Grade 7 Middle School Math Solution Alignment to Oklahoma Academic Standards

Transcription

1 7.N.1 Read, write, represent, and compare rational numbers, expressed as integers, fractions, and decimals 7.N.2 Calculate with integers, with and without positive integer exponents, to solve real-world and mathematical problems; explain the relationship between absolute value of a rational number and the distance of that number from zero 7.N N N N N N N.2.4 Know that every rational number can be written as the ratio of two integers or as a terminating or repeating decimal. Compare and order rational numbers expressed in various forms using the symbols >, <, or = Recognize and generate equivalent expressions of rational numbers, including equivalent fractions Estimate solutions to multiplication and division of integers in order to assess the reasonableness of results Illustrate multiplication and division of integers using a variety of representations Solve real-world and mathematical problems involving addition, subtraction, multiplication, and division of rational numbers; use efficient and generalizable procedures including but not limited to standard algorithms Raise integers to positive integer exponents 4: Moving Beyond Positive 1: Signed 1: Adding and Subtracting 1: Expressions 2: Be (M2-103) 1: Human Line (M4-7) 1: Equal Groups (M2-89) 2: Be (M2-103) 3: Building a Wright Brothers Flyer (M2-113) 1: Equal Groups (M2-89) 2: Be (M2-103) 1: Equal Groups (M2-89) 2: Be (M2-103) 5: Negative and the Four Quadrants 3: 2: Walk The Line (M2-17) 3: Two-Color Counters (M2-31) 4: What s the Difference (M2-49) 5: All Mixed Up (M2-69) 3: 1: Equal Groups (M2-89) 2: Be! (M2-103) 3: Building a Wright Brothers Flyer (M2-113) 1: Matter (M3-7) 3: s 2: Representing on Lines 3: Multiplying and Dividing 1: Adding and Subtracting 2: Using Lines to Add and Subtract 3: Multiplying and Dividing to Simplify to Simplify Grade 7 Middle School Math Solution: Alignment to OAS 1

2 7.N.2 (cont d) 7.A.1 Understand the concept of proportionality in real-world and mathematical situations, and distinguish between proportional and other relationships 7.N N A A.1.2 Solve Real world and mathematical problems involving calculations with rational numbers and positive integer exponents Explain the relationship between absolute value of a rational number and the distances of that number from zero on a number line. Use the symbol for absolute value. Describe that the relationship between two variables, x and y, is proportional if it can be expressed in the form y/x = k or y = kx; distinguish proportional relationships from other relationships, including inversely proportional relationships xy=k or y = k/x Recognize the graph of a proportional relationship is a line through the origin and the coordinates (1,r) where both r and the slope are the unit rate (constant of proportionality, k) 4: Moving Beyond Positive 1: Expressions 1: Signed 3: Proportionality 3: Proportionality 1: Matter (M3-7) 3: Building a Wright Brothers Flyer (M2-113) 2: Magnificent Magnitude (M4-23) 1: How Does Your Garden Grow (M1-91) 2: Complying with Title IX (M1-109) 4: Minding Your Ps and Qs (M1-139) 1: How Does Your Garden Grow (M1-91) 3: Fish-Inches (M1-127) 4: Minding Your Ps and Qs (M1-139) 3: 5: Negative and the Four Quadrants 1: Proportional 1: Proportional to Simplify to Simplify s 3: Using Absolute Value 3: Representing Proportional 3: Representing Proportional 1: Introduction to Direct Variation 2: Writing Direct Variation 3: Converting between Proportions and Direct Variation 4: Modeling Direct Variation 5: Determining Characteristics of Direct Variation Graphs Grade 7 Middle School Math Solution: Alignment to OAS 2

3 7.A.2 Recognize proportional relationships in real-world and mathematical situations; represent these and other relationships with tables, verbal descriptions, symbols, and graphs; solve problems involving proportional relationships and interpret results in the original context 7.A A A.2.3 Represent proportional relationships with tables, verbal descriptions, symbols, and graphs; translate from one representation to another. Determine and compare the unit rate (constant of proportionality, slope, or rate of change) given any of these representations Solve multi-step problems involving proportional relationships involving distance-time, percent increase or decrease, discounts, tips, unit pricing, similar figures, and other real-world and mathematical situations Use proportional reasoning to solve real-world and mathematical problems involving ratios 3: Proportionality 4: Proportional 2: Fractional Rates 1: How Does Your Garden Grow (M1-91) 2: Complying with Title IX (M1-109) 3: Fish-Inches (M1-127) 4: Minding Your Ps and Qs (M1-139) 1: Markups and Markdowns (M1-161) 2: Perks of Work (M1-177) 3: No Taxation without Calculation (M1-197) 4: More Ups and Downs (M1-209) 5: Pound for Pound, Inch for Inch (M1-223) 1: Making Punch (M1-51) 2: Eggzactly (M1-59) 3: Tagging Sharks (M1-69) 1: Proportional 2: Proportional Reasoning and Percents 3: Representing Proportional by 2: Proportional Reasoning and Percents 3: Problem Solving with Percents using Proportional 5: Geometry 2: Scale Drawings 1: Proportional 1: Problem Solving using Ratio and Rate Reasoning 2: Proportional Reasoning 1: Introduction to Direct Variation 2: Writing Direct Variation 3: Converting between Proportions and Direct Variation 4: Modeling Direct Variation 5: Determining Characteristics of Direct Variation Graphs 1: Using Proportions to Solve Percent Problems 2: Solving Percent Problems 1: Calculating Percent Change and Final Amounts 2: Using Percents and Percent Change 1: Using Scale Drawings 2: Using Scale Factor 1: Problem Solving with Equivalent Ratios and Rates using Tables 2: Problem Solving with Equivalent Ratios and Rates using Double Lines 3: Problem Solving with Equivalent Ratios and Rates Using Graphs 1: Solving Proportions using Equivalent Ratios 2: Solving Proportions using Means and Extremes Grade 7 Middle School Math Solution: Alignment to OAS 3

