GrUber (Grades 6-8)

So today in math lab, we made a fake company named Gruber. First we needed to find out how much to charge for going to where the person is, so I thought it would be good to charge $1.00 to pick up. Then each mile to get to their destination is going to be $.50. 

- Chloe (Grade 6) 

In the first situation, I asked the students to decide two things: a flat pick up cost and a price per mile. We constructed a table of values (assuming each part of a mile would be rounded up to whole miles).

Then we created an algebraic rule for when the flat rate is $2.00 and the price per mile is $1.50. Where x (the independent variable) is the number of miles, and y (the dependent variable) is the cost, y=1.5x+2. Next, we looked at what would happen if we changed just the flat pick up rate. Using desmos.com, we were able to compare the lines.

y=1.5x+2
x	y
independent	dependent
miles	cost
0	$2.00
1	$3.50
2	$5.00
3	$6.50
4	$8.00
5	$9.50
6	$11.00
7	$12.50
8	$14.00
9	$15.50
10	$17.00

The lines were parallel and moved up and down based on the flat pick up rate.

Then we looked at what would happen if the flat rate remained the same but the price per mile changed.


Every equation crossed 2 on the y-axis, but the angle (or slope) changed. The higher the value, the steeper the slope.

Stage three was to design their own company. What variables would be important to them? Would they change the price based on weather, time in the car, number of people in the car, size of the car....? What would their service be called? How would they market the company to attract customers?



Hi, and welcome to YOUBER! Youber is where it's all about you! Yay! So the cost for the pick up is $1.00. The cost per mile is $1.50 because mine is a Youber black. 

- Chloe

To be continued...

One Grain of Rice (Grades 1-4)

On the first day, give me one grain of rice. On the second day, give me two grains of rice. On the third day, give me four grains of rice. Do this for 30 days. 

On day 30 the girl got 536,870,912 grains of rice. 

AMAZING!!!!!!!!!

Actually, I kinda expected that. I have read another story like this...

- Serena (Grade 3) 


To read the full story of One Grain of Rice, go here.

One Grain of Rice (Grades 6-8)

There was a king who made a deal with the people that he would collect rice each day, and would give up rice to the people if there was a famine. So one day there was a famine, and the people were complaining because of hunger. But the king said that it wasn't a big enough famine. So the king got the grains of rice from the storage and put them in buckets on elephants to carry to the palace. But some buckets had holes, so the rice was falling out. A girl was collecting the rice that was falling using her skirt. When she went to the palace, she got caught, and she said that she was saving it for the king so he wouldn't lose any rice. So once the king heard, he made a deal with the girl. The girl said she wanted 1 grain of rice and 2 times as much each day for 30 days. "I think it's easy!" the king said, so the deal was made. 

I predict it would be about 240 grains of rice. 
I wonder how much rice is in the storage. 
I wonder who got the better deal. 

- Hendon (Grade 8) 

day	rice	total
1	1	1
2	2	3
3	4	7
4	8	15
5	16	31
6	32	63
7	64	127
8	128	255
9	256	511
10	512	1023

rice = 2 to the power of (day-1)
Total rice = one more than the previous day's rice amount.

Resources: https://illuminations.nctm.org/uploadedFiles/Content/Lessons/Resources/6-8/OneGrainRice-AS-OGR.pdf

Class Pet (Grades 1-3)

Blog by Kristanna (grade 3):
"Today we talked about which class pet we should get, and put sticky notes with animals on them. We divided them into interesting, boring, safe, and dangerous boxes."

Students wrote 5 possible class pets on sticky notes and put them on an x-axis ranging from dangerous to safe.

The positive-positive quadrant was the top right. Animals should be chosen from this box. Bottom left was negative-negative. These animals wouldn't be considered. They could also be sorted by other criteria: expense, size, friendly...

"I think we should get two guinea pigs because they are interesting and cute, and I have two of my own. They are kind of expensive." - Kristanna 
Other objects could be sorted too, like books.

After we stepped back, we noticed that kids usually like to pick interesting books to talk about, not boring ones.

Kenyan Handshake (Grades 4-8)

Blog by Jacob (grade 7)

"In Kenya, everyone in the congregation shakes hands with each other after church. To do this, at the end of the service, the pastor walks out. The next person walks by and shakes his hand, then goes next to the pastor. Third person shakes the pastor's hand and then lines up behind the second person. This goes on until the whole congregation is in a circle. Our job is to find out how many handshakes will happen if there were 50 people. 

My prediction is 100."



The students brainstormed ways to model this problem. Acting it out, making a table, making a graph, make a smaller (easier) problem and multiplying it to get the final answer.









After making a long chart, they discovered that number of handshakes was 1225. They also discovered that the handshakes didn't grow at the same rate, so an easier problem wouldn't work.

The next day we modeled the handshakes with polygons. Each dot was a person, each line was a handshake.



Each new person (n) shook hands (n-1) times. The 6th person shook hands with 5 people and this happened 6 times. Because this method counts each handshake twice, we divided it by 2.

Handshakes = n(n-1)/2

For more information about the math behind the handshake problem, go here.