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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?

You've reached the finish line!

April Solutions

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