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					                                                                      CORRELATION
                                                                             of
                                          the Understanding Numeration PLUS & Understanding Math PLUS programs
                                                                            with
                                                       New York State Math Core Curriculum Standards
                                                                       Grade Seven
                                                                      November 2007

Note: a. The Understanding Math PLUS series of programs consist of 10 programs written for Kindergarten to 10th Grade.

The 10 programs are:
       Understanding Fractions           Understanding Whole Numbers and Integers
       Understanding Probability         Understanding Percent
       Understanding Exponents           Understanding Equations
       Understanding Algebra             Understanding Graphing
       Understanding Numeration
       Understanding Measurement and Geometry

Note: b. The Understanding Numeration software for K to 3 is set up so that the teacher selects items in the following order:
Concept .. from 5 concepts .. Counting, Comparing & Ordering, Place Value, Operations and Problem Solving.
Skill .. chosen from the list of specific learning expectations
Level .. indicates the levels of development for Kindergarten to 3rd grade.

                 Level                Upper Range of Number
                 A                    10
                 B                    20
                 C                    100
                 D                    1000

Lesson .. 250 lessons are sequenced to build understanding of concepts.
A detailed Lesson Synopsis on the website www.neufeldmath.com to assist the teacher by stating the lesson contents but also by giving lesson suggestions.
Worksheet .. off computer worksheets are selected from the CD by a code.
Note: c. The remaining 9 Understanding Math programs for 4th to 10th grade are set up so that they can be used in a variety of teaching and learning environments
ranging from a teacher centered approach with 1 computer to a student centered lab approach. The lessons can also be used in remediation, tutorial, intervention,
resource, fast-tracking.
Each topic has:
..an interactive concept introduction, usually with a variety of graphic approaches.
..a number of particular examples
..practice questions with random questions but particular feedback
..a topic test with random questions and tracking
..off computer worksheets selected from the website .. www.neufeldmath.com




Neufeld Learning Systems Inc. November 2007                                                                                                                         1
Source: Mathematics Core Curriculum MST Standard 3
Problem Solving Strand

Students will build new mathematical knowledge through problem solving.
Students will solve problems that arise in mathematics and in other contexts.
Students will apply and adapt a variety of appropriate strategies to solve problems.
Students will monitor and reflect on the process of mathematical problem solving.

                                      Strand                                                                 Neufeld Learning Systems Inc.
                                                                                                              Understanding Math PLUS
                                                                                                                       Lessons
7.PS.1 Use a variety of strategies to understand new
       mathematical content and to develop more efficient methods

7.PS.2 Construct appropriate extensions to problem situations

7.PS.3 Understand and demonstrate how written symbols                                  Understanding Algebra
       represent mathematical ideas                                                    Topic 4. Patterns, Formulas, Substitution
                                                                                       Expressions, Terms, Variables
                                                                                       Definitions
                                                                                       Summary
                                                                                       Patterns to Formulas
                                                                                       Example... Hockey Standings
                                                                                       Example... Counting Money
                                                                                       Example... Angles in a Polygon

7.PS.4 Observe patterns and formulate generalizations

7.PS.5 Make conjectures from generalizations

7.PS.6 Representproblem situations verbally, numerically,                              Understanding Algebra
       algebraically, and graphically                                                  Topic 4. Patterns, Formulas, Substitution
                                                                                       Expressions, Terms, Variables
                                                                                       Definitions
                                                                                       Summary
                                                                                       Patterns to Formulas
                                                                                       Example... Hockey Standings
                                                                                       Example... Counting Money
                                                                                       Example... Angles in a Polygon

7.PS.7 Understand that there is no one right way to solve
       mathematical problems but that different methods haveadvantages and
       disadvantages



Neufeld Learning Systems Inc. November 2007                                                                                                  2
Source: Mathematics Core Curriculum MST Standard 3
                                      Strand                                                      Neufeld Learning Systems Inc.
                                                                                                   Understanding Math PLUS
                                                                                                            Lessons
7.PS.8 Understand how to break a complex problem into simpler
       parts or use a similar problem type to solve a problem
7.PS.9 Work backwards from a solution

7.PS.10 Use proportionality to model problems                               Understanding Percent
                                                                            Topic 4. Ratios and Proportions
                                                                            What is a Proportion?
                                                                            Proportions
                                                                            Example 1
                                                                            Example 2 – Lemonade
                                                                            Example 3 – Marbles
                                                                            Example 4 – Trout

7.PS.11 Work in collaboration with others to solve problems
7.PS.12 Interpret solutions within the given constraints of a
       problem

7.PS.13 Set expectations and limits for possible solutions

7.PS.14 Determine information required to solve the problem

7.PS.15 Choose methods for obtaining required information

7.PS.16 Justify solution methods through logical argument

7.PS.17 Evaluate the efficiency of different representations of a problem




Neufeld Learning Systems Inc. November 2007                                                                                       3
Source: Mathematics Core Curriculum MST Standard 3
Reasoning and Proof Strand

Students will recognize reasoning and proof as fundamental aspects of mathematics.
Students will make and investigate mathematical conjectures.
Students will develop and evaluate mathematical arguments and proofs.
Students will select and use various types of reasoning and methods of proof.

