Download Math Curriculum Document

Mathematics is the study of patterns in
quantity and space.
Mahesh Sharma
Math Curriculum Document
Orleans Southwest Supervisory Union
Version 3.0
May, 2011
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Table of Contents
1. Statements of Vision, Mission, and Learning Principles .......................................................................... 3
Vision ........................................................................................................................................................ 3
Mission...................................................................................................................................................... 3
Learning Principles ................................................................................................................................... 3
2. K-12 Enduring Understandings and Essential Questions for Mathematics .............................................. 5
K-12 Enduring Understandings ................................................................................................................ 5
Essential Questions ................................................................................................................................... 5
3. Curriculum Mapping: Course/ Grade Level Benchmarks ....................................................................... 6
4. Cornerstone Assessments ....................................................................................................................... 15
Evidence of Benchmark Obtainment ......................................................... Error! Bookmark not defined.
Grade Level Assessments ………………..………………………………………………………………………………………………. 33
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1. Statements of Vision, Mission, and Learning Principles
Vision

All students will graduate with passing Algebra II.

Fifty percent of the student will graduate with taking a calculus level course.
Mission
The OSSU PreK-12 Math Program is committed to ensuring an educational experience
that provides our students with the tools and strategies necessary to be lifelong learners,
consumers of information and productive members of our ever changing society. All
students will be capable of reasoning and thinking mathematically, able to apply
mathematical knowledge, will be mathematically literate, and will use technology
(computers, calculators, etc.) and manipulatives to enhance their learning.
Learning Principles
Math Learning Principles
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Math is best learned through discovery of concepts. Therefore we need vertical
alignment of materials and manipulatives.
Math is a language. Therefore, we must have vertical alignment of vocabulary.
Students need automatic with skills to support high level conceptual thinking and
problem solving. Therefore, instruction must focus on the development of automaticity
of key skills while teaching higher level concepts.
Assessment drives instruction. Therefore, teachers will use formative assessment
throughout their instruction to inform them of the next learning step for each child.
Students need to learn new math concepts in an intentional method starting with intuitive,
concrete, pictorial, abstract, procedural, application and communication. Therefore,
teachers will make sure their instruction progress through this continuum for each
concept they teach.
District Learning Principles
Transfer is the goal - The ultimate goal is for learners to apply their knowledge, skills and
understanding of big ideas to new contexts.
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Curriculum - Learners will make connections through their interests, strengths and prior
knowledge to gain a deep understanding of cross-curricular concepts. Curriculum must focus on
BIG IDEAS that are spiraled, aligned and logically connected throughout PreK-12 education.
Assessment /Feedback - Learners need regular non-judgmental and constructive feedback.
They also need timely opportunities to use the feedback to understand goals and to produce
quality work. Learners should experience multiple forms of assessment that is conducted by
both teachers and learners.
Instruction - Learners make connections to the larger world of ideas when the instruction is
guided by clear expectations, and models for learners to follow. When instruction is rooted in
inquiry and application, learners gain a deeper level of understanding of the big ideas.
Environment - Learners perform best in communities of trusted adults and peers. They take
risks and achieve their personal best in safe and supportive school-wide environments. Learners
transfer their understanding across environments when learning is personalized and feedback is
supportive and instructive.
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2. K-12 Enduring Understandings and Essential Questions for Mathematics
K-12 Enduring Understandings
(Draft for committee to approve)

Students will understand that internalizing the language of mathematics will help them
communicate how they have solved problems in quantities and/or space.

Students will understand that constructing mathematical concepts will give them a deeper
knowledge of how to apply their knowledge to solve problems.

Students will understand that being fluent with mathematical procedures will help them apply
their knowledge to solve problems in quantity and/or space.

Students will understand that being automatic with their mathematics skills will allow them to
apply concepts to solve problems in quantity and space.
Essential Questions
To be developed from look at list from Grand Island, NE web site of their curriculum to start the
conversations.
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3. Curriculum Mapping: Course/ Grade Level Benchmarks
Math Grade Level Benchmarks
Grade K
Guaranteed Benchmarks for all students
Number and Operations
1. Count by ones, forward and backward, starting at a number between 1 and
100.
2. Count by 10 and 5 to 100.
3. Automatize the integration of number symbol, cluster, value, and name to
numbers up to 10 (able to decompose the number into its components).
4. Automatize combinations that equal 10, number +/-1, and single-digit number
+10.
