1. The South Mississippi Science and Mathematics Partnership Program (SMP) 2 Supported by The U.S. Department of Education and Administered by The Mississippi Department of Education (MDE)

2. 2 Our Team Dr. Myron Henry (Co-Director), Mathematics Dr. Sherry Herron (Co-Director), Science Education Dr. Sharon Walker (Co-Director), Science Education Dr. Shelia Brown, Science Education Ms. Lida McDowell, Mathematics Ms. Mary Peters, Mathematics Dr. David Beckett, Science The most important members of our team? Your teachers who were participants and their students, which is you! 15.Area, multiplication of integers, fractions, sequences, irrational numbers

6. Mini Mathematics Lessons 1.Area and perimeter, a chart 2.Product of two negative numbers is a positive number, it is not magic. 3.Fraction Earth 4.Fibonacci Sequence and the Golden Ratio or Divine Proportion from the Da Vinci Code

7. 7 Mathematics Topics area compared to perimeter multiplication of negative real numbers fractions Arithmetic and Fibonacci sequences irrational numbers

8. 8 Partial Objectives from the 2007 Mississippi Mathematics Objectives (Revised) 6 th grade 1d (Compute using basic operations with fractions), 1f [Explain the relationship(s) among fractions, decimals, and percents and model and represent a specific quantity in multiple ways], 4b (Calculate the perimeter and area of regular and irregular shapes using a variety of methods) 7 th grade 1b (Solve problems involving operations of rational numbers), 2a (Recognize, describe, and state the rule of generalized numerical and geometric patterns using tables, words, and symbols), 2e (Identify and apply properties in solving problems) Pre-Algebra 1a (Define, classify, and order rational and irrational numbers and their subsets), 2b (Apply properties of real numbers with an emphasis on the distributive properties of multiplication over addition and subtraction), 4a (Solve real-world application problems that include length and area using standard measurements Transition to Algebra 1a (Compare and contrast the subsets of real numbers)

10. 3 –1? 3 –2? Table 1 – 6 2 1 3 Complete Table 1. 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). What do you notice about the product of a positive integer and a negative integer? Multiplying Integers Activity You can use patterns to find rules for multiplying integers. ExpressionProduct 3 9 3 2? 3 1? 3 0? 6 3 0 – 3

11. Look at Table 2. Then use your answer from Step 3 to complete the table. 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). What do you notice about the product of two negative integers? –3 (–1) –3 (–2) ExpressionProduct –3 3 –3 2 –3 1 –3 0 4 5 6 Table 2 Activity You can use patterns to find rules for multiplying integers. Multiplying Integers -9 -6 -3 0 3 6

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

13. Small Mathematics Lesson: the product of two negative integers is a positive integer? Says who? Distributive law of multiplication

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

15. Small Mathematics Lesson: Fractional distribution of the Earth’s natural resources = water = land Land ( )

16. Fractional distribution of the Earth’s natural resources = water = land Uninhabitable Land ( ) Habitable Land ( )

17. Fractional distribution of the Earth’s natural resources = water = land Uninhabitable Land ( ) Habitable Land ( ) Supports Food Growth ( )

18. Fractional distribution of the Earth’s natural resources In the whole Earth, there are 8 ( ). Each eighth is divided into 4 equal parts giving 32 ( ) in the Earth. Stated another way,

19. Fractional distribution of the Earth’s natural resources = water = land Uninhabitable Land ( ) Habitable Land ( ) Supports Food Growth ( ) Contains Drinkable Water ( )

20. 6 th Grade Benchmark: State a rule to explain a number pattern; 7 th Grade Benchmark: Describe and extend patterns in sequences. nfnfn 1f 1 =1 2f 2 =1+3 3f 3 =1+3+3 4f 4 =1+3+3+3 5f 5 =1+4·3 A number pattern {1, 4, 7, 10, 13, 16, …, 82}. Question? What is the rule that describes this number pattern or sequence? In terms of previous entries? The ultimate rule for f n (this is worth $1 to the student that discovers it first)? What value of n gives f n = 82? nfnfn 6 7 8 9 n

21. nfnfn 1f 1 =1 2f 2 =1 3f 3 =2 4f 4 =3 5f 5 =5 nfnfn 6 7 8 9 10 6 th Grade Benchmark: State a rule to explain a number pattern; 7 th Grade Benchmark: Describe and extend patterns in sequences. 1.Fibonacci Sequence 2.What is the n-th term? 3.What is the ratio of [(f n+1 )/(f n )] for n large? 4.What is the “Divine Proportion” (from the DaVinci Code) or Golden Ratio? 5.Let’s build a spreadsheet.