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1 THANK YOU FOR YOUR PURCHASE! The resources included in this purchase were designed and created by me. I hope that you find this resource helpful in your classroom. Please feel free to contact me with any questions as you implement this in your class. Maneuvering the Middle is an education blog with valuable tips for lesson planning, teacher organization, and math concepts in the middle school classroom. /ManeuveringTheMiddle maneuveringthemiddle.com PLEASE Print and copy this resource for your personal classroom use only. Save this to both home and school computers. Only post this only for students on a password protected class website. PLEASE DO NOT Reproduce or distribute this resource to other colleagues. Post this on the internet in any form, including classroom/personal websites, network drives, or other sharing websites (i.e. Amazon Inspire, etc). Maneuvering the Middle LLC, 2012-Present Products by Maneuvering the Middle, LLC may be used by the purchaser for their classroom use only. This is a single classroom license only. All rights reserved. If you wish to share this product with your team or colleagues, you may purchase additional licensing at a discounted rate. PAGE ONE

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3 NUMEBRS AND OPERATIONS CHEAT SHEET - A Rational numbers C B A ADDITION If the signs are the SAME, ADD and use the same sign. If the signs are DIFFERENT, SUBTRACT and TAKE THE SIGN of the number with the GREATEST ABSOLUTE VALUE. SUBTRACTION Rewrite the problem to ADD THE OPPOSITE. Then, follow the rules for adding rational numbers. A. WHOLE: positive counting numbers starting with 0 B. INTEGER: whole numbers and their opposites C. RATIONAL: fractions, repeating decimals and terminating decimals MULTIPLICATION & DIVISION If there is an EVEN NUMBER of signs, the solution is POSITIVE. If there is an ODD NUMBER of signs, the solution is NEGATIVE. Signed numbers Rational number classification 14 : 9 1 : 0 : : 27 : scientific 2.7 : notation 6 3 : 1 : 1 2 : A B A C A C B B C Rational number operations

4 PROPORTIONAL RELATIONSHIPS CHEAT SHEET - A RATE: a ratio with TWO DIFFERENT UNITS $ LB UNIT RATE: a ratio with a quantity of ONE PRICE 1 LB 250 MI 4 HRS MILES 1 HR PROPORTION: two EQUAL ratios MILES HR Rate & PROPORTIONS 49 FT 5 SEC FEET 1 SEC Can be used to find a missing quantity Must be setup correctly; be sure to use labels 432 X 6 8 3,456 6X 576 X 576 MILES IN 8 HOURS Percent vocabulary MARKUP DISCOUNT OTHER tax tip mark up gratuity increase sale price amount off decrease mark down discount whole sale PERCENT: a QUANTITY out of100 commission interest Set up a percent proportion or an equation Solve for the missing quantity Reread the problem to make sure you answer the question Measurement conversions % 100 PART WHOLE PART % WHOLE (as a decimal) MEASUREMENT CONVERSION: converting one measurement system to another Label the various units Use the measurement chart if necessary to find the conversion Set up and solve the proportion IN CM INCHES TO CENTIMETERS KILOGRAMS TO POUNDS X 12.7 X 5 X 5 IN 12.7 CM PERCENT OF CHANGE: the percent GAINED or LOST over a period of time Determine the change Set up a percent proportion Solve for the missing quantity Reread the problem to make sure you answer the question % 100 CHANGE ORIGINAL percent

5 PROPORTIONALITY & SIMILAR SHAPES CHEAT SHEET - A similarity CIRCUMFERENCE Circles SIMILAR FIGURES have CORRESPONDING: 1. PROPORTIONAL sides 2. EQUAL angles DIAMETER C πd C 2πr D A C 12 B H I G J A G B H The FORMULA for the circumference of a circle can be MANIPULATED to solve for π. π 3.14 π 22 7 Scale Factor ENLARGEMENT scale factor is greater than 1 NEW ORIGINAL REDUCTION scale factor is less than 1 The SCALE FACTOR is the ratio in which a figure is DILATED. 3 FT 5 FT SCALE FACTOR OF 1.5 X Y X 4.5 FT Y 7.5 FT scientific notation SCALE DRAWING: uses a SCALE to convert measurements 1 CM 2.5 MILES 1 IN 300 FEET Frequently used on MAPS and BLUEPRINTS Label the various units The conversion will be given Set up and solve the proportion IN FT Scale drawings X X 7 X 7 IN FT

