Math CC 7: ACCENTUATE THE NEGATIVE INV. 3 Name: Per: INVESTIGATION 3: MULTIPLYING AND DIVIDING RATIONAL NUMBERS Date Learning Target/s Classwork Homework Self-Assess Your Learning Day 1 Thursday Students will multiply rational 9/29 numbers, including fractions. Day 2 Friday 9/30 Day 3 Monday 10/3 Day 4 Tuesday 10/4 ATN Investigation 3 Common Core Standards Students will play the Integer Product Game to extend their knowledge of integers (and for fun!). Students will divide rational numbers, including fractions. Students will demonstrate understanding of + / - / x / of rational numbers through a check up quiz Pg. 2-3: ATN 3.2 Multiplying rational numbers Pg. 6-7: ATN 3.4 PRODUCT INTEGERS GAME Pg. 9-10:ATN 3.3 Dividing rational numbers ATN Check Up Quiz #2 Pg 4: Love story worksheet Correct online Pg. 8: Multiplying and Dividing Integers practice Correct with EDpuzzle Pg. 11: Multiplying and Dividing Integers practice Correct online pg. 12: PEMDAS Investigation 4 preparation Correct online 7.NS.2b. 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. 7.NS.12c Apply properties of operations as strategies to multiply and divide rational numbers. 7.NS.1d 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. Student Signature: Due: Wed. Oct 5, 2016 Parent/Guardian Signature: Date: 1
Day 1 ATN 3.2: Multiplication of Rational Numbers 1. Complete the tables in each group based on the highlighted algorithm. Group 1 4 * 3=12 5*9= 5.1*1= 3 4 1 2 = a. What do the examples in group 1 have in common? Group 2 4 * 3= 12 5* 9= 5.1*1= 3 4 1 2 = What do the examples in group 2 have in common? Group 3 4 * 3= 12 5* 9= 5.1* 1= 3 4 1 2 = What do the examples in group 3 have in common? b. Write and solve two additional problems for each group. 1. 2. b. Write and solve two additional problems for each group. 1. 2. b. Write and solve two additional problems for each group. 1. 2. Based on your conclusion above, what is the rule of multiplication for each set of signs? Positive x Positive = Positive x Negative = Negative x Positive = Negative x Negative = 2
For each of the products below predict the sign: 7 ( 8) ( 3) 12 ( 5) ( 4) 1 2 ( 2 3 ) 3 Explain how you used what you know about multiplying two rational numbers to multiply 3 rational numbers: Predict whether the sign of each product is positive or negative. Explain your thinking. Equation Sign Explanation Positive Negative Positive Positive Positive Positive Negative Negative Negative Negative Find the product in each group 2 x 3 and 3 x 2 2 x 3 and 3 x 2 2 x 3 and 3 x 2 Equal Not equal Equal Not equal Equal Not equal Define commutative property: What operations are commutative? Addition Subtraction Multiplication Division 3
Day 1 ATN 3.2 Homework (Online CORRECT your errors with a red pen): 4
EXTRA PRACTICE 5
Day 2 ATN 3.4: Applying Mulitiplication of Integers Rules: Integer Product Game 1)Player A puts a paper clip on a number in the factor list. 2) Player B puts the other paper clip on any number on the factor list, including the number chosen by Player A. Player B then marks the product of the 2 factors on the product grid. 3) Player A moves either one of the paper clips to another number. He or she then marks the new product with a different color than player B. 4) Each payer takes turns moving a paper clip and marking a product. A product can only be marked by one player. 5) The winner is the first player to mark 4 squares in a row (up, down, across, diagonally) 6
