Visualizing Addition of Dissimilar Fractions Without and With Regrouping
Objective: Visualize addition of dissimilar fractions without and with regrouping.

Mother has one whole cake. First she sliced 1 and then 1 of the cake. What part of the cake did she slice? 2 4 Let’s solve the problem following the steps in problem solving.
1. What is asked for?
The part of the cake that was sliced.
2. What are the given data?
1 was the first sliced , and 1 was the second sliced 2 4 3. What is the mathematical sentence?
1 + 1 = n

2 4
1
4
1
2
1
8
1
8
4. So 1 + 1 = 3
2 4 4
* How can we add fractions if they are dissimilar?
* Change the fractions to similar then add.
...Lesson 3
Topic: Fractions
Subtopic: Addition and Subtraction of Fractions
Materials
• A set of paper strips with words written on it
• Fish bowl
Objectives
• To guess the word written on the paper strip
• To practice patience and understanding to those who can not get the answer correctly
Control of Error
• Teacher
Presentation
• The teacher will introduce the activity and give the instruction on what to do.
• She will ask for 5 pairs of volunteers from the class. One volunteer will pick a paper strip from the bowl and the other will guess the word. Then they will exchange places. If they can get the answer correctly, they will receive a prize.
Work by 4’s
Materials
• A set of fraction paper strips
• A box
Objectives
• To add similar and dissimilarfractions
• To participate actively in the activity
Control of Error
• Teacher
• Key cards
Presentation
• The class will form groups of 4 members.
• The group will discuss the steps in adding fractions.
• Each member will get 1 paper strip from the box.
• They will add the fractions on the paper strips.
• Then they will do LAS 1a – 1c.
Learning Activity Sheet 1a
Recall
Add the following fractions. Express the sum to lowest term if needed.
3/6 + 2/6
3/13 + 4/13
2/9 + 6/9
4/16 + 12/16
6/17 + 5/17
6/12 + 8/12
5/15 + 7/15
2/7 + 11/7
8/5 + 6/5...
...Fraction (mathematics)
A fraction (from Latin: fractus, "broken") represents a part of a whole or, more generally, any number of equal parts. When spoken in everyday English, a fraction describes how many parts of a certain size there are, for example, onehalf, eightfifths, threequarters. A common, vulgar, or simple fraction (examples: \tfrac{1}{2} and 17/3) consists of an integer numerator, displayed above a line (or before a slash), and a nonzero integer denominator, displayed below (or after) that line. Numerators and denominators are also used in fractions that are not common, including compound fractions, complex fractions, and mixed numerals.
The numerator represents a number of equal parts, and the denominator, which cannot be zero, indicates how many of those parts make up a unit or a whole. For example, in the fraction 3/4, the numerator, 3, tells us that the fraction represents 3 equal parts, and the denominator, 4, tells us that 4 parts make up a whole. The picture to the right illustrates \tfrac{3}{4} or 3/4 of a cake.
Fractional numbers can also be written without using explicit numerators or denominators, by using decimals, percent signs, or negative exponents (as in 0.01, 1%, and 10−2 respectively, all of which are equivalent to 1/100). An integer such as the number 7 can be thought of as having an implied...
...indirectly affects the climate patterns.
3. Environmental Impact
* To begin with, the green cover is reduced. Trees and plants help balance the atmosphere, without them we are subjected to various concerns like Global warming, the green house effect, irregular rainfall and flash floods among other imbalances.
4. Effect on human health
* The land when contaminated with toxic chemicals and pesticides lead to problem of skin cancer and human respiratory system.
* The toxic chemicals can reach our body through foods and vegetables that we eat as they are grown in polluted soil.
5. Cause Air pollution
* Landfills across the city keep on growing due to increase in waste and are later burned which leads to air pollution.
* They become home for rodents, mice etc which in turn transmit diseases.
6. Distraction for Tourist
* The city looses its attraction as tourist destination as landfills do not look good when you move around the city.
* It leads to loss of revenue for the state government.
7. Effect on wildlife
* The animal kingdom has suffered mostly in the past decades.
* They face a serious threat with regards to loss of habitat and natural environment.
Preventions/Solutions
5. Buy biodegradable products.
6. Do Organic gardening and eat organic food that will be grown without the use of pesticides.
7. Create dumping ground away from residential areas....
...Fractions
The problem here is to add and 
These two fractions do not have the same denominators (lower numbers), so we must first find a common denominator of the two fractions, before adding them together.
For the denominators here, the 8 and 14, a common denominator for both is 56.
With the common denominator, the
becomes a
and the
becomes a
So now our addition problem becomes this...
The problem here is to add and 
Since these two fractions have the same denominators (the numbersunder the fraction bar), we can add them together by simply adding the numerators (the 21 and 36 = 57), while keeping the same denominator (the 56).
Our answer here is:
The fraction is an improper fraction (the numerator is greater than the denominator).
While there is nothing incorrect about this, an improper fraction is typically
simplified further into a mixed number.
The whole number part of the mixed number is found by dividing the 57 by the 56.
In this case we get 1.
