New User Special Price Expires in

Let's log you in.

Sign in with Facebook


Don't have a StudySoup account? Create one here!


Create a StudySoup account

Be part of our community, it's free to join!

Sign up with Facebook


Create your account
By creating an account you agree to StudySoup's terms and conditions and privacy policy

Already have a StudySoup account? Login here

MAT 105 Chapter 3 notes

Star Star Star Star Star
1 review
by: Catherine Notetaker

MAT 105 Chapter 3 notes BIO 104-A

Marketplace > The College of New Jersey > Biology > BIO 104-A > MAT 105 Chapter 3 notes
Catherine Notetaker
GPA 3.6
View Full Document for 0 Karma

View Full Document


Unlock These Notes for FREE

Enter your email below and we will instantly email you these Notes for INQUIRIES IN THE LIFE SCIENCES

(Limited time offer)

Unlock Notes

Already have a StudySoup account? Login here

Unlock FREE Class Notes

Enter your email below to receive INQUIRIES IN THE LIFE SCIENCES notes

Everyone needs better class notes. Enter your email and we will send you notes for this class for free.

Unlock FREE notes

About this Document

Chapter 3 notes
Dr. Wund
Class Notes




Star Star Star Star Star
1 review
Star Star Star Star Star
"No all-nighter needed with these notes...Thank you!!!"


Popular in Biology

This 6 page Class Notes was uploaded by Catherine Notetaker on Monday January 11, 2016. The Class Notes belongs to BIO 104-A at The College of New Jersey taught by Dr. Wund in Spring 2016. Since its upload, it has received 53 views. For similar materials see INQUIRIES IN THE LIFE SCIENCES in Biology at The College of New Jersey.

Similar to BIO 104-A at TCNJ


Reviews for MAT 105 Chapter 3 notes

Star Star Star Star Star

No all-nighter needed with these notes...Thank you!!!



Report this Material


What is Karma?


Karma is the currency of StudySoup.

You can buy or earn more Karma at anytime and redeem it for class notes, study guides, flashcards, and more!