A. What strategies did you find useful in playing the game? B. What pair(s) of numbers from the factor list will give each product? a. 5 b. -12 c. 12 d. -25 C. Your opponent puts a paper clip on -4. List 5 products that you can form, assuming they are not marked. Tell where you would need to put your paper clip in each case. 1. 2. 3. 4. 5. D. Describe the moves to make in each case. 1. The paper clips are on -5 and -2. You want a product of -15. 2. The paper clips are on -3 and -2. You want a product of -6. 3. Your opponent will win with 24. What numbers should you avoid with your paper clip moves? E. Mia thinks the game could be called the Division game. Explain why Mia might think this. 7
Day 2 Homework. ATN Inv 2/3 PRACTICE: CORRECT with the EDpuzzle (with red pen): Write a number sentence for each and solve: 1) Madison eats 2 cups of popcorn every day. How many cups of popcorn are gone after 6 days? Number Sentence: Answer: 2) If she started with 24 cups of popcorn, how many days will it take to eat all of the popcorn? Number Sentence: Answer: 3) Tyler, Marco, Ryan and William want to buy a pizza that cost $16. How much money will they each owe if they divide the debt for the pizza evenly? (Think cost) Number Sentence: Answer: Solve: 18 + 6 = 12 + -3 = 18 6 = 12 ( 3) = 18 x 6 = 12 x 3 = 18/6 = 12/ 3 = 8
Day 3 ATN 3.3: Division of Rational Numbers 2. Complete the tables in each group based on the highlighted algorithm. Group 1 12 3 = 4 30 6 = 5 15 5 = 9 4.5 = 5 1 2 = a. What do the examples in group 1 have in common? Group 2 12 3 = 4 30 6 = 5 15 5 = -9 4.5 = 5 1 2 = What do the examples in group 2 have in common? Group 3 12 3 = 4 30 6 = 5 15 5 = -9 4.5 = 5 1 2 = What do the examples in group 3 have in common? b. Write and solve two additional problems for each group. 1. b. Write and solve two additional problems for each group. 1. b. Write and solve two additional problems for each group. 1. 2. 2. 2. Based on your conclusion above, what is the rule of division for each set of signs? Positive Positive = Positive Negative = Negative Positive = Negative Negative = 9
Find the product in each group 12 4 = 4 12 = 3 2 = 2 3 = 16 8 = 8 16 = Equal Not equal Equal Not equal Equal Not equal Define communitive property: What operations are commutative? Addition Subtraction Multiplication Division Solve: 1) 5 + 5= 2) 7.3 + 7.3= 3) 9 + 9= The examples above are examples of additive inverse. In your own words explain what the additive inverse is: Recall that some fractions have decimals that terminate. For example, 3 =.75. Other fractions have 4 decimals that repeat. For example, 1 =.33333. =.3. The 3 repeats. 3 1) State whether each fraction will terminate or repeat. The write each fraction as a decimal. 2 = Terminate Repeat 5 3 8 = Terminate Repeat 5 6 = Terminate Repeat 35 10 = Terminate Repeat 8 9 = Terminate Repeat 3 11 = Terminate Repeat List two other fractions that will terminate, give their decimal representations: 1) List two other fractions that will repeat, five their decimal representations: 1) 2) 2) 10
Day 3 ATN 3.3 Homework. Multiplying and Dividing Integers practice. SHOW YOUR WORK! (Online CORRECT your errors with a red pen): Solve using the algorithms from class: 1) 11 * 9 = 2) 8 * 10 = 3) 4 * 3 = 4) 15 * 2 = 5) 1( 6) = 6) ( 8.1) 1 = 7) 2.4( 1.2) = 8) 1.5*4 = 9) 1 2 3 4 = Solve the equations using the algorithms from class. 10) 12 3 = 11) 64 8 = 12) 2.5 5= 13) 1 1 6 14) 108 24 15) 19.5-3 16) 2 3 = 17) 7 10 = 11
Day 4 ATN Investigation 4 PREPARATION. Online CORRECT your errors with a red pen. Solve the equations. SHOW YOUR WORK! 1) ( 6 x 9) + (10 x 2) = 2) 2(6-1) (14 2) = 3) (66 6) x (17 5) = 4) (41 11) x 2² = 5) (10 + 2)² (12 3) = 12