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QPA First Nine Weeks Review

QPA First Nine Weeks Review. MCC7.NS 1 Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.

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QPA First Nine Weeks Review

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  1. QPA First Nine Weeks Review MCC7.NS 1 Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. MCC7.NS 2 Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. MCC7.NS 3 Solve real-world and mathematical problems involving the four operations with rational numbers.

  2. MCC7.NS.1.a  Describe situations in which opposite quantities combine to make 0. If you are playing a board game and advance 3 on your first place and go back three on your second play, how much of a gain have you made? +3 -3 = 0; No gain

  3. MCC7.NS.1.a  Describe situations in which opposite quantities combine to make 0. 1 1 2) What is -5 + 5, - (- ) - , or 3.4 – 3.4? 5 5 Opposites make zero

  4. MCC7.NS.1b Understand p + q as the number located a distance |q | from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts. 3) Adding the value of what points would result in a sum of zero? A B C D 1 -1 0 1 6 A & D both equal 5/6 away from zero and combine to make zero.

  5. MCC7.NS.1b Understand p + q as the number located a distance |q | from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts. 4) Remember: Distance is always positive. We can not travel negative distances. What is the distance from 6 to -6? -6 0 6 Distance is always positive: 12

  6. MCC7.NS.1b Understand p + q as the number located a distance |q | from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts. 5) Remember: Distance is always positive. We can not travel negative distances. What is the distance from A to B? A B -1 0 1 2 2 3 3 Distance is always positive: 4/3

  7. MCC7.NS.1b Understand p + q as the number located a distance |q | from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts. 6) If your checking account has a balance of $425.23 and you write a check for $98.95 and make a deposit of 324.92, what is your balance? $425.23 - 98.95 $326.28 +324.92 $651.20 Subtract checks & add deposits to your balance.

  8. MCC7.NS.1.c Understand subtraction of rational numbers as adding the additive inverse, p – q = p + (-q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts. 7) Remember: Adding a negative is the same as subtracting a positive. 13 – 19 = 13 + (-19) = -19 + 13 -6

  9. MCC7.NS.1.c Understand subtraction of rational numbers as adding the additive inverse, p – q = p + (-q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts. 8) You are in a hot air balloon in Death Valley (where land is at 86 meters below sea level). You are at 48 feet above sea level. Your best friend is at 25 feet below sea level. How far apart are you? Distance is positive. 48 to zero + 25 feet below = 73 feet apart.

  10. MCC7.NS.1.c Understand subtraction of rational numbers as adding the additive inverse, p – q = p + (-q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts. 9) Remember: Adding a negative is the same as subtracting a positive. a – b = a + (-b) = -b + a -b –(-a)

  11. MCC7.NS.1.c Understand subtraction of rational numbers as adding the additive inverse, p – q = p + (-q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts. 10) Remember: Distance is always positive. What is the distance between point A and point B. A B C D -1 0 1 Point A -5/6, Point B -1/3, Distance 3/6 = 1/2

  12. M7N1.d. Apply properties of operations as strategies to add and subtract rational numbers. 11) -22.23 + 18.98 Same signs, sum and keep. Different signs, subtract. Remember to put the larger absolute value on top. -22.23 +18.98 -3.25 Keep the sign that’s further out (larger absolute value), then you will be exact.

  13. M7N1.d. Apply properties of operations as strategies to add and subtract rational numbers. 2 3 -3 - (-1 ) 12) Solve. 5 4 8 15 -3 + 1 20 20 28 15 -2 + 1 20 20 13 -1 20

  14. M7N1.d. Apply properties of operations as strategies to add and subtract rational numbers. 13) Is -34.4 + 72 greater than or less than 23 – (-15)? 72. 23 -34.4 +15 37.6 38 <

  15. M7N1.d. Apply properties of operations as strategies to add and subtract rational numbers. 14) Again in Death Valley you are in a hot air balloon. You start at 80 feet above sea level and descend (go down) 75 feet, then 25 feet and 8 feet more. What is position in reference to sea level? 80 – (75 + 25 + 8) 80 – (108) -28 or 28 feet below sea level

  16. MCC7.NS.2.a  Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (-1)(-1) = 1and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts. 15) Your extended family is going to the Columbia County Fair. If there are 2 adults who are not going to ride anything and only pay $8 each for admission and 7 who pay $19.50 each to get a ride everything ticket, how much will it cost to get into the fair? 2  $8 + 7  $19.50 $16 + 136.50 $152.50

  17. MCC7.NS.2.a  Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (-1)(-1) = 1and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts. 16) 4 (23) = 4  20 + 4  3 because of the what property? Distributive property What does this equal? 92