5. Fluently calculate combinations within 10.
6. Represent and solve addition and subtraction word problems within 10.
Geometry and Measurement
1. Identify common 2-D and 3-D shapes and their attributes.
2. Measure items using body parts or other nonstandard units.
Functions and Algebra
1. Identify and extend patterns in numbers and space.
2. Apply commutative property to addition.
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Math Grade Level Benchmarks
Grade 1
Guaranteed Benchmarks for all students
Number and Operations –
1. Extend counting sequence forward and backward, starting at a number between 1
and 120, by 1’s and 10’s.
2. Count by 2 and 5 to 120.
Automatize 100 addition facts up to 20 (10 by 10 grid)
Fluently calculate subtraction facts 1-20.
3. Identify and explain place value to the hundreds.
4. Understand the property of zero in addition and subtraction.
Represent and solve word problems with addition and subtraction.
Geometry and Measurement –
1. Identify the common 2-D and 3-D shapes and their attributes
2. Calculate perimeter of 2-D shapes.
Functions and Algebra
1. Apply patterns of commutative and associative properties to addition and
subtraction
2. Demonstrate understanding of equality between two addition expressions.
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Math Grade Level Benchmarks
Grade 2
Guaranteed Benchmarks for all students
Number and Operations
1. Automatize 100 addition and 100 subtraction facts within 20 (10 by 10 grid).
2. Solve 2-digit addition and subtraction problems using standard procedures
(algorithm) with fluency and place value understanding.
3. Identify and explain place value to the thousands.
4. Work with equal groups of objects to gain foundations for multiplicative
reasoning.
Geometry and Measurement
1. Describe shapes based on their attributes.
2. Calculate perimeter of simple shape when given all lengths or calculate an
unknown length when given the perimeter.
3. Work with time and money.
Functions and Algebra
1. Apply patterns of commutative and associative property to addition (25 + 72=
72+25; 25 + 17 + 5 +33 = 17 + 33 + 25 + 5)
2. Understand the inverse relationship between addition and subtraction.
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Math Grade Level Benchmarks
Grade 3
Guaranteed Benchmarks for all students
Number and Operations
1. Recognize, express and use place value beyond one cycle of three digits and extend
the pattern.
2. Automatize multiplication facts 10 by 10 and fluently calculate division facts 10 by
10.
3. Represent and solve whole number word problems.
4. Fluently execute multi-digit addition and subtraction using standard procedures with
understanding.
5. Fluently estimate and execute 2 digit by1 digit multiplication.
6. Describe fractions as a number on the number line
Geometry and Measurement
1. Efficiently calculate perimeter of any shape, area of a rectangle and volume of a
rectangular prism.
2. Solve problems involving measurement and estimations of intervals of time, liquid
volumes and mass of objects
3. Construct and calculate the volume of a rectangular prism with cubes.
Functions and Algebra
1. Apply patterns of distributive (145 x 2 = 100x2 + 40x2 + 5x2), commutative and
associative properties to addition, subtraction and multiplication operations.
2. Demonstrate understanding of equality between two expressions (any combination of
addition, subtraction and multiplication).
Data, Statistics and Probability
1. Represent and interpret data
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Math Grade Level Benchmarks
Grade 4
Guaranteed Benchmarks for all students
Number and Operations
1. Automatize multiplication and division facts 12 by 12.
2. Recognize, express and use place value for any number of cycles.
3. Use place value and properties of operations to perform multi-digit arithmetic
4. Fluently execute 2 digit by 2 digit multiplication and 3 digit by 1 digit division
using standard procedures (algorithm).
5. Use the four operations with whole numbers to solve problems.
6. Determine multiples and factors of whole numbers.
7. Automatize and apply divisibility rules for 2, 4, 5, 10.
8. Find equivalent fractions, order fractions and convert to decimal for 1/2, 1/4, 1/5,
1/10, 1/100.
Geometry and Measurement
1. Use multiplication and division to find the dimensions of common shapes. (Given
the length of one side and the total area, calculate the missing side using division)
2. Draw and identify lines and angles and classify shapes by properties of their lines
and angles.
Explain and demonstrate line of symmetry.
Functions and Algebra
1. Apply patterns of distributive, commutative and associative property to addition
(234 + 345; 45 + 89 + 55), subtraction (901 -345; 345 – 123 + 55),
Multiplication (16 x 14; 25 x 45 x 4) and division (345 ÷ 5)
2. Demonstrate understanding of the inverse relationship between multiplication and
division.
