
scalene triangle.
D4 Identify and define relationships between planes; i.e., parallel, perpendicular,
and
intersecting.
H5 Predict and describe sizes, positions and orientations of two-dimensional
shapes
after transformations such as reflections, rotations, translations and dilations.
EFJ6 Draw similar figures that model proportional relationships; e.g., model
similar
figures with a 1 to 2 relationship by sketching two of the same figures, one
with
corresponding sides twice the length of the other.
I7 Build three-dimensional objects with cubes, and sketch the two-dimensional
representations of each side; i.e., projection sets.
SIXTH GRADE
PATTERNS, FUNCTIONS AND ALGEBRA STANDARD ACTIVITIES RESOURCES
A1 Represent and analyze patterns, rules and functions, using physical materials,
tables and graphs.
ABEJ2
Use words and symbols to describe numerical and geometric patterns, rules
and functions.
D3 Recognize and generate equivalent forms of algebraic expressions, and explain
how the commutative, associative and distributive properties can be used to
generate equivalent forms; e.g., perimeter as 2 (l+w) or 2l +2w.
HK4 Solve simple linear equations and inequalities using physical models,
paper and
pencil, tables and graphs.
FK5 Produce and interpret graphs that represent the relationship between two
variables.
CGJ6 Evaluate simple expressions by replacing variables with given values,
and use formulas
in problem-solving situations.
L7 Identify and describe situations with constant or varying rates of change,
and compare
them.
M8 Use technology to analyze change; e.g., use computer applications or graphing
calculators to display and interpret rate of change.
SIXTH GRADE
DATA ANALYSIS AND PROBABILITY STANDARD ACTIVITIES RESOURCES
A1 Read, construct and interpret line graphs, circle graphs and histograms.
E2 Select, create and use graphical representations that are appropriate for
the type of
data collected.
D3 Compare representations of the same data in different types of graphs,
such as a bar
graph and circle graph.
F4 Understand the different information provided by measures of center (mean,
mode,
and median) and measures of spread (range).
B5 Describe the frequency distribution of a set of data, as shown in a histogram
or
frequency table, by general appearance or shape; e.g., number of modes, middle
of
data, level of symmetry, outliers.
G6 Make logical inferences from statistical data.
K7 Design an experiment to test a theoretical probability and explain how
the results
may vary.
Top
Secondary Mathematics Course Schedule
Content and instructional strategies have been explored to raise the level
of student performance in preparation for the Ohio Graduation Test and other
state and national assessments. Implementation of the more rigorous mathematics
courses of study will be progressive beginning with the current eighth grade
class. The following schedule outlines the course transitions. The courses
will continue to have traditional titles to comply with post secondary institutions.
The benchmarks and indicators for each of the six mathematics standards are
incorporated into the individual courses of study. Three mathematics credits
are mandatory to fulfill graduation requirements.
7th – 8th Grade Mathematics
Students in grades seven and eight will be scheduled into sections based on
their past performance and teacher recommendation.
Algebra I – 8th Grade
Students who perform at an accelerated pace may be recommended to take Algebra
I in the 8th grade. These students will
qualify for an elective high school credit if they achieve an A or B average
for the yearlong course.
Algebra I, Algebra I Basic
Students are advised to select Algebra I/Algebra I Basic for the 9th grade
year.
Geometry, Geometry Basic
Students who successfully completed Algebra I, Algebra I Basic are advised
to select Geometry, Geometry Basic for the 10th
grade year. Students who completed Algebra in the 8th grade are advised to
take Geometry in the 9th grade year.
Algebra II, Algebra II Basic
Students who successfully completed Algebra I and Geometry are advised to
select Algebra II for the 3rd math credit. Selecting
this course for the 11th grade would allow time for additional courses listed
below.
Advanced Mathematics
Students who excel in mathematics are encouraged to select Advanced Mathematics
for the 11th or 12th grade years with teacher recommendation.
Statistics, Probability & Data Analysis
This course may be selected as an elective mathematics course following the
completion of Algebra II and with teacher
recommendation. This course may be taken consecutively with Advanced Mathematics
or Calculus by students who wish to
study mathematics extensively.
Calculus
Students who successfully complete Advanced Mathematics may schedule Calculus
with teacher recommendation.
Top
SEVENTH GRADE
NUMBER, NUMBER SENSE AND OPERATIONS STANDARD ACTIVITIES RESOURCES
A1 Demonstrate an understanding of place value using powers of 10 and
write large numbers in scientific notation.
AI2 Explain the meaning of exponents that are negative or 0.
B3 Describe differences between rational and irrational numbers; terminating
terminating and repeating decimals vs. non-terminating and non-repeating decimals.
E4 Use order of operations and properties to simplify numerical expressions
involving integers, fractions and decimals.
H5 Explain the meaning and effect of adding, subtracting, multiplying and
dividing
integers; show how adding two integers can result in a lesser value.
I6 Simplify numerical expressions involving integers and use integers to solve
real-life problems.
I7 Solve problems using the appropriate form of a rational number (fraction,
decimal or
percent.)
H8 Develop and analyze algorithms for computing with percents and integers,
and demonstrate fluency in their use.
