document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1189804>Question 1189804</A>: <I><SPAN STYLE=\"word-break: break-all;\"> There is one bus driver, two coaches, and three teams, each with four dancers going to a competition. Nia writes the expression 1 + 2 + 3 ∙ 4 to represent everyone that will be on the bus and solves it using the following steps:\r<BR>\n" );
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document.write( "1 + 2 + 3 ∙ 4\r<BR>\n" );
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document.write( "= 3 + 3 ∙ 4\r<BR>\n" );
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document.write( "= 6 ∙ 4\r<BR>\n" );
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document.write( "=24 <BR>\n" );
document.write( "A. Nia concludes that 24 people will be on the bus going to the competition. Describe the mistake Nia made when solving her expression. Then write an explanation and draw a picture to help Nia understand how to solve her expression correctly.\r<BR>\n" );
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document.write( "B. How would you write this expression if n represents the number of teams?\r<BR>\n" );
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document.write( "C. How would this expression be different if there were two coaches for each team? Write an expression and draw a picture to support your expression. </SPAN>\n" );
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document.write( "Part A\r<BR>\n" );
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document.write( "Nia made the mistake in line 3<BR>\n" );
document.write( "She went from 3+3*4 to 6*4 which is not correct<BR>\n" );
document.write( "It's a common mistake students make at first is that they add before multiplying. Refer to PEMDAS or BODMAS or \"order of operations\" for more information.\r<BR>\n" );
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document.write( "Nia should have simplified the 3*4 into 12 first before adding later.<BR>\n" );
document.write( "So,<BR>\n" );
document.write( "3+3*4 = 3+12 = 15<BR>\n" );
document.write( "There are 15 people going on the bus.\r<BR>\n" );
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document.write( "One way to draw a picture is to have 3 circles and four dots per circle. That will represent the 3*4 = 12 dancers. Then have 1 dot to represent the driver, and 2 more dots for the coaches. Count out all the dots and you should find there are 15 dots total.<BR>\n" );
document.write( "The driver and coaches are not in any of the circles.\r<BR>\n" );
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document.write( "Part B\r<BR>\n" );
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document.write( "The 3*4 means we have 3 circles of 4 dots per circle.<BR>\n" );
document.write( "If we had say 5 circles, each four dots, then we'd have 5*4 = 20 dots in all the circles combined.\r<BR>\n" );
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document.write( "The question is: what if we don't know how many teams there are? Since this is unknown, we refer to it as the variable n.\r<BR>\n" );
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document.write( "The general rule is that having n circles means there are 4n dots overall in the circles alone. Simply multiply the number of dots per circle with the number of circles.\r<BR>\n" );
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document.write( "The original expression of<BR>\n" );
document.write( "1+2+3*4<BR>\n" );
document.write( "would turn into<BR>\n" );
document.write( "1+2+n*4<BR>\n" );
document.write( "which is the same as<BR>\n" );
document.write( "1+2+4n<BR>\n" );
document.write( "since we can multiply in any order\r<BR>\n" );
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document.write( "Then to tidy things up just a bit, the 1+2 becomes 3<BR>\n" );
document.write( "So we end up with 3+4n as the expression to reprsent the total number of people going on the bus. Where n is the number of teams.\r<BR>\n" );
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document.write( "The expression 3+4n means we have 4 dots per circle (n number of circles) and 3 extra dots outside all the circles to represent the 1 driver + 2 coaches.\r<BR>\n" );
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document.write( "Answer: 3+4n\r<BR>\n" );
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document.write( "Part C\r<BR>\n" );
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document.write( "If we had 2 coaches per team, and not just 2 coaches flat, then we'd have 2n coaches for n number of teams.\r<BR>\n" );
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document.write( "The expression <BR>\n" );
document.write( "1+2+4n<BR>\n" );
document.write( "would become<BR>\n" );
document.write( "1+2n+4n<BR>\n" );
document.write( "and that simplifies to<BR>\n" );
document.write( "1+6n\r<BR>\n" );
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document.write( "Each circle now has 6 dots to represent the 4 dancers + 2 coaches per circle. Like before, n is the number of teams and it's some positive whole number (eg: n = 5). Outside all the circles is one single dot to represent the driver.\r<BR>\n" );
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document.write( "Answer: 1+6n<BR>\n" );
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