6 EQUATIONS AND INEQUALITIES CHEAT SHEET - A Solving equations Use INVERSE OPERATIONS to UNDO the equation. undo addition or subtraction undo multiplication or division isolate the variable check your work 6x+731 6x24 x4 6(4)+731 GRAPH the inequality statement on a number line to represent THE POSSIBLE SOLUTIONS. VALUE IS INCLUDED VALUE IS NOT INCLUDED Graphing inequalities SAME STEPS as SOLVING EQUATIONS! inequalities When dividing by a negative number, flip the inequality symbol. To check your work, choose a value that is within the constraints of the inequality and plug in the number. If it is correct, then you should get a true statement. 1 2 x 5 > x > 30 x < 60 CHECK 1 (10) 5 > (10) > < 60 INEQUALITY VOCABULARY scientific notation Remember that each term can represent a different inequality symbol when writing inequalities. < < > > less than is fewer than is smaller than below less than or equal to maximum at most is not more than is not greater than greater than or equal to minimum at least is not less than is not smaller than greater than is more than is larger than above equal is same Determine what is being solved for and choose a variable (number of rides, number of feet, etc). Determine the result of the situation (total cost, total height, difference in weight, etc). $5 fee $2 per total pounds + person cost pounds per month total weight 5 2x x 60 If it is not equal, then use the appropriate inequality symbol. Writing equations & inequalities

7 LINEAR RELATIONSHIPS CHEAT SHEET - A Graphing equations RATE OF CHANGE y mx + b y -2x + 2 Y-INTERCEPT EXAMPLES: MILES PER HOUR COST PER ITEM FEET PER SECOND d rt Rate of change You can solve for any of the variables above, if you know the other two values MILES d rt 150 r(2) 75 r HOUR scientific notation Constant of proportionality CONSTANT OF PROPORTIONALITY: the ratio of the y-value to the x-value, represented by k, it is equal to the rate of change EXAMPLE: k y x X Y k 62 2 k 31 X-VALUE independent measured x-axis left side of table top row of table TOTAL SAVINGS ($) Tables & graphs 0 MONTHS Y-VALUE dependent varies y-axis right side of table bottom row of table

8 PERSONAL FINANCIAL LITERACY CHEAT SHEET - A taxes SALES TAX: a percentage of the total amount of a purchase INCOME TAX: a percentage that the government imposes on an individuals earnings % 100 PART PART % WHOLE WHOLE (as a decimal) incentives REBATE: a fixed amount of money that is refunded after a purchase COUPONS: used to discount the price of an item at the time of the sale SALE: a type of discount, typically a percentage off of a purchase SIMPLE: I p r t COMPOUND: A P (1 + r) t interest I interest p principal r annual interest rate (as a decimal) t time (in years) A the future value P principal r annual interest rate (as a decimal) t time (in years) The equations can be used to solve for any missing piece of information. Be sure to change the rate to a decimal and convert any number of months to years. Read carefully for what the question asks. Net worth ASSET: something you OWN LIABILITY: something you OWE ANNUUAL INCOME NECESSARY MONTHLY BUDGET 12 NET WORTH ASSETS LIABILITIES ASSESTS cash in a checking account cash in a savings account investments car (current value) house (current value) LIABILITITES personal loan credit-card debt student loan debt If not given, find the total amount of the monthly budget. To determine the percentage of the budget for each category, set up a percent proportion. % 100 CATEGORY TOTAL $ budgets

9 PROBABILITY CHEAT SHEET - A PROBABILITY PROBABILITY is the LIKELIHOOD of an event occurring. EXPERIMENAL PROBABILITY The ratio of the number of times an event occurs to the total number of trials Based on data Often displayed in tables P(EVENT) # OF WAYS IT OCCURS POSSIBLE OUTCOMES THE COMPLEMENT of an event is the probability of the event NOT occurring. # OF WAYS IT CANNOT OCCUR P(EVENT) POSSIBLE OUTCOMES SAMPLE SPACE is all of the possible outcomes. Create a list, a table, or a tree diagram Multiply the various numbers of options together to get the total outcomes Types of probability A NUMBER CUBE IS ROLLED AND LANDS ON 4 3 OUT OF 17 SWITCHES ARE DEFECTIVE THEORETICAL PROBABILITY The probability of an event happening based on possible outcomes Based on theory 1 THE PROBABILITY OF ROLLING A 4 IS 6 A 50% CHANCE OF A COIN LANDING ON TAILS As the NUMBER OF TRIALS INCREASES, the experimental probability APPROACHES the theoretical probability. INDEPENDENT EVENTS Two or more events in which the results do not impact one another Events where the item is replaced A SPINNER IS SPUN AND A NUMBER CUBE IS ROLLED DEPENDENT EVENTS Two or more events in which the results of the first impact the results of the second Events where the item is not replaced TWO NAMES ARE DRAWN FROM A HAT WITHOUT REPLACEMENT INDEPENDENT VS. DEPENDENT ACE, NOT REPLACING IT, AND DRAWING A QUEEN 2 6 (ace) (queen) SPADE, REPLACING IT, AND DRAWING A TWO (spade) (2)