GI9 Represent and solve problem situations that can be modeled by and solved
using
concepts of absolute value, exponents and square roots (for perfect squares).
SEVENTH GRADE
MEASUREMENT STANDARD ACTIVITIES RESOURCES
A1 Select appropriate units for measuring derived measurements; miles per
hour,
revolutions per minute.
B2 Convert units of area and volume within the same measurement system using
proportional reasoning and a reference table when appropriate; square feet
to
square yards, cubic meters to cubic centimeters.
D3 Estimate a measurement to a greater degree of precision than the tool provides.
E4 solve problems involving proportional relationships and scale factors;
scale
models that require unit conversions within the same measurement system.
A5 Analyze problem situations involving measurement concepts, select appropriate
strategies, and use an organized approach to solve narrative and increasingly
complex problems.
CJ6* Use strategies to develop formulas for finding area of trapezoids and
volume of
cylinders and prisms.
C7 Develop strategies to find the area of composite shapes using the areas
of
triangles, parallelograms, circles and sectors.
G8 Understand the difference between surface area and volume and demonstrate
that
two objects may have the same surface area, but different volumes may have
the
same volume, but different surface areas.
F9 Describe what happens to the surface area and volume of a three-dimensional
object
when the measurements of the object are changed; length of sides are doubled.
*This J Benchmark references the Patterns, Functions and Algebra Standard
SEVENTH GRADE
GEOMETRY AND SPATIAL SENSE STANDARD ACTIVITIES RESOURCES
EJ1 Use proportional reasoning to describe and express relationships between
parts
and attributes of similar and congruent figures.
D2 Determine sufficient properties that define a specific two-dimensional
figure or
three-dimensional object. For example:
a. Determine when one set of figures is a subset of another, e.g., all squares
are
rectangles.
b. Develop a set of properties that eliminates all but the desired figure;
e.g.,
only squares are quadrilaterals with all sides congruent and all angles congruent.
GJ3* Use and demonstrate understanding of the properties of triangles.
a. Use Pythagorean Theorem to solve problems involving right triangles.
b. Use triangle angle sum relationships to solve problems.
F4 Determine necessary conditions for congruence of triangles.
GJ5 Apply properties of congruent or similar triangles to solve problems involving
missing lengths and angle measures.
EJ6 Determine and use scale factors for similar figures to solve problems
using
proportional reasoning.
F7 Identify the line and rotation symmetries of two-dimensional figures to
solve problems.
H8 Perform translations, reflections, rotations and dilations of two-dimensional
figures
using a variety of methods (paper folding, tracing, graph paper).
I9 Draw representations of three-dimensional geometric objects from different
views.
*This J Benchmark references the Patterns, Functions and Algebra Standard
SEVENTH GRADE
PATTERNS, FUNCTIONS AND ALGEBRA STANDARD ACTIVITIES RESOURCES
BG1 Represent and analyze patterns, rules and functions with words, tables,
graphs
and simple variable expressions.
AB2 Generalize patterns by describing in words how to find the next term.
AE3 Recognize and explain when numerical patterns are linear or nonlinear
progressions; e.g. 1,3,5,7…is linear and 1,3,4,8,16…is nonlinear.
FHI4 Create visual representations of equation-solving processes that model
the use of
inverse operations.
FK5 Represent linear equations by plotting points in the coordinate plane.
FK6 Represent inequalities on a number line or a coordinate plane.
G7 Justify that two forms of an algebraic expression are equivalent and recognize
when an expression is simplified.
J8 Use formulas in problem-solving situations.
D9 Recognize a variety of uses for variables.
L10 Analyze linear and simple nonlinear relationships to explain how a change
in one
variable results in the change of another.
FM11 Use graphing calculators or computers to analyze change; e.g., distance-time
relationships.
SEVENTH GRADE
DATA ANALYSIS AND PROBABILITY STANDARD ACTIVITIES RESOURCES
A1 Read, create and interpret box-and-whisker plots, stem-and-leaf plots,
and other
types of graphs, when appropriate.
EG2 Analyze how decisions about graphing affect the graphical representation;
e.g.,
scale, size of classes in a histogram, number of categories in a circle graph.
F3 Analyze a set of data by using and comparing combinations of measures of
a
center (mean, mode, median) and measures of spread (range, quartile, interquartile
range), and describe how the inclusion or exclusion of outliers affects those
measures.
B4 Construct opposing arguments based on analysis of the same data, using
different
graphical representations.
D5 Compare data from two or more samples to determine how sample selection
can
influence results.
G6 Identify misuses of statistical data in articles, advertisements, and other
media.
I7 Compare probabilities of compound events, multiple coin tosses or multiple
rolls
of number cubes, using such methods as organized lists, tree diagrams and
area models.
KJ8* Make predictions based on theoretical probabilities, design and conduct
an
experiment to test the predictions, compare actual results to predicted results,
and explain differences. * The J Benchmark references the Patterns, Functions
and Algebra Standard
Top
EIGHTH GRADE
NUMBER, NUMBER SENSE AND OPERATIONS STANDARD ACITIVITIES RESOURCES
A1 Use scientific notation to express large numbers and small numbers between
0 and 1.
B2 Recognize that natural numbers, whole numbers, integers, rational numbers
and
irrational numbers are subsets of the real number system.
