Accelerated Math INB.notebook 1 November 05, 2014 Table of Contents Left Page Right Page Nuggets of Knowledge 0 Table of Contents 1 Table of Contents 2 Table of Contents 3 Module 1 Learning Targts 4 Rate/Ratio/Percent Notes 5 Lesson 6 Gallery Walk 6 Proportional Relationships Notes 7 Graphs of Proportional & Not proportion Relationships 8 Percent Notes 9 Costa's Levels of Questioning 10 Proportional Relationship Notes 11 Entry Squares 12 Lesson 20 & 21 Notes 13 Module 1 Quiz Refection 14 Lesson 21 Notes 15 Percent Notes (Simple Interest) 16 Percent Notes Continued 17 Classroom Scale factor table 18 Lesson 16 & Lesson 17 Notes 19 Classroom scale factor drawing 20 Lesson 18 & Lesson 19 Notes 21 Module 2 Learning Targets 22 7M2 Lesson 1 Video Notes 23 Real Number Sense Graphic 24 7M2 Lesson 2 Video Notes 25 Practice Adding/Subtracting Rational #s 26 7M2 Lesson 3/4 Notes 27 Foldable for Integers 28 7M2 Lesson 5/6 Notes 29 Integer Quick Drills 30 7M2 Lesson 7 Notes 31 32 7M2 Lesson 8/9/10 Notes 33 34 7M2 Lesson 11/12/15/16 Notes 35 36 37 38 39 40 41 42 43 44 45 46 47 Accelerated Math INB.notebook 2 November 05, 2014 Table of Contents Right Page Left Page 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 Accelerated Math INB.notebook 3 November 05, 2014 Table of Contents Left Page Right Page 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 Accelerated Math INB.notebook 4 November 05, 2014 Module 1—Ratio & Proportions Learning Targets and scoring Rubric Track your progress after each assessment Quiz 1 Quiz 2 Test 7.RP.1 Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. 7.RP.2 Recognize and represent proportional relationships between quantities. a. Decide whether two quantities are in a proportional relationship b. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. c. Represent proportional relationships by equations. d. Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate 7.RP.3 Use proportional relationships to solve multistep ratio and percent problems. 7.EE.3 Solve multistep reallife and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. 7.EE.4a Use variables to represent quantities in a realworld or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. a. Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Score of 1 Score of 2 Score of 3 Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. Score of 4 I cannot: I can only partially: I can with minor errors: I can with no errors: Reason quantitatively & use Reason quantitatively & use Reason quantitatively & use Reason quantitatively & use •7.G.1 Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas • • • units to solve problems units to solve problems units to solve problems units to solve problems from a scale drawing and reproducing a scale drawing at a different scale. Interpret structure of Interpret structure of Interpret structure of Interpret structure of • • • • expressions expressions expressions expressions Create equations that describe • Create equations that describe • Create equations that describe • Create equations that describe • #s or relationships #s or relationships #s or relationships #s or relationships Understand solving equations • Understand solving equations • Understand solving equations • Understand solving equations • as process of reasoning & explain as process of reasoning & explain as process of reasoning & explain as process of reasoning & explain reasoning reasoning reasoning reasoning Solve equations in one variable • Solve equations in one variable • Solve equations in one variable • Solve equations in one variable • Represent & solve equations Represent & solve equations Represent & solve equations Represent & solve equations • • • • Interpret functions that arise in • Interpret functions that arise in • Interpret functions that arise in • Interpret functions that arise in • applications applications applications applications Analyze functions using Analyze functions using Analyze functions using Analyze functions using • • • • different representations different representations different representations different representations Build a function that models a • Build a function that models a • Build a function that models a • Build a function that models a • relationship between two quantities relationship between two quantities relationship between two quantities relationship between two quantities Accelerated Math INB.notebook November 05, 2014 5 Questions What are the 3 ways to write a ratio? Rate / Ratios / Percents Percent per hundred **write percent as % P pecent is the same as Three ways to write % How are a ratio and a rate the same and different? fraction decimal percent Ratiocomparing 2 numbers s fraction English colon ay 3 w Equivalent Ratios Rateratio with units Unit Raterate with denominator of one ex To compareDIVIDE 225 cans 977 cans 3 hours 8 hours 75 cans per hour 1 122 