Challenge Problems level 1 Number Sense

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Challenge Problems level 1Number Sense

• These exercises are primarily based on the Number
  Sense Thread
• This is defined in the New Jersey Core Curriculum
  Standards (NJCCS) http//www.state.nj.us/njded/fra
  meworks/math/ .
• Use these exercises to practice your open ended
  problem solving skills. See next page for
  guidelines.
• Use View -gt Normal to work on a problem.
• To print one problem
• Go To File -gt Print
• Click on Current slide button
• Click OK

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Problem Solving Guidelines for OPEN ENDED (OE)
Math Problems

• Read the problem twice.
• 1. Restate/underline the QUESTION.
• 2. Summarize/underline the important FACTS.
• 3. Show your SOLUTION.
• (Briefly, explain your math reasoning. Use a
  figure with labels or table if possible).
• 4. Write the ANSWER.
• (Be sure to include units of measure, double
  check that you answered the question being asked
  (in step 1) and check that it is reasonable.)

3

• If half the people in a room leave at the end of
  every five-minute interval and at the end of
  twenty minutes the next to the last person
  leaves, how many people were in the room to start
  with? (Assume that no one enters the room once
  the process begins.)
• 32
• 28
• 16
• 12
• 8

4

• ½ x 2/3 x ¾ x 4/5 x 5/6 x 6/7
• 1/7
• 3/7
• 21/27
• 6/7
• 7/8

5

• If 0.036 3.6 10t, what is the value of t?
• 3
• 2
• 1
• 2
• 3

6

• In a supermarket, Shakira bought 5 items from
  aisles 1 through 7, inclusive, and 7 items from
  aisles 4 through 10, inclusive. Which of the
  following could be the total number of items that
  Shakira bought?
• 9
• 10
• 11
• II only
• I and II only
• I and III only
• II and III only
• I, II, and III

7

• The table shows the attendance at the home games
  of the Hunterdon Central High School football
  team. If the median attendance for the five games
  was 456, and no two games had the same
  attendance, what is the greatest possible value
  for n?
• 400
• 455
• 457
• 478
• 549

8

• Ten cars containing a total of 32 people passed
  through a checkpoint. If none of these cars
  contained more than 4 people, what is the
  greatest possible number of these cars that could
  have contained exactly 2 people?
• One
• Two
• Three
• Four
• Five

9

• Miguel is 180 centimeters tall. At 200 pm one
  day, his shadow is 60 centimeters long, and the
  shadow of a nearby fence post is t centimeters
  long. In terms of t, what is the height, in
  centimeters, of the fence post?
• t 120
• t/3
• 3t
• 3 Sqrt(T)
• (t/3)2

10

• What is the sum of 5 consecutive integers if the
  middle one is 70?

11

• Add 8x to 2x and then subtract 5 from the sum. If
  x is a positive integer, the result must be an
  integer multiple of
• 2
• 5
• 8
• 10
• 15

12

• If 44 is the average (arithmetic mean) of x, x,
  x, 35, and 65, then x

13

• A mechanic can install carburetors in 3 cars
  every 4 hours. At that rate, how long will it
  take the mechanic to install carburetors in 5
  cars?

14

• 3, 6, 11, 18, ...
• The first four terms of a sequence are shown
  above. Which of the following could be the
  formula that gives the nth term of this sequence
  for all positiveintegers n?
• 2n
• 2n 1
• 3n
• n2 1
• n2 2

15

• If N (5/14) (5/14) (7/9), then N
• 7/9
• 9/7
• 5
• 7
• 14

16

• If x is a number from Column X and y is a number
  from Column Y in the table above, how many
  different values are possible for x y?
• Nine
• Eight
• Seven
• Six
• Five

17

• The perimeter of a 7-sided figure is 15. If the
  length of each side of the figure is increased by
  2 units, what is the perimeter of the new figure?

18

• Every student who studies art in a certain school
  receives exactly one of the grades A, B, C, or D.
  If 1/5 of the students receive A's, 1/4 receive
  B's, 1/2 receive C's, and 10 students receive
  D's, how many students in the school study art?

19

• In an 8-gram solution of water and alcohol, the
  ratio by mass of water to alcohol is 3 to 1. If
  12 grams of a solution consisting of 2 grams
  water for each gram of alcohol is added to the
  8-gram solution, what fraction by mass of the new
  solution is alcohol?