I3 Apply order of operations to simplify expressions and perform computations
involving integer exponents and radicals.
C4 Explain and use the inverse and identity properties and use inverse relationships
(addition/subtraction, multiplication/division, squaring/square roots) in
problem
solving situations.
G5 Determine when an estimate is sufficient and when an exact answer is needed
in
problem situations, and evaluate estimates in relation to actual answers;
e.g., very close, less than, greater than.
G6 Estimate, compute and solve problems involving rational numbers, including
ratio,
proportion and percent, and judge the reasonableness of solutions.
H7 Find the square root of perfect squares, and approximate the square root
of
non-perfect squares as consecutive integers between which the root lies.
I8 Add, subtract, multiply, divide and compare numbers written in scientific
notation.
EIGHTH GRADE
NUMBER, NUMBER SENSE AND OPERATIONS STANDARD ACTIVITIES RESOURCES
A9 Demonstrate an understanding of place value using powers of 10 and
(1)* write large numbers in scientific notation.
AI10 Explain the meaning of exponents that are negative or 0.
(2)
B11 Describe differences between rational and irrational numbers; terminating
and
(3) and repeating decimals vs. non-terminating and non-repeating decimals.
C12 Use order of operations and properties to simplify numerical expressions
involving integers, fractions and decimals.
F13 Explain the meaning and effect of adding, subtracting, multiplying and
dividing integers; show how adding two integers can result in a lesser value.
G14 Solve problems using the appropriate form of a rational number (fraction,
(7) decimal or percent).
I15 Represent and solve problem situations that can be modeled by and solved
using
(9) concepts of absolute value, exponents and square roots (for perfect squares).
*The numbers in parentheses are references to the Seventh Grade Indicators
with 8th-10th Grade Benchmarks under the
Number, Number Sense, and Operations Standard.
EIGHTH GRADE
MEASUREMENT STANDARD ACTIVITIES RESOURCES
D1 Compare and order the relative size of common U. S. customary units and
metric
units; e.g., mile and kilometer, gallon and liter, pound and kilogram.
D2 Use proportional relationship and formulas to convert units from one
measurement system to another; e.g., degrees Fahrenheit to degrees Celsius.
BE3 Use appropriate levels of precision when calculating with measurements.
B4 Derive formulas for surface area and volume and justify them using geometric
models
and common materials. For example:
a. the surface area of a cylinder as a function of its height and radius;
b. that the volume of a pyramid (or cone) is one-third of the volume of a
prism
(or cylinder) with the same base area and height.
C5 Determine surface area for pyramids by analyzing their parts.
AF6 Solve and determine the reasonableness of the results for problems involving
rates
and derived measurements, such as velocity and density, using formulas, models
and graphs.
D7 Apply proportional reasoning to solve problems involving indirect measurements
or rates.
E8 Find the sum of the interior and exterior angles of regular convex polygons
with
and without measuring the angles with a protractor.
BC9 Demonstrate understanding of the concepts of perimeter, circumference
and area
by using established formulas for triangles, quadrilaterals, and circles to
determine
the surface area and volume of prisms, pyramids, cylinders, spheres and cones.
(Note: Only volume should be calculated for spheres and cones.)
BE10 Use conventional formulas to find the surface area and volume of prisms,
pyramids
and cylinders and the volume of spheres and cones to a specified level of
precision.
EIGHTH GRADE
MEASUREMENT STANDARD ACITIVITIES RESOURCES
E11 Solve problems involving proportional relationship and scale factors;
(4)* e.g., scale models that require unit conversions within the same measurement
system.
A12 Analyze problem situations involving measurement concepts, select appropriate
(5) strategies, and use an organized approach to solve narrative and increasingly
complex problems.
C13 Develop strategies to find the area of composite shapes using the areas
of
(7) triangles, parallelograms, circles and sectors.
*The numbers in parentheses reference Seventh Grade Indicators with 8th –10th
Grade Benchmarks
in the Measurement Standard.
EIGHTH GRADE
GEOMETRY AND SPATIAL SENSE STANDARD ACTIVITIES RESOURCES
BDH1 Make and test conjectures about characteristics and properties (sides,
angles,
symmetry) of two-dimensional figures and three-dimensional objects.
C2 Recognize the angles formed and the relationship between the angles when
two
lines intersect and when parallel lines are cut by a transversal.
B3 Use proportions in several forms to solve problems involving similar figures
(part-to-part, part-to-whole, corresponding sides between figures.)
D4 Represent and analyze shapes using coordinate geometry; e.g., given three
vertices and the type of quadrilateral, find the coordinates of the fourth
vertex.
F5 Draw the results of translations, reflections, rotations and dilations
of objects in
the coordinate plane, and determine properties that remain fixed; e.g., lengths
of sides
remain the same under translations.
E6 Draw nets for a variety of prisms, pyramids, cylinders and cones.
EIGHTH GRADE
GEOMETRY AND SPATIAL SENSE STANDARD ACTIVITIES RESOURCES
B7(1)* Use proportional reasoning to describe and express relationships between
parts
and attributes to similar and congruent figures.