cans per hour 1 Summary Unit rate is for comparing rations and their rates (when using different units). Unit rate allows us to compare varying sizes by dividing ratios to get 1 as denominator. Accelerated Math INB.notebook 6 November 05, 2014 Accelerated Math INB.notebook November 05, 2014 7 Proportional Relationships Questions Measures in one amount are PROPORTIONAL to another amount if there is a positive number that for each first # you can multiply you get the 2nd #. How does a table show a proportional relationship? Explain the elements of a proportional relationship? EX X y 2 10 3 15 4 20 for each x value, you get the y value by multiplying by 5 A relationship is proportional IF your 1st number gets multiplied or divided by the same number each time. EX (students create own example here) Summary You get a proportional relationship when you multiply values by the same constant. Accelerated Math INB.notebook November 05, 2014 8 Not proportional Not proportional Not proportional proportional Accelerated Math INB.notebook 9 Questions November 05, 2014 Percent Notes Equation used to solve % problems How do you find the price of something given the original amount and the percent? How do you know when to multiply or divide when solving % problems? Whole x Percent = Part decimal form Finding % of a whole. Percent Increase and Decrease Quantity = Percent x whole Jon has 15 original cards. He increased his collection by 5 cards. What is the % increase? Bob's tires...Fred sold 165 tires which was 60% of the tires sold that month. What was the number of record tires sold? Summary You can find the amount of a discount given the % off and original amount. If you don't know the original price you can find it by knowing the the % and sale price and dividing. Accelerated Math INB.notebook 10 November 05, 2014 Accelerated Math INB.notebook November 05, 2014 11 Proportional Relationships Questions What do you see in a proportional graph? Tables Graphs My x gets multiplied by same value each time to get my y →passes through origin →straight line Explain how you find the constant of proportion with table or equation? Equations y=k x VOCAB constanta specific number Variablea letter that represents a number (we can change it) Constant of proportionalitythe number in a proportional relationship that is being multipled Summary A proportional relationship can be represented in a table, graph, or equation. The constant of proportionality can be used to create tables, graphs, and equations. Accelerated Math INB.notebook 12 November 05, 2014 Identify the categories that apply to the given value. Express 9 hours as a percentage of 3 days. The price of a tent was decreased by 15% and sold for $76.49. What was the original price? Accelerated Math INB.notebook 13 November 05, 2014 Lesson 20 Summary: Scale Drawing Process: 1. Measure lengths and widths carefully with a ruler or tape measure. Record in an organized table. 2. Calculate the scale drawing lengths, widths and areas using what was learned in previous lessons. 3. Calculate the actual areas. 4. Begin by drawing the perimeter, windows and doorways. 5. Continue to draw the pieces of furniture making note of placement of objects (distance from nearest wall). 6. Check for reasonableness of measurements and calculations. Lesson 21 Changing Scale Factors: 1. To produce a scale drawing at a different scale, you must determine the new scale factor. The new scale factor is found by dividing the different (new drawing) scale factor by the original scale factor. 2. To find each new length, you can multiply each length in the original scale drawing by this new scale factor. Accelerated Math INB.notebook 14 November 05, 2014 Module 1 Quiz Reflection What did I do well? What did I not do so well? What is my plan to improve what I did not do well? Accelerated Math INB.notebook 15 November 05, 2014 Steps: 1. Find each scale factor. 2. Divide new scale factor by original scale factor. 3. Divide the given length by the new scale factor (the quotient from the prior step) Lesson 21 Summary: Variations of Scale Drawings with different scale factors are scale drawings of an original scale drawing. From a scale drawing at a different scale, the scale factor for the original scale drawing can be computed without information of the actual object, figure or picture. Accelerated Math INB.notebook 16 November 05, 2014 Lesson Summary: § Discount price = original price – rate original price OR (1 rate) original price § Commission = rate total sales amount § Markup price = original price + rate original price OR (1 + rate) original price § r is the percent of the principal that is paid over a period of time (usually per year). § t is the time. § P is the principle or the starting amount. § r and t must be compatible. For example, if r is an annual interest rate, then t must be written in