20

• The sum of the digits of a three-digit number is
  12. If the hundreds digit is 3 times the tens
  digit and the tens digit is 1/2 the units digit,
  what is the tens digit of the number?
• 2
• 3
• 4
• 6
• 9

21

• The population of Norson, the largest city in
  Transitania, is 50 percent of the rest of the
  population of Transitania. The population of
  Norson is what percent of the entire population
  of Transitania?
• 20
• 25
• 30
• 33 1/3
• 50

22

• The price of 10 pounds of apples is d dollars. If
  the apples weigh an average of 1 pound for every
  6 apples, which of the following is the average
  price, in cents, of a dozen such apples?
• 20d
• 50d/3
• 5d
• 5d/3
• d/20

23

• To make an orange dye, 3 parts of red dye are
  mixed with 2 parts of yellow dye. To make a green
  dye, 2 parts of blue dye are mixed with 1 part of
  yellow dye. If equal amounts of green and orange
  are mixed, what is the proportion of yellow dye
  in the new mixture?
• 3/16
• 1/4
• 11/30
• 3/8
• 7/12

24

• A group of workers can harvest all the grapes
  from 10 square meters of a vineyard in 1/2
  minute. At this rate, how many minutes will the
  group need to harvest all the grapes from 100
  square meters of this vineyard?
• 5
• 10
• 20
• 50
• 60

25

• In a community of 416 people, each person owns a
  dog or a cat or both. If there are 316 dog owners
  and 280 cat owners, how many of the dog owners
  own no cat?
• 36
• 100
• 136
• 180
• 316

26

• If p is an odd integer, which of the following is
  an even integer?
• p 2
• p2
• p2 2
• (p 2)2
• p2 p

27

• If it takes 10 people 12 hours to do a certain
  job, how many hours would it take 6 people,
  working at the same rate, to do 1/4 of the same
  job?
• 6
• 5
• 4 and 1/2
• 4
• 3 and 3/4

28

• If x/3 x2 , the value of x can be which of the
  following?
• I. - 1/3
• II. 0
• III. 1/3
• I only
• II only
• III only
• II and III only
• I, II, and III

29

• Seven cards in a pile are numbered 1 through 7.
  One card is drawn. The units digit of the sum of
  the numbers on the remaining cards is 7. What is
  the number on the drawn card?
• 1
• 3
• 5
• 6
• 7

30

• The odometer of a new automobile functions
  improperly and registers only 2 miles for every 3
  miles driven. If the odometer indicates 48 miles,
  how many miles has the automobile actually been
  driven?

31

• If United States imports increased 20 percent and
  exports decreased 10 percent during a certain
  year, the ratio of imports to exports at the end
  of the year was how many times the ratio at the
  beginning of the year?
• 12/11
• 4/3
• 11/8
• 3/2
• 2

32
A newspaper reported that one weekend the movie
Batman Returns earned 14.8 million. According to
that newspaper, the figure represented 42 of the
previous weekend's earnings. Approximately how
much did Batman Returns earn during the previous
weekend?
33
Driving home, Karen came to a sign that said
traffic would be reduced to one lane for the next
7 miles due to road construction. Cars were only
moving at about 5 miles per hour. How long would
it take Karen to get through the construction
zone?
34
Sample MC ItemLiang got an answer of about 3.87
when she entered 15 on her calculator and pressed
the (   ) key. As usual, she stopped to think
briefly about whether or not her calculator's
answer was reasonable. Which of the following
statements is the most likely explanation for her
to believe that her calculator's answer is or is
not reasonable?
35
Using a standard procedure for rounding, (i.e.,
if the digit in the hundreds place is five or
more, round up otherwise round down), a data
analyst rounds the population of a city to the
nearest thousand and records it as 50,000. What
is the greatest possible value for the actual
population?
36
Sample MC ItemWhich of these numbers has the
greatest number of different prime factors? a.
30      b. 50      c. 99       d.  121
37
Every number is divisible by itself and 1. The
number 24 is the smallest positive integer that
is divisible by six other positive integers,
namely 2, 3, 4, 6, 8, and 12. What is the
smallest positive integer that is divisible by
itself, 1, and seven other positive integers? a.
30        b. 36     c. 40      d.  48
38

• A train traveling 60 miles per hour for 1 hour
  covers the same distance as a train traveling 30
  miles per hour for how many hours?

39
Today we will make even more precise estimates
than in the first Getting Close game. Let's
practice an example from the Getting Close
game. Suppose a friend from another school visits
to play Getting Closer. Two cards are turned
over Write an explanation for your friend
about how you can quickly estimate whether the
sum of the two numbers is closest to 0, 1 or 2.
1/3

.75
40

• A florist buys roses at 0.50 a piece and sells
  them for 1.00 a piece. If there are no other
  expenses, how many roses must be sold in order to
  make a profit of 300?
• 100
• 150
• 200
• 300
• 600

41

• If it is now 400 p.m. Saturday, in 253 hours
  from now, what time and day will it be? (Assume
  no daylight saving time changes in the period.)
• 500 a.m. Saturday
• 100 a.m. Sunday
• 500 p.m. Tuesday
• 100 a.m. Wednesday
• 500 a.m. Wednesday