A8(2) Determine sufficient properties that define a specific two-dimensional
figure or
three-dimensional object. For example:
a. determine when one set of figures is a subset of another; e.g., all
squares and rectangles.
b. develop a set of properties that eliminates all but the desired figure;
e.g.,
only squares are quadrilaterals with all sides congruent and all angles congruent.
B9(5) Apply properties of congruent or similar triangles to solve problems
involving
missing lengths and angle measures.
F10(8) Perform translations, reflections, rotations and dilations of two-dimensional
figures
using a variety of methods (paper folding, tracing, graph paper.)
*The number in parentheses references the Seventh Grade Indicators with
8th – 10th Grade Benchmarks
in the Geometry and Spatial Sense Standard.
EIGHTH GRADE
PATTERNS, FUNCTIONS AND ALGEBRA STANDARD ACTIVITIES RESOURCES
C1 Relate the various representations of a relationship; e.g., relate a table
to graph, description and symbolic form.
A2 Generalize patterns and sequences by describing how to find the nth term.
B3 Identify functions as linear or nonlinear based on information given in
a table,
graph or equation.
D4 Extend the uses of variables to include covariants where y depends on x.
D5 Use physical models to add and subtract monomials and polynomials, and
to
multiply a polynomial by a monomial.
E6 Describe the relationship between the graph of a line and its equation,
including
being able to explain the meaning of slope as a constant rate of change and
y-intercept in real-world problems.
DF7 Use symbolic algebra (equations and inequalities), graphs and tables to
represent situations and solve problems.
D8 Write, simplify and evaluate algebraic expressions (including formulas)
to
generalize situations and solve problems.
F9 Solve linear equations and inequalities graphically, symbolically and using
technology.
H10 Solve 2 by 2 systems of linear equations graphically and by simple substitution.
H11 Interpret the meaning of the solution of a 2 by 2 system of equations;
i.e.,
point, line, no solution.
G12 Solve simple quadratic equations graphically; e.g., y+x -16.
J13 Compute and interpret slope, midpoint and distance given a set of ordered
pairs.
I14 Differentiate and explain types of changes in mathematical relationship,
such as
linear vs. nonlinear, continuous vs. noncontinuous, direct variation vs. inverse
variation.
EIGHTH GRADE
PATTERNS, FUNCTIONS AND ALBEGRA STANDARD ACTIVITIES RESOURCES
J15 Describe and compare how changes in an equation affects the related graphs;
e.g.,
for a linear equation changing the coefficient of x affects the slope and
changing constant
affects the intercepts.
J16 Use graphing calculators or computers to analyze change; e.g., interest
compounded
over time as a nonlinear growth pattern.
EIGHTH GRADE
DATA ANALYSIS AND PROBABILITY STANDARD ACTIVITIES RESOURCES
A1 Use, create and interpret scatterplots and other types of graphs as appropriate.
B2 Evaluate different graphical representations of the same data to determine
which is the most appropriate representation for an identified purpose; e.g.,
line graph for change over time, circle graph for part-to-whole comparison,
scatterplot for relationship between two variants.
B3 Differentiate between discrete and continuous data and appropriate ways
to
represent each.
D4 Compare two sets of data using measure of center (mean, mode, median) and
measure of spread (range, quartiles, interquartile range, percentiles).
C5 Explain the mean’s sensitivity to extremes and its use in comparison
with the
median and mode.
F6 Make conjectures about possible relationship in a scatterplot and approximate
line of best fit.
G7 Identify different ways of selecting sample, such as survey response, random
sample, representative sample and convenience sample.
E8 Describe how the relative size of a sample compared to the target population
affects the validity of predictions.
F9 Construct convincing arguments based on analysis of data and interpretation
of graphs.
EIGHTH GRADE
DATA ANALYSIS AND PROBABILITY STANDARD ACTIVITIES RESOURCES
H10 Calculate the number of possible outcomes for a situation, recognizing
and
accounting for when items may occur more than once or when order is
important.
J11 Demonstrate an understanding that the probability of either of two disjoint
events occurring can be found by adding the probabilities for each and that
the probability of one independent event following another can be found by
multiplying the probabilities.
Top
ALGEBRA I
ALGEBRA I BASIC
NUMBER, NUMBER SENSE AND OPERATIONS STANDARD ACTIVITIES RESOURCES
C1 Identify and justify whether properties (closure, identity, inverse,
commutative and associative) hold for a given set and operations;
e.g., even integers and multiplication.
E2 Compare, order and determine equivalent forms for rational and
irrational numbers.
F3 Explain the effects of operations such as multiplication or division,
and of computing powers and roots on the magnitude of quantities.
G4 Demonstrate fluency in computations using real numbers.
I5 Estimate the solutions for problem situations involving square and
cube roots.
ALGEBRA I
ALBEGRA I BASIC
MEASUREMENT STANDARD ACTIVITIES RESOURCES
D1 Convert rates within the same measurement system; e.g., miles per
hour to feet per second; kilometers per hour to meters per second.
D2 Use unit analysis to check computations involving measurement.
D3 Use the ratio of length in similar two-dimensional figures or
three-dimensional objects to calculate the ratio of their areas or
volumes respectively.