4 1: Circles and Ratios 1: Pi: The Ultimate Ratio (M1-7) 2: Fractional Rates 1: Making Punch (M1-51) 2: Eggzactly (M1-59) 3: Tagging Sharks (M1-69) 7.A.2 (cont d) 7.A.2.4 Use proportional reasoning to assess the reasonableness of solutions 3: Proportionality 4: How Does Your Garden Grow? (M1-91) 5: Complying with Title IX (M1-109) 6: Fish-Inches (M1-127) 7: Minding Your Ps and Qs (M1-139) 4: Proportional 1: Markups and Markdowns (M1-161) 2: Perks of Work (M1-177) 3: No Taxation without Calculation (M1-197) 4: More Ups and Downs (M1-209) 5: Pound for Pound, Inch for Inch (M1-223) 2: Picture Algebra 1: Using Picture Algebra with 2: Modeling Two-Step 7.A.3 Represent and solve linear equations and 7.A.3.1 Write and solve problems leading to linear equations with one variable in the form px+q=r and p(x+q) = r, where p, and q are non-negative rational numbers 3: Reasoning Algebraically 2: Two-Step 1: Picture Algebra (M3-53) 2: Expressions that Play Together (M3-65) 3: Formally Yours (M3-77) 4: Two-Step 3: Solving Two- Step 2: Solving with Multiplication 3: Solving with Multiplication 4: Solving with Division 5: Solving with Division 6: Solving Two-Step Grade 7 Middle School Math Solution: Alignment to OAS 4

5 7.A.3 (cont d) 7.A A.3.3 Represent, write, solve, and graph problems leading to linear inequalities with one variable of the form x + p >q and x+p<q, where p and q are nonnegative rational numbers Represent real-world or mathematical situations using equations and inequalities involving variables and rational numbers 3: Reasoning Algebraically 3: Reasoning Algebraically 2: 2: Two-Step 2: Two-Step 3: Multiple Representations of 1: First Among Equals (M3-87) 4: Be Greater Than (M3-95) 1: Picture Algebra (M3-53) 2: Expressions that Play Together (M3-65) 3: Formally Yours (M3-77) 4: Be Greater Than (M3-95) 1: Put It On the Plane (M3-125) 2: Stretches, Stacks, and Structure (M3-139) 3: Deep Flight I (M3-155) 4: One-Step 4: Two-Step 4: Two-Step 3: Solving One-Step 2: Picture Algebra 2: Picture Algebra 3: Solving Two- Step 4: Problem Solving with Two-Step 1: Graphing with positive 2: Solving One-Step Linear 1: Using Picture Algebra with 2: Modeling Two-Step 3. Solving with Multiplication 4: Solving with Multiplication 5: Solving with Division 6: Solving with Division 7: Solving Two-Step 1: Using Picture Algebra with 2: Modeling Two-Step 2: Solving with Multiplication 3: Solving with Multiplication 4: Solving with Division 5: Solving with Division 6: Solving Two-Step 1: Using Linear and 2: Solving Problems with 3: Solving Problems with Decimals and Fractions Grade 7 Middle School Math Solution: Alignment to OAS 5