10 2D GEOMETRY CHEAT SHEET - A polygons AREA OF A TRIANGLE b h 2 CIRCUMFERENCE DIAMETER Circles h h h h b Ab h b b b QUADRILATERALS h h b b 1 b 2 A h(b 1+b 2 ) 2 C πd A πr 2 The AREA of a SEMICIRCLE can be found by DIVIDING THE AREA of the whole circle by TWO. Ab h π 3.14 π 22 7 COMPOSITE FIGURE: a figure that can be DECOMPOSED into basic shapes. Composite figures Find the AREA of the various shapes and then ADD or SUBTRACT. scientific notation Angle relationships The THREE ANGLES in a triangle have a SUM OF180 O. 33 o X X X 72 o 75 o X o D E C A B F COMPLEMENTARY ANGLES: <DBE and <EBF SUPPLEMENTARY ANGLES: <ABC and <CBF

11 VOLUME AND SURFACE AREA CHEAT SHEET - A Volume THE AMOUNT OF SPACE A 3D OBJECT OCCUPIES (UNITS 3 ) PRISMS A prism has two parallel bases that do not touch. Named according to the shape of the base B the area of the base V Bh PYRAMIDS One base, faces come together at a vertex Named according to the shape of the base B the area of the base V 3 Bh HEIGHT OF TRIANGLE BASE h h h h HEIGHT OF PRISM BASE BASE BASE THE TOTAL COVERING ON THE FACES OF A 3D OBJECT EX: WRAPPING A PRESENT, A CARDBOARD NET, PAINTING THE SIDES OF A 3D FIGURE Surface area (UNITS 2 ) TOTAL SURFACE AREA The sum of the area of all of the faces and bases in a 3D figure LATERAL SURFACE AREA The sum of the area of all of the faces, not including bases, in a 3D figure HEIGHT OF TRIANGLE HEIGHT OF TRIANGLE BASE BASE BASE HEIGHT OF TRIANGLE

12 DATA AND STATISTICS CHEAT SHEET - A STATISTICS VOCABULARY MEAN: the average MEDIAN: middle value when ordered from least to greatest MODE: most often repeated RANGE (SPREAD): the difference between the greatest and least values SHAPE: describes the type of graph, including symmetric and skewed SYMMETERICAL DATA: the data is evenly balanced around the mean SKEWED LEFT SKEWED RIGHT CIRCLE GRAPHS: display part-to-whole and part-to-part relationships through percentages. THE ENTIRE CIRCLE HAS A SUM OF 100%. If the total budget is $2,400, then how much is saved? % PART WHOLE X X X $360 Savings 15% Food 25% CIRCLE GRAPHS Mortgage 25% Utilities 15% Insurance 20% If $525 is spent on food, then what is the monthly budget? % PART WHOLE 525 x 25X X $2,100 BOX PLOTS BOX PLOTS are used to compare the SPREAD and DISTRIBUTION in a set of data. MIN Q1 MEDIAN Q3 MAX INTERQUARTILE RANGE: the difference between Q3 and Q1 RANGE: the difference between the maximum and the minimum MIN MODE MEDIAN: the middle value (numbers are already ordered in a dot plot) MAX DOT PLOTS DOT PLOTS are used to display the SPREAD OF THE DATA along an axis.