D4 Use scale drawings and right triangle trigonometry to solve problems
that include unknown distances and angle measures.
D5 Solve problems involving unit conversion for situations involving
distances, areas, volumes and rates within the same measurement system.
ALGEGRA I
ALGEBRA I BASIC
GEOMETRY AND SPATIAL SENSE STANDARD ACTIVITIES RESOURCES
I1 Define the basic trigonometric ratios in right triangles: sine,
cosine and tangent.
I2 Apply proportions and right triangle trigonometric ratios to solve problems
involving missing lengths and angle measures in similar figures.
DG3 Analyze two-dimensional figures in a coordinate plane; e.g.,
use slope and distance formulas to show that a quadrilateral is a
parallelogram.
ALGEBRA I
ALBEGRA I BASIC
PATTERNS, FUNCTIONS AND ALGEBRA STANDARD ACTIVITIES RESOURCES
B1 Define function with ordered pairs in which each domain element is
assigned exactly one range element.
CA2 Generalize patterns using functions or relationships (linear,
quadratic and exponential), and freely translate among tabular,
graphical and symbolic representations.
B3 Describe problem situations (linear, quadratic and exponential) by
using tabular, graphical and symbolic representations.
E4 Demonstrate the relationship among zeros of a function, roots of
equations, and solutions of equations graphically and in words.
E5 Describe and compare characteristics of the following families of functions:
linear, quadratic and exponential functions; e.g., general shape,
number of roots, domain, range, rate of change, maximum or minimum.
F6 Write and use equivalent forms of equations and inequalities in
problem situations; e.g., changing a linear equation to the slope-
intercept form.
D7 Use formulas to solve problems involving exponential growth and decay.
F8 Find linear equations that represent lines that pass through a given set
of ordered pairs, and find linear equations that represent lines
parallel or perpendicular to a given line through a specific point.
H9 Solve and interpret the meaning of 2 by 2 systems of linear
equations graphically, by substitution and by elimination, with and
without technology.
ALGEBRA I
ALGEBRA I BASIC
PATTERNS, FUNCTIONS AND ALGEBRA STANDARD ACTIVITIES RESOURCES
G10 Solve quadratic equations with real roots by factoring, graphing,
using the quadratic formula and with technology.
D11 Add, subtract, multiply and divide monomials and polynomials
(division of polynomials by monomials only).
D12 Simplify rational expressions by eliminating common factors and
applying properties of integer exponents.
I13 Model and solve problems involving direct and inverse variation
using proportional reasoning.
I14 Describe the relationship between slope and the graph of a direct
variation and inverse variation.
J15 Describe how a change in the value of a constant in a linear or
quadratic equation affects the related graphs.
ALGEBRA I
ALGEBRA I BASIC
DATA ANALYSIS AND PROBABILITY STANDARD ACTIVITIES RESOURCES
A1 Classify data as univariate (single variable) or bivariate (two
variables) and as quantitative (measurement) or qualitative
(categorical) data.
A2 Create a scatterplot for a set of bivariate data, sketch the line of best
fit, and interpret the slope of the line of best fit.
A3 Analyze and interpret frequency distributions based on spread,
symmetry, skewness, clusters and outliers.
E4 Describe and compare various types of studies (survey, observation,
experiment), and identify possible misuses of statistical data.
G5 Describe characteristics and limitations of sampling methods, and
analyze the effects of random versus biased sampling; e.g.,
determine and justify whether the sample is likely to be
representative of the population.
F6 Make inferences about relationships in bivariant data, and recognize
the difference between evidence of relationship (correlation) and
causation.
H7 Use counting techniques and the Fundamental Counting principle to
determine the total number of possible outcomes for mathematical
situations.
ALGEBRA I
ALGEBRA I BASIC
DATA ANALYSIS AND PROBABILITY STANDARD ACTIVITIES RESOURCES
I8 Describe, create and analyze a sample space and use it to calculate
probability.
J9 Identify situations involving independent and dependent events,
and explain differences between, and common misconceptions about,
probabilities associated with those events.
K10 Use theoretical and experimental probability, including simulations or
random numbers, to estimate probabilities and to solve problems
dealing with uncertainty; e.g., compound events, independent events,
simple dependent events.
Top
GEOMETRY
GEOMETRY BASIC
NUMBER, NUMBER SENSE AND OPERATIONS STANDARD ACTIVITIES RESOURCE
D1 Connect physical, verbal and symbolic representations of irrational
numbers; e.g., construct ÷`2 as a hypotenuse or on a number line.
D2 Explain the meaning of the nth root.
C*3 Use factorial notation and computations to represent and solve
problem situations involving arrangements.
I4 Approximate the nth root of a given number greater than zero
between consecutive integers when n is an integer; e.g., the 4th
root of 50 is between 2 and 3.
*This capital letter is a reference to the 12th Grade Benchmark for the
Number, Number Sense and Operations Standard. All other capital letter references
for Geometry
refer to the 8th – 10th Grade Benchmarks.
GEOMETRY
GEOMETRY BASIC
MEASUREMENT STANDARD ACTIVITIES RESOURCES
A*1 Explain how a small error in measurement may lead to a large error
in calculated results.
A*2 Calculate relative error.
