Document Sample

MULTIPLICATION Definition – Multiplication of whole numbers is repeated addition: 3x5=5+5+5 In this example 3 and 5 are factors; 15 is the product. Three Models of Multiplication Set model: 3 x 5 is interpreted as 3 groups of 5 objects. Measurement model 3 x 5 is interpreted as a bar diagram with 3 sections of length 5. Or using a number line, start at 0 and take 3 hops of length 5. Rectangular array model 3 x 5 is interpreted as 3 rows of 5 objects. The objects could be dots, stars or boxes. While this is often called the area model, you should not use this term with students until you have introduced the concept of area in 3rd or 4th grade. Properties of Multiplication 1. Multiplicative Identity: 1 x 8 = 8 1 group of 8 2. Commutative Property: 3 x 5 = 5 x 3 Which model would you use to explain this? 3. Associative Property: (2 x 3) x 4 = 2 x (3 x 4) See graphic with 2 shelves each with 3 boxes of 4 flowers on page 26. • Together the associative and commutative properties give us an “any order” property for multiplication of a list of factors 4. Distributive Property 3 x (12) = 3 x (10 +2) = 3 x 10 + 3 x 2 This can be explained nicely using rectangular arrays. 3 10 2 Important These properties should be taught as principles about the ways numbers behave, illustrated with models and practiced with mental math exercises and word problems. They are not simply rules to memorize. Teaching Multiplication Three Overlapping Stages Before starting students should be able to: 1. Count to 100. 2. Know basic addition doubles 1+1= up to 10 + 10 = 3. Be able to skip count by 2, 3, 5, and 10. Stage 1 - (End of grade 1) –Focuses on the meaning of multiplication as repeated addition. Uses rectangular array model. Stage 2 – (Grades 2 and 3) – Focuses on increased computational proficiency and conceptual understanding. Use of word problems, mental math and practice work sheets. Stage 3 – (End of third grade) Mastery of single digit multiplication. Example – Mr. Bisk buys 2 boxes of pies. Each box has 4 pies. If the pies cost $3 each, how much did he pay. Note that this is a two step problem. Examples – Mental Math • 6 x 20 = 6 x (2 x 10) = (6 x 2) x 10 = 12 tens = 120 • 8 x 9 = 8 x (10 – 1) = (8 x 10) – (8 x 1) = 80 – 8 = 72 DIVISION Definition – Division is defined by missing factors. The number 56 ÷ 8 is the missing factor in ____ x 8 = 56. Multiplication and Division are opposite operations. Interpretations of 20÷4 • Partitive Model: “20 is 4 groups of what unit?” • Measurement Model: “20 is how many groups of 4?” It is important to use both models. Which model works for division by a fraction? Example: 12 pounds of flours is put into bags weighing 1 ½ pounds each. How many bags are there? Quotient Remainder Theorem Pretend you are in third grade. Find: Quotient Remainder Theorem For any two whole numbers A and k with k≠0, there are unique whole numbers q and r such that A=k·q+r where 0 ≤ r < k How would you illustrate 20 ÷ 3 with a “rectangular array with remainder?” Division by Zero 10 ÷ 0 = ? 0÷0=? Why is it undefined? Case 1: Suppose 10 ÷ 0 = ?. Then ? x 0 = 10. Can’t be! Case 2: Suppose 0 ÷ 0 = ?. Then ? x 0 = 0. Anything works here. But our answer is supposed to be unique. Homework Read sections 1.5, 1.6 and 1.7 HW Set 5 - Problems 1, 2cd, 4, 6, 7, 8, 9a HW Set 6 - Problems 1, 2ab, 3ab, 6 1. Write as a base 10 number: 431five 2. Write short word problems illustrating: a. The comparison model for 12-5 b. The part-whole model for 17-9

DOCUMENT INFO

Shared By:

Categories:

Tags:

Stats:

views: | 126 |

posted: | 11/25/2011 |

language: | English |

pages: | 24 |

OTHER DOCS BY 177P72yh

How are you planning on using Docstoc?
BUSINESS
PERSONAL

By registering with docstoc.com you agree to our
privacy policy and
terms of service, and to receive content and offer notifications.

Docstoc is the premier online destination to start and grow small businesses. It hosts the best quality and widest selection of professional documents (over 20 million) and resources including expert videos, articles and productivity tools to make every small business better.

Search or Browse for any specific document or resource you need for your business. Or explore our curated resources for Starting a Business, Growing a Business or for Professional Development.

Feel free to Contact Us with any questions you might have.