Grade Five Problems
Grade Five Problems
Let's do some fun problems!
1)
How many addition signs should be put between digits of the
number 987654321 and where should we put them to get a total
of 99?
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Answer
2)
Divide the face of the clock into three parts with two lines
so that the sum of the numbers in the three parts are equal.
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3)
According to experts the first 4 moves in a chess game can
be played in 197299 totally different ways. If it takes 30
seconds to make one move, how long would it take one player
to try every possible set of 4 moves?
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4)
Batman has been imprisoned by the Riddler. To escape he must
find the quickest way to move the tower of plutonium disks
from one post to another so that the disks have the same
arrangement as on the original post. He may move only one
disk at a time. What is the minimum number of moves he
must make in order to move the ten disk tower and have it appear the
same?
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Answer
5)
A man has to be at work by 9:00 a.m. and it takes him 15
minutes to get dressed, 20 minutes to eat and 35 minutes to
walk to work. What time should he get up?
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Answer
6)
Replace each blank with the correct digit.
4 3 _ 2
4 5 _
_ 1 2 7
---------
8 8 9 3
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Answer
7)
In the first year of production a play sells 1572 tickets,
in its second year it sells 1753 tickets, in its third year
it sells 152 less than in its second year. How many tickets
are sold in 3 years?
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8)
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9)
Scientists have just discovered people on Neptune. There
are 3 villages, 2 cities and 1 super city on Neptune. These
are the populations in 1994 and 1996.
1994 1996
Eilosa 129 204
Vertu 308 292
Pridi 90 50
Dedrun 500 600
Antran 700 693
Maran 1200 1500
List the places in order of increasing size in 1994 and 1996.
In which year was the population of the planet greater?
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10)
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11)
The mass of the Great Pyramid is 557t greater than that of
the Leaning Tower of Pisa. Stone Henge has a mass of 2695t
which is 95t less than the Leaning Tower of Pisa. There once was
a Greater Pyramid which had a mass twice that of the
Great Pyramid, what was the mass of the Greater Pyramid.
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12)
Find the number of faces, edges and vertices on the figure
shown.
- What would this figure be called?
- What would the two figures contained in it be called?
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13)
Given a cube, draw a second figure with a square base,
having 8 edges, 5 vertices and 5 faces.
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14)
Given a cone having one edge and one vertex and two faces, make two
intersecting cuts through the flatside and find the number of vertices,
edges and faces each piece will have.
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15)
How many different cubes can you make if each face of a
given cube has a line connecting the center points of two
opposite edges?
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16)
If every vertex of a regular pentagon is connected to every
other vertex, how many triangles are formed?
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17)
The weather during Pith Possum's vacation was strange. It
rained on 15 different days, but it never rained for a whole
day.
- Rainy mornings were followed by clear afternoons.
- Rainy afternoons were preceeded by clear mornings.
- There were 12 clear mornings and 13 clear afternoons in all.
- How long was the vacation?
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18)
Festival Antigonish keeps a set of five counter weights to
help stagehands move heavy props. The weights can balance
exactly any load that is a multiple of 10kg, from 10kg up to
a total of the five weights. Give the masses of weights
which meet these conditions and allow the stagehands to
counterbalance the max possible load.
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19)
If you begin with a one digit integer, multiply by 3, add 8,
divide by 2 and subtract 6, you will get the integer back.
Find the number.
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20)
This stairway is made of cubes. How many cubes would be
needed to make the steps 9 steps high?
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Answer
21)
4 5 9 16 7
2 2 4 5 7 1
2 3 5 6 8 4
4 6 20 42 25 63 2
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22)
This is a turtle graphics problem.
A bug is walking across the doorstep of a house. When he
starts out he is facing the house at the opposite side of
the doorstep. If he goes 3 units left, 1 unit right, 2
units left, 8 units left, what will the bug
have to do to get back where he started as quickly as
possible without retracing his steps?
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23)
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24)
There are 12 people in a room. 6 people are wearing socks
and 4 people are wearing shoes, 3 people are wearing both.
How many people are in bare feet?
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25)
One morning grasshopper fell down a hole 2 metres deep. He would
climb 1/4 of a metre every day but at night he slid down 1/8
pf a metre. At this rate, how many days until the
grasshopper gets out?