13 NUMEBRS AND OPERATIONS CHEAT SHEET - B Rational numbers A. : positive counting numbers starting with 0 B. : whole numbers and their opposites C. : fractions, repeating decimals and terminating decimals C B A ADDITION If the signs are the, and use the same sign. If the signs are, and take the sign of the number with the. SUBTRACTION Rewrite the problem to. Then, follow the rules for adding rational numbers. MULTIPLICATION & DIVISION If there is an even number of signs, the solution is. If there is an odd number of signs, the solution is. Signed numbers Rational number classification 14 : 9 1 : 0 : : 14 : scientific 2.7 : notation 6 3 : 1 : 1 2 : Rational number operations

14 PROPORTIONAL RELATIONSHIPS CHEAT SHEET - B RATE: a ratio with $ LB 250 MI 4 HRS 49 FT 5 SEC UNIT RATE: a ratio with a quantity of Percent vocabulary MARKUP DISCOUNT OTHER PRICE 1 LB MILES 1 HR FEET 1 SEC PROPORTION: two ratios Can be used to find a missing quantity Must be set up correctly; be sure to use labels MILES HR Rate & PROPORTIONS X 8 PERCENT: a out of Set up a percent proportion or an equation Solve for the missing quantity Reread the problem to make sure you answer the question Measurement conversions % 100 PART PART % WHOLE WHOLE (as a decimal) MEASUREMENT CONVERSION: INCHES TO CENTIMETERS KILOGRAMS TO POUNDS Label the various units Use the if necessary to find the conversion Set up and solve the proportion PERCENT OF CHANGE: Determine the change Set up a Solve for the missing quantity Reread the problem to make sure you answer the question IN CM X % 100 CHANGE ORIGINAL percent

15 PROPORTIONALITY & SIMILAR SHAPES CHEAT SHEET - B similarity Circles SIMILAR FIGURES have CORRESPONDING: 1. sides 2. angles C πd C 2πr D A C 12 B H I G J The for the circumference of a circle can be to solve for. π 3.14 π 22 7 Scale Factor ENLARGEMENT NEW ORIGINAL REDUCTION The is the ratio in which a figure is. 3 FT 5 FT SCALE FACTOR OF 1.5 X Y scientific notation measurements SCALE DRAWING: uses a to convert 1 CM 2.5 MILES 1 IN 300 FEET Frequently used on and Label the various units The conversion will be given Set up and solve the proportion IN FT Scale drawings X

16 EQUATIONS AND INEQUALITIES CHEAT SHEET - B Solving equations Use to the equation. undo addition or subtraction undo multiplication or division isolate the variable check your work 6x+731 the inequality statement on a number line to represent. SAME STEPS as SOLVING EQUATIONS! inequalities When dividing by a, flip the inequality symbol. To check your work, choose a value that is within the of the inequality and plug in the number. If it is correct, then you should get a true statement. 1 2 x 5 > 25 INEQUALITY VOCABULARY scientific notation Graphing inequalities Remember that each term can represent a different inequality symbol when writing inequalities. < < > > Determine what is being solved for and choose a variable. Determine the result of the situation. + If it is not equal, then use the appropriate inequality symbol. Writing equations & inequalities

17 LINEAR RELATIONSHIPS CHEAT SHEET - B Graphing equations y mx + b 8 EXAMPLES: MILES PER HOUR COST PER ITEM FEET PER SECOND d rt Rate of change You can solve for any of the variables above, if you know the other two values MILES HOUR scientific notation Constant of proportionality CONSTANT OF PROPORTIONALITY: EXAMPLE: k y x X-VALUE independent measured x-axis left side of table top row of table TOTAL SAVINGS ($) Y-VALUE dependent varies y-axis right side of table bottom row of table X Y Tables & graphs 0 MONTHS

18 PERSONAL FINANCIAL LITERACY CHEAT SHEET - B taxes SALES TAX: REBATE: incentives INCOME TAX: COUPONS: SALE: SIMPLE: I p r t COMPOUND: A P (1 + r) t interest I p r t Be sure to change the rate to a and convert any number of months to. Read carefully for what the question asks. A P r t Net worth ASSET: something you LIABILITY: something you ANNUUAL INCOME NECESSARY MONTHLY BUDGET 12 NET WORTH ASSETS LIABILITIES ASSESTS LIABILITITES If not given, find the of the monthly budget. To determine the of the budget for each category, set up a percent proportion. budgets

