2008 USM Summer Math Institute Co-Sponsored by Institutions of Higher Learning (IHL) U.S. Department of Education (No Child Left Behind Funding) The Center for Science and Mathematics Education The Department of Mathematics College of Science and Mathematics College of Education and Psychology Day Six PowerPoint Presentations, Integers, and Enrichment

2008 USM Summer Math Institute Your Mathematics Instructors, Staff and Partners Ms. Michelle Green, Co-Director and Co-Instructor for (SM)2I Stringer Attendance Center National Board Certified/Early Adolescence Email mgreen@westjasper.k12.ms.us , Phone 601-428-5508 Dr. Myron Henry, Director and Co-Instructor for (SM)2I Department of Mathematics and the Center for Science and Mathematics Education Johnson Science Tower 314 Email myron.henry@usm.edu, Phone 601-266-4739 or 266-6516 All Participants (that’s you)

Day six. Pp presentations built by us. Let's present! Day Six of (SM)2I Day six. Pp presentations built by us. Let's present! Finish Power Point Slides Power Point Presentations (15 minutes per team) Enrichment: Even Numbers and Sums of Primes Goldbach’s conjecture Even numbers (2-60) as the sum of primes

Multiplying Integers You can use patterns to find rules for multiplying integers. Activity 1 Complete Table 1. Table 1 Expression Product 3 • 3 9 3 • 2 ? 3 • 1 3 • 0 2 What pattern do you see as you read down the Product column in Table 1? Extend Table 1 using this pattern to find the next two products, 3 • (–1) and 3 • (–2). 6 3 3 What do you notice about the product of a positive integer and a negative integer? 3 •( –1) ? 3 • (–2) – 3 – 6

Multiplying Integers -9 -6 -3 3 6 You can use patterns to find rules for multiplying integers. Activity Table 2 4 Look at Table 2. Then use your answer from Step 3 to complete the table. Expression Product –3 • 3 –3 • 2 –3 • 1 –3 • 0 -9 5 What pattern do you see as you read down the Product column in Table 2? Extend Table 2 using this pattern to find the next two products, –3 • (–1) and –3 • (–2). -6 -3 –3 • (–1) –3 • (–2) 3 6 What do you notice about the product of two negative integers? 6

Multiplying Integers Multiplying Integers Words Numbers NOTE BOOK Words Numbers Same Sign The product of two integers with the same sign is positive. 4 • 2 = 8 –4 • (–2) = 8 Different Sign The product of two integers with different signs is negative. 4 • (–2) = –8 –4 • 2 = –8 Zero The product an integer and 0 is 0. 4 • 0 = 0 –4 • 0 = 0

Small Mathematics Lesson: the product of two negative integers is a positive integer? Says who? Distributive law of multiplication ..\..\..\..\All Users\Desktop\Notebook Software.lnk

The Product of two negative integers is a positive integer! Negative times a positive is a negative! The Product of two negative integers is a positive integer!

Lets build a test in Microsoft Word with Equation Editor sm2itest08.docx

For those who finish building the test using Microsoft Equation Editor. Do the Numbers Activity. Does it relate to the 2007 Mathematics Framework Revised (see for example Fifth Grade 1d)? Build a lesson plan and power point for this Numbers Activity.

Answers for even numbers 6 through 60