**By: Carolyn Howell**

Kelsea Manning

Esmari Venter

AnnaMarie Fazzino

Kelsea Manning

Esmari Venter

AnnaMarie Fazzino

**Drinking the Tang, HW #8**

1. Use common benchmarks to select appropriate methods for estimating measurements.

2. Select and apply techniques and tools to accurately find length, area, volume, and angle measures to appropriate levels of precision.

3. Understand, select, and use units of

appropriate size and type to measure angles,

perimeter, area, surface area, and volume.

NCTM Standards (6-8)

TEKS

The boy starts out with a 20 oz bottle of juice. He drinks 1 oz of juice mixture every day until the bottle is empty. He adds one ounce of water to the bottle after every drink he has. So if he drinks 0 ounces of water the first day, then he would drink 1 ounce of water the second day. 0+1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16+17+18+19= 190 oz. of water total. The amount of fluids (water and /or juice) he drinks is this 1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16+17+18+19+20= 210 oz. This makes sense because he actually drinks one more ounce of juice than water every time. That extra ounce totals up to 20 oz.

Step 4: Looking Back

Johnny Manziel's Gatorade

a. So Tang boy drinks one ounce of pure juice the first day then adds one ounce of water. The second day he drinks two ounces of mixture and adds two oz of water. This process continues till there is no more juice left.

Step 3: Carry out the plan

Johnny Manziel is given one small 17 oz. Gatorade and an endless amount of water to drink during the NFL Combine. Before the game starts, Johnny drinks 1 oz of Gatorade and fills the bottle back up with water. After the first round, he drinks 2 oz of Gatorade and fills the bottle up again with water. He continues this process until the bottle is empty.

How much water does Johnny drink during the Combine?

Johnny drinks 136 oz of water + what is in the Gatorade mixture

16 + 15 + 14 + 13 + 12 + 11 + 10 + 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 = 136 oz

Explanation

The Problem

So, the boy drank 1 ounce of juice the first day and 0 ounces of water on the first day. The second day he drank 2 ounces of juice and 1 ounces of water. When we add the ounces of individual fluids together we get 210 oz. of juice and 190 oz. of water respectively in the 20 days he took to drink all of the juice. This makes sense because the boy drinks 1 more ounce of juice than water on the first day, so by the 20th day he has consumed 20 oz more juice than water.

So, to answer the given question, the boy drank 190 oz. of water.

What are the knowns and unknowns of the problem?

Knowns

: -The bottle can hold 20 oz.

Day 1: drinks 1 oz of juice then refills

Day 2: drinks 2 oz of juice then refills

Day 3: drinks 3 oz of juice then refills

He drinks an extra ounce of tang everyday

The bottle is refilled with water everyday

Unknowns

: Number ounces of water he drinks

Connection between knowns and unknowns?: The bottle has to be refilled with water each day and has to have 20 ounces of fluid before he can drink out of it. Also, he will consume more tang than water because he's drinking more and more tang each day.

To conserve the contents of a 20 oz. bottle of Tang, a tang drinker adopts the following procedure: On the first day, he drinks 1 oz. of Tang and then refills the bottle with water. On the second day, he drinks 2 oz. of the mixture and then refills the bottle with water. On the third day, he drinks 3 oz. of the mixture and again refills the bottle with water. The procedure is continued for succeeding days until the bottle is empty.

How many ounces of water does he drink?

Step 1: Understand the problem

Step 2: devise a plan

In order to help us visualize the problem we will construct a table.

Create a table with 3 columns and 22 rows. On the upper left hand side we will label a column "day", next to that will be the "ounces of juice he drank", and next to that will be the "ounces of water he drank." Once we get to 20 ounces at the very bottom of our table we will add up all the numbers in the 2nd column (which should start with 20 oz) , and then add up all the numbers in the 3rd column (which should start with 0 oz). Then we should have our answer!

It should look a little something like this.........

Measurement. The student solves application problems involving estimation and measurement of length, area, time, temperature,

volume, weight, and angles. The student is expected to:

(A) estimate measurements (including circumference) and

evaluate reasonableness of results;

(B) select and use appropriate units, tools, or formulas to

measure and to solve problems involving length (including

perimeter), area, time, temperature, volume, and weight;

(C) measure angles; and

(D) convert measures within the same measurement system

(customary and metric) based on relationships between units.