                                     Strand                                                          Neufeld Learning Systems Inc.
                                                                                                      Understanding Math PLUS
                                                                                                               Lessons
7.RP.1 Recognize that mathematical ideas can be supported by a variety
of strategies

                                                                                  Understanding Math PLUS
7.RP.2 Use mathematical strategies to reach a conclusion                          All Sections


7.RP.3 Evaluate conjectures by distinguishing relevant from
irrelevant information to reach a conclusion or make appropriate estimates

7.RP.4 Provide supportive arguments for conjectures

7.RP.5 Develop, verify, and explain an argument, using                            Understanding Math PLUS
appropriate mathematical ideas and language                                       All Sections

7.RP.6 Support an argument by using a systematic approach to
test more than one case



7.RP.7 Devise ways to verify results or use counterexamples to refute incorrect
       statements

7.RP.8 Apply inductive reasoning in making and supporting
mathematical conjectures




Neufeld Learning Systems Inc. November 2007                                                                                          4
Source: Mathematics Core Curriculum MST Standard 3
Communication Strand

Students will organize and consolidate their mathematical thinking through communication.
Students will communicate their mathematical thinking coherently and clearly to peers, teachers, and others.
Students will use the language of mathematics to express mathematical ideas precisely.

                                     Strand                                                                    Neufeld Learning Systems Inc.
                                                                                                                Understanding Math PLUS
                                                                                                                         Lessons
7.CM.1 Provide a correct, complete, coherent, and clear rationale for
       thought process used in problem solving



7.CM.2 Provide an organized argument which explains rationale for
       strategy selection

7.CM.3 Organize and accurately label work

7.CM.4 Share organized mathematical ideas through the manipulation of               Understanding Math PLUS
       objects, numerical tables, drawings, pictures, charts, graphs,               All Sections
       tables, diagrams, models and symbols in written and verbal form

7.CM.5 Answer clarifying questions from others

7.CM.6 Analyze mathematical solutions shared by others



7.CM.7 Compare strategies used and solutions found by others in relation
       to their own work

7.CM.8 Formulate mathematical questions that elicit, extend, or challenge
       strategies, solutions, and/or conjectures of others

7.CM.9 Increase their use of mathematical vocabulary and language when              Understanding Math PLUS
       communicating with others                                                    All Sections

7.CM.10 Use appropriate language, representations, and terminology
        when describing objects, relationships, mathematical solutions, and
        rationale

7.CM.11 Draw conclusions about mathematical ideas through decoding,
        comprehension, and interpretation of mathematical visuals,symbols, and
        technical writing

Neufeld Learning Systems Inc. November 2007                                                                                                    5
Source: Mathematics Core Curriculum MST Standard 3
Connections Strand

Students will recognize and use connections among mathematical ideas.
Students will understand how mathematical ideas interconnect and build on one another to produce a coherent whole.

                                    Strand                                                               Neufeld Learning Systems Inc.
                                                                                                          Understanding Math PLUS
                                                                                                                   Lessons
7.CN.1 Understand and make connections among multiple representations
of the same mathematical idea



7.CN.2   Recognize connections between subsets of mathematical ideas

7.CN.3   Connect and apply a variety of strategies to solve problems             Understanding Math PLUS
                                                                                 All Sections
7.CN.4 Model situations mathematically, using representations to draw
conclusions and formulate new situations


7.CN.5 Understand how concepts, procedures, and mathematical results             Understanding Math PLUS
in one area of mathematics can be used to solve problems in other                All Sections
areas of mathematics

7.CN.6 Recognize and provide examples of the presence of mathematics
in their daily lives




7.CN.7 Apply mathematical ideas to problem situations that develop
outside of mathematics

7.CN.8 Investigate the presence of mathematics in careers and areas of
interest

7.CN.9 Recognize and apply mathematics to other disciplines, areas of
interest, and societal issues




Neufeld Learning Systems Inc. November 2007                                                                                              6
Source: Mathematics Core Curriculum MST Standard 3
Representation Strand

Students will create and use representations to organize, record, and communicate mathematical ideas
Students will select, apply, and translate among mathematical representations to solve problems.
Students will use representations to model and interpret physical, social, and mathematical phenomena.

                                      Strand                                                            Neufeld Learning Systems Inc.
                                                                                                          Understanding Math PLUS
                                                                                                                  Lessons
7.R.1 Use physical objects, drawings, charts, tables, graphs, symbols,             Understanding Math PLUS
       equations, or objects created using technology as representations           Understanding Algebra
                                                                                   Understanding Equations
                                                                                   Understanding Graphing
                                                                                   ALL SECTIONS
7.R.2 Explain, describe, and defend mathematical ideas using
     representation
7.R.3 Recognize, compare, and use an array of representational forms
7.R.4 Explain how different representations express the same relationship

7.R.5 Use standard and non-standard representations with accuracy and
detail

7.R.6 Use representations to explore problem situations
7.R.7 Investigate relationships between different representations and
their impact on a given problem
7.R.8 Use representation as a tool for exploring and understanding
mathematical ideas
7.R.9 Use mathematics to show and understand physical phenomena                    Understanding Fractions
(e.g., make and interpret scale drawings of figures or scale models of objects)    Topic 7. Ratios and Proportions
                                                                                   What is a Proportion?
                                                                                   Proportions
                                                                                   Example 1
                                                                                   Example 2 - Lemonade
                                                                                   Example 3 - Marbles
                                                                                   Example 4 - Scale Drawing