years. Accelerated Math INB.notebook 17 November 05, 2014 Lesson Summary § Percent means “per hundred”. percent is the same as Write as short for percent. Usually there are three ways to write a number: a percent, a § fraction, and a decimal. Fractions and decimals are related to the ratio of percent over . Lesson Summary § Visual models or numeric methods can be used to solve percent problems. § Equaons can be used to solve percent problems using the basic equaon: OR . Accelerated Math INB.notebook November 05, 2014 18 Classroom Bookshelf Actual length Actual width Scale length Scale width Actual area Scale area 348" 372" 29 31 12946 in squared 899 Back table cabinet storage desk Accelerated Math INB.notebook 19 November 05, 2014 Key Idea: Scale Drawing: a reduced or enlarged twodimensional drawing of an original two dimensional drawing. Lesson 16 Summary: Scale Drawing: A drawing in which all lengths between points or figures in the drawing are reduced or enlarged proportional to the lengths in the actual picture. A constant of proportionality exists between corresponding lengths of the two images. Reduction: The lengths in the scale drawing are smaller than those in the actual object or picture. Enlargement/Magnification: The lengths in the scale drawing are larger than those in the actual object or picture. Onetoone Correspondence: Each point in one figure corresponds to one and only one point in the second figure. Lesson 17 Steps to check for proportionality for scale drawing and original object/picture: 1. Measure lengths of scale drawing. Record on table. 2. Measure corresponding lengths on actual picture/drawing. Record on table. 3. Check for constant of proportionality. Accelerated Math INB.notebook 20 November 05, 2014 Scale Drawing of classroom Accelerated Math INB.notebook 21 November 05, 2014 Key Idea: The scale factor can be calculated from the ratio of any length in the scale drawing to its corresponding length in the actual picture. The scale factor corresponds to the unit rate and the constant of proportionality. Scaling by factors greater than 1 enlarge the segment and scaling by factors less than 1 reduce the segment. Lesson 19 Summary: Given the scale factor r representing the relationship between scale drawing length and actual length, the square of this scale factor, r2, represents the relationship between scale drawing area and actual area. For example, if 1 inch on the scale drawing represents 4 inches of actual length, then the scale factor, r, is . On this same drawing, 1 square inch of scale drawing area would represent 16 square inches of actual area since r2 is . Accelerated Math INB.notebook 22 November 05, 2014 Accelerated Math INB.notebook 23 November 05, 2014 Accelerated Math INB.notebook 24 November 05, 2014 Accelerated Math INB.notebook 25 November 05, 2014 Accelerated Math INB.notebook 26 Practice with Integers November 05, 2014 Practice with Rational Numbers Accelerated Math INB.notebook 27 November 05, 2014 Accelerated Math INB.notebook 28 November 05, 2014 Accelerated Math INB.notebook 29 November 05, 2014 Accelerated Math INB.notebook 30 Students tape their Integer Quick drills here. completed ______ correct _______ percent (correct/completed)=_______ November 05, 2014 Accelerated Math INB.notebook 31 November 05, 2014 Accelerated Math INB.notebook 32 November 05, 2014 Accelerated Math INB.notebook 33 November 05, 2014 Accelerated Math INB.notebook 34 November 05, 2014 Accelerated Math INB.notebook November 05, 2014 35 Questions What sign of a multiplicaation problem would you get if the signs were different? What is the difference between multi/dividing numbers and add/ subtrating rational numbers? Summary When multiplying and dividing positive and negative numbers, the same signes give us positive #s, different signs give us a negative number. Accelerated Math INB.notebook 36 November 05, 2014 Accelerated Math INB.notebook November 05, 2014 Accelerated Math INB.notebook November 05, 2014 Accelerated Math INB.notebook November 05, 2014 Accelerated Math INB.notebook November 05, 2014 Accelerated Math INB.notebook November 05, 2014 Accelerated Math INB.notebook November 05, 2014 Blackboard Teacher Website 3 things you learned from this page 3 things you learned from this page Current INB can watch videos about things learned in class teacher contact information when absent can get caught up links to online book & blackboard can pause videos and watch again Office 365 Engage NY 3 things you learned from this page can see lessons at Enage NY website www.365login.com/ Student Login Info: Username: last name ‐last four digits of ID @sps81.org when absent can get caught up example: [email protected] can print pages of problems sets when absent Password (birthdate): mmddyyyy Accelerated Math INB.notebook November 05, 2014 0
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