WIS PS Library - Level 2

I am a big fan of pesto, so every year I plant tons of basil. You don't know what pesto is? Well let me tell you, it's the best pasta sauce ever! The basic pesto recipe includes basil, parsley, garlic, Parmesan cheese, butter, pine nuts, and salt and pepper to taste. Boy, am I getting a craving for some just describing it to you. Add some homegrown tomatoes on the side (they're so much better than store-bought)... yum!

In one of my 10-foot by 15-foot garden beds I will plant two packets of basil. Each packet holds enough seeds for one row 75 feet long. I always plant marigolds around the borders of my gardens; besides being pretty, they attract bugs that are good for gardens. Because of this, I will start the basil rows 1 foot from the edges.

The directions on the seed packets say the rows should be planted 1 foot apart. After the seeds sprout and reach a height of 2 to 3 inches, they are to be thinned so there are 6 inches between plants.

Now I have some thinking to do, and I'd like you to help me. Depending on the way I plant my rows of basil, what is the maximum number of basil plants I might have after thinning?

I keep a jar on my dresser for collecting the coins I find when I empty my pockets. This morning I counted my coins and found out the following:

One-fifth of the coins in my jar are dimes.
One-sixth of them are nickels.
One-tenth are quarters
The rest are pennies.

The total value is $3.52.

How many of each coin do I have?

Tell how you got your answer and how you know it is correct.

Extra: I went to the bank and got coin wrappers. It takes $10 worth of quarters to fill a quarter wrapper, $5 worth of dimes to fill a dime wrapper, $2 worth of nickels to fill a nickel wrapper, and $0.50 worth of pennies to fill a penny wrapper.

How many more of each coin do I need before I can fill one wrapper of each?

The workers at Amy's Barn Company usually work in teams of 5. It takes a crew of 5 workers 9 days to build a barn.

A crew lost two of its workers. How many days should it take the remaining 3 workers to build a barn?

Extra: If a customer needs to have a barn built in 7 days, what is the minimum number of workers that Amy would need to put on the job?

One of my favorite places to visit in Nova Scotia is the Museum of Industry in Stellarton. On my last trip I enjoyed a special exhibit on antique bed quilts.

One quilt in particular grabbed my attention. It was rectangular and was made entirely of one-inch squares, 5467 of them according to the description next to it. I wondered if I could determine the length and width of the quilt with only that information. I did, and I bet you can, too!

What are the most likely dimensions of the quilt?

Be sure to explain how you found them and how you know you have found the best answer.

Extra: If you spread this quilt evenly on a standard double bed, 54" wide and 75" long, with the shorter edge of the quilt along the head of the bed, how much would hang down on each side?

Jonathan and Hazel love to drink tea. When they are both at home, a pound of tea lasts two weeks. Occasionally Hazel visits her mother in Australia. It takes six weeks for Jonathan alone to use up a pound of tea.

How long should a pound of tea last Hazel if she were alone?

Extra: In 2019 Hazel visited her mother for six weeks in the spring. In the summer Jonathan gave up drinking tea for six weeks. Their favorite tea costs $9.00 per pound. About how much did the couple spend on tea during the year?

Luis wants to play basketball but is supposed to finish his math assignment first. Ms. Barajas, his teacher, offers him a bargain that he can cut his assignment short on the condition that he determine the exact number of balls that are in the ball closet. Ms. Barajas informs him that

there are fewer than thirty balls;
if he were to take out two balls at a time, there would be one ball left in the closet;
if he takes out three balls at a time, there would be no balls left in the closet;
if he takes out four balls at a time, there will be three balls left over;
if he takes out five balls at a time, there would be no balls left in the closet.

Luis smiles as he tells her how many balls are in the closet. Ms. Barajas returns his smile, picks up his paper, and sends him to the court.

Question: How many balls are in the closet?

Extra: Which one of the following statements could NOT be true? Why?

10% of the balls are basketballs
60% of the balls are soccer balls

This year Anthony's family is hosting the big Thanksgiving dinner. That means his grandmother, aunts, uncles, and cousins will all be coming to his house. There will be 12 adults and 15 children, so they're going to need a lot of food!

Anthony is in charge of making the rolls. His mom wants him to make enough so that there will be 3 rolls for every 2 adults and 4 rolls for every 3 children. She also told him to bake one extra roll for each person to make a turkey sandwich the next day.

She advised him not to make partial recipes because recipes with yeast often turn out better if you follow the directions exactly. With all the leftovers that could spoil, refrigerator space will be precious, so Anthony doesn't want to save any dough to bake later -- he wants to bake it all at once.

His recipe makes 2 dozen rolls. How many rolls will he make if he follows all of his mother's suggestions? Explain how you arrived at your answer.

Extra: Anthony's Famous Butter Rolls Recipe

5 1/2 cups all-purpose flour 3 tablespoons white sugar 2 teaspoons salt 1 1/2 teaspoons active dry yeast 1 1/2 cups milk 1/2 cup water 3/4 cup butter Makes 2 dozen rolls

Ben was helping the school custodian set up chairs in the gym for an assembly. They needed to seat 180 students and put the same number of chairs in each row.

After hearing the custodian's plan and doing some quick mental math, Ben suggested a different arrangement for the same number of seats. He explained that, by putting 5 more chairs in each row, they could have 3 fewer rows, and students in the back row would be able to see better.

How many chairs were in each row of Ben's plan?

Extra: Write a similar problem involving two possible sets of rows and seats per row for 270 students. Show a solution for your problem.

Ms. Juncos is the lead teacher for the fourth grade team at Newton Elementary School. One week before Halloween, the team teachers assigned all of the fourth graders a new project. They thought that the students might enjoy making geometric jack-o-lanterns, so they planned a field trip to Anderson's Pumpkin Patch to hunt, clean, and create the jack-o-lanterns.

Looking at the class lists the night before the trip, Ms. Juncos decided to put the students into groups so no one would have to work in the pumpkin patch alone. Her first attempt using pairs did not work - one person was left out. Next she tried groups of five, but that didn't work either. Then she tried groups of three and again had someone left over. Still no luck when she tried groups of four. Each attempt ended with one person left out.

If each grade at Ms. Juncos's school has fewer than 80 students, how many pupils are on her team?

Bonus: What number of group members should Ms. Juncos use to make this work?

10)

Shawn gets an allowance of $5 every other Sunday for doing chores. He likes to stop on his way home from school and buy a healthy snack. His favorite treat costs $0.65.

How many of these snacks can Shawn afford every two weeks?

After buying as many of these snacks with his $5 as possible, Shawn puts his left over allowance in his piggy bank. He is saving to buy a new calculator. The model he wants costs $8.95. (It performs integer division and operations with fractions!)

How many weeks will it take him to save enough for the calculator?

[Hint: Try estimating the answer before calculating it, so you will know if your answer is reasonable.]

Be sure to explain how you solved the problem and how you know you are right.

Extra: Shawn's mother tells him that, if he just gives up one of those snacks each week, he'll be able to buy the calculator in less than three months and have it in time for the annual math contest. Can you do the math to prove whether Mom is right or not? Explain your steps.

11)

Tabitha's job is putting numbers on the apartments in a new building. The apartments are numbered consecutively starting at 1. At the hardware store the digits cost $1 apiece. The bill for the digits came to $282.

How many apartments will Tabitha be numbering?

Be sure to explain how you found your answer.

Extra: On Mondays the store sells 1s for half price. How much could Tabitha save by buying the digits on Monday?

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