Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Abuse of notation wikipedia , lookup
Bra–ket notation wikipedia , lookup
Large numbers wikipedia , lookup
History of mathematical notation wikipedia , lookup
Musical notation wikipedia , lookup
Big O notation wikipedia , lookup
Location arithmetic wikipedia , lookup
Positional notation wikipedia , lookup
Moiré pattern wikipedia , lookup
Unit 2: Assignment Name: _______________________ Class: _______________________ Assignment Booklet The following booklet will provide each of you the opportunity to achieve the appropriate outcomes in this unit. Work through each page and provide answers on the each page where space is provided. Use pencil Each booklet will remain in the Math classroom Make sure your name is on the front along with your homeroom class Contents Covered in Booklet Patterns Exponents Square Roots Scientific Notation Create your own questions Mental Math Outcomes the booklet addresses: SCO A1 SCO A2 SCO A3 SCO A4 SCO A5 SCO A6 model and link various representations of square root of a number recognize perfect squares between 1 and 144 and apply patterns related to them distinguish between an exact square root of a number and its decimal approximation find the square root of any number, using an appropriate method demonstrate and explain the meaning of negative exponents for base ten represent any number written in scientific notation in standard form, and vice versa Patterns 1. What would come next in this pattern? 5, 10, 15, 20, 25, 30 … _____________________________________________________________ 2. If I make the pattern 2, 4, 6, 8, 10, what will come next? And then what? What is the rule? ____________________________________________ _____________________________________________________________ 3. My pattern is 0, 4, 8, 12, 16. What are the next three numbers in my pattern? How do you know? ___________________________________ ____________________________________________________________ 4. My pattern is 1, 4, 7, 10. What are the next five numbers in my pattern? What is the rule for my pattern? How would you make a table to show that? _______________________________________________________________ _______________________________________________________________ 5. What would the pattern be if you started at five and added two each time? _______________________________________________________________ 6. Here is how the Fibonacci pattern begins: 1, 1, 2, 3, 5, 8. What comes next? Then what? How do you know? Can you state the rule in words? _______________________________________________________________ _______________________________________________________________ _______________________________________________________________ The above cartoon (Amend 2005) shows an unconventional sports application of the Fibonacci numbers (left two panels). (The right panel instead applies the Perrin sequence). Perfect Squares List the first 12 perfect squares in the table provided. Use a pattern to fill in the table up to 20. Use computations in n n2 1 1 Pattern n2 1 the to write n2 in a different way 1x1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Explain the pattern you found between the perfect squares. _____________________________ _____________________________________________________________________________ _____________________________________________________________________________ _____________________________________________________________________________ _____________________________________________________________________________ Use a drawing (grid) to calculate the approximate value of 6.22 Use the number line to solve: 45 124 149 Scientific Notation Scientists have a need to express very large (or very small numbers) in some convenient way. For example, astronomers measure the distance to stars in light years, a unit of distance which suitably expresses the huge distances which are involved. A light year is the distance which light travels in one year. Let us see how many meters there are in one light year. Light travels at a speed of 300000000 m/s (three hundred million meters per second). Definitions: Coefficient ___________________________________________________________________ _____________________________________________________________________________ Base 10 Power ________________________________________________________________ _____________________________________________________________________________ Scientific Notation ______________________________________________________________ _____________________________________________________________________________ _____________________________________________________________________________ Express the following in scientific notation: 1. 6,000,000,000,000,000,000,000 _____________________________________________ 2. 547,000 _____________________________________________ 3. 3,500,000,000 _____________________________________________ 4. 0.00000000000463 _____________________________________________ 5. 0.00090674 _____________________________________________ 6. 790,640,000 _____________________________________________ 7. 0.000047906 8. 198,000,000,000,000,000,000,000,000,000,000 ________________________________ 9. 0.000000049744 _____________________________________________ 10. 0.0014650 _____________________________________________ _____________________________________________ Express the following in standard form: 1. 2. 3. 4. 5. 6. 7. 3.4067 x 107 _____________________________________________ 19 _____________________________________________ 9 _____________________________________________ -6 _____________________________________________ -5 _____________________________________________ 5.0400 x 10 4.0689 x 10 1.0015 x 10 8.0000 x 10 6.4523 x 10 2 8.213 x 10 _________________________________________ -4 _____________________________________________ 1a) __________________ b) __________________ c) __________________ d) __________________ 2) Draw a line from the letter side to the roman numeral side. 3a) __________________ b) __________________ c) __________________ d) __________________ e) __________________ f) __________________ g) __________________ h) __________________ 4a) _________________ b) __________________ c) __________________ d) __________________ e) __________________ f) __________________ On this page create three questions that have to do with patterns, exponents, square roots and/or scientific notation and then answer them. Consideration will be given to questions that are well thought out, and those questions may be added to an upcoming assessment. Be creative and come up with examples from area that you are passionate about. (Example: NBA question I made up last Friday). 1. 2. 3. 4. 5. 6. Journal Space Journal # _______ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ Journal # _______ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ Journal # _______ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ Journal # _______ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ Journal # _______ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ Journal # _______ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ Mental Math Sheet Date: Date: Date: 1 1 1 2 2 2 3 3 3 4 4 4 5 5 5 6 6 6 7 7 7 8 8 8 9 9 9 10 10 10 Date: Date: Date: 1 1 1 2 2 2 3 3 3 4 4 4 5 5 5 6 6 6 7 7 7 8 8 8 9 9 9 10 10 10 Mental Math Sheet Date: Date: Date: 1 1 1 2 2 2 3 3 3 4 4 4 5 5 5 6 6 6 7 7 7 8 8 8 9 9 9 10 10 10 Date: Date: Date: 1 1 1 2 2 2 3 3 3 4 4 4 5 5 5 6 6 6 7 7 7 8 8 8 9 9 9 10 10 10 Mental Math Sheet Date: Date: Date: 1 1 1 2 2 2 3 3 3 4 4 4 5 5 5 6 6 6 7 7 7 8 8 8 9 9 9 10 10 10 Date: Date: Date: 1 1 1 2 2 2 3 3 3 4 4 4 5 5 5 6 6 6 7 7 7 8 8 8 9 9 9 10 10 10 Grade 8 Math JMJH