The Problem of the Week presents an opportunity for 1st to 12th graders to apply their creativity to mathematical problem solving. It is NOT a required assignment. It is available to those students who find the question interesting and who are looking to stretch their imagination.

1)

Mrs. Martinez planted a lovely vegetable garden in her backyard. Many pesky critters have been sneaking into the garden at night to snack on some of her fresh vegetables. Mrs. Martinez decided she would build a fence around her garden to keep the critters out. She measured one side of her square garden and it was 12 feet long.

How much fencing will she need altogether to protect her vegetable garden?

Extra: The next year Mrs. Martinez grew a bigger garden. This time she decided to build a new fence right away to keep those critters away. The length of her garden is now 16 feet and the width is 12 feet.

How much fencing will she need in all for her new garden? What shape is her garden now?

2)

Here's one pattern:

4, 14, 24, 34, 44, 54, 64, . . .

Can you find these numbers on a number grid?

Here's a similar pattern:

9, 19, 29, 39, 49, . . .

Find another similar pattern. Can you describe what all these patterns have in common?

Write a number model or sentence that shows the addition that must be done to move from one number to the next in the pattern.

3)

Ben wants an ice cream cone, but he is having trouble deciding which flavor and topping to get!

He can get either cookie dough ice cream or chocolate ice cream, and either cookie crumbles or sprinkles for a topping.

How many different choices of ice cream cone with topping does Ben have?

4)

Three of Miss Smith's students helped her put away all the basketballs the class had been playing with during P.E. Miss Smith wanted to reward them for their kindness. She went home and baked one yummy brownie for each of them. One of the students was absent the next day, and Miss Smith let the two who were at school share all of the brownies she had baked.

How can the two students share the three brownies equally?

Extra

What if Miss Smith made 7 brownies instead and only 2 helpers were in school? How many brownies would each student get?

5)

There was a piñata at Drew's birthday party. The 3 Gonzalez sisters collected 4 packs of bubblegum that fell from the piñata. When they got home, they decided to split the 4 packs of gum evenly. They opened each pack and counted 6 pieces of gum in each.

How can the 3 sisters divide the bubblegum evenly? How do you know?

Extra: What if their mother tells them they must share the packs of gum with their 3 cousins as well? How many pieces would each child get?

6)

Manuela has to earn 10 tickets to get a prize from the prize box. She earned 3 tickets yesterday by cleaning up after an art project. Today she earned 4 more for raising her hand instead of calling out.

How many more tickets does she need before she can get a prize from the box?

Extra: If Manuela saves her tickets until she has 20 tickets, she can get a bigger prize. How many more will she need for the bigger prize?

7)

Jayoniece's family planted an apple tree right outside her window when she was born. It was 10 feet tall when they planted it.

On Jayoniece's first birthday they measured the height. The apple tree was 12 feet tall.

When she turned two, it had grown to 14 feet.

On Jayoniece's third birthday, the tree was 16 feet tall.

If this pattern continues, how tall will the tree be on her fourth birthday? About how many feet does the tree grow every year?

Extra: How tall will the tree be by Jayoniece's tenth birthday? At that time, how much will the tree have grown since they planted it?

8)

A dog takes three steps to walk the same distance for which a cat takes four steps. Suppose one step of the dog covers 1/2 foot. How many feet would the cat cover in taking 24 steps?

9)

It is Halloween, and Shawn and his five friends want to dress up as bats.

They have been researching bats at school and learned that the largest bats in the world live in Asia and are called flying foxes. These bats can have a wingspan of 2 meters. Shawn and his five friends decide they want to be flying foxes for Halloween.

Their mothers made the costumes with wingspans of 3 feet (2 meters was way too big for them). If Shawn and his five friends stretched out all of their wings tip to tip, how far would they reach?

Explain your thinking.

10)

It's September, and Mr. Gonzalez wants to buy special gifts to welcome his new second grade students. He found sparkly pencils that said "Second Graders are #1," and he wants to buy one for each student.

There are 6 pencils in a pack and he will have 22 students in his class.

• How many packs does he need to buy?

• Will he have any leftover pencils?

• How do you know?