Data, Statistics, and Probability
1. Represent and interpret data.
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Math Grade Level Benchmarks
Grade 5
Guaranteed Benchmarks for all students
Number and Operations
1. Recognize, represent, order, and compare fractions in the four forms: part to whole
(fractions, probability), comparison of two quantities (ratio), comparison of a quantity
with standard (decimal and percent), and comparison of comparison (proportion).
2. Fluently execute multi-digit by multi-digit multiplication and division including
decimals using standard procedures
3. Know and apply divisibility rules (3, 6, 8, and 9,) and prime factorization to find
greatest common factor (GCF) and lowest common denominator (LCD).
4. Execute all operations on fractions (addition, subtraction, multiplication, and
division).
Geometry and Measurement
1. Know, relate, and apply formulas for perimeter and area of common figures
(triangles and polygons(? Should be rectangles only))
2. Graph points on a coordinate plane in first quadrants.
3. Classify polygons based on their attributes
Functions and Algebra
1. Know and apply reversibility of operations (addition and subtraction, multiplication
and division).
2. Use properties of numbers to calculate efficiently (e.g. 4 x 8 x 5 x 3 x 2- compatible
numbers, understanding and applying cross simplification of fraction operations).
Data, Statistics, and Probability
1. Calculate mean, median and mode and state range.
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Math Grade Level Benchmarks
Grade 6
Guaranteed Benchmarks for all students
Number and Operations
1. Fluently operate on integers (addition, subtraction, multiplication, and division)
with understanding.
2. Express a number in exponential form (including scientific notation), rules of
exponents.
3. Find, express, and use the concept of rate of change (increase, decrease, scale
factor, graphing, similarity)
Geometry and Measurement
1. Know and apply formulas for perimeter and area of circles, triangles and derived
figures (combined and extended figure).
2. Calculate surface area and volume of prisms.
3. Graph points on a coordinate plane in all quadrants.
Functions and Algebra
1. Recognize, express, and evaluate simple linear relationships (e.g. linear
equations—from graphical, tabular, numerical, and algebraic forms) and apply the
concept of linear relationship.
Data, Statistics, and Probability
1. Analyze and interpret data in terms of center, spread, and overall shape.
2. Decide when mean, median, or mode best represent data set.
3. Summarize and describe distributions.
4. Decide when mean, median or mode best represents data set
5. Summarize and describe distributions.
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Math Grade Level Benchmarks
Grade 7
Guaranteed Benchmarks for all students
Number and Operations
1. Add, subtract, multiply, and divide algebraic expressions with rational coefficients.
2. Translate a written phrase and/or word problem into an algebraic expression or
equation.
Geometry and Measurement
1. Calculate the area of composite, two-dimensional figures and the surface area and
volume of three-dimensional figures.
2. Understand and apply concepts of congruence and similarity (apply scale factor in
linear, area, and volume).
3. Dilate, translate, rotate, and reflect two-dimensional figures and describe how these
transformations affect congruence and similarity.
4. Write and solve equations involving properties of sides and angles of geometric
figures (e.g. vertical, complementary, supplementary, adjacent, interior/exterior,
and parallel lines cut by a transversal).
Functions and Algebra
1. Solve one-variable equations with rational coefficients and constants.
Data, Statistics, and Probability
1. Calculate simple probability (including from geometric figure).
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Math Grade Level Benchmarks
Grade 8
Guaranteed Benchmarks for all students
Number and Operations
1. Add, subtract, multiply, and divide numeric and algebraic expressions with real
coefficients.
Geometry and Measurement
1. Apply and extend the concepts of transformations to include compositions.
2. Understand the relationship of sides and angles in triangles (e.g., special right
triangles, Pythagorean Theorem, triangle inequality theorem).
3. Calculate the surface area and volume of cylinders, spheres, and cones.
Functions and Algebra
1. Solve one-variable equations with real coefficients and constants.
2. Analyze and model linear functions as graphs, tables, and equations and apply them
to real-world problems.
3. Solve systems of linear equations by graphing.
4. Identify linear and non-linear functions
Data, Statistics, and Probability
1. Model real-life data on scatter plots
2. Identify correlations.
3. Use lines of best fit to make predictions.
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4. Cornerstone Assessments
Evidence of achieving grade level benchmarks
Grade K
Guaranteed Benchmarks for all students
Number and Operations
7. Count by ones, forward and backward, starting at a number between 1 and
100.
8. Count by 10 and 5 to 100.
9. Automatize the integration of number symbol, cluster, value, and name to
numbers up to 10 (able to decompose the number into its components).