19 PROBABILITY CHEAT SHEET - B PROBABILITY PROBABILITY: P(EVENT) # OF WAYS IT OCCURS POSSIBLE OUTCOMES THE COMPLEMENT: # OF WAYS IT CANNOT OCCUR P(EVENT) POSSIBLE OUTCOMES SAMPLE SPACE: Create a list, a table, or a tree diagram Multiply the various number of options together to get the total outcomes Types of probability EXPERIMENAL PROBABILITY The of the number of times an event occurs to the total number of trials Based on Often displayed in A NUMBER CUBE IS ROLLED AND LANDS ON 4 3 OUT OF 17 SWITCHES ARE DEFECTIVE THEORETICAL PROBABILITY The probability of an event happening based on all Based on 1 THE PROBABILITY OF ROLLING A 4 IS 6 A 50% CHANCE OF A COIN LANDING ON TAILS As the NUMBER OF TRIALS INCREASES, the experimental probability the theoretical probability. INDEPENDENT EVENTS Two or more events in which the results impact one another Events where the item is A SPINNER IS SPUN AND A NUMBER CUBE IS ROLLED DEPENDENT EVENTS Two or more events in which the results of the first the results of the second Events where the item is replaced INDEPENDENT VS. DEPENDENT ACE, NOT REPLACING IT, AND DRAWING A QUEEN (ace) (queen) SPADE, REPLACING IT, AND DRAWING A TWO. TWO NAMES ARE DRAWN FROM A HAT WITHOUT REPLACEMENT (spade) (2)

20 2D GEOMETRY CHEAT SHEET - B polygons Circles TRIANGLES h h h b b b C πd A πr 2 QUADRILATERALS h b h b h b 1 b 2 The of a can be found by dividing the area of the whole circle by. π 3.14 π 22 7 COMPOSITE FIGURE: a figure that can be into basic shapes. Composite figures Find the of the various shapes and then or. scientific notation Angle relationships The in a triangle have a. 33 o 75 o X o A C COMPLEMENTARY ANGLES: SUPPLEMENTARY ANGLES: D B E F

21 VOLUME AND SURFACE AREA CHEAT SHEET - B Volume THE AMOUNT OF A 3D OBJECT OCCUPIES (UNITS 3 ) PRISMS PYRAMIDS A prism has two that do not touch. Named according to the of the base B V Bh One base, faces come together at a Named according to the of the base B V 3 Bh THE ON THE FACES OF A 3D OBJECT Surface area EX: (UNITS 2 ) TOTAL SURFACE AREA The of the area of all of the faces and bases in a LATERAL SURFACE AREA The sum of the area of all of the faces,, in a 3D figure

22 DATA AND STATISTICS CHEAT SHEET - B STATISTICS VOCABULARY MEAN: MEDIAN: MODE: RANGE (SPREAD): CIRCLE GRAPHS: display and part-to-part relationships through percentages. THE ENTIRE CIRCLE HAS A SUM OF. Savings 15% Food 25% CIRCLE GRAPHS Mortgage 25% Utilities 15% Insurance 20% SHAPE: SYMMETERICAL DATA: If the total budget is $2,400, then how much is saved? If $525 is spent on food, then what is the monthly budget? BOX PLOTS BOX PLOTS are used to compare the and in a set of data. INTERQUARTILE RANGE: RANGE: MEDIAN: the middle value (numbers are already ordered in a dot plot) DOT PLOTS DOT PLOTS are used to display the along an axis.

23 NUMEBRS AND OPERATIONS CHEAT SHEET - C Rational numbers ADDITION SUBTRACTION MULTIPLICATION & DIVISION Signed numbers Rational number classification scientific notation Rational number operations

24 PROPORTIONAL RELATIONSHIPS CHEAT SHEET - C Percent vocabulary Rate & PROPORTIONS Measurement conversions percent

25 PROPORTIONALITY & SIMILAR SHAPES CHEAT SHEET - C similarity Circles Scale Factor Scale drawings

26 EQUATIONS AND INEQUALITIES CHEAT SHEET - C Solving equations inequalities Graphing inequalities INEQUALITY VOCABULARY scientific notation Writing equations & inequalities

27 LINEAR RELATIONSHIPS CHEAT SHEET - C Graphing equations Rate of change Constant of proportionality Tables & graphs

28 PERSONAL FINANCIAL LITERACY CHEAT SHEET - C taxes incentives interest Net worth budgets

29 PROBABILITY CHEAT SHEET - C PROBABILITY Types of probability INDEPENDENT VS. DEPENDENT

30 2D GEOMETRY CHEAT SHEET - C polygons Circles Composite figures scientific notation Angle relationships

31 VOLUME AND SURFACE AREA CHEAT SHEET - C Volume Surface area

32 DATA AND STATISTICS CHEAT SHEET - C STATISTICS VOCABULARY CIRCLE GRAPHS BOX PLOTS DOT PLOTS