7.R.10 Use mathematics to show and understand social phenomena
(e.g., determine profit from sale of yearbooks)
7.R.11 Use mathematics to show and understand mathematical phenomena               Understanding Algebra
         (e.g., use tables, graphs, and equations to show a pattern underlying a   Topic 1. Introduction to Algebraic Thinking
         function)                                                                 Function Machine
                                                                                   Introduction
                                                                                   Find Output
                                                                                   Find Input
                                                                                   Find The Rule
                                                                                    Rules 1, 2, 3, 4
Neufeld Learning Systems Inc. November 2007                                                                                             7
Source: Mathematics Core Curriculum MST Standard 3
Number Sense and Operations Strand

Students will understand numbers, multiple ways of representing numbers, relationships among numbers, and number systems.
Students will understand meanings of operations and procedures, and how they relate to one another.
Students will compute accurately and make reasonable estimates.

                                     Strand                                                                Neufeld Learning Systems Inc.
                                                                                                            Understanding Math PLUS
                                                                                                                     Lessons
7.N.1 Distinguish between the various subsets of real numbers                     Understanding Whole Numbers and Integers
      (counting/natural numbers, whole numbers, integers, rational numbers, and   Topic 4. The Meaning of Integers
      irrational numbers)                                                         The Integer Line
                                                                                  Opposite Integers
                                                                                  Examples 1, 2
                                                                                  Absolute Values
                                                                                  Examples 1, 2
                                                                                  Comparing Integers
                                                                                  Examples 1, 2, 3, 4
                                                                                  Example Questions
                                                                                  Examples 1, 2, 3, 4, 5, 6
                                                                                  Practice Questions

7.N.2   Recognize the difference between rational and irrational numbers (e.g.,   Understanding Measurement and Geometry
        explore different approximations of π )                                   Topic 3. The Circle
                                                                                  PI... A Special Number
                                                                                  Introduction
                                                                                  How do we Measure Circumference?
                                €                                                 Measuring Circles
                                                                                  Summary

7.N.3   Place rational and irrational numbers (approximations) on a number line
        and justify the placement of the numbers

7.N.4   Develop the laws of exponents for multiplication and division             Understanding Exponents
                                                                                  Topic 3. The Exponent Rules
                                                                                  Multiplication of Powers with the Same Base
                                                                                  Expanding the Exponents
                                                                                  The Pattern
                                                                                  In General
                                                                                  Division of Powers with the Same Base
                                                                                  Expanding the Exponents
                                                                                  The Pattern
                                                                                  In General


Neufeld Learning Systems Inc. November 2007                                                                                                8
Source: Mathematics Core Curriculum MST Standard 3
                                      Strand                                                             Neufeld Learning Systems Inc.
                                                                                                           Understanding Math PLUS
                                                                                                                   Lessons
7.N.5   Write numbers in scientific notation                                   Understanding Exponents
                                                                               Topic 4. Scientific Notation
7.N.6   Translate numbers from scientific notation into standard form          Why Use Scientific Notation?
                                                                               Scientific Notation for Large Numbers
7.N.7   Compare numbers written in scientific notation                         Introduction
                                                                               Chart
                                                                               The Rule
                                                                               The Steps
                                                                               Scientific Notation for Small Numbers
                                                                               Introduction
                                                                               Chart
                                                                               The Steps
                                                                               Examples
                                                                               1. Number Question
                                                                               2. Park Question
                                                                               3. Sun Question
                                                                               4. Kitchen Question
                                                                               Practice Questions

7.N.8   Find the common factors and greatest common factor of two or           Understanding Fractions
        more numbers                                                           Topic 3. Equivalent Fractions
                                                                               Greatest Common Factor
                                                                               12 and 18
                                                                               30 and 40
                                                                               70 and 42

7.N.9   Determine multiples and least common multiple of two or more numbers

7.N.10 Determine the prime factorization of a given number and write in
       exponential form

7.N.11 Simplify expressions using order of operations Note: Expressions        Understanding Whole Numbers and Integers
may include absolute value and/or integral exponents greater than 0.           Topic 9. Order of Operations
                                                                               Why use Order of Operations?
                                                                               BEDMAS
                                                                               Example Questions
                                                                               Examples 1, 2, 3, 4, 5, 6, 7, 8, 9, 10
                                                                               Word Problems
                                                                               Shipping
                                                                               Babysitting
                                                                               Garbage
                                                                               Practice Questions
Neufeld Learning Systems Inc. November 2007                                                                                              9
Source: Mathematics Core Curriculum MST Standard 3
                                     Strand                                                                  Neufeld Learning Systems Inc.
                                                                                                               Understanding Math PLUS
                                                                                                                         Lessons
7.N.12 Add, subtract, multiply, and divide integers                                Understanding Whole Numbers and Integers
                                                                                   Topic 5. Adding Integers
7.N.13 Add and subtract two integers (with and without the use of a number line)   In This Topic
                                                                                   Elevators... An Introduction to Addition
                                                                                    Examples 1, 2, 3, 4
                                                                                    Summary... Using Elevators
                                                                                   Markers... An Introduction to Addition
                                                                                    Opposites
                                                                                    Examples 1, 2, 3, 4
                                                                                   Going for a Walk... An Introduction to Addition
                                                                                    Examples 1, 2, 3
                                                                                   Number Line... An Introduction to Addition
                                                                                    Examples 1, 2, 3
                                                                                    Summary... Using a Number Line

