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Division: Part A (Dividing with basic facts, with and without remainders) (A6: demonstrate (with & without concrete materials) and understanding of ÷ (3digit by 1digit) & remainders) Big Idea: the inverse of multiplication - when we divide a number or group of things into equal parts - e.g. your mom bakes a dozen muffins and there are six of you, how many muffins will you each get Related Vocabulary: quotient, front-end estimation (rounding), estimate, multiplication, division, dividend, divisor Model: Division is the inverse of multiplication. http://www.harcourtschool.com/glossary/math2/index5.html See the following link for an introductory lesson: showing where we are going http://www.learnalberta.ca/ Grade 5 / Mathematices/ Division of Whole Numbers lessons Lesson: (adapted from Saxon Math) We will use basic facts that you already know to help us getting ready for complicated division questions. Look at two ways you see basic multiplication facts written: 1) 2 X 4 = 8 2) 4 X2 3) 4(2) You will also see division questions written different ways. Here are three of them: 1) 8 ÷ 2 = 4 2) 8/2 _ 4_ 3) 2) 8 These numbers all have names. For example, …..in the equation 2 X 4 = 8 factor X factor = product If we know one factor, we can find out the other factor. For example, ….. 2 X ? = 8 ?X4=8 The process of finding a missing factor is called division. 1 _ 4_ * the 2 is now called the divisor 8÷2=4 or as we will be writing it, 2) 8 ** the 8 is called the dividend *** the answer (4) is the quotient If we know that the product is 8 and one factor is 2, then we are asking “2 times what number equals 8? ” Since we know our multiplication facts, we know that the missing number is 4. A division problem is like a miniature multiplication table. Do you see where the factors are? 0 1 2 3 4 5 6 7 8 0 0 0 0 0 0 0 0 0 0 1 0 1 2 3 4 5 6 7 8 2 0 2 4 6 8 10 12 14 16 3 0 3 6 9 12 15 18 21 24 4 0 4 8 12 16 20 24 28 32 5 0 5 10 15 20 25 30 35 40 6 0 6 12 18 24 30 36 42 48 7 0 7 14 21 28 35 42 49 56 8 0 8 16 24 32 40 48 56 64 Practice: Let’s solve the following orally. Please watch where we write our answer. check out http://www.rainforestmaths.com/ (grade 5 > division) How many times does the divisor go into dividend for each question below? ____ _____ _____ _____ 2)12 3) 6 7)21 5)25 These work out nicely! Here we have our original division question. We have 8 stars divided neatly into groups of 2. We can divide our 8 stars into equal groups of 2. 4_ 2)8 8_ (We write the product of 2 X 4 just below our 8. As you can see, 0 we have nothing left over. Practice: ____ _____ _____ _____ _____ _____ 3)12 2) 6 8)24 5)35 7)63 8)72 2 However, sometimes the number inside is not an even product and we discover that we have a remainder, something left over. Here we have 9 stars. If I want to divide them into groups of 2, we will have 1 remaining. We can divide our 8 stars into equal groups of 2 but then we have 1 left over. 4_ 2)9 8 (Again, we write the product of 2 X 4 just below the 8. 1 However, this time we have 1 left over, the remainder) We write our final answer the following way: 4 r 1_ 2)9 8 . 1 view http://www.ronblond.com/MathGlossary/ (see division) and http://new.learnalberta.ca/content/memg/Division02/Divide%20-%20Division/index.html Some more practice……… check out http://www.rainforestmaths.com/ (grade 5 > division > 2 digit with remainder) In pairs (someone beside or near you), estimate the following (without a remainder). ____ _____ _____ _____ 2)13 3) 11 7)25 5)24 ____ _____ _____ _____ 4)7 6)13 9)29 8)35 3 Lock Down What You Know: Rewrite the following questions and solve. Remember to line up your place value columns and write your numbers in the correct spot. This activity is just to let you practice what you already know. a) 14 ÷ 7 = b) 24 ÷ 8 = c) 34 ÷ 4 = d) 69 ÷ 8 = e) 36 ÷ 9 = f) 24 ÷ 7 = g) 37 ÷ 5 = h) 49 ÷ 7 = i) 85 ÷ 9 = 4