10. Automatize combinations that equal 10, number +/-1, and single-digit number
+10.
11. Fluently calculate combinations within 10.
12. Represent and solve addition and subtraction word problems within 10.
Geometry and Measurement
3. Identify common 2-D and 3-D shapes and their attributes.
4. Measure items using body parts or other nonstandard units.
Functions and Algebra
3. Identify and extend patterns in numbers and space.
4. Apply commutative property to addition.
These benchmarks are evident by students being able to:
Number and Operations
 Identify and construct sets when given the number symbols 1-10.
 Read, write and compare numbers to 20.
 Recognize and name the number clusters 0-10.
 Orally state the missing addend in a sum of 10. “What goes with 8 to make 10?” (9 facts)
 Orally state the sum of 10 plus a single digit number. (18 facts)
 Orally state sums of addition facts with sums 2- 9. (36 facts)
 Orally state one more from any number within 50.
 Orally state one less from any number within 50.
 Represent addition/subtraction problems with manipulatives, drawings and/or equations.
Geometry and Measurement
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Create or draw given shapes.
o 2-D: circle, square, triangle, rectangle
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o 3-D: cube, cone, cylinder, sphere
Identify some basic attributes of the shape:
o Number of sides
o Number of vertices/“corners”
o Curved or straight lines
Compose simple shapes to form larger shapes
Demonstrate the inverse relationship that a larger unit will result in a smaller number
representing the measurement.
Algebra and Functions
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Identify and extend patterns in numbers (2 + 1; 22 + 1; 42 + 1) and space (floor patterns,
quilt patterns, etc.)
Apply commutative property to addition (2 + 8 = 8 + 2).
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Grade 1
Guaranteed Benchmarks for all students
Number and Operations –
5. Extend counting sequence forward and backward, starting at a number between 1
and 120, by 1’s and 10’s.
6. Count by 2 and 5 to 120.
Automatize 100 addition facts up to 20 (10 by 10 grid)
Fluently calculate subtraction facts 1-20.
7. Identify and explain place value to the hundreds.
8. Understand the property of zero in addition and subtraction.
Represent and solve word problems with addition and subtraction.
Geometry and Measurement –
3. Identify the common 2-D and 3-D shapes and their attributes
4. Calculate perimeter of 2-D shapes.
Functions and Algebra
3. Apply patterns of commutative and associative properties to addition and
subtraction
4. Demonstrate understanding of equality between two addition expressions.
These benchmarks are evident by students being able to:
Number and Operations
 Automatize addition facts up to 20, orally in 2 seconds each or written in 3 minutes per
100 facts.
 Demonstrate place value understanding of 2 digit numbers
o Build and write a 2 digit number with base ten materials or Cuisenaire rods
o Identify and explain the value of each digit
o Write 2 digit numbers in expanded notation.
o Read and write numbers within 99.
 Order a set of non-sequential numbers, 1-100 from least to greatest.
Geometry and Measurement
 Identify the common shapes by name and attribute.
o 2-D: hexagon, rhombus, trapezoid
o 3-D: rectangular prisms
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Create or draw the shape.
Identify some basic attributes of the shape.
o Sides
o Angles
Calculate the perimeter
o Given a simple figure and measurements
o Given Cuisenaire Rods, other manipulatives or graph paper, to construct the shape
Construct a rectangle with a given perimeter.1
Algebra and Functions
 State and explain the commutative property when given a simple addition fact.
 Explain two ways to solve a problem using the associative property when given 3
addends (3 + 4 + 7 = 3 + 7 + 4).
 Solve two expressions with one missing addend to show understanding of equality
o (5 + 3 = 6 + ___)
 Write two expressions that show equality using addition.
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Grade 2
Guaranteed Benchmarks for all students
Number and Operations
5. Automatize 100 addition and 100 subtraction facts within 20 (10 by 10 grid).
6. Solve 2-digit addition and subtraction problems using standard procedures
(algorithm) with fluency and place value understanding.
7. Identify and explain place value to the thousands.
8. Work with equal groups of objects to gain foundations for multiplicative
reasoning.
Geometry and Measurement
4. Describe shapes based on their attributes.
5. Calculate perimeter of simple shape when given all lengths or calculate an
unknown length when given the perimeter.