                                                                                   Topic 6. Subtracting Integers
                                                                                   In This Topic
                                                                                   Markers... An Introduction to Subtraction
                                                                                    Markers Help Us Understand
                                                                                   Review Opposites
                                                                                    Examples 1, 2, 3, 4, 5, 6, 7, 8
                                                                                    The Pattern
                                                                                   Elevators... An Introduction to Subtraction
                                                                                    Examples 1, 2, 3, 4
                                                                                    Summary... Using Elevators
                                                                                   Summary... Add the Opposite
                                                                                   Example Questions
                                                                                    Example 1 – With Brackets
                                                                                    Example 2 – With Brackets
                                                                                    Example 3 – Meaning of... 2 – 5
                                                                                    Example 4 – Meaning of... -7 – 3
                                                                                    Example 5 – Meaning of... -7 + 9 – 18
                                                                                    Example 6 – Meaning of... -4 – 9 + 2 – 8




Neufeld Learning Systems Inc. November 2007                                                                                                  10
Source: Mathematics Core Curriculum MST Standard 3
                                   Strand                                                                Neufeld Learning Systems Inc.
                                                                                                          Understanding Math PLUS
                                                                                                                   Lessons
                                                                                Understanding Whole Numbers and Integers
                                                                                Topic 7. Multiplying Integers
                                                                                Multiplication Is...
                                                                                Examples 1, 2
                                                                                The Multiplication Table
                                                                                Instructions
                                                                                Patterns
                                                                                Practice 1, 2
                                                                                Order in Multiplication
                                                                                The Multiplication Table
                                                                                Examples 1, 2, 3
                                                                                Summary #1... Signs

                                                                                Topic 8. Dividing Integers
                                                                                Division to Multiplication
                                                                                The Division Table
                                                                                Instructions
                                                                                Patterns
                                                                                Practice
                                                                                The Inverse of Multiplication
                                                                                Examples 1, 2
                                                                                Summary #1... Signs
                                                                                Summary #2... Signs
                                                                                Example Questions
                                                                                Examples 1, 2, 3, 4

7.N.14 Develop a conceptual understanding of negative and zero exponents with   Understanding Exponents
                                                                   -2
       a base of ten and relate to fractions and decimals (e.g., 10 = .01 =     Topic 3. The Exponent Rules
       1/100)                                                                   A Power with Exponent 0
                                                                                Explanation with b; Explanation with a
                                                                                Summary
                                                                                A Power with a NEGATIVE Exponent
                                                                                Method 1: Explanation with b
                                                                                Method 2: Explanation with k
                                                                                Method 3: Bacteria Doubling
                                                                                Summary




Neufeld Learning Systems Inc. November 2007                                                                                              11
Source: Mathematics Core Curriculum MST Standard 3
                                    Strand                                                               Neufeld Learning Systems Inc.
                                                                                                           Understanding Math PLUS
                                                                                                                   Lessons
7.N.15 Recognize and state the value of the square root of a perfect square (up   Understanding Exponents
       to 225)                                                                    Topic 5. Square Roots
                                                                                  Squaring Numbers
7.N.16 Determine the square root of non-perfect squares using a calculator        Square Roots
                                                                                  Radical Signs
                                                                                  Square Roots of Negative Numbers
                                                                                  Example Questions
                                                                                  1. Radicals First
                                                                                  2. The Four Equations
                                                                                  3. Lawn Question
                                                                                  4. Make a Square
                                                                                  Practice Questions

7.N.17 Classify irrational numbers as non-repeating/non-terminating decimals

7.N.18 Identify the two consecutive whole numbers between which the
       square root of a non-perfect square whole number less than 225 lies
       (with and without the use of a number line)


7.N.19 Justify the reasonableness of answers using estimation




Neufeld Learning Systems Inc. November 2007                                                                                              12
Source: Mathematics Core Curriculum MST Standard 3
Algebra Strand

Students will represent and analyze algebraically a wide variety of problem solving situations.
Students will perform algebraic procedures accurately.
Students will recognize, use, and represent algebraically patterns, relations, and functions.

