An argument is a discussion in which a disagreement is expressed.  It is important to have facts to support your argument.

In math you can explain an argument using oral, written, concrete, pictorial, or graphical forms.

Example
Maria and her brother Michael are trying to determine whose bedroom has the greatest perimeter.  Maria's room dimensions are 10 feet for length and 12 feet for width.  Michael's room is 9 feet long and 11 feet wide.  Determine which bedroom has the largest perimeter. 

Oral- explaining your answer by talking to another person Maria would explain the formula for perimeter is side + side + side.  She would tell her brother that the perimeter of her room is 44 feet.  Michael's perimeter of his room is 40 feet.  Maria would argue that her room has the largest perimeter because
44 > 40.

Example
Riley and her friend Elizabeth are trying to determine who spent more time on the bus.  Riley gets on the bus at 7:15 a.m. and gets to school at 8:35 a.m.  Elizabeth gets on the bus at 7:30 a.m. and gets to school at 8:45 a.m.  Determine who spent more time on the bus.

Written- writing your facts down on a piece of paper
  Get on bus Arrive at school Time on bus
Riley 7:15 a.m. 8:35 a.m. 1 hr 20 min.
Elizabeth 7:30 a.m. 8:45 a.m. 1 hr 15 min.

Riley spends 5 minutes longer on the bus than Elizabeth.

Example
Trey and his brother Scott are trying to determine who spent more at the store.  Trey bought 2 shirts that cost $14.76 and a pair of pants for $22.30.  Scott bought a pair of sandals for           $19.87, shorts for $12.56, and 3 pairs of socks for $3.65.  Determine who spent more at the store.

Concrete- having definite facts to support your argument

 

 

 

 

 

 

 

Trey    $14.76 shirt
     $14.76 shirt
 
+ $22.30
pants
     $51.82  
     
Scott   $19.87 sandals
    $12.56 shorts
    $3.65 socks
    $3.65 socks
 
+$3.65
socks
  $43.38  

Trey spent more at the store than Scott.

$51.82 > $43.38

Example
Tiffany wants to figure out how many different combination of outfits she can make from 3 shirt and 3 pants.   Robin tells her she can make 9 different combinations.
Determine if Robin is correct.

Pictorial- drawing a picture to show your facts

 

 

 

 

 

 

Robin is correct there are 9 different outfits that Tiffany can make.

Example
Mary wants to determine how many more cookies she sold on Friday than on Wednesday. On Monday she sold 20 cookies, Tuesday she sold 32 cookies, Wednesday 45 cookies, Thursday 25 cookies, and Friday 55 cookies.  Use the line graph to determine the difference between the two days.

Graphical- drawing a graph or table to show your facts.

 

 

 

 

 

 

 

  55
- 45
  10

Mary sold 10 more cookies on Friday than on Wednesday.

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