6. Work with time and money.
Functions and Algebra
3. Apply patterns of commutative and associative property to addition (25 + 72=
72+25; 25 + 17 + 5 +33 = 17 + 33 + 25 + 5)
4. Understand the inverse relationship between addition and subtraction.
These benchmarks are evident by students being able to:
Number and Operations
 Automatize subtraction facts, orally in 2 seconds each or written in 3 minutes per 100
facts.
 Respond accurately to a mix of 100 addition and subtraction facts written in 5 minutes.
 Solve 2-digit addition and subtraction problems using the standard procedure and
demonstrate understanding by solving it a second way.
 Demonstrate place value understanding of 3-digit numbers
o Build and write a 3 digit number with base ten materials, Cuisenaire Rods or
representations
o Identify and explain the value of each digit
o Write in expanded notation
o Read and write numbers within 99.
 Order a set of non-sequential numbers, 1-1000 from least to greatest.
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Geometry and Measurement
 Calculate the perimeter
o Given one side of an equilateral triangle, rhombus, or regular hexagon.
o Given the total perimeter and one side of a rectangle.
 Construct a figure given the total perimeter and one side using a standard unit of inches.
 Work with time and money to apply number operations and concepts.
Algebra and Functions
 State and explain the commutative property when given a 2-digit addition fact.
 Explain 2 ways to solve a problem with three 2-digit addends using the associative
property.
 Solve two expressions of equality with a missing addend or subtrahend (12 – __ = 3 + 5)
 Write two expressions that show equality using addition and a subtraction expression.
 Write an addition equation that is the inverse of a subtraction equation; write a
subtraction equation that is the inverse of an addition equation.
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Grade 3
Guaranteed Benchmarks for all students
Number and Operations
7. Recognize, express and use place value beyond one cycle of three digits and extend
the pattern.
8. Automatize multiplication facts 10 by 10 and fluently calculate division facts 10 by
10.
9. Represent and solve whole number word problems.
10. Fluently execute multi-digit addition and subtraction using standard procedures with
understanding.
11. Fluently estimate and execute 2 digit by1 digit multiplication.
12. Describe fractions as a number on the number line
Geometry and Measurement
4. Efficiently calculate perimeter of any shape, area of a rectangle and volume of a
rectangular prism.
5. Solve problems involving measurement and estimations of intervals of time, liquid
volumes and mass of objects
6. Construct and calculate the volume of a rectangular prism with cubes.
Functions and Algebra
3. Apply patterns of distributive (145 x 2 = 100x2 + 40x2 + 5x2), commutative and
associative properties to addition, subtraction and multiplication operations.
4. Demonstrate understanding of equality between two expressions (any combination of
addition, subtraction and multiplication).
Data, Statistics and Probability
2. Represent and interpret data
These benchmarks are evident by students being able to:
Number and Operations
 Orally read numbers from 1,000 to 999,999.
 Write numbers from 1,000 to 999,999 in standard form.
 Identify the digit's value and place for numbers from 1,000 to 999,999.
 Count forward or backwards by any multiple of 10 starting at any number between 1000
and 999,999.
 Express multiplication facts (10 X10) orally (2 seconds) and/or written (3 seconds).
 Demonstrate and explain the standard procedure for addition and subtraction of multidigit numbers.
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Demonstrate and explain the standard procedure for 2 digit by 1 digit multiplication.
Geometry and Measurement
 Find the perimeter of a simple figure given the measurements of the sides and the
formula.
 Find the area of a rectangle given its measurements and the formula.
 Construct, measure, and calculate the perimeter of a simple figure.
 Construct, measure, and calculate the area of a rectangle.
 Construct a figure with a given perimeter.
 Construct all possible rectangles with a given area.
 Construct, measure, and calculate the volume of a rectangular prism with cubes.
 Construct all possible rectangular prisms with a given volume using cubes.
Algebra and Functions
 Compute a 2 digit by 1 digit multiplication problem, using the distributive property (28 x
7 = (20 + 8) x 7).
 Compute addition problems of 3 or more numbers using the associate property (ex.
making 10s strategy)

Explain an efficient method to add a column of multi-digit numbers.
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Grade 4
Guaranteed Benchmarks for all students
Number and Operations
9. Automatize multiplication and division facts 12 by 12.
10. Recognize, express and use place value for any number of cycles.
11. Use place value and properties of operations to perform multi-digit arithmetic
12. Fluently execute 2 digit by 2 digit multiplication and 3 digit by 1 digit division
using standard procedures (algorithm).
