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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 Neufeld Learning Systems Inc. November 2007 18 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 Neufeld Learning Systems Inc. November 2007 19 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 Neufeld Learning Systems Inc. November 2007 21 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 Neufeld Learning Systems Inc. November 2007 24 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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10Th Grade Mathematical Worksheets document sample

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