6.1+Scaling+Up+or+Down+1011

Comparing and Scaling Tasnim Mostafa Math 7D Scaling Up or Down Investigation 6 Problem 6.1

Many important practical and mathematical applications involve comparing quantities of one kind or another; it is important to know which method to use and how we should use them.
 * BIG IDEA:**

Which comparing strategies work best in which situations?
 * Investigation 6 Essential Question:**

**Notes:** To make things larger or smaller you can use a scale factor.

Problem 6.1

__T.rex__ (average count) Weight: 8100 kilograms Height: 6 meters Skull length: 1 meter Incisors length: 15 centimeters

__Lager then Average Human__ (average count) Weight: 90 kilograms Height: 2 meters Skull length: 20 centimeters Incisors length: 1 centimeter

//The T.rex was MUCH bigger then a “larger than average” human being. Everything that was measured of a T.rex was bigger then everything measured for a “larger than average” human.//
 * How big was T. rex compared to a “larger than average” human being?**

T. rex weighed 8010 kilograms more than a “larger than average” human 90kg >human weight, x 90 equals 8100kg < T-Rex Weight

T. rex was 4 meters taller than a “larger than average” human 2m> human height, x 3 equals 6m human skull length x 5 equals 1m Rex Incisor length.

So basically the T.rexes were/had 90 times heavier than a “larger than average” human. 3 times taller than a “larger than average” human. 5 times bigger skulls then a “larger than average” human’s skull 15 times larger teeth then a “larger than average” human’s teeth.


 * Write a paragraph to help someone younger then you understand how the size of T.rex compares to the size of a human. Be specific about the comparisons you are making.**

Some of our favorite stories have to do with Dinosaurs and how they lived on our earth a long, long time ago. We know that Dinosaurs were big from what we’ve heard but wouldn’t we like to know exactly how big? Well no problem we can know now. Archeologists (people who study old things and history) dug up various parts of a dinosaur’s body. Not just any dinosaur but a special one. His name is T.rex, he was a very big guy. Now imagine a pretty big human guy like your dad but slightly bigger. So this T.rex dinosaur was 3 times his height. So if you stacked up 3 of those big humans you would be able to see how tall T.rex was. The T.rex also weighed a lot! About 8100 kilograms! We’re talking like 6 really fat people combined. Of course to weigh so much they must have ate a lot of different things and to help them do that they had huge teeth (called incisors). Their teeth were about 14 times a big human tooth. To be able to have these teeth the T.rex had a big head/skull too. His skull was 80 centimeters more then a big human skull. So now we know that dinosaurs especially T.rex’s were really big! And since they were so much bigger then humans they could have harmed us if they were still around. But luckily there not. So we have nothing to worry about.


 * __Follow up:__**

The infants height is same as “larger than average” and the T.rex is three times that height. So the scale factor would be 1/3
 * 1. Suppose an infant T. rex was the same height as the “larger than average” human described in the problem above, but he was still similar to an adult T.rex. What would be the scale factor between a grown T. rex and the infant T.rex?**

Grown T-Rex’s incisors= 15cm Scale Factor=1/3 1/3 of 15cm=5cm Incisors were 5 cm
 * 2. How long were the incisors of this young T.rex?**


 * 3. How long was the skull of this young T.rex?**

Grown T-Rex’s skull=1 meter Scale Factor=1/3 1/3 of a meter=33cm Skull is 33 cm

Vocab words: __Population Density__- measurement of population per unit area __Rate__- frequency relative to a time unit __Ratio__- relative magnitudes of two quantities __Scale, Scaling__- scale is an ordered reference standard, scaling is the act of arranging in a graduated series __Unit Rate__- A rate with the second term being one unit __Decimal__- A linear array of digits that represents a real number __Difference__- the quality of being unlike or dissimilar __Equation-__ a mathematical statement that two expressions are equal __Equivalent ratio__-two ratios that have the same value __Fraction__- a component of a mixture __Graph, Coordinate graph__- chart the data, grid with x and y axes crossing through the center __Percent__- a proportion in relation to a whole __Scale Factor-__ A number which scales or multiplies some quantity __Proportion-__ the quotient obtained when the magnitude of a part is divided by the magnitude of the whole