A*3 Explain the difference between absolute error and relative error in
measurement.
A*4 Give examples of how the same absolute error can be problematic in
one situation but not in another; e.g., compare "accurate to the
nearest foot" when measuring the height of a person versus when
measuring the height of a mountain.
DC5 Determine the measures of central and inscribed angles and their
associated major and minor arcs.
*This capital letter refers to the 12th Grade Benchmark in the Measurement
Standard.
GEOMETRY
GEOMETRY BASIC
GEOMETRY AND SPATIAL SENSE STANDARD ACTIVITIES RESOURCES
A1 Formally define and explain key aspects of geometric figures,
including:
a. interior and exterior angles of polygons;
b. segments related to triangles (median, altitude, midsegment);
c. points of concurrency related to triangles (centroid, incenter,
orthocenter, circumcenter);
d. circles (radius, diameter, chord, circumference, major arc, minor arc,
sector, segment, inscribed angle).
A2 Recognize and explain the necessity for certain terms to remain undefined,
such as point, line and plane.
H3 Make, test and establish the validity of conjectures about geometric
properties and relationships using counterexample, inductive and
deductive reasoning, and paragraph or two-column proof, including:
a. prove the Pythagorean Theorem;
b. prove theorems involving triangle similarity and congruence;
c. prove theorems involving properties of lines, angles, triangles and
quadrilaterals;
d. test a conjecture using basic constructions made with a compass and
straightedge or technology
E4 Construct right triangles, equilateral triangles, parallelograms,
trapezoids, rectangles, rhombuses, squares and kites, using compass
and straightedge or dynamic geometry software.
GEOMETRY
GEOMETRY BASIC
GEOMETRY AND SPATIAL SENSE STANDARD ACTIVITIES RESOURCES
E5 Construct congruent figures and similar figures using tools, such
as compass, straightedge, and protractor or dynamic geometry software.
FA6 Identify the reflection and rotation symmetries of two- and three-
dimensional figures.
E7 Perform reflections and rotations using compass and straightedge
constructions and dynamic geometry software.
F8 Derive coordinate rules for translations, reflections and rotations of
geometric figures in the coordinate plane.
F9 Show and describe the results of combinations of translations,
reflections and rotations (compositions); e.g., perform compositions
and specify the result of a composition as the outcome of a single motion,
when applicable.
C10 Solve problems involving chords, radii and arcs within the same circle.
GEOMETRY
GEOMETRY BASIC
PATTERNS, FUNCTIONS AND ALGEBRA STANDARD ACTIVITIES RESOURCES
B1 Define function formally and with f(x) notations.
B2 Describe and compare characteristics of the following families of
functions: square root, cubic, absolute value and basic trigonometric functions;
e.g., general shape, possible number of roots, domain and range.
D3 Solve equations and formulas for a specified variable; e.g., express
the base of a triangle in terms of the area and height.
D4 Use algebraic representations and functions to describe and
generalize geometric properties and relationships.
D5 Solve simple linear and nonlinear equations and inequalities having
square roots as coefficients and solutions.
D6 Solve equations and inequalities having rational expressions as
coefficients and solutions.
H7 Solve systems of linear inequalities.
G8 Graph the quadratic relationship that defines circles.
J9 Recognize and explain that the slopes of parallel lines are equal and
the slopes of perpendicular lines are negative reciprocals.
G10 Solve real-world problems that can be modeled using linear,
quadratic, exponential or square root functions.
H11 Solve real-world problems that can be modeled, using systems of
linear equations and inequalities.
J12 Describe the relationship between slope of a line through the origin
and the tangent function of the angle created by the line and the
positive x-axis.
GEOMETRY
GEOMETRY BASIC
DATA ANALYSIS AND PROBABILITY STANDARD ACTIVITIES RESOURCES
C1 Describe measures of center and the range verbally, graphically and
algebraically.
A2 Represent and analyze bivariate data using appropriate graphical
displays (scatterplots, parallel box-and-whisker plots, histograms
with more than one set of data, tables, charts, spreadsheets) with
and without technology.
A3 Display bivariate data where at least one variable is categorical.
A4 Identify outliers on a data display; e.g., use interquartile range to
identify outliers on a box-and-whisker plot.
G5 Provide examples and explain how a statistic may or may not be an
attribute of the entire population; e.g., intentional or unintentional bias
may be present.
D6 Interpret the relationship between two variables using multiple graphical
displays and statistical measures; e.g., scatterplots, parallel box-and-whisker
plots, and measures of center and spread.
J7 Model problems dealing with uncertainty with area models
(geometric probability).
K8 Differentiate and explain the relationship between the probability of an
event and the odds of an event, and compute one given the other.
Top
ALGEBRA II
ALGEBRA II BASIC
NUMBER, NUMBER SENSE AND OPERATIONS STANDARD ACTIVITIES RESOURCES
AB1 Determine what properties hold for matrix addition and matrix
multiplication; e.g., use examples to show addition is commutative and
when multiplication is not commutative.
AB2 Determine what properties hold for vector addition and multiplication,
and for scalar multiplication.
E3 Represent complex numbers on the complex plane.
D4 Use matrices to represent given information in a problem situation.
B5 Model, using the coordinate plane, vector addition and scalar multiplication.
