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 Technology College of Education and Psychology Day Seventeen More Principal + Interest--on Excel, English and metric units, dilations, reflections, translations, rotations

USM Summer Math Institute Your Mathematics Instructors, Staff and Partners Ms. Michelle Green, Co-Director and Co-Instructor for (SM) 2 I –Stringer Attendance Center –National Board Certified/Early Adolescence – Phone Dr. Myron Henry, Director and Co-Instructor for (SM) 2 I –Department of Mathematics and the Center for Science and Mathematics Education –Johnson Science Tower 314 – Phone or 266- All Participants (that’s you)

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4 Day Seventeen of (SM) 2 I 1.Compound and simple interest 2.and principal in Excel 3.Ratcheting down and up for metric and English measurement conversions 4.Transformations through Cabri Jr. Geometry: reflection, dilation, translation, rotation

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6 Jim wants to deposit money in a account to buy an antique Studebaker car in six years. The following interest rates are available to him % simple interest % compounded annually % compounded semiannually % compounded quarterly. Find out how much will Jim have after six years if he invests $15,000. Which account should he choose to maximize his return? Use your spreadsheet with appropriate substitutions to help Jim decide how to invest. Simple Interest: A = P·( 1 + n · r)

7 A measurement chart for the 2008 USM Summer Mathematics Institute. Below are some helpful measurement comparisons that you may useful.. Metric System of Measure Some Conversions Circular Stuff Volume of a pyramid = Volume of a sphere = SA of a sphere = Volume of a right prism or cylinder = (area of B)·h. Sum of the interior angles of an n-gon: (n-2)*180 Euler’s formula for Polyhedra: V + F = E

8 Miles to km by ratcheting down and then up

9 km to miles by ratcheting down and then up

Reflecting the triangle ABC about the given line (what is the line?) results in a new triangle A', B', and C'. The line segments connecting corresponding vertices are perpendicular to the line of reflection, and the line of reflection bisects the line segments. by line segments.

12 Translation of 5 cm through an angle of 45 

13 Three dilations

Rotation through an angle of 90 

15 Rotation through an angle of 45 

16 Reflections through Cabri Jr 1.Construct a triangle with F2 2.Construct your reflection line or segment with F2 3.Choose Reflection with F4 4.Select triangle with curser press enter 5.Then select line or segment with curser press enter 6.Choose F3 for perpendicular line

17 Same distance Always 90 o

18 1.Construct a triangle with F2 2.Go to F5 and choose alpha-num and press enter 3.Press alpha to change to number mode 4.Enter a scale factor 5.Go to F4 and choose dilation 6.Select the triangle press enter, then insert a point press enter, then move arrow to the number and press enter. Dilations through Cabri Jr

19 Dilation of Dilation of 2

20 Translations through Cabri Jr 1.Construct a triangle with F2 2.Choose Translation with F4 3.Select triangle with curser press enter 4.Then select one vertex of the triangle and press enter 5.Move curser to where you want to translate shape to and press enter

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22 Rotations through Cabri Jr 1.Construct a line with F2 2.Choose perpendicular with F3 to form perpendicular lines 3.In one Quadrant construct a triangle with F2 4.Then select intersection point of lines for point of rotation press enter 5.Select triangle press enter 6.Then you have to mark the angle you want to rotate and press enter.

23 90 o

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