orderofoperations

media type="custom" key="1620543"toc

 **Order of Operations** Adapted from “Order of Operations,” //Exploring Algebra I with the Geometer’s Sketchpad//,, Tim Erikson, Key Curriculum Press, 2006 =Assessment Anchors = **M11.A.1 ** Demonstrate an understanding of numbers, ways of representing numbers, relationships among numbers and number systems. 
 * M11.D.2 ** Represent and/or analyze mathematical situations using numbers, symbols, words, tables and/or graphs. 
 * M11.D.4 ** Describe or use models to represent quantitative relationships. 

 = Purpose   =

In this activity, you will explore the importance of agreeing on and following the standard rule for order of operations: 1.   First do operations that occur within grouping symbols. 2.   Then evaluate powers. 3.   Then do multiplications and divisions from left to right. 4.   Finally, do additions and subtractions from left to right.

=Introduction=

In our entire known galaxy, everyone follows the exact same steps #1 and #2.While on Earth, we follow the Terran order described above. In other parts of the galaxy, however, different rules are followed! Today, we are going to explore the orders of operations of the Vulcans and the Klingons. You are working out math problems with your two best friends, Spock (a Vulcan) and Worf (a Klingon). Because you are working differently, you will get different answers to the same math problems. =The File=

Please open the following file on one of the computers:

=Setting Up the Problem=

1)   On the first page, you will evaluate the expression 1+3*2   in all 3 systems. Think of this expression as a+b*c  . To prepare for this work, drag point a   to 1, <span style="FONT-SIZE: 11pt; LINE-HEIGHT: 115%; FONT-FAMILY: 'Calibri','sans-serif'; POSITION: relative; TOP: 4.5pt; mso-fareast-font-family: 'Times New Roman'; mso-bidi-font-family: 'Times New Roman'; mso-bidi-theme-font: minor-bidi; mso-ascii-theme-font: minor-latin; mso-fareast-theme-font: minor-fareast; mso-hansi-theme-font: minor-latin; mso-text-raise: -4.5pt; mso-ansi-language: EN-US; mso-fareast-language: EN-US; mso-bidi-language: AR-SA">  b to 3, and <span style="FONT-SIZE: 11pt; LINE-HEIGHT: 115%; FONT-FAMILY: 'Calibri','sans-serif'; POSITION: relative; TOP: 4.5pt; mso-fareast-font-family: 'Times New Roman'; mso-bidi-font-family: 'Times New Roman'; mso-bidi-theme-font: minor-bidi; mso-ascii-theme-font: minor-latin; mso-fareast-theme-font: minor-fareast; mso-hansi-theme-font: minor-latin; mso-text-raise: -4.5pt; mso-ansi-language: EN-US; mso-fareast-language: EN-US; mso-bidi-language: AR-SA">  c to 2. =Solving the Problem=

On Earth, multiplication and division must be done first, from left to right, before addition and subtraction. You’ll do this calculation on the Terran number line. 1)   <span style="FONT-FAMILY: 'Times New Roman', Times, serif">On the Terran number line, you must calculate b*c first. Press and hold the **Custom** tools icon, choose the **Multiply** tool, and click on points b and c <span style="FONT-SIZE: 11pt; LINE-HEIGHT: 115%; FONT-FAMILY: 'Calibri','sans-serif'; POSITION: relative; TOP: 4.5pt; mso-fareast-font-family: 'Times New Roman'; mso-bidi-font-family: 'Times New Roman'; mso-bidi-theme-font: minor-bidi; mso-ascii-theme-font: minor-latin; mso-fareast-theme-font: minor-fareast; mso-hansi-theme-font: minor-latin; mso-text-raise: -4.5pt; mso-ansi-language: EN-US; mso-fareast-language: EN-US; mso-bidi-language: AR-SA">  <span style="FONT-FAMILY: 'Times New Roman', Times, serif">.

<span style="FONT-FAMILY: 'Times New Roman', Times, serif"> 1)   Now calculate a+b*c on the Terran number line by choosing the **Add** custom tool and clicking first on point <span style="FONT-SIZE: 11pt; LINE-HEIGHT: 115%; FONT-FAMILY: 'Calibri','sans-serif'; POSITION: relative; TOP: 4.5pt; mso-fareast-font-family: 'Times New Roman'; mso-bidi-font-family: 'Times New Roman'; mso-bidi-theme-font: minor-bidi; mso-ascii-theme-font: minor-latin; mso-fareast-theme-font: minor-fareast; mso-hansi-theme-font: minor-latin; mso-text-raise: -4.5pt; mso-ansi-language: EN-US; mso-fareast-language: EN-US; mso-bidi-language: AR-SA">  a and then on point (b*c) .     2)     Change the color of the resulting marker. (Display>Color) 3) In the Vulcan system, they do addition and subtraction first, before multiplication and division. Use the **Add** and **Multiply** custom tools to do the Vulcan calculation of the second number line. Color the final result marker to match the color of the Terran answer. 4) Similarly, do the Klingon calculation and color its final result marker. <span style="FONT-FAMILY: 'Times New Roman', Times, serif"><span style="FONT-SIZE: 11pt; LINE-HEIGHT: 115%; FONT-FAMILY: 'Calibri','sans-serif'; mso-fareast-font-family: Calibri; mso-bidi-font-family: 'Times New Roman'; mso-bidi-theme-font: minor-bidi; mso-ascii-theme-font: minor-latin; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-ansi-language: EN-US; mso-fareast-language: EN-US; mso-bidi-language: AR-SA"> =<span style="FONT-FAMILY: 'Times New Roman', Times, serif"><span style="FONT-SIZE: 11pt; LINE-HEIGHT: 115%; FONT-FAMILY: 'Calibri','sans-serif'; mso-fareast-font-family: Calibri; mso-bidi-font-family: 'Times New Roman'; mso-bidi-theme-font: minor-bidi; mso-ascii-theme-font: minor-latin; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-ansi-language: EN-US; mso-fareast-language: EN-US; mso-bidi-language: AR-SA">First Question =

Now, please answer the following question media type="custom" key="1916261"

=Another Problem=

<span style="FONT-FAMILY: 'Times New Roman', Times, serif">Now, go to page 2 in the sketch and evaluate the expression given at the top of the page in all three systems.

=Final Questions=

Now, answer the folllowing questions: media type="custom" key="1916755"