                                      Strand                                                                    Neufeld Learning Systems Inc.
                                                                                                                  Understanding Math PLUS
                                                                                                                          Lessons
7.A.1   Translate two-step verbal expressions into algebraic expressions              Understanding Algebra
                                                                                      Topic 4. Patterns, Formulas, Substitution
                                                                                      Expressions, Terms, Variables
                                                                                      Definitions
                                                                                      Summary
                                                                                      Patterns to Formulas
                                                                                      Example... Hockey Standings
                                                                                      Example... Counting Money
                                                                                      Example... Angles in a Polygon
                                                                                      Substitution is... Math Scrabble
                                                                                      Scrabble 1, 2, 3
                                                                                      Challenge
                                                                                      Substitution Examples
                                                                                      Examples 1, 2, 3, 4
                                                                                      Practice Questions

7.A.2   Add and subtract monomials with exponents of one                              Understanding Algebra
                                                                                      Topic 5. Adding Expressions
7.A.3   Identify a polynomial as an algebraic expression containing one or more       Our Problem
        terms                                                                         Adding Expressions with X and Y Tiles
                                                                                      Examples 1, 2, 3
                                                                                      Adding Expressions with X-Squared Tiles
                                                                                      Examples 1, 2, 3
                                                                                      Adding Expressions without Tiles
                                                                                      Examples 1, 2
                                                                                      Practice Questions with Tiles
                                                                                      Practice Questions without Tiles
                                                                                      Topic Test




Neufeld Learning Systems Inc. November 2007                                                                                                     13
Source: Mathematics Core Curriculum MST Standard 3
                                      Strand                                                            Neufeld Learning Systems Inc.
                                                                                                           Understanding Math PLUS
                                                                                                                    Lessons
                                                                                Understanding Algebra
                                                                                Topic 6. Subtracting Expressions
                                                                                Our Problem
                                                                                Subtracting Expressions with X and Y Tiles
                                                                                Concept
                                                                                Examples 1, 2
                                                                                Subtracting Expressions with X-Squared Tiles
                                                                                Examples 1, 2
                                                                                Subtracting Expressions without Tiles
                                                                                Practice Questions with Tiles
                                                                                Practice Questions without Tiles

7.A.4 Solve multi-step equations by combining like terms, using the             Understanding Equations
      distributive property, or moving variables to one side of the equation    Topic 4. Solving Multi-Step Equations
                                                                                Our Problem
                                                                                Concepts – Examples with Tiles
                                                                                Concepts – Examples without Tiles
                                                                                Examples 1, 2, 3, 4, 5
                                                                                Summary
                                                                                Literal Equations
                                                                                What Are They?
                                                                                How do you solve them?
                                                                                Why Solve the Literal Equations?
                                                                                A Perimeter Example
                                                                                A Temperature Example

7.A.5   Solve one-step inequalities (positive coefficients only) (See 7.G.10)   Understanding Equations
                                                                                Topic 7. Solving Inequalities
                                                                                Comparing Integers
                                                                                 The Integer Line
                                                                                 Example 1... Greater Than; Example 2... Less Than
                                                                                 Explanation
                                                                                 Example 3... Greater Than; Example 4... Less Than
                                                                                 Greater Than or Less Than
                                                                                Inequalities
                                                                                 What Are They?
                                                                                 Inequality vs. Equation
                                                                                 Summary of Relationships
                                                                                Inequality on the Number Line
                                                                                 Examples 1, 2, 3, 4
                                                                                Solving Inequalities
                                                                                 Examples 1, 2, 3, 4, 5, 6
Neufeld Learning Systems Inc. November 2007                                                                                             14
Source: Mathematics Core Curriculum MST Standard 3
                                     Strand                                                                 Neufeld Learning Systems Inc.
                                                                                                             Understanding Math PLUS
                                                                                                                      Lessons
7.A.6   Evaluate formulas for given input values (surface area, rate, and density   Understanding Measurement and Geometry
        problems)                                                                   Topic 3. Solids…Volume and Surface Area
                                                                                    Surface Area of a Solid
                                                                                    The Concept
                                                                                    Surface Area of a Pyramid

7.A.7   Draw the graphic representation of a pattern from an equation               Understanding Graphing
        or from a table of data                                                     Topic 5. Relations, Equations, Functions
                                                                                    Relations
7.A.10 Write an equation to represent a function from a table of values             What is a Relation?
                                                                                    Domain and Range
                                                                                    Example 1 – Triangles
                                                                                    Example 2 – Tiles, Part 1
                                                                                    Example 3 – Tiles, Part 2
                                                                                    Example 4 – Running
                                                                                    Example 5 – Hit the Ball
                                                                                    Functions
                                                                                    What is a Function? – Examples 1, 2, 3
                                                                                    Vertical Line Test
                                                                                    Examples 1, 2, 3
                                                                                    Function Notation
                                                                                    Examples 1, 2
                                                                                    Patterns to Words to Equations
                                                                                    Examples 1, 2, 3, 4

7.A.8   Create algebraic patterns using charts/tables, graphs, equations, and       Understanding Algebra
        expressions                                                                 Topic 3. Patterns, Patterns, Patterns
                                                                                    Patterns to Formulas
                                                                                    Examples 1, 2, 3
                                                                                    Factor Pairs in Arrays
                                                                                    Factors of 8, 12, 16, 20, 5, 15, 18
                                                                                    Prime and Composite
                                                                                    Prime Numbers
                                                                                    Composite Numbers
                                                                                    Common Factors/GCF
                                                                                    Examples 1, 2
                                                                                    Patterns in the Multiplication Table
                                                                                    Sieve of Eratosthenes
                                                                                    Patterns With 9
                                                                                    Practice Questions



