Read the questions carefully. Take your time and write a complete answer on your paper before
checking your answers by clicking on the answer ink
28. Esther shot two arrows at a target. The picture below shows where the
arrows landed.
Esther calculated her score by adding the number of points for each ring in
which an arrow landed. For the two arrows above, her score was 35 points
(25 + 10).
a. In your Student Answer Booklet, make a list of all the possible scores
Esther could have gotten by shooting two arrows that hit the target.
b. Is it possible for Esther to score a total of 235 points using only 5 arrows?
Show your work or explain your answer.
c. What is the fewest number of arrows required for Esther to score a total of
240 points? Show your work or explain your answer.
link to answer for test item 28
29. Molly formed three polygons—a triangle, a rectangle, and a pentagon—with
string. She calculated the sum of the measures of the interior angles for each
polygon and entered her data in the chart shown below.
a. What is the sum of the measures of the interior angles of a hexagon?
b. What is the sum of the measures of the interior angles of an octagon?
c. How many sides does an unnamed polygon have if the sum of the measures
of the interior angles is 2340°?
d. Explain how you would find the sum of the measures of the interior angles
of an n-sided polygon.
link to answer for test item 29
a. The possible scores are
| 10+10=20 | 10+25 =35 | 10+50 = 60 | 10+100= 110 |
| 25+25 =50 | 25+ 50=75 | 25+ 100=125 | |
| 50+50= 100 | 50+ 100= 150 | ||
| 100+100=200 |
If you make a table it is easy to see the repeats and avoid them. 10+25 would be the same as 25+10 because order does not matter.
b. It is possible for Esther to score a total of 235 points using only 5 arrows!
the highest possible score if all hit the 100 would be 500
if all 5 hit 50 it would be 250
if all 5 hit 25 it would be 125
if all 5 hit 10 it would be 50
so the answer has to be a combination of different scores.
235 in expanded form is 200 + 30 + 5
| arrows | 10 | 25 | 50 | 100 | |
| one | 100 | ||||
| two | 50 | ||||
| three | 50 | ||||
| four | 25 | ||||
| five | 10 |
My thinking was that 100+100+ 25 +10 made 235 but that was only 4 arrows. But if i substituted two 50's for a 100 then I'd have my 5 arrows. 100 +50+50 +25 +10 =235
c. The fewest number of arrows required for Esther to score a total of 240 points
240 =200+40
there is no "40" score
25+ 10= 35 and there is no 5 to make the 40--so I know I can't do it this
way
240 is also 24 x 10 so 24 would be the most arrows. I will group the tens in fifties and hundreds.
100+ 140 = 240
140= 100+10+10+10+10
that's 6
a. I can use my calculator for this question so I will
follow the pattern and each time I add a side I add 180 degrees.
I know 5 sides is 504 degrees.
540+180=720 for six sides
b. an octagon is eight sides which is two more than 6 so I
add 180 twice to the last answer.
720 +180+180=1080
for eight sides
c. 2340 is more than 8 sides. To find out how much
more I can use the calculator
2340- 1080 =1260 then divide that by 180
1260÷ 180 =7 more or
15 sides in all
d. A polygon has to have at least 3 sides so we start with 180
as the smallest degrees of interior angles.
each time I add a side I add 180 more.
A two sided polygon is not possible so .
three sides starts it all so let's call n-2 our
start of 180's.
180 (n-2) = the sum of the interior angles.
For your information
There is a formula you can memorize that finds the sum of the interior angles
|
Sum of Interior Angles |
= 180(n-2) |
| A hexagon has 6 sides. So n = 6. Using our formula from above, that gives us 180(6-2) = 180(4) = 7200 |
| An octagon has 8 sides. So n = 8. Using our formula from above, that gives us 180(8-2) = 180(6) = 10800 |
using it you can see that the answers to part-a and part-b come out the same as they did with our add 180 per side method.