  18. MCC7.NS.2.a  Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (-1)(-1) = 1and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts. 17) Again in Death Valley you are in a hot air balloon. You are at 2 feet below sea level and cut off the heat. You start to descend at a rate of 5 feet per minute for 10 minutes. What is your position in relation to sea level? -2 + (-5  10) -2 - 50 52 below sea level or -52

  19. MCC7.NS.2.a  Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (-1)(-1) = 1and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts. 1 1 -3  -1  - 5 18) Solve. 5 4 16 5 5 -  -  - 5 4 1 1 4 16 5 5 - ¢ - ¢ - 5 4 1 1 1 -20

  20. MCC7.NS.2.b       Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers then –(p/q) = (-p)/q = p/(-q). Interpret quotients of rational numbers by describing real-world contexts. 19) What does the word quotient mean? Answer to a division problem Solve the following: -17.64 ÷ -2.1 = 8.4 -125 ÷ .25 = -500 ⅝ ÷ -½ = -1¼

  21. MCC7.NS.2.b       Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers then –(p/q) = (-p)/q = p/(-q). Interpret quotients of rational numbers by describing real-world contexts. 20) We have 20 pounds of sugar. There are roughly 2 cups per pound of sugar. If we are making candy that calls for 1⅓ cups per batch, how many batches can we make with 20 pounds of sugar? 1 20 lbs.  2 cups per pound ÷ 1 per batch 3 1 80 cups ÷ 1 cups per batch 3 80 4 ÷ 1 3 20 80 3 = 60 batches 1 4 1

  22. MCC7.NS.2.b       Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers then –(p/q) = (-p)/q = p/(-q). Interpret quotients of rational numbers by describing real-world contexts. 21) Match the following to the property that it demonstrates. Commutative property a + b = b + a a + 0 = a a(b + c) = a b + a c a + (b + c) = (a + b) + c Identity property Distributive property Associative property

  23. MCC7.NS.2.c Apply properties of operations as strategies to multiply and divide rational numbers 1 -10  -1 22) Solve. 4 10 5  - - 1 4 5 10 5 - ¢ - 1 4 2 25 12½ or 2

  24. MCC7.NS.2.c Apply properties of operations as strategies to multiply and divide rational numbers 23) If book soxs cost $.75 each and we spent $6.75 on book soxs, how many did we buy? $6.75 ÷ $.75 $.75 $6.75 9 book soxs

  25. MCC7.NS.2.c Apply properties of operations as strategies to multiply and divide rational numbers 24) The cheerleaders are selling spirit tattoos. If they make $.20 profit on each on, how many do they have to sell to make $300 profit? $300 ÷ $.20 $.20 $300 1500 Go Team

  26. MCC7.NS.2.c Apply properties of operations as strategies to multiply and divide rational numbers 3 25) What decimal and percent equal ? 8 .3 7 5 375 . % 8 3.00 -2 4 60 56 40 0.375 and 37.5%

  27. MCC7.NS.2d Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats. 1 3 26) 1 - equals what as a decimal? 4 8 .8 7 5 3 2 1 - 8 8 8 7.00 -6 4 3 10 0 - 60 8 8 56 7 40 8 0.875

  28. MCC7.NS.2d Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats. 27) In Mrs. Cason’s homeroom 14 out of 26 are boys. What percent are boys? Round to the nearest whole percent. .5 3 8 26 14.00 -130 100 78 220 0.538 equals about 54%

  29. MCC7.NS.3 Solve real-world and mathematical problems involving the four operations with rational numbers. 28) We start out with $45 spend $8 and spend $9 more. Then we earn $25. What do we have now? 45 – 8 - 9 + 25 37 – 9 + 25 28 + 25 53

  30. MCC7.NS.3 Solve real-world and mathematical problems involving the four operations with rational numbers. 29) The highest temperature on record for Africa is 136° F recorded in Libya, Africa. The lowest temperature on record for Africa is -11° F recorded in Morocco, Africa. What is the difference between these two temperatures? 136 - (-11) 136 + 11 147 difference

  31. MCC7.NS.3 Solve real-world and mathematical problems involving the four operations with rational numbers. 30) Remember: Distance is always positive. What is the distance between point A and point C. A B C D -5 0 5 6

  32. MCC7.NS.3 Solve real-world and mathematical problems involving the four operations with rational numbers. 31) What integer would be 15 to the right of point A? 10 A B C D -5 0 5 What integer would be 15 to the left of point A? -20

  33. MCC7.NS.3 Solve real-world and mathematical problems involving the four operations with rational numbers. 32) Kaylee has four textbooks each weighing 1 ¾ pounds. How much do they weigh altogether? 3 4  1 4 4 7  1 4 1 4 7  1 4 1 7 pounds

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