13. Use the four operations with whole numbers to solve problems.
14. Determine multiples and factors of whole numbers.
15. Automatize and apply divisibility rules for 2, 4, 5, 10.
16. Find equivalent fractions, order fractions and convert to decimal for 1/2, 1/4, 1/5,
1/10, 1/100.
Geometry and Measurement
3. Use multiplication and division to find the dimensions of common shapes. (Given
the length of one side and the total area, calculate the missing side using division)
4. Draw and identify lines and angles and classify shapes by properties of their lines
and angles.
Explain and demonstrate line of symmetry.
Functions and Algebra
3. Apply patterns of distributive, commutative and associative property to addition
(234 + 345; 45 + 89 + 55), subtraction (901 -345; 345 – 123 + 55),
Multiplication (16 x 14; 25 x 45 x 4) and division (345 ÷ 5)
4. Demonstrate understanding of the inverse relationship between multiplication and
division.
Data, Statistics, and Probability
2. Represent and interpret data.
These benchmarks are evident by students being able to:
Number and Operations
 Count forward or backward by any multiple of 10 starting at any number between 1,000
and 1,000,000
 Express multiplication facts (12 X12) orally (2 seconds) and written (3 seconds).
 Demonstrate and explain the standard procedure for 2 digit by 2-digit multiplication
either written or by observation.
 Demonstrate and explain the standard procedure for 3 digit by 1 digit division either
written or by observation.
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Find all factor pairs for a whole number up to 100.
Determine whether a given whole number, from 1 – 100, is a multiple of a given 1-digit
number.
Generate a four, five or six digit number that is divisible by 2, 4, 5 and 10.
Generate a four-digit number that is not divisible by 2, 4, 5 and 10.
Identify equivalent fractions and a decimal equivalent for the benchmark fractions, 1/100,
1/10, 1/5, 1/4, 1/2.
Represent and solve multi-step word problems using any combination of the four basic
operations.
Geometry and Measurement
 Calculate the missing sides of a rectangle when given the length of one side and the total
area.
 Create all the rectangles with a given perimeter and solve for the areas.
 Calculate the volume of a rectangular prism when given the dimensions and the formula.
 Create all possible rectangular prisms given the total volume.
 Draw all lines of symmetry of a given figure.
 Draw a 2-dimension figure with at least one line of symmetry.
 Draw points, lines, line segments, rays, angles (right, acute, obtuse) and perpendicular
and parallel lines. Identify these in 2 dimensional figures.
Algebra and Functions
 Solve 2 digit by 2-digit multiplication problem using the distributive property. (partial
products)
 Describe the pattern in a series of numbers that are divisible by any pairing of the factors
of 2, 4, 5 or 10.
 Explain an efficient method (through use of the associate property) to add a column of
multi-digit numbers.
 Find an unknown factor given the product and a known factor.
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Grade 5
Guaranteed Benchmarks for all students
Number and Operations
5. Recognize, represent, order, and compare fractions in the four forms: part to whole
(fractions, probability), comparison of two quantities (ratio), comparison of a quantity
with standard (decimal and percent), and comparison of comparison (proportion).
6. Fluently execute multi-digit by multi-digit multiplication and division including
decimals using standard procedures
7. Know and apply divisibility rules (3, 6, 8, and 9,) and prime factorization to find
greatest common factor (GCF) and lowest common denominator (LCD).
8. Execute all operations on fractions (addition, subtraction, multiplication, and
division).
Geometry and Measurement
4. Know, relate, and apply formulas for perimeter and area of common figures
(triangles and polygons(? Should be rectangles only))
5. Graph points on a coordinate plane in first quadrants.
6. Classify polygons based on their attributes
Functions and Algebra
3. Know and apply reversibility of operations (addition and subtraction, multiplication
and division).
4. Use properties of numbers to calculate efficiently (e.g. 4 x 8 x 5 x 3 x 2- compatible
numbers, understanding and applying cross simplification of fraction operations).
Data, Statistics, and Probability
2. Calculate mean, median and mode and state range.
These benchmarks are evident by students being able to:
Number and Operations
 Compute factor and quotient in multi-digit multiplication and division problems using
standard algorithms.
 Find the prime factorization string of a number with multiple factors.
 Given a picture of a shaded shape or a divided set, label with correct fraction
 Draw a representation of a fraction
 Find probability of selecting a certain number of items from a set
 Place given fractions, decimals, percents on a number line.
 Order a given list of fractions, decimals, and percents from least to greatest.
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Apply prime factorization, divisibility rules, and LCD to add and subtract fractions.