D6 Compute sums, differences and products of matrices using paper and
pencil calculations for simple cases, and technology for more complicated
cases.
E7 Compute sums, differences, products and quotients of complex numbers.
C8 Use fractional and negative exponents as optional ways of
representing and finding solutions for problem situations;
e.g., 27 2/ 3 = (27 1/ 3) 2 =9
D9 Use vector addition and scalar multiplication to solve problems.
C10 Explain the meaning of the nth root.
C11 Use factorial notation and computations to represent and solve problem
situations involving arrangements.
C12 Approximate the nth root of a given number greater than zero between
consecutive integers when n is an integer; e.g., the 4th root of 50 is
between 2 and 3.
ALGEBRA II
ALBEGRA II BASIC
MEASUREMENT STANDARD ACTIVITIES RESOURCES
A1 Determine the number of significant digits in a measurement.
B2 Use radian and degree angle measures to solve problems and perform
conversions as needed.
C3 Derive a formula for the surface area of a cone as a function of its slant
height and the circumference of its base.
C4 Calculate distances, areas, surface areas and volumes of composite
three-dimensional objects to a specified number of significant digits.
D5 Solve real-world problems involving area, surface area, volume and density
to a specified degree of precision.
A6 Explain how a small error in measurements may lead to a large error in
calculated results.
A7 Calculate the relative error.
A8 Explain the difference between absolute error and relative error in
measurement.
A9 Give examples of how the same absolute error can be problematic in one
situation but not in another; e.g., compare "accurate to the nearest
foot" when
measuring the height of a person versus when measuring the height of a
mountain.
ALGEBRA II
ALGEBRA II BASIC
GEOMETRY AND SPATIAL SENSE STANDARD ACTIVITIES RESOURCES
B1 Use polar coordinates to specify locations on a plane.
B2 Represent translations using vectors.
B3 Describe multiplication of a vector and a scalar graphically and
algebraically, and apply to problem situations.
A4 Use trigonometric relationships to determine lengths and angle
measures; i.e., Law of Sines and Law of Cosines.
ADE5 Identify, sketch and classify the cross sections of three-dimensional
objects.
ALGEBRA II
ALGEBRA II BASIC
PATTERNS, FUNCTIONS AND ALGEBRA STANDARD ACTIVITIES RESOURCES
C1 Identify and describe problem situations involving an iterative process
that can be represented as a recursive function; e.g., compound interest.
C2 Translate a recursive function into a closed form expression or formula
for the nth term to solve a problem situation involving an iterative
process; e.g., find the value of an annuity after 7 years.
A3 Describe and compare the characteristics of the following families of
functions: quadratics with complex roots, polynomials of any degree,
logarithms, and rational functions; e.g., general shape, number of roots,
domain and range, asymptotic behavior.
A4 Identify and maximum and minimum points of polynomial, rational and
trigonometric functions graphically and with technology.
A5 Identify families of functions with graphs that have rotation symmetry
or reflection symmetry about the y-axis, x-axis or y=x.
A6 Represent the inverse of a function symbolically and graphically as a
reflection about y=x.
D7 Model and solve problems with matrices and vectors.
B8 Solve equations involving radical expressions and complex roots.
D9 Solve 3 by 3 systems of linear equations by elimination and using
technology, and interpret graphically what the solution means
(a point, line, plane, or no solution).
A10 Describe the characteristics of the graphs of conic sections.
A11 Describe how a change in the value of a constant in an exponential,
logarithmic or radical equation affects the graph of the equation.
ALGEBRA II
ALGEBRA II BASIC
DATA ANALYSIS AND PROBABILITY STANDARD ACTIVITIES RESOURCES
CD1 Design a statistical experiment, survey or study for a problem; collect
data for the problem; and interpret the data with appropriate graphical
displays, descriptive statistics, concepts of variability, causation,
correlation and standard deviation.
CD2 Describe the role of randomization in a well-designed study, especially
as compared to a convenience sample, and the generalization of
results from each.
B3 Describe how a linear transformation of univariate data affects range,
mean, mode and median.
AB4 Create a scatterplot of bivariate data, identify trends, and find a function
to model the data.
AB5 Use technology to find the Least Squares Regression Line, the
regression coefficient, and the correlation coefficient for bivariate data
with a linear trend, and interpret each of these statistics in the context
of the problem situation.
B6 Use technology to compute the standard deviation for a set of data, and
interpret standard deviation in relation to the context or problem situation.
A7 Describe the standard normal curve and its general properties, and
answer questions dealing with data assumed to be normal.
AB8 Analyze and interpret univariate and bivariate data to identify patterns,
note trends, draw conclusions, and make predictions.
ALGEBRA II
ALGEBRA II BASIC
DATA ANALYSIS AND PROBABILITY STANDARD ACTIVITIES RESOURCES
CD9 Evaluate validity of results of a study based on characteristics of the
study design, including sampling method, summary statistics and data
analysis techniques.
A10 Understand and use the concept of random variable, and compute and
interpret the expected value for a random variable in simple cases.
D11 Examine statements and decisions involving risk; e.g., insurance rates
and
medical decision.
