# Problem of the Week Archive: 4-6

## Problem of the Week 12_30

1. Can you write 1/2 as the sum of two unit fractions? 1/(2 ) = 1/a+ 1/b

How many combinations can you find?

2. Are there any rectangles whose area and perimeter have the same numerical value? How many can you find?

3. How do think question 1 and 2 relate to one another?

Fresno County Office of Education • Larry Powell, Superintendent

Carl Veater, Math on Call Program Producer, cveater@fcoe.org, (559) 265-3065

Fax: (559) 265-3041

2011-2012

## Problem of the Week 12_26

The table shows a list of numbers. For every number listed in the table, multiply by 2 and record the result on the right.

1. What is the result of multiplying an even or odd number by 2? Will this always happen? Draw a picture to show why or why not.

2. Create a new table with the same numbers in the left column. This time, multiply the number by 2 and then add 1. Record this result on the right.

3. How do the results from the first table relate to the results in your new table? Why do you think that is?

4. What conclusions can you make about how even and odd numbers work?

## Problem of the Week 12_22

I am a number that can be written as a decimal or as a fraction. I am less than ½ and more than 1/3. As a decimal, all three of my digits are different and odd. The sum of my tenths’ and hundredths’ digits is less than 9. The sum of my tenths’ and thousandths’ digits is less than seven.

1.Who am I? Describe me as a decimal, a fraction, and in words. How are these descriptions related?

2.Draw a number line to show my location. What is my exact distance from one?

Show all steps and thinking used to find the mystery number.

## Problem of the Week 12_18

The students in Roberto’s class are growing wheatgrass seedlings in different conditions for a science project. Roberto noticed that Patricia’s seedlings are 1 1/2 times a tall as his own. He also notices that Cody’s seedlings are 3/4 as tall as his own.

1. Which of the seedling cups must belong to each student? Explain your reasoning.

2. Roberto’s seedlings are 8 inches tall. Find the height in inches of the wheatgrass in the other two cups. Solve the problem in at least two ways.

Fresno County Office of Education • Larry Powell, Superintendent

## Problem of the Week 12_14

Your classmate Evelyn says,

When you multiply by a number, you will always get a result larger than the number you start with. Look, I can show you.

Start with 7.

Multiply by 5. 7×5=35

The answer is 35, and 35 >7

35 is bigger than 7.

It even works for fractions.

Start with 1/2.

Multiply by 4. 1/2 × 4 = 2

The answer is 2, and 2 > 1/2

2 is bigger than 1/2.

Do you agree with Evelyn? Why or why not? For what numbers will Evelyn's rule work? For what numbers will Evelyn's rule not work? Explain and give examples.

Attach additional pages as necessary.

## Problem of the Week 12_10

1. A student claims that 4/5 is closer to one than 5/4, do you agree? Explain why or why not using a number line.

2. Find four fractions equivalent to the number five. Use a number line to explain why they are equivalent.

Fresno County Office of Education • Larry Powell, Superintendent

Carl Veater, Math on Call Program Producer, cveater@fcoe.org, (559) 265-3065

Fax: (559) 265-3041

## Problem of the Week 12_6

1. Create a number line and use it to demonstrate why -6 -4 = -10.

2. On the same number line show why 2(-4) = -8.

Explain your process completely.

Fresno County Office of Education • Larry Powell, Superintendent

Carl Veater, Math on Call Program Producer, cveater@fcoe.org, (559)265-3065

Fax: (559) 265-3041

2011-2012

## Problem of the Week 12_2

Susie has 200 beads and 120 of them are red. What percent of her beads are red and what percent are not red?

Pam is going to give Susie some of her green beads, how many green beads would she have to give Suzie so that she would have 40% red beads?

Fresno County Office of Education • Larry Powell, Superintendent

Melinda Riccardi, Math on Call Program Producer, mriccardi@fcoe.org (559) 265-4044

Fax: (559) 265-3041

## Problem of the Week 11_29

If a dart is thrown at the following tangram dartboard and we assume the dart lands at random on the board, what is the probability of the dart landing in each of the identified areas?

1. Area A 2. Area B 3. Area C

Be sure to show all thinking used to solve each part of the problem.

Fresno County Office of Education, Larry Powell, Superintendent

Melinda Riccardi, Math on Call Program Producer, mriccardi@fcoe.org

(559) 265-4044 FAX: (559) 265-3041

2010-2011

## Problem of the Week 11_26

Xavier wants to join a basketball league this summer. There are three different teams that have openings. Xavier was able to collect data for the last five games that each of the teams played and organize it in a table.

1. If Xavier uses the mean to rank the teams, which team will he join?

2. If he uses the median to rank the teams, which team will he join?

3. If you are the coach of the Stars team, what kind of data would you use to get Xavier to join your team? Why?

4. Represent this data in your choice of a type of a graph.

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