Fun at the Fair

Essential Questions: Math EQs How can an area model help us solve multiplication problems? Why does decomposing a factor work when multiplying a multidigit number? Robotics EQs How do you know the Ferris Wheel that you built and programmed is a robot? How does the worm gear affect the movement of the Ferris Wheel? How does modeling help engineers?

What property is being used? How can you decompose 13? ? + ? = 13 How many ways are there? What property is being used?

Abe Froman, owner of the town carnival needs Mia and Max’s help. The most popular ride at the carnival is the upside down Ferris wheel, but the lines at this ride are always way too long. Mr. Froman needs Mia and Max’s help to build a model of the upside down Ferris wheel so that they can use it to collect some data that will help Mr. Froman.

What is a Ferris Wheel? The Ferris wheel was originally called the Great Chicago Wheel It was built by George Ferris in 1893

Ferris Wheels Today Today Ferris wheels are always one of the most popular rides at amusement parks, fairs, etc. The London Eye, a giant Ferris wheel, was a popular attraction for visitors at the 2012 Olympics.

Upside Down Ferris Wheel None of these rides, however, are as exciting as Abe Froman’s wild, upside-down Ferris Wheel.

Math Solves Everything Let’s take a look at how we can use Math to investigate what happens with the lines at some of Mr. Froman’s rides. Three people can fit in each car of the “Looper” roller coaster, so the ride attendant lines people up in rows of 3. (The first row is modeled below.) If there are 6 rows of people, how many people are waiting in line for the Looper ?

Scenario #1 a. What mathematical operation could be used to solve this problem? b. What type of shape have you created with your unit cubes? c. What equation would represent your array?

Scenario #2 There are 9 rows of people waiting in line to ride the “Ragin’ Rapids”. Each row contains 6 people. How many people in all are waiting in line?

Scenario #2 What equation could be used to solve this problem?   If you didn’t know what 9 × 6 was, what else could you do to solve this? How can an area model help us to solve multiplication problems?

What happens to the array in this scenario? It is the grand opening of the “Twister”! 4 people can ride in each car so the ride attendant lines people up in rows of 4. There are 16 rows of people in line. Due to space and safety concerns however, only 10 rows of people can wait in line next to the ride while the rest of the group must wait a little distance away. Use your cubes or grid to model what the people waiting in line would look like. What happens to the array in this scenario?

Scenario #3 How many people are waiting in line next to the Twister?   How many people need to wait a little distance away from the Twister? How many people in all are waiting on line for the Twister? What two multiplication expressions can help you find the total product?

Scenario #3 “4 × 16 is the same as (4 × 10) + (4 × 6)” Do you agree with this statement? Why or why not? “7 × 15 is the same as (7 × 5) + (7 × 3)”

Scenario #4 5 people can ride the “Mindbender” at one time so the ride attendant lines people up in rows of 5. There are 18 total rows of people in line. How could you split the line into groups of people to make it easier to find the total number of people waiting in line?

Scenario #4 What multiplication equation models the total number of people waiting in line? How could you separate one of the factors to make it easier to find the product? Write the expressions.   How many total people are waiting in line? How do you know which is the most efficient way to break apart the factor?

Mr. Froman’s Upside-Down Ferris Wheel Mr. Froman has asked Mia and Max to use their new knowledge to help him with the biggest problem at the fair. The upside down Ferris wheel at the fair is always the most popular ride and has the longest lines. Abe would like Mia and Max to build a model of the real life upside down Ferris wheel so that they can use it to answer questions about how many revolutions the Ferris wheel completes in a certain amount of time and how quickly they can move people on and off of the ride.

2 x 6 bricks

Pose a Problem What equation represents the story? Kyle went to a fruit market. The market sells a wide variety of fruits and vegetables. The picture at the right shows a display of oranges. Write a problem that can be solved using the picture. What equation represents the story? How can we decompose one of the factors to make this problem simpler?

Models… and models How are these two models alike? How are they different? When we talk about models in math, what do we mean? When we talk about making or using models in engineering, what do we mean?

Engineers and Models Why are models important to engineers? Why don’t they just build a full size Ferris wheel to investigate with? How can models help engineers answer questions about real life problems?

Area (array) model What multiplication expression could this area model represent? Why could breaking the factor 143 into 100 + 40 + 3 make it easier to solve? What is the total product represented by the model? Why wouldn’t I want to draw every single square needed to cover the entire array?

Mr. Froman’s Upside-Down Ferris Wheel After you finish constructing the Ferris Wheel, explore the programming. Try to develop a program that will turn the Ferris Wheel at different speeds. What would we need to include, in a program that could detect and count the number of riders on the Ferris Wheel? Let’s look at the Ferris Wheel Follies handout…

Fun at the Fair Journal Questions Mathematics Concepts: 1. What operation helped you to predict how many riders would pass by the motion sensor in one minute? Would any other operation work? 2. How can decomposing a factor help make a multiplication problem easier to solve? Use words, numbers, symbols, and or pictures to explain your thinking. Robotics Concepts: 1. What part of your Ferris wheel build made it a robot? 2. How do you think the worm gear affected the motion of the Ferris wheel?