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STATISTICS, PROBABILITY & DATA
ANALYSIS
PATTERNS, FUNCTIONS AND ALGEBRA STANDARD ACTIVITIES RESOURCES
A1* Find the equation of the regression line of given data.
*The grade level indicators for Statistics, Probability & Data Analysis
were written specifically for this course
and do not correlate with the ODE 11th and 12th grade level indicators.
STATISTICS, PROBABILITY & DATA ANALYSIS
DATA ANALYSIS AND PROBABILITY STANDARD ACTIVITIES RESOURCES
C1* Distinguish between a sample and a population.
A2 Classify data by type and level of measurement.
D3 Identify uses and abuses of statistics
C4 Define various sampling methods.
A5 Utilize technology (including calculators and computer spreadsheets) to
organize,
summarize, analyze and perform calculations with data.
A6 Organize raw data into a frequency table, histogram, frequency polygon,
ogive, dotplot,
stem-and-leaf plot, bar graph, pie chart, boxplot and scatterplot.
A7 Rank scores in ascending or descending order and group large sets of data
into intervals.
B8 Calculate measures of central tendency (the median, mode, midrange and
weighted mean)
from a set of data.
B9 Calculate range, mean absolute deviation, standard deviation and variance
from a set of data.
B10 Interpret results of a procedure or situation using the range rule of
thumb.
A11 Convert values into corresponding "z" scores (standard scores)
and percentile values
for comparisons.
B12 Identify minimum/maximum values and outliers.
A13 List the sample space of an event.
B14 Assign probabilities to single events.
B15 Calculate the odds in favor and odds against an event.
B16 Calculate the probability of the union of two events.
B17 Determine whether events are mutually exclusive.
*The grade level indicators for Statistics, Probability & Data Analysis
were written specifically for this course and
do not correlate with the ODE 11th and 12th grade level indicators.
STATISTICS, PROBABILITY & DATA ANALYSIS
DATA ANALYSIS AND PROBABILITY STANDARD ACTIVITIES RESOURCES
B18* Calculate the probability of the complement of an event.
A19 Draw a tree diagram to show the possible outcomes of a procedure.
B20 Determine whether events are independent.
B21 Calculate the probability of the intersection of two events.
B22 Calculate the conditional probability of an event’s occurrence, given
that another event
has already occurred.
C23 Use a simulation to estimate the probability of a real-life situation.
A24 Distinguish between a permutation and a combination.
B25 Determine the total number of outcomes in a situation using the fundamental
counting
rule, factorial rule, permutations and combinations.
A26 Identify a random variable as discrete or continuous.
B27 Identify a probability distribution and calculate its mean and standard
deviation.
A28 Identify a binomial distribution.
D29 Use a binomial distribution to find probabilities in a problem-solving
situation.
B30 Find the mean and standard deviation of a binomial distribution.
B31 Analyze continuous distributions of two types: uniform and normal.
A32 Graph a normal distribution.
B33 Use a standard normal distribution table (normal curve) to find probabilities.
A34 Standardize a random variable on the normal curve with a standard deviation
of one.
B35 Find probabilities and values using standardized normal distributions.
D36 Apply the Central Limit Theorem to practical problems.
*The grade level indicators for Statistics, Probability & Data Analysis
were written specifically for this course
and do not correlate with the ODE 11th and 12th grade level indicators.
STATISTICS, PROBABILITY & DATA ANALYSIS
DATA ANALYSIS AND PROBABILITY STANDARD ACTIVITIES RESOURCES
B37* Approximate a binomial distribution with a normal distribution.
C38 Calculate critical values that correspond to a given degree of confidence.
D39 Compute the margin of error in the sample mean from the population mean.
D40 Find the confidence interval for the population (a) mean, (b) proportion,
and
(c) standard deviation using a given degree of confidence and sample data.
C41 Construct and interpret confidence intervals in problem situations.
C42 Determine appropriate sample size.
C43 Define statistical hypothesis.
C44 Identify the null and alternative hypotheses about a population.
C45 Find the value of a test statistic.
C46 Distinguish between two-tailed, right-tailed and left-tailed statistical
tests.
C47 Distinguish between Type I and Type II errors in hypothesis testing.
C48 Test a claim about the population mean, proportion or standard deviation
using both the
traditional and the P-value methods of testing hypotheses.
D49 Find the value of the linear correlation coefficient and use a given significance
level to
determine whether there is a significant linear correlation between two variables.
D50 Predict values using a regression equation.
D51 Calculate the coefficient of determination and the percentage of total
variation that
can be explained by the linear relationship between two variables.
D52 Compute the explained variation, unexplained variation, total variation
and standard error
of estimate in a set of data.
*The grade level indicators for Statistics, Probability & Data Analysis
were written specifically for this course and
do not correlate with the ODE 11th and 12th grade level indicators.
Top
ADVANCED MATHEMATICS
NUMBER, NUMBER SENSE AND OPERATIONS STANDARD ACTIVITIES RESOURCES
E1 Determine what properties (closure, identity, inverse, commutative and
associative) hold for operations with complex numbers.
C2 Apply combinations as a method to create coefficients for the Binomial
Theorem,
and make connections to everyday and workplace problem situations.
ADVANCED MATHEMATICS<
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