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April Problems
Number Theory | Measurement | Geometry |
Patterns, Algebra, and Functions | Data,
Statistics, and Probability
Number Theory
Start out simple...
Mowing Lawns
1. Ron and Darrell mow lawns to earn money in the summer.
Ron has a riding mower. He charges $18 a yard and pays his
little brother $7 to help. He is able to do 9 yards in a
day.
Darrell has a walking mower. He charges $20 a yard and does
8 yards a day. Who do you think does better? Explain your
answer.
Turkey Time
2. Julia Child was roasting a turkey. It has been out of the
oven for 20 minutes. The turkey was roasting for 4 hours and
15 minutes. The oven was preheated for 10 minutes. If it is
5:00 now, then what time did Julia put the turkey in the
oven?
Now try to work this out...
Jumping Frogs
3. A frog jumped on several stones on his way to the pond.
He did not land on the same stone twice. The product of all
of the stones that he hopped on was 19,635. On which stones
did he jump?
Multiplication Madness
4. Use multiplication to solve these arrays:
This will really challenge
you...
Birthday Beach Bash (from Math
Forum)
5. Twins Maggie and Dana and their friend Rebecca were
celebrating their tenth birthdays with a party at the beach.
The first fun activity was water games. As Chelsea arrived,
she observed that 1/3 of the kids were playing with beach
balls, 40% were exploring underwater with goggles, and .25
were floating on tubes.
The party continued with many games, presents, and the ever
popular cake and ice cream. When the party was over, each
kid received a party bag and a balloon to take home. There
were even 3 left for Maggie, Dana, and Rebecca.
How many balloons were needed for the beach party?
Measurement
Start out simple...
Trees
6. The perimeter of a square lot is lined with trees. There
are 3 yards between the centers of the trees. There are 8
trees on each side and a tree is at each corner. What is the
number of yards in the perimeter of the lot? Explain how you
got your answer.
Now try to work this out...
Baking Bonanza
7. Jan is baking. She needs 4 cups of sugar. Her problem is
that she only has a 1/2 cup measure and a 3/4 cup measure.
What is the least number of scoops that she could make in
order to get 4 cups? Explain your answer.
This will really challenge
you...
Circles and Leaves
8. A circular table has an area of 1256 sq. in. The table
opens in the middle to allow the addition of leaves. Each
leaf is 12 " wide and is rectangular in shape. How many
leaves must be added to change the area of the table to 2696
sq. in.? Work backwards
and remember these formulas:
Area of rectangle = length x width
Area of a circle = pi x radius squared
Geometry
Start out simple...
Parallelogram Per Cents
9. What per cent of the quadrilaterals in this diagram are
parallelograms?
Now try to work this out...
Use Your Imagination
10. Create a symmetrical design with a perimeter of:
10cm
20cm
36cm
Do you think the perimeter is always even? Could there be a
way for the perimeter to be odd?
This will really challenge
you...
Inscribing Squares
11. Each of the squares shown is inscribed in a larger
square so that the vertices of the inscribed square bisect
the sides of the larger square. What fraction of the area of
the largest square is shaded? Express your answer in
simplest form.
Patterns, Algebra, And Functions
Start out simple...
Slipping Snails
12. Upon your arrival on Monday morning, you observe a snail
making its way up the wall of your cabin. Each day, it
carefully works its way 30 inches up the wall. At night,
though, it slips back down 12 inches. The cabin wall is 9
feet high. If the snail
started on Monday, will it reach the top of the cabin wall
before you leave
on Friday afternoon?
Now try to work this out...
Pascal's Triangle
13. Fill in the blanks in this diagram. Tell the strategy
you used to do this. Show 3 different patterns that you
notice.
This will really challenge
you...
Moving Cows
14. There are cows in each of these pastures. The pastures
are connected by bridges. The number on each bridge tells
the total number of cows in the 2 connecting pastures. Hint:
no pasture has more than 20 or less than 10 cows.
Data, Statistics, And
Probability
Start out simple...
The Whole Thing
15. Two numbers are chosen at random with replacement from
this set: (1, 2, 3, 4). The 2 chosen numbers are used as
numerator and denominator of a fraction. What is the
probability that the fraction represents a whole number?
Express your answer as a fraction in simplest form.
Now try to work this out...
Building Bacteria
16. Consider 2 bacteria on a surface. The number of bacteria
doubles every hour. Make a table and graph the results for n
hours. Analyze the results.
This will really challenge
you...
What's My Score?
17. Mrs. O. Angle has 12 students in her advanced algebra
class. On a recent test, the average was 80. When Beth asked
for her score, Mrs. Angle could not find it, but she did
remember adding Beth's score in the average. She also
remembered that Beth had passed.
These are the scores of the other students:
65, 65, 70, 70, 80, 85, 85, 90, 90,
90, 100
Tell how Mrs. Angle can figure out the missing score. What
is that score?
April
Solutions
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