Transcript ppDivPart1
Multiplication and Division • In mathematics, we say that addition and subtraction are inverse operations. This is why there are related facts: 3+4=7 7-4=3 7-3=4 • In this same way, multiplication and division are inverse operations: 3 • 4 = 12 12 ÷ 4 = 3 12 ÷ 3 = 4 Exploration 3.15 • Make up a story problem for 15 ÷ 3. • Share them with your group. • Sort them into two or more piles. Select one from each pile, and read it to the class. Different Word Problems • In any division problem: • Dividend ÷ Divisor = Quotient. • In word problems, we usually have a rate as part of the problem (apples per person). Where the rate appears determines the type of word problem. Models for Division • Carlos has 24 apples. If it takes 4 apples per pie, how many pies can he make? This is repeated subtraction. • Carlos has 24 apples. If he wants to make 4 pies, how many apples will be in each pie? This is partitioning. Missing Factor Model of Division 28 ÷ 4 = Can be thought of as 4 X ? = 28 Terminology • • • • • b ÷ n = a iff a∙n = b b is the dividend n is the divisor a is the quotient a and n are the factors of b and b is a multiple of a and n. The number line! • We use the number line with multiplication when we think about continuous models, or multiplication as repeated addition. • We can use the number line here to show division as repeated subtraction. What Properties Hold for Division? Dividing by Zero No calculators! Do the following division problem 159 ÷ 13 Division • Can you divide without using the Long Division Algorithm? • Hint: the answer is YES! • Let’s see what students do. Strategies • Amelinda and Alosha both used repeated subtraction. • Elaine and Thomas used a combination of repeated subtraction and something else. Describe this. For this weekend • You will finish pages 1 - 15 in your packet. • This will count as a project grade, not a homework grade--there are 41 total questions that need to be answered. A total of 40 points. • For each question, be sure to explain both how the student answered the question, and why the mathematics is appropriate. • The length of the answer is not what will get you a good grade!!!