Find the prime factorization string when given a number with multiple factors.
Apply divisibility rules to simplify and multiply fractions.
Given a picture of a shaded shape or a divided set, label with correct fraction and vice
versa; also find probability of selecting certain items from set.

Use equivalent fraction as a strategy for add and subtract fractions.

Construct and solve equations from story problems containing fraction operations, and
write story problems around fraction equations with all four operations.
Geometry and Measurement
 Calculate the perimeter of a rectangle when provided the area and length of one side that
is expressed as a fraction.
 Find the width of a rectangle given the length and total perimeter (using fractions as
dimensions).
 Given the side lengths of a rectangle or base and height of a triangle (where each side is
greater than 99, or given in fraction or decimal form), calculate the area and perimeter in
a context of a story problem.
o Multiple figures (e.g. many packages to the post office with combined girdle of
360).
o Decimals (e.g., Xerox machine accepts x size paper, my drawing is 18 x 26, what
reduction should I make?).
 Calculate area of a shaded section (obvious fraction) of a simple figure (triangle, square)
 Calculate the volume of a 3D figure with correct units labeled, given necessary side
lengths.
 Calculate the other sides of a simple figure larger than 99 square units with one side less
than 10 units, in fraction or decimal form, when given the area.
 Find all dimensions (factor pairs) possible to form a rectangle and designate the pair,
which provides the greatest area when given the total perimeter.
 Calculate volume ???
Algebra and Functions
 Solve for one unknown quantity in a one operation equation
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Grade 6
Guaranteed Benchmarks for all students
Number and Operations
4. Fluently operate on integers (addition, subtraction, multiplication, and division)
with understanding.
5. Express a number in exponential form (including scientific notation), rules of
exponents.
6. Find, express, and use the concept of rate of change (increase, decrease, scale
factor, graphing, similarity)
Geometry and Measurement
4. Know and apply formulas for perimeter and area of circles, triangles and derived
figures (combined and extended figure).
5. Calculate surface area and volume of prisms.
6. Graph points on a coordinate plane in all quadrants.
Functions and Algebra
6. Recognize, express, and evaluate simple linear relationships (e.g. linear
equations—from graphical, tabular, numerical, and algebraic forms) and apply the
concept of linear relationship.
Data, Statistics, and Probability
1. Analyze and interpret data in terms of center, spread, and overall shape.
7. Decide when mean, median, or mode best represent data set.
8. Summarize and describe distributions.
These benchmarks are evident by students being able to:
Number and Operations
 Automatize
facts using
operations).
9. Decide when
mean,integers
median (all
or mode
best represents data set
 Given a story problem containing positive and negative integers, write and solve an
10. Summarize and describe distributions.
equation.
 Write a story problem based on an equation.
 Place negative integers on a number line.
 Express large numbers in exponential form and scientific form and vice versa
 What number should I multiply 128 by to get a perfect square? The new number is a
square of what?/cube Wording?
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Geometry and Measurement
 Calculate area and perimeter of circles, triangles and combined simple labeled figures.
 Given two similar figures with corresponding measurement (e.g., base and area on both),
find remaining measurements (e.g., perimeter and height).
 Create a smaller scale figure based on larger diagram using grid paper.
 Solve real world and mathematical problem involving area, surface area and volume
Algebra and Functions
 Solve for unknown quantities in equations with two or more operations.
 Apply distributive property in multiplication of a whole number by a mixed number.
 Extend mathematical patterns and write a rule, then solve for the nth term; complete a
table based on a given rule. (e.g. -2, 4, -8, 16, -32…; t = -2(n-1))
 Graph an equation by plotting points and describing trends when given a data set
occurring over time.
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Grade 7
Guaranteed Benchmarks for all students
Number and Operations
3. Add, subtract, multiply, and divide algebraic expressions with rational coefficients.
4. Translate a written phrase and/or word problem into an algebraic expression or
equation.
Geometry and Measurement
5. Calculate the area of composite, two-dimensional figures and the surface area and
volume of three-dimensional figures.
6. Understand and apply concepts of congruence and similarity (apply scale factor in
linear, area, and volume).
7. Dilate, translate, rotate, and reflect two-dimensional figures and describe how these
transformations affect congruence and similarity.
8. Write and solve equations involving properties of sides and angles of geometric
figures (e.g. vertical, complementary, supplementary, adjacent, interior/exterior,
and parallel lines cut by a transversal).