Neufeld Learning Systems Inc. November 2007                                                                                                 15
Source: Mathematics Core Curriculum MST Standard 3
                                      Strand                                                                  Neufeld Learning Systems Inc.
                                                                                                                 Understanding Math PLUS
                                                                                                                         Lessons
                                                                                    Understanding Algebra
                                                                                    Topic 4. Patterns, Formulas, Substitution
                                                                                    Patterns to Formulas
                                                                                    Examples 1, 2, 3
                                                                                    Factor Pairs in Arrays
                                                                                    Factors of 8, 12, 16, 20, 5, 15, 18
                                                                                    Prime and Composite
                                                                                    Prime Numbers
                                                                                    Composite Numbers
                                                                                    Common Factors/GCF
                                                                                    Examples 1, 2
                                                                                    Patterns in the Multiplication Table
                                                                                    Sieve of Eratosthenes
                                                                                    Patterns With 9
                                                                                    Practice Questions
                                                                                    Expressions, Terms, Variables
                                                                                    Definitions
                                                                                    Summary
                                                                                    Patterns to Formulas
                                                                                    Example... Hockey Standings
                                                                                    Example... Counting Money
                                                                                    Example... Angles in a Polygon

7.A.9   Build a pattern to develop a rule for determining the sum of the interior   Understanding Measurement and Geometry
        angles of polygons                                                          Topic 6. Angles and Polygons
                                                                                    Angles in Polygons
                                                                                    Methods 1, 2
                                                                                    Exterior Angles in a Polygon




Neufeld Learning Systems Inc. November 2007                                                                                                   16
Source: Mathematics Core Curriculum MST Standard 3
Geometry Strand

Students will use visualization and spatial reasoning to analyze characteristics and properties of geometric shapes.
Students will identify and justify geometric relationships, formally and informally.
Students will apply coordinate geometry to analyze problem solving situations.

                                     Strand                                                                  Neufeld Learning Systems Inc.
                                                                                                               Understanding Math PLUS
                                                                                                                       Lessons
7.G.1 Calculate the radius or diameter, given the circumference or area of           Understanding Measurement and Geometry
      a circle                                                                       Topic 3. The Circle
                                                                                     Circumference of a Circle
                                                                                     Circumference
                                                                                     Example 1 – Egg
                                                                                     Example 2 – The Well
                                                                                     Example 3 – The Rolling Coin
                                                                                     Example 4 – The Semi-Circle
                                                                                     Area of a Circle
                                                                                     Recall Area
                                                                                     Area Exploration #1
                                                                                     Area Exploration #2
                                                                                     Example 1 – Wheel
                                                                                     Example 2 – Pizza
                                                                                     Example 3 – The Semi-Circle
                                                                                     Example 4 – The Dog’s Run
                                                                                     Example 5 – The Hockey Rink
                                                                                     Practice Questions

7.G.2   Calculate the volume of prisms and cylinders, using a given formula and      Understanding Measurement and Geometry
        a calculator                                                                 Topic 4. Solids…Volume and Surface Area
                                                                                     Volume of a Solid
                                                                                     The Concept
                                                                                     Volume of a Prism: Examples 1, 2
                                                                                     Volume of a Cylinder
7.G.3   Identify the two-dimensional shapes that make up the faces and bases of      Understanding Measurement and Geometry
        three-dimensional shapes (prisms, cylinders, cones, and pyramids)            Topic 2. Perimeter and Area of Polygons
                                                                                     Polygons... What Are They?
                                                                                     Concept
                                                                                     A Triangle is
                                                                                     A Quadrilateral is
                                                                                     A Pentagon is
                                                                                     A Hexagon is
                                                                                     An Octagon is
                                                                                     Classify Polygons


Neufeld Learning Systems Inc. November 2007                                                                                                  17
Source: Mathematics Core Curriculum MST Standard 3
                                      Strand                                                                 Neufeld Learning Systems Inc.
                                                                                                              Understanding Math PLUS
                                                                                                                       Lessons
7.G.4   Determine the surface area of prisms and cylinders, using a calculator       Understanding Measurement and Geometry
        and a variety of methods                                                     Topic 4. Solids…Volume and Surface Area
                                                                                     Surface Area of a Solid
                                                                                     The Concept
                                                                                     Surface Area of a Pyramid
                                                                                     Surface Area of a Cylinder

7.G.5   Identify the right angle, hypotenuse, and legs of a right triangle           Understanding Exponents
                                                                                     Topic 6. Pythagorean Theorem
                                                                                     In This Topic
                                                                                     The Right Triangle
                                                                                     Math or Magic?
                                                                                      Introduction
                                                                                      Omar’s Rope Trick #1, #2
                                                                                      Our Rope Trick
                                                                                     Squares on a Grid
                                                                                      Examples 1, 2, 3, 4
                                                                                     Squares on the Sides of a Right Triangle
                                                                                      Triangles 1, 2, 3

7.G.6   Explore the relationship between the lengths of the three sides of a right   Understanding Exponents
        triangle to develop the Pythagorean Theorem                                  Topic 6. Pythagorean Theorem
                                                                                     The Pythagorean Theorem
7.G.9   Determine whether a given triangle is a right triangle by applying the       The Pattern
        Pythagorean Theorem and using a calculator                                   In General
                                                                                     Theorem
                                                                                     Example Questions
                                                                                     Example 1... Pole Example
                                                                                     Example 2... Tower Example
                                                                                     Example 3... Walking Example
                                                                                     Example 4... Lake Example
                                                                                     Example 5... Geometric Example

