Once students get to the fourth grade, learning equivalence in fractions with unlike denominators is something that they can look forward to...or not look forward to. It can be a very tough lesson and something that is hard for the children to understand. They need to have a simple understanding of fractions already. They need to know what they are and how they add up together. Meaning that they need to understand that fractions are a part of a whole...a fraction of something, and that if the fractions are equal they can add up to create a whole. The easiest way to describe this and review it is with a circle representing a pie. Each slice comes from the pie and all put together its a whole. Also the stronger the students is with their multiplication tables and the corresponding division facts, the easier this lesson is going to be for them. But by the time the students get to the fourth grade they should have already been introduced to them and have a firm understanding of what they are and how to identify them.

One of the best ways to introduce the ideas of equialent fractions with unlike denominators are with visual aids. A fantastic way to introduce this is with a hands on activity for the children. Each child will have a baggie of "pie pieces" or wedge pieces of a circle in different fractions, and a sheet of paper with a whole circle drawn on it. (I have attached a photo of a set I made for better understanding). The teacher would work with the same pieces on the over head. Teacher pieces would be made with transparency and colored to match the students, but still see through on the overhead. Together the teacher and students would work through some example of equivalent fractions with unlike denominators. For example students would be instructed to place their 1/2 piece in their circle and than two 1/4th pieces on the other side. They would be able to see that two 1/4th pieces equal the 1/2 piece and that all that together equals a whole, or 1....

...In elementary math there are several concepts about fractions. One concept students in fourth grade will need to master is learning how to tell if fractions are equivalent with unlikedenominators. There are a few prerequisite skills that are necessary in order for the students to understand this concept. The first thing students need to know is what fractions are. Fractions are a way of counting parts of a whole. Secondly, the students need to know how to identify parts of a fraction. The top number in a fraction is the numerator. The numerator is the number of parts in a whole (Eather). The bottom number in a fraction is the denominator. The denominator is the number of parts the whole is divided into (Eather). Lastly, the student will need to have a basic knowledge of their multiplication and division facts. This will help the students in deciding whether or not the fraction is indeed equivalent or not.
The first step in teaching students about equivalent fractions is to have a whole class conversation using manipulatives or visual aides. I would start the lesson with an overhead projection or use of a mimeo board in order to show the students what equivalent fractions look like. I would start with two circles on the board, one divided into two pieces and one...

...Teaching First Graders to Count
A. Counting Principles
Counting is a skill that is practiced throughout a student’s education using a variety of methods. One particular method is rote counting or standard order principle. The standard order principle is an understanding that counting is a sequence pattern that is consistent. It always begins with the number 1, then 2 follows, 3,4,5,6, etc. Sequential counting is taught by counting by ones, fives and tens. Circle time in the beginning of the day can incorporate to do daily calendar group activity. The day of the week, the number of days in a week as well as counting the number of school days since the first day of school are all part of the daily calendar math. Counting school days can begin by counting in standard order with the first day of school. Each day can be represented by using a picture or symbol such as a picture of an apple. One green apple for each day, then a yellow apple for every 5th day and on every 10th day, a red apple is used. This visual display of counting will show student which apples to count by 1’s, 5’s and 10’s as the school year progresses.
In a small group setting with about 10 students, we will first establish that students can identify numbers on a one to one correspondence by counting to 20. Manipulatives such as 20 counting bears in random colors will be placed in zip lock baggies and passed out to the group. Students will be asked to sort the bears...

...Samantha Meyer
MATH 334
Reflection 5
Date of Observation: Friday, May 1, 2015
Grade Level Observed: 4th grade
Math concept covered: Multiplying fractions using a number line
Mentor teacher’s name: Jessica Ross
Intern (your) name: Samantha Meyer
Reflection 5: Reflecting on your personal growth
This semester I interned at Hawthorne Elementary School in Ms. Ross’ fourth grade classroom. Each week I observed the class for two and a half hours and participated in helping instruct the math lesson. While at my math internship, I have learned tools to help me become an effective elementary mathematics teacher. In my opinion, this internship has been helpful but I believe it could have been even more beneficial. Compared to my internship in level one and science, interning at Hawthorne has been much less involved and hands on. Before starting this internship, I was very nervous because I have never taught fourth grade before. I was even more nervous because math has always been my weakest subject and I was very nervous to teach fourth grade math. This internship has made me realize that it is okay to be nervous, but as long as you love to teach it is always a good experience no mater what subject or grade. This internship has taught me the importance of patience, classroom management, differentiation, and effective ways to teach fourth grade mathematics.
Ms. Ross teaches the lowest level of fourth grade math at Hawthorne Elementary. This was...

...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, one-half, eight-fifths, three-quarters. 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 non-zero 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...

...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...

...In order to teach students the concept of equivalence when working with fractions with unlikedenominators or finding equivalent fractions, there are some skills that the students must already possess. These are as follows:
Students are able to both recognize and write fractions
Students understand the ‘breakdown’ of a fraction where the top is the numerator and the bottom is thedenominator
Students must have some understanding of equivalence and what it means
Students must be able to both multiply and divide with relative ease
The concept of finding equivalent fractions could be introduced using manipulative. One of these manipulative that would be extremely useful would be the pies. The ‘pie kit’ could be made or purchased, but both would include a large amount of pies with each being cut into different sizes with each ‘slice’ having a specific value on it (i.e. 1/3, 1/4, 1/2, 1/16, etc.). Using this visual manipulative, students would able to see the equivalent of various fractions (i.e. 1/2 is equivalent to 2/4 and 3/3 is equivalent to 16/16).
The steps for finding equivalent fractions would begin by having an overhead (for a large class) or having the children at a large group table (for a smaller class). Either one of these ways would allow the teacher to utilize the pie manipulative...

...Lacsap’s Fractions
IB Math 20 Portfolio
By: Lorenzo Ravani
Lacsap’s Fractions Lacsap is backward for Pascal. If we use Pascal’s triangle we can identify patterns in Lacsap’s fractions. The goal of this portfolio is to ﬁnd an equation that describes the pattern presented in Lacsap’s fraction. This equation must determine the numerator and the denominator for every row possible.
Numerator
Elements of the Pascal’s triangle form multiple horizontal rows (n) and diagonal rows (r). The elements of the ﬁrst diagonal row (r = 1) are a linear function of the row number n. For every other row, each element is a parabolic function of n. Where r represents the element number and n represents the row number. The row numbers that represents the same sets of numbers as the numerators in Lacsap’s triangle, are the second row (r = 2) and the seventh row (r = 7). These rows are respectively the third element in the triangle, and equal to each other because the triangle is symmetrical. In this portfolio we will formulate an equation for only these two rows to ﬁnd Lacsap’s pattern. The equation for the numerator of the second and seventh row can be represented by the equation: (1/2)n * (n+1) = Nn (r) When n represents the row number. And Nn(r) represents the numerator Therefore the numerator of the sixth row is Nn(r) = (1/2)n * (n+1) Nn(r) = (1/2)6 * (6+1) Nn(r) = (3) * (7) Nn(r) = 21 Figure 2: Lacsap’s...

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