The fractional part of the mixed number is found by using the remainder of the division,
which in this case is 1 (57 divided by 56 is 1 remainder 1).
The final answer is: 
The problem here is to add and 
These two fractions do not have the same denominators (lower numbers), so we must first find a common denominator of the two...
...Subtraction with Regrouping
Abstract
This literature review focuses on twodigit subtraction with regrouping. Many students struggle with this concept and place value is a major stumbling block for students trying to master subtraction. This paper will also show that delaying the introduction to the traditional algorithm and allowing students to use their invented strategies as well as paying attention to the concreterepresentationalabstract instructional sequence help students overcome the obstacles to learning subtraction computations. In addition, studies by Ma, Chick, Pham, and Baker show that teacher content knowledge also effects how students learn twodigit subtraction.
Subtraction with Regrouping
Introduction
Research shows that many students struggle with learning subtraction with regrouping. This difficulty typically arises because the students do not understand the concept of place value in addition to composing and decomposing numbers. This document examines the importance of place value understanding, the use of invented strategies and the utilization of concreterepresentationalabstract (CRA) instructional sequence as well as the traditional subtraction strategy. This literature review also discusses how teacher content knowledge impacts student learning of subtraction with regrouping.
The Importance of Place Value
Developing students’...
...Title of Lesson: Subtracting by Regrouping
Objectives:
The students will be able to:
• Subtract by going from right to left, subtract the ones, then the tens, then the hundreds
• Subtract by regrouping the tens, then the hundreds
GPS Standards:
MCC.3.NBT.2 Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.
Preparation:
In preparation for this lesson, I will review the rules for regrouping, new methods, and fun interacting games or examples that may be useful in teaching this lesson. I will print worksheets, one for practice in the classroom and one for assessment.
Materials/Resources:
• Lollipops
• Practice worksheet
• Assessment worksheet
• Pencils
• Smart Board
• manipulatives
Procedures:
I. Introduction
To begin this lesson, I will tell the students that we will be working on subtracting by regrouping with tens and hundreds. Then, I will write a problem on the board. I will divide the class into three groups by giving the students cards of three different colors. Group 1 – blue, group 2 – red, group 3 green. Group one will be the ones place, group two will be the tens place, and group three will be the hundreds place. This will help students get a visual of the math problems. We will “borrow” from one another, but first we needed to separate...
...ELECTROPHILIC ADDITION
PURPOSE
The purpose of this lab is to learn how to synthesize 2methyl2butene into 2bromo2methylbutane using addition of hydrogen bromide.
THEORY
Chemical Compound Molecular Formula Molecular Weight Boiling Point Melting Point Density
Amylene CH3CH=C(CH3)2 70.13 g/mol 36 oC 134 oC 0.662 g/ml
Hydrobromic Acid HBr 80.91 g/mol 126 oC 11 oC 1.490 g/ml
2Bromo2MethylButane C5H11Br 151.05 g/mol 107 oC 1.18 g/ml
Sodium bicarbonate NaHCO3 84.007 g/mol Decomposes at melting point unknown 2.159 g/ml
Diethyl ether C2H5OC2H5 74.12 g/mol 34.6 °C −116.3 °C 0.7134 g/ml
In this lab we use electrophilic addition of a hydrogen halide to an alkene to make 2bromo2methylbutane. Electrophilic addition is an addition reaction where a pi bond is removed to create two new covalent bonds, YZ + C=C → YCCZ. Electrophilic addictions can also be the reverse of dehydrohalogenation. Dehydrohalogenation is when a double bond is formed between the α and βcarbon. In this lab the addition of hydrogen bromide produces a more substituted alkyl halide with respect to Markovnikov's rule where the Bromine atom attaches to the more substituted carbon.**
**According to lab manual, www.wikipedia.com
PROCEDURE
First we mixed 25ml of hydrobromic acid and 10mlof amylene in a 50ml flask. Then we attach the apparatus and reflux the solution...
...Addiction as Choice?
Andria Burgess
Introduction to Psychology
Addiction as Choice?
Substance abuse is a pervasive problem throughout the United States. It affects all populations, socioeconomic groups, ages, and races. Within the community of substance abuse treatment providers, there is an ongoing debate on whether addiction is a disease, or whether individuals who abuse substances choose to engage in the behavior. There is evidence to support both positions. This paper will examine the controversy surrounding the issue of whether addiction is a choice, and examine the arguments presented by both sides.
Addiction is a Choice
Many individuals view substance abuse and drug addiction as a choice. These individuals argue that addicts choose to put the addictive substance in their body, therefore triggering the subsequent chemical reaction that occurs (Schaler, 2000) Individuals who argue that addiction is a choice, do not dispute that there is a physiological reaction when the drug or alcohol enters the body, and that longterm use alters the addicts brain chemistry. What they take issue with is the disease concept of addiction. Proponents of the choice theory argue that by labeling addiction as a disease, personal responsibility is removed from the equation, thereby allowing the addict to justify continued use as they are "unable" to stop (Schaler, 2000).
Experience with addiction treatment confirms the choice theory, according to proponents of this...
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