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26)
Kim, Raelene, Jim and Rick finished first, second, third and
fourth in a motor bike race. If their numbers were 5, 17,
1 and 7, use the following clues to find out who had what number
and what order they finished in.
- 17 said she would have placed higher if her bike had not
stalled at the start.
- Rick finished before 7 but after Raelene.
- 1's father, said he was very proud of his daughter's finish.
- Kim finished after 5.
- Jim wasn't third.
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Answer
27)
An ice cream stand has nine different flavours. A group of
children come to the stand and each buys a double scoop cone
with two flavours of ice cream. If none of the children
choose the same combination of flavours, and every different
combination of flavors is chosen, how many children are there?
FLAVOURS
1 Vanilla
2 Maple
3 Chocolate
4 Tiger
5 Raspberry
6 Strawberry
7 Coffee
8 Moon Mist
9 Cherry Vanilla
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28)
Place the digits 9,4, 7, 6, 5, 1, in the boxes in order to
get the largest result.
[ ][ ] x [ ][ ] + [ ] x [ ] = ?
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29)
Four boys work together painting houses for the summer. For
each house they paint they get $256.00. If the boys work
for 4 months of summer and their expenses are $152.00 per
month, how many houses must they paint for each of them to
have one thousand dollars at the end of the summer?
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Answer
30)
In her first year a dog breeder's dogs produce 2 puppies. In her
second year her dogs produce three-times as many puppies. In her
third year her dogs produce 5 times as many puppies as the first year. How many puppies will the
breeder have produced in her first 3 years?
If she sells the puppies for $200.00 each, how much will she
have made?
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Answer
31)
Two frogs are hopping along a path one lily pad wide, going
in the same direction. There are 18 lily pads and one frog
jumps 3 lily pads at a time, the other jumps two lily pads
at a time. If the frogs leave the shore one after the
other, how many lily pads will be jumped on by both frogs?
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32)
A grocery store has a sale on bananas. If you buy six
bananas you get the sale price. If the grocer has 489
bananas how many bunches of six can he sell at his sale
price? In this case how many can be sold at the regular price?
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33)
Some students hold a bake sale to raise money for their
school library. They sold fudge and squares and cookies.
One of each type of treat was put into 95 paper bags and the
students were allowed to keep the left overs. If they
started out with 110 cookies, 130 pieces of fudge and 116
squares, the students put the same number of each kind of treat
in each bag(eg. 2cookies, 1 fudge, 1 square.
How many of each treat did they keep?
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34)
Describe the shaded area of the following figure in terms of
a fraction.
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35)
Sixteen players enter a tennis tournament. If there can be
no draws how many games must be played if each player can be
eliminated by one loss.
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36)
If a man can walk 4km in 1 hour and his wife can walk 5km in
1 hour, how many minutes will it take them to meet if they begin
walking at the same time at opposite ends of a 12km road, and have
agreed to meet at the half way point?
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37)
In how many different ways can the cars of a three car train
be arranged?
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38)
In 1989 the price of a soccer ball was $8.00. A financial
analyst predicted that the price would rise $0.25/year for
the next 10 years. In what year will the price be $9.75?
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39)
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40)
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41)
How many unit cubes are needed to build this solid figure?
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42)
See how many triangles you can draw using any three of the
five points on the circle as vertices.
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43)
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44)
If a ball is dropped from a height of 100m, each time it hits
the ground it bounces 3/5 of the height it fell. How far
will the ball have travelled in the 5th bounce?
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45)
Two girls went on a vacation together and they agreed to
split all expenses. They trip was prepaid so Mary wrote a
cheque for food and one for lodging. Clare wrote the
cheques for gas and entertainment. How much does Clare owe
Mary?
FOOD LODGING
Mary: $56.97 $83.29
GAS ENTERTAINMENT
Clare: $41.96 $37.47
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46)
The record for the greatest number of consecutive jumping
jacks is 14500 in 5 hours and 35 minutes. If Joe does 55
jumping jacks per minute, how long will it take Joe to tie
the record?
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47)
A line of length 4 is divided into nine equal segments.
Find a fraction to describe the length AB.
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48)
Rachel opened her math book and found that the sum of the facing pages
was 243. What pages did she open to?
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