6 7.A.4 Use order of operations and properties of operations to generate equivalent numerical and algebraic expressions containing rational numbers and grouping symbols; evaluate such expressions 7.GM.1 Develop and Understand the concept of surface area and volume of rectangular prisms 7.GM.2 Determine the area of trapezoids and area and perimeter of composite figures 7.A A GM GM.2.2 Use Properties of operations (limited to associative, commutative, and distributive) to generate equivalent numerical and algebraic expressions containing rational numbers, grouping symbols and whole number exponents Apply understanding of order of operations and grouping symbols when using calculators and other technologies Using a variety of tools and strategies, develop the concept that volume of a rectangular prism with rational-valued edge lengths can be found by counting the total number of same-sized units cubes that fill a shape without gaps or overlap. Use appropriate measurements such as cm^3 Find the Area and perimeter of composite figures to solve real-world and mathematical problems 3: Reasoning Algebraically 1: Composing and Decomposing 1: Composing and Decomposing 1: Composing and Decomposing 1: Expressions 1: Expressions 1: Algebraic Expressions 3: Decimals and Volume 1: Factors and Area 1: Factors and Area 1: Circles and Ratio 3: Building a Wright Brothers Flyer (M2-113) 1: Matter (M3-7) 2: Into the (M3-23) 3: Second Verse, Same as the First (M3-35) 4: Are They Saying the Same Thing? (M3-53) 1: Matter (M3-7) 1: No Substitute for Hard Work (M3-7) 2: Mathematics Gymnastics (M3-19) 3: All My Xs (M3-33) 1: Length, Width, and Depth (M1-115) 2: All About that Base and Height (M1-15) 3: Slicing and Dicing (M1-51) 2: That s a Spicy Pizza (M1-19) 3: Circular Reasoning (M1-33) 3: 4: Two-Step 3: 3: 6: Geometric Measurement 6: Geometric Measurement 6: Geometric Measurement 1: Variable Expressions 3: Volume and Surface Area 2: Area 2: Area 3: Circles to Simplify to Simplify 1: Factoring Linear Expressions 2: Using Order of to Simplify Algebraic Expressions 3: Using Order of to Simplify Algebraic Expressions to Simplify to Simplify to Simplify to Simplify 1: Calculating Volume of Right Prisms 1: Developing Area Formulas 2: Calculating Area of Various Figures 4: Calculating Area of Composite Figures 1: Calculating Circumference and Area of Circles Grade 7 Middle School Math Solution: Alignment to OAS 6

7 7.GM.3 Use reasoning with proportions and ratios to determine measurements justify formulas, and solve real-world and mathematical problems involving circles and related geometric figures 7.GM.4 Analyze the effects of dilations, translations, and reflections on the attributes of two-dimensional figures on and off the coordinate plane 7.D.1 Display and analyze data in a variety of ways 7.GM GM D D D.2.1 Describe the properties of similarity, compare geometric figures for similarity, and determine scale factors resulting from dilations Graph and describe translations and reflections of figures on a coordinate plane and determine the coordinates of the vertices of the figure after the transformation Design simple experiments, collect data and calculate measures of central tendency and spread (range). Use these quantities to draw conclusions about the data collected and make predictions Use Reasoning with proportions to display and interpret data in circle graphs and histogram. Choose the appropriate data display and know how to create the display using a spreadsheet or other graphing technology Determine the probability of an event using the ratio between the size of the event and the size of the sample space; represent probabilities as percents, fractions, and decimals between 0 and 1 Course 3* Course 3* 1: Transforming Geometric Objects 1: Transforming Geometric Objects 5: Describing Variability of 5: Describing Variability of 4: Analyzing Populations and 2: Similarity 4: Proportional 1: Rigid Motion Transformations 2: Numerical Summaries of Data 1: The Statistical Process 1: Introduction to 2: Compound 1: Pinch-Zoom Geometry (M1-109) 2: Rising, Running, Stepping, Scaling (M1-125) 3: From Here to There (M1-141) 5: Pound for Pound, Inch for Inch (M1-223) 3: Lateral Moves (M1-39) 4: Mirror Mirror (M1-53) 1: In the Middle (M5-71) 2: Box it Up (M5-87) 1: What s Your Question (M5-7) 3: Using Histograms to Display Data (M5-47) 1: Rolling, Rolling, Rolling (M4-7) 2: Give Models a Chance (M4-23) 3: Toss the Cup (M4-33) 4: A Simulating Conversation (M4-47) 1: Evens or Odds (M4-73) 2: Three Girls and No Boys (M4-89) 4: Geometric Transformations 1: Transformations on the Coordinate Plane 5: Geometry 2: Scale Drawings 4: Geometric Transformations 7: Measures of Central Tendency and Data Displays 7: Measures of Central Tendency and Data Displays 6: Data Comparisons and 1: Transformations on the Coordinate Plane 1: Measures of Central Tendency 2: Displays of Numerical Data 2: Introduction to 4: Dilating Plane Figures 1: Using Scale Drawings 2: Using Scale Factor 1: Translating Plane Figures 3: Reflecting Plane Figures 5: Performing One Transformation 1: Calculating Mean, Median, Mode, and Range 3: Creating and Interpreting Histograms 1: Determining Grade 7 Middle School Math Solution: Alignment to OAS 7

8 7.D.2 Calculate probabilties and reason about probabilities using proportions to solve real-world and mathematical problems 7.D D.2.3 Calculate the probability as a fraction of a sample space or as a fraction of area. Express as percents, decimals, or fractions Use proportional reasoning to draw conclusions about and predict relative frequencies based on probabilities 4: Analyzing Populations and 4: Analyzing Populations and 1: Introduction to 2: Compound 1: Introduction to 2: Compound 1: Rolling, Rolling, Rolling (M4-7) 2: Give Models a Chance (M4-23) 3: Toss the Cup (M4-33) 4: A Simulating Conversation (M4-47) 1: Evens or Odds (M4-73) 2: Three Girls and No Boys (M4-89) 6: Data Comparisons and 3: Toss the Cup (M4-33) 6: Data Comparisons 1: Evens or Odds (M4-73) and 2: Introduction to 1: Introduction to 1: Determining 1: Determining Grade 7 Middle School Math Solution: Alignment to OAS 8