7.G.7   Find a missing angle when given angles of a quadrilateral                    Understanding Measurement and Geometry
                                                                                     Topic 6. Angles and Polygons
                                                                                     Angles in Polygons
                                                                                     Methods 1, 2
                                                                                     Exterior Angles in a Polygon
7.G.8   Use the Pythagorean Theorem to determine the unknown length of a side        Understanding Exponents
        of a right triangle                                                          Topic 6. Pythagorean Theorem
                                                                                     Practice Questions

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Source: Mathematics Core Curriculum MST Standard 3
                                      Strand                                                          Neufeld Learning Systems Inc.
                                                                                                          Understanding Math PLUS
                                                                                                                   Lessons
7.G.10 Graph the solution set of an inequality (positive coefficients          Understanding Equations
       only) on a number line (See 7.A.5)                                      Topic 7. Solving Inequalities
                                                                               Graphing Linear Inequalities in Two Variables
                                                                               Concepts 1, 2
                                                                               Examples 1, 2, 3
                                                                               Solving Systems of Linear Inequalities by Graphing
                                                                               Examples 1, 2


Measurement Strand

Students will determine what can be measured and how, using appropriate methods and formulas.
Students will develop strategies for estimating measurements.

                                      Strand                                                         Neufeld Learning Systems Inc.
                                                                                                      Understanding Math PLUS
                                                                                                               Lessons
7.M.1   Calculate distance using a map scale

7.M.2   Convert capacities and volumes within a given system                   Understanding Measurement and Geometry
                                                                               Topic 3. Solids…Volume and Surface Area
                                                                               Volume of a Solid
                                                                               The Concept
                                                                               Volume of a Prism: Examples 1, 2
                                                                               Volume of a Cylinder

7.M.3   Identify customary and metric units of mass                            Understanding Measurement and Geometry
                                                                               Topic 1. An Introduction to Measurement
                                                                               Metric and U.S.A Standard Measurement Systems
                                                                               Searching for the Standard Unit
                                                                               Related Units from Metric Prefixes
                                                                               Metric Prefixes at Work
                                                                               Converting Between Metric Units
                                                                               The Ruler

7.M.4   Convert mass within a given system




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Source: Mathematics Core Curriculum MST Standard 3
                                      Strand                                                            Neufeld Learning Systems Inc.
                                                                                                         Understanding Math PLUS
                                                                                                                  Lessons
7.M.5   Calculate unit price using proportions                                   Understanding Percent
                                                                                 Topic 4. Ratios and Proportions
                                                                                 What is a Proportion?
                                                                                 Proportions
                                                                                 Example 1
                                                                                 Example 2 – Lemonade
                                                                                 Example 3 – Marbles
                                                                                 Example 4 – Trout
                                                                                 Example 5 – Tree Height
                                                                                 Example 6 – Map
                                                                                 Example 7 – Scale Drawing

7.M.6   Compare unit prices

7.M.7   Convert money between different currencies with the use of an exchange
        rate table and a calculator

7.M.8   Draw central angles in a given circle using a protractor (circle         Understanding Graphing
        graphs)                                                                  Topic 2. Statistics
                                                                                 Circle or Pie Graphs
                                                                                  Example 1... Radio Station
                                                                                  Example 2... Health Survey

7.M.9 Determine the tool and technique to measure with an appropriate
      level of precision: mass

7.M.10 Identify the relationships between relative error and magnitude
      when dealing with large numbers (e.g., money, population)



7.M.11 Estimate surface area                                                     Understanding Measurement and Geometry
                                                                                 Topic 4. Solids…Volume and Surface Area
                                                                                 Surface Area of a Solid
                                                                                 The Concept
                                                                                 Surface Area of a Pyramid
                                                                                 Surface Area of a Cylinder




Neufeld Learning Systems Inc. November 2007                                                                                             20
Source: Mathematics Core Curriculum MST Standard 3
                                    Strand                                                         Neufeld Learning Systems Inc.
                                                                                                     Understanding Math PLUS
                                                                                                             Lessons
7.M.12 Determine personal references for customary /metric units of mass   Understanding Measurement and Geometry
                                                                           Topic 1. Introduction to Measurement
                                                                           Benchmarks
                                                                           Establishing Benchmarks
                                                                           Meter Benchmarks
                                                                           Foot Benchmarks
                                                                           Centimeter Benchmarks
                                                                           Inch Benchmarks
                                                                           Yard Benchmarks
                                                                           Our Benchmarks
                                                                           Using Benchmarks
                                                                           Converting Between Metric Units

7.M.13 Justify the reasonableness of the mass of an object




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Source: Mathematics Core Curriculum MST Standard 3
Statistics and Probability Strand

Students will collect, organize, display, and analyze data.
Students will make predictions that are based upon data analysis.
Students will understand and apply concepts of probability.