Functions and Algebra
2. Solve one-variable equations with rational coefficients and constants.
Data, Statistics, and Probability
2. Calculate simple probability (including from geometric figure).
These benchmarks are evident by students being able to:
Number and Operations
 Use a variable in place of a word, phrase or situation.
 Translate words into simple numerical and algebraic expressions.
 Translate expressions into words.
 Translate a written phrase into an algebraic expression and solve when this expression is
part of an equation.
 Represent the area model through the use of algebra tiles.
 Demonstrate an understanding of like terms through the use of manipulatives.
 Accurately describe coefficient, constant, and like terms through oral assessment and
modeling the operations.
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Geometry and Measurement
 Determine the proportional relationship between similar shapes in terms of dimensions,
area, surface area, or volume (by constructing shapes that are decreased or increased in
size by a common factor).
 Draw three triangles with the same perimeter with three different areas. (Pythagorean
theorem). use this as assessment question-determine one side
 Make a model of area, surface area and volume through the use of manipulatives. Is this
correct?
 Construct various shapes given the same area.
 Make 3-D shapes of a certain surface area.
 Determine the area of the rectangle, given its perimeter and one side length.
 Identify the rotational symmetry and the relationship between the interior angles of a
trapezoid or parallelogram with a diagonal.
Algebra and Functions:
 Translate words into simple numerical and algebraic expressions.
 Translate expressions into words.
 Accurately describe coefficient, constant, like terms through recall and oral assessment
and though modeling the operations.
 Demonstrate knowledge of slope through dilation.
 Solve multi-step equations with algebra tiles.
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Grade 8
Guaranteed Benchmarks for all students
Number and Operations
2. Add, subtract, multiply, and divide numeric and algebraic expressions with real
coefficients.
Geometry and Measurement
4. Apply and extend the concepts of transformations to include compositions.
5. Understand the relationship of sides and angles in triangles (e.g., special right
triangles, Pythagorean Theorem, triangle inequality theorem).
6. Calculate the surface area and volume of cylinders, spheres, and cones.
Functions and Algebra
5. Solve one-variable equations with real coefficients and constants.
6. Analyze and model linear functions as graphs, tables, and equations and apply them
to real-world problems.
7. Solve systems of linear equations by graphing.
8. Identify linear and non-linear functions
Data, Statistics, and Probability
4. Model real-life data on scatter plots
5. Identify correlations.
6. Use lines of best fit to make predictions.
These benchmarks are evident by students being able to:
Number and Operations
 Accurately place a set of real numbers on a number line given a set interval.
Geometry and Measurement:
 Transform using graph paper.
 Display knowledge of transformations (translation, reflection, rotation, and dilation)
through the use of tessellations.
 Transform a shape in the following ways:
o a horizontal rotation
o a scale factor of two
o a reflection.
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

4. Rotate a shape 90 degrees into each successive quadrant from quadrant 1, dilated by a
given factor.
Given an inscribed regular polygon inside a circle, determine the area and perimeter of
the polygon.
Algebra and Functions
 Given an equation of a line such as y=x, explain the behavior of lines written in point
slope form and how changing values dilates, reflects, and translates the graph.
 Graph and explain the effect of stretching, shrinking, and flipping an equation.
 Given a quadratic equation y = x2, understand dilation, translation, and reflection when
changing the values for y – y1 = a(x – x1)2.Wording?
 Convert between the different forms of a linear function (graphical, tabular, equation and
verbal/words)
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Assessments
For the 2010-2011 school, we will be using a mixture of assessments, screening, progress
monitoring and end of year assessments. For the screening and progress monitoring
assessments we will be using AIMSweb assessment system. At the end of the year, we will be
adding our own items to the AIMSweb, to measure the effectiveness of our instruction on the
standards that AIMSweb does not measure or does not have the cognitive complexity.
During May of 2011 the math committee audited AIMSweb assessments and mapped these
items to the grade level benchmarks. As we studied AIMSweb, we found that as the grade
levels increase the gap between what AIMSweb items asked of students was below what the
OSSU curriculum and the common core demanded of students. In the 4th grade AIMSweb, we
determined that there benchmark assessments were a grade level below OSSU curriculum and
at 6th grade it was 2 grade levels below our benchmarks.
For the screening assessments we will be augmenting the administrative procedures to gather
item level information for each student, to support flexible grouping. It has been found with
successful implementation of Response to Instruction, the teachers who do an item level
review of student work and then provide instruction to students in flexible groups have a
greater student achievement.
Please see the following pages of the end of year assessments for each grade.
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