Unit 1 Number System Fluency Greatest Common Factor (GCF) Common Multiple (LCM) Long Division Operations with Decimals Math 6/7 Unit 1 Calendar 7/30 7/31 8/1 8/2 8/3 Rules and Procedures; Getting to Know You! Rules and Procedures; Group Work Task Unit 1 Pre-test; Problem Solving Task 8/6 8/7 8/8 8/9 8/10 MSG Set-up; GCF & LCM Problem Solving with GCF & LCM Problem Solving with GCF & LCM Long Division Problem Solving with Long Division; Short Quiz 8/13 8/14 8/15 8/16 8/17 Operations with Decimals Operations with Decimals It! Challenge; Operations with Decimals Problem Solving with GCF/LCM, Long Division, & Decimals Review Activity, Quiz 8/20 8/21 8/22 8/23 8/24 Dividing Fractions with Models & Algorithms Dividing Fractions with Models & Algorithms Dividing Fractions with Models & Algorithms Unit 1 Review Unit 1 Test
# of red streamers __________ # of blue streamers __________ Long Division The purpose of division is to determine how many times the divisor fits into the dividend. Division is the inverse (opposite operation) of multiplication. You can use multiplication to “undo” or check your answer. Multiply the quotient by the divisor and you should get the dividend. Example: Long Division and Remainders What is a remainder? A __________ exists when your __________ doesn’t go into your __________ evenly, meaning that you don’t have enough remaining to make another group. It is the “_________ __________” amount after you have divided. Example: 1) 23 4 = 4 goes into 23 five whole times, but there are three more left. Those three won’t allow us to make another group of 4, so 3 is the remainder. How do we write remainders? Up until this point, you have probably been writing remainders as “R 3”. Now that you know more about what a remainder is, you will need to write your remainders differently to reflect what a remainder actually represents. We can work with remainders in one of two ways: Remainders as Fractions Divide: 139 6 Note: When you divide, the divisor (6) goes into the dividend (139), 23 whole times, but there is 1 left over that won’t make another group of 6. 1 is the remainder. We it as a fraction with the remainder over the divisor. “There is one left when we needed six to make another whole.” Remainders as Decimals When you want to write your remainder as a decimal, you add a zero and continue to divide until you get a remainder of zero or you round your answer according to your instructions. If there is no decimal, you must add a decimal before you add a zero. You Try: Find the quotient and write the remainder as a fraction. 1) 154 ÷ 4 = 2) 121 ÷ 8 =
5) _____ ÷ _____ = _____ 6) _____ ÷ _____ = _____ 7) _____ ÷ _____ = _____ Dividing Fractions Using Common Denominators Example: You Try: 1) 2) 3) 4) 5) 6) Reciprocals A _______________ is one of two numbers whose product is 1. It is the result of “flipping” a fraction. Examples of reciprocals: 1) and 2) and 3) = and You Try: Find the reciprocals: 1) 2) 3) 4) 4 5) 6) 7
7) 8) 9) = Dividing Fractions Using SOAR S – First fraction stays the SAME. (But make sure you change all mixed numbers to improper fractions first.) O – OPPOSITE operation (division to MULTIPLICATION). AR – AND RECIPROCAL Example: S (Same) 0 (Opposite Operation) AR (And Reciprocal) You Try: 1) = 2) = 3) = 4) = 5) = 6) = 7) = 8) = 9) = Dividing Fractions Practice Divide. Use any of the methods we have learned to find the quotient. Answer as a mixed number if possible. 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12)