Date Created: 01/11/16
Mat 105 end of chapter 2 notes Characteristics of our Base-10 system 1. It has 10 symbols which can be used to represent any amount 2. The value of each place is 10 times that of the previous place 3. Each place contains only one symbol 4. The value of the numeral depends on its place in the number 5.The value of a number is determined by multiplying each numeral by its place value and then adding the sum 6. Zero represents both an empty place and an actual amount Mat 105 chapter 3 notes Chapter 3 The Four Fundamental Operations of Arithmetic Key idea: Numbers can be composed and decomposed and research shows that the ability to compose and decompose numbers is critical in elementary school mathematics. Section 3.1 Understanding Addition Words for addition: combine, join, put together Addition of Roman numerals: xxxviii + xxvi Four example problems: 1. Andy has 3 marbles and his older sister Bella gives him 5 more. How many does he have now? 2. Keesha and Jose each drank 6 ounces of orange juice. How much juice did they drink in all? 3. Linnea has 4 feet of yellow ribbon and 3 feet of red ribbon. How many feet of ribbon does she have? 4. Josh has 4 red trucks and 2 blue trucks. How many trucks does he have altogether? Discrete and Continuous amounts Model or drawings to represent each and general or “bar”model (a+b=c) Part Part Whole This general model can represent each of the problems above and all of the 4 operations of arithmetic. Some stages for addition: x x x x x x x x a) combine all and count, b) count on 3and45678, c) know that 3 + 5 = 8 Note that problem 1. above can be modeled by the union of the elements of two sets. Addition: If A and B are disjoints sets, containing a and b elements, respectively, then a + b = n (A union B). Number line model is often problematic 100 addition facts: Table 0 to 9 horizontal and 0 to 9 vertical. Using properties can benefit students Identity property of addition Commutative property of addition Associative property of addition Closure property of addition-unique and existence Regroup when adding and subtracting e.g. 36 + 28 = and 64 - 36 = In addition 6+8 > 9 in subtraction 6 > 4 but in both an amount is moved from one place to another and the amount always represents a 10-for-1 exchange ( 10 for 1 or 1 for 10) Trading, exchanging or regrouping rather than carry or borrow. Investigation 3.1b Mental Addition 1. 39 + 57 2. 68 + 35 3. 66 + 19 4. 545 + 228 5. 186 + 125 Leading digit or front end: 68+35 = 60+30+8+5 Compensation: 68+35 = 70+33 Break and bridge: 68+35 = 68+30+5 Compatible numbers: 68+35=65+35+3 Children’s strategies for addition: 48 + 26 a) add up to 10:48 58 68 68 + 6 b) Break second number apart: 48 + 20 = 68, 68 + 6 = 74 c) Use partial sums: 48  26 60 14 74 Partial Sums: 48+26 number line Base 10 blocks More difficult three-digit addition with Base-10 blocks Numbers Base-10 blocks Words 267 2 hundreds, 6 tens, 7 ones 133 1 hundred, 3 tens, 3 ones An algorithm is a single, clearly described method that works in all cases. There are many efficient algorithms used around the world not just the ones you learned. Investigation 3.1d Alternate Algorithm - Lattice Algorithm for addition 6 4 5 +7 2 8 Estimation; The NCTM standards note that students need to develop, analyze and explain procedures for computation and estimation. Addition in base-5: 43+24 Number and operation sense. 1. To take numbers apart and put them back together 2. To move fluently among different representations 3. To recognize when one representation is more useful than another 4. To perform mental computation and estimation flexibly 5. To determine whether an answer is reasonable 6. To understand the effect of different operations on numbers Section 3.2 Understanding Subtraction Five example subtraction problems: 1. Joe had 7 marbles. He lost 2 in a game. How many does he have left? 2. Billy has 2 marbles and Yaka has 7. How many more does Yaka have? 3. At the beginning of the week, the hospital had 7 ounces of insulin. During the week, 2 ounces of insulin were used. How much insulin did the hospital have at the end of the week? 4. You need $7 to go to the movie and you only have $2. How much more do you need? 5. Tom has 7 feet of bubblegum rope and Meg has 2 feet. How much more does Tom have? Which are discrete and continuous (measurement)? Some are “Take-away” and some are “Comparison” Set model and linear (measurement) model. Also missing addend. x x x x x x x x x x x x x x minuend - subtrahend = difference C – B = A Whole C Part A Part B Number line Whole number Properties: no identity, not commutative or associative, not closed Investigation 3.2a Mental Subtraction 1. 65 – 28  65 – 30 =35, 35+2 = 37 compensation 2. 62 – 29  29 + 10 = 39, 39 + 10 = 49, 49 + 10 = 59, 59 + 3 = 62 adding up 33 3. 184 – 125 125 + 60 = 185 60 – 1 = 59 compensation 4. 132 – 36  64 + 36 = 100 so 100 - 36 = 64 64 + 32 = 96 compatible numbers 5. 1000 – 648 648 + 300 = 948 300 + 52 = 352 adding up 64 – 27 Base-10 number line 64 - (20 + 7) 64 -7 -20 57 – 20 37 Base-10 blocks Subtraction 300 – 148 = Investigation 3.13 Alternate Algorithm – European Subtraction Algorithm used other countries 9 8 4 _ 3 6 8 ______________ You can’t take 8 from 4 cross out the 6 and put 7 now subtract 14 – 8 is 6, 8 – 7 is 1 and 9 – 3 = 6 6 2 3 - 1 5 8 . _______________ You can’t take 8 from 3 so cross out 5 and make 6, 13 – 8 = 5. You can’t take 6 from 2 so cross out 1 and make it 2 now 12 – 6 = 6 and 2 from 6 = 4 Words “Borrow” and “Carry” would better describe the process as Exchange, Regroup or Trade. Subtraction in Base-5 321-142


Buy Material

Are you sure you want to buy this material for

0 Karma

Buy Material

BOOM! Enjoy Your Free Notes!

We've added these Notes to your profile, click here to view them now.


You're already Subscribed!

Looks like you've already subscribed to StudySoup, you won't need to purchase another subscription to get this material. To access this material simply click 'View Full Document'

Why people love StudySoup

Steve Martinelli UC Los Angeles

"There's no way I would have passed my Organic Chemistry class this semester without the notes and study guides I got from StudySoup."

Amaris Trozzo George Washington University

"I made $350 in just two days after posting my first study guide."

Jim McGreen Ohio University

"Knowing I can count on the Elite Notetaker in my class allows me to focus on what the professor is saying instead of just scribbling notes the whole time and falling behind."

Parker Thompson 500 Startups

"It's a great way for students to improve their educational experience and it seemed like a product that everybody wants, so all the people participating are winning."

Become an Elite Notetaker and start selling your notes online!

Refund Policy


All subscriptions to StudySoup are paid in full at the time of subscribing. To change your credit card information or to cancel your subscription, go to "Edit Settings". All credit card information will be available there. If you should decide to cancel your subscription, it will continue to be valid until the next payment period, as all payments for the current period were made in advance. For special circumstances, please email


StudySoup has more than 1 million course-specific study resources to help students study smarter. If you’re having trouble finding what you’re looking for, our customer support team can help you find what you need! Feel free to contact them here:

Recurring Subscriptions: If you have canceled your recurring subscription on the day of renewal and have not downloaded any documents, you may request a refund by submitting an email to

Satisfaction Guarantee: If you’re not satisfied with your subscription, you can contact us for further help. Contact must be made within 3 business days of your subscription purchase and your refund request will be subject for review.

Please Note: Refunds can never be provided more than 30 days after the initial purchase date regardless of your activity on the site.