Mathematics is the study of patterns in quantity and space.

Mahesh Sharma

Math Curriculum Document

Orleans Southwest Supervisory Union

Version3.0

May, 2011

Table of Contents

1. Statements of Vision, Mission, and Learning Principles

Vision

Mission

Learning Principles

2. K-12 Enduring Understandings and Essential Questions for Mathematics

K-12 Enduring Understandings

Essential Questions

3. Curriculum Mapping: Course/ Grade Level Benchmarks

4. Cornerstone Assessments

Evidence of Benchmark Obtainment

Grade Level Assessments ………………..………………………………………………………………………………………………. 33

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

  • 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.

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.

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.

3. Curriculum Mapping: Course/ Grade Level Benchmarks


Math Grade Level Benchmarks

Grade K

Math Grade Level Benchmarks

Grade 1


Math Grade Level Benchmarks

Grade 2



Math Grade Level Benchmarks

Grade 3

Math Grade Level Benchmarks

Grade 4


Math Grade Level Benchmarks

Grade 5


Math Grade Level Benchmarks

Grade 6


Math Grade Level Benchmarks

Grade 7


Math Grade Level Benchmarks

Grade 8

4. Cornerstone Assessments

Evidence of achieving grade level benchmarks


Grade K

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

  • Create or drawgiven shapes.
  • 2-D: circle, square, triangle, rectangle
  • 3-D: cube, cone, cylinder, sphere
  • Identify some basic attributes of the shape:
  • Number of sides
  • Number of vertices/“corners”
  • 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

  • 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).

Grade 1


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
  • Build and write a 2 digit number with base ten materials or Cuisenaire rods
  • Identify and explain the value of each digit
  • Write 2 digit numbers in expanded notation.
  • 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.
  • 2-D: hexagon, rhombus, trapezoid
  • 3-D: rectangular prisms
  • Create or draw the shape.
  • Identify some basic attributes of the shape.
  • Sides
  • Angles
  • Calculate the perimeter
  • Given a simple figure and measurements
  • 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 commutativeproperty when given a simple addition fact.
  • Explain two ways to solvea problemusing 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
  • (5 + 3 = 6 + ___)
  • Write two expressions that show equalityusing addition.

Grade 2


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
  • Build and write a 3 digit number with base ten materials, Cuisenaire Rods or representations
  • Identify and explain the value of each digit
  • Write in expanded notation
  • Read and write numbers within 99.
  • Order a set of non-sequential numbers, 1-1000 from least to greatest.

Geometry and Measurement

  • Calculate the perimeter
  • Given one side of an equilateral triangle, rhombus, or regular hexagon.
  • 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.


Grade 3

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 multi-digit numbers.
  • 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.


Grade 4

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.
  • 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.


Grade 5

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.
  • 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 perimeterof 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 sideis greater than99, or given in fraction or decimal form), calculate the area and perimeterin a context of a story problem.
  • Multiple figures (e.g. many packages to the post office with combined girdle of 360).
  • 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 thegreatest area when given the total perimeter.
  • Calculate volume ???

Algebra and Functions

  • Solve for one unknown quantity in a one operation equation


Grade 6

These benchmarks are evident by students being able to:

Number and Operations

  • Automatize factsusingintegers (all operations).
  • Given a story problem containing positive and negative integers, write and solve an 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?/cubeWording?

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.


Grade 7

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.
  • Translateawrittenphrase 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.

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 shapesof 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-stepequations with algebra tiles.


Grade 8

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:
  • a horizontal rotation
  • a scale factor oftwo
  • a reflection.
  • 4. Rotatea 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