                                         Strand                                                    Neufeld Learning Systems Inc.
                                                                                                    Understanding Math PLUS
                                                                                                             Lessons
7.S.1 Identify and collect data using a variety of methods               Understanding Graphing
                                                                         Topic 2. Statistics
                                                                         Data... What is it?
                                                                         Examples of Data
                                                                         Example 1... Fast Food Earnings
                                                                         Example 2... Infant’s Walk
                                                                         Example 3... Canada and U.S.A. Forecast
                                                                         Example 4... King of the Strike Out
                                                                         Example 5... U.S.A. Stake in India
                                                                         Example 6... Allergy Troubles
                                                                         A Summary: Examples
                                                                         Statistics... What is it?
                                                                         Collecting Data
                                                                         Throw a Die
                                                                         Throw 2 Dice
                                                                          Voting
                                                                         Primary Data - Gathering Methods
                                                                         Secondary Data - Gathering Methods

7.S.2   Display data in a circle graph                                   Understanding Graphing
                                                                         Topic 2. Statistics
                                                                         Circle or Pie Graphs
                                                                          Example 1... Radio Station
                                                                          Example 2... Health Survey

7.S.3   Convert raw data into double bar graphs and double line graphs   Understanding Graphing
                                                                         Topic 2. Statistics
                                                                         Bar Graph
                                                                          Example 1... Energy
                                                                          Example 2... Lengths of Rivers
                                                                         Line Graph
                                                                          Example 1... Life Expectancy
                                                                          Example 2... Software Profits

7.S.4   Calculate the range for a given set of data


Neufeld Learning Systems Inc. November 2007                                                                                        22
Source: Mathematics Core Curriculum MST Standard 3
                                      Strand                                                             Neufeld Learning Systems Inc.
                                                                                                          Understanding Math PLUS
                                                                                                                   Lessons
7.S.5   Select the appropriate measure of central tendency                        Understanding Graphing
                                                                                  Topic 2. Statistics
                                                                                  Measures of Central Tendency
                                                                                  Introduction
                                                                                   The Mean Average
                                                                                   The Median average
                                                                                   The Mode
                                                                                   Summary
                                                                                   Another Example
                                                                                   Adding Data Points

7.S.6   Read and interpret data represented graphically (pictograph, bar graph,   Understanding Graphing
        histogram, line graph, double line/bar graphs or circle graph)            Topic 2. Statistics
                                                                                  Bar Graph
                                                                                   Example 1... Energy
                                                                                   Example 2... Lengths of Rivers
                                                                                  Histogram
                                                                                   Example 1... Heights of Students
                                                                                   Example 2... Roll a Die
                                                                                  Line Graph
                                                                                   Example 1... Life Expectancy
                                                                                   Example 2... Software Profits
                                                                                  Circle or Pie Graphs
                                                                                   Example 1... Radio Station
                                                                                   Example 2... Health Survey

7.S.8 Interpret data to provide the basis for predictions and to establish        Understanding Probability
       experimental probabilities                                                 Topic 1. Introduction to Probability
                                                                                  Possible Outcomes... Examples
                                                                                  What are they?
                                                                                  1. Coin
                                                                                  2. Picking One Ball
                                                                                  3. Picking Two Balls
                                                                                  4. Eye Test
                                                                                  5. Coin and Die
                                                                                  6. Travel
                                                                                  7. Rabbits
                                                                                  8. Forest




Neufeld Learning Systems Inc. November 2007                                                                                              23
Source: Mathematics Core Curriculum MST Standard 3
                                    Strand                                                      Neufeld Learning Systems Inc.
                                                                                                  Understanding Math PLUS
                                                                                                          Lessons
7.S.9   Determine the validity of sampling methods to predict outcomes   Understanding Probability
                                                                         Topic 2. What’s the Chance?
                                                                         Experiments with Spinners
                                                                          Experiments 1
                                                                          Experiments 2
                                                                          Experiments 3
                                                                          Experiments 4
                                                                          Experiments 5
                                                                          Experiments 6
                                                                         The Spinner Game
                                                                          Board 1
                                                                          Board 2
                                                                         IT’s in the Bag

7.S.10 Predict the outcome of an experiment                              Understanding Probability
                                                                         Topic 2. What’s the Chance?
                                                                         Probability
                                                                         What is it?
                                                                         Introduction 1
                                                                         Introduction 2
                                                                         Probability Examples
                                                                         1. Coin Toss
                                                                         2. Picking One Ball
                                                                         3. Picking Two Balls
                                                                         4. Travel Example
                                                                         5. Number Example
                                                                         6. Rabbit Example
                                                                         7. Mailing Letters
                                                                         8. Forest
                                                                         9. Ahmed’s Maze
7.S.11 Design and conduct an experiment to test predictions              Understanding Probability
                                                                         Topic 2. What’s the Chance?
                                                                         The Probability Scale
                                                                         Examples
                                                                         Summary
                                                                         Follow Up
                                                                         Soccer Example
                                                                         Experimental Probability
                                                                         Introduction
                                                                         Examples 1, 2
7.S.12 Compare actual results to predicted results

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Source: Mathematics Core Curriculum MST Standard 3
Neufeld Learning Systems Inc. November 2007          25
Source: Mathematics Core Curriculum MST Standard 3

				
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Description: 10Th Grade Mathematical Worksheets document sample