Article Analysis: 'Representations In Teaching And Learning Fractions'

The learning provision for numeracy development for children is very important from the beginning of their learning platform as maths is a key in every day live for everyone.

In the chapter, “Equal Sharing Problems and Children’s Strategies for Solving them” the authors recommend fractions be introduced to students through equal sharing problems that use countable quantities because they can be shared by people or other groupings. In other words, quantities can be split, cut, or divided. Additionally, equal sharing problems assist children to create “rich mental models “for fractions (p.10).

Many students get confused when learning about fractions. At our grade level we teach about parts of a whole, equal shares, and partitioning.

Goal: At the end of the lesson the students will be able to evaluate twenty five fraction problems, and some of the fraction problems will include word problems

Fractions are a concept that many people would not normally associate with kindergartners. Typically, fractions are not formally introduced and taught to children until around third grade. However, the question remains; Are kindergartners capable of solving fraction problems even though they have not been formally introduced to the concept yet? This article explores whether or not preschool and kindergarten children aged 3 years 8 months to 6 years 6 months can solve fractional problems using their limited knowledge about partitioning objects. This investigation took place over the course of two months at a Montessori school in Mississippi where children could move freely from one content area to the next.

Learning about the long and tiresome process of transforming ordinary fractions into decimal fractions has made me realize how much I had taken for granted using calculator for the past decade. There are downsides to relying more on the calculator than relying on “old-fashioned” mind. “Patterns as Aids” becomes a problem when a student follows rules without understanding and calculates large numbers mentally using tricks but fails to understand the purpose of the processes or steps. Therefore it is better to understand less but thoroughly, than to be an expert in memorizing tricks and rules without any understanding. Principles must be taken apart, and each ingredient learned and taught individually. When something sounds hard or difficult, it usually means we did not break the problem into portions. Often I take for granted and overlooked simple aspects of math that I automatically perform. This book also mentions the importance of using word

The pre-assessment used to establish students' baseline knowledge and skills for this lesson was a comparing fractions pre-test. Students compared the following types of fraction comparisons: unit fractions, benchmark fractions, normal fractions, equivalent fractions, improper fraction vs. normal fractions, and improper vs. improper fractions. I have taken the information and used it to figure out which types of comparisons the students understand and using it to work on increasing the students' ability to include the other types. I use the information to accommodate what the students already know about the target. It showed me that students do not understand how to compare fractions, when they have a different denominator.

During the sixty-minute lesson, the students will determine one, ten, or one hundred more or less than a given number. This lesson teaches students how to determine one, ten, or one hundred more or less using the DWS (draw it, write it, solve it) strategy, a place vale chart, and expanded form (391, expanded form = 300+90+1). This lesson builds on the student’s prior knowledge of place value disks, and helps them to make connections between a representational drawing and expanded number form. The place value chart and place value disks are used to help students visualize one, ten, or one hundred more or less than a number in connection to place value understanding (ones, tens, hundreds place). The goal of this lesson is for students to apply their knowledge of place value understanding in order to determine one, ten, or one hundred more or less of a given number, using the lesson strategies to help them explain their

In conclusion, the general capability of numeracy can be at times difficult to implement. This is because numeracy is often stigmatized to the sciences and math subjects. However, numeracy is another way which students can communicate and demonstrate their historical skills. Through seeing numeracy in this light, enables teachers and students an opportunity to cater for students with diverse learning needs, including those with ESL/D or with a disability.

Fractions can also be used to represent ratios or even division equations and all rational numbers. While fractions come in many different forms such as mixed numbers, improper, vulgar and proper fractions, the function of a fraction is generally the same—to represent parts of a whole. To simplify the matter further—if you can solve a division problem, then you are able to use fractions. In fact, you use fractions all the time without a hint of doubt. For instance, when we tell the time, use or recipe or figure out the price of an object after a sale—it is all fractions. We use them every day, but why? What is the inclination to measure ingredients in halves, quarters and two-thirds? Why do we reflexively say “Half past 3” when telling the time? It is all because parts of a whole are far more common than complete collectives of any one thing. So let us take a step back and analyze a fraction: 2/5. 2 is considered the numerator, and 5 is the denominator. 5 would be the whole—for instance, there are 5 stuffed bears in total. But then 2 is the amount we have from the whole—as in, we only have 2 of the 5 stuffed bears. A slightly more challenging problem would be saying that a $50 shirt is ½ price. To solve this, we would simply convert 50 into an improper fraction (a fraction in which the numerator is larger than the denominator), 50/1 and multiply it by ½. This would result in the improper fraction, 50/2. You would then simplify

This is a 30-minute lesson designed for a 5th grade maths class mastering to multiply the usage of fractions is some thing students learn at the beginning of sixth grade, but is a great manner to check department and pictorial representations of mathematics.

Teaching the concept of integers and number theory is a fundamental part of math curriculum. The ability of a professional mathematics teacher to tie in real world experiences, using hand on activities and manipulatives is essential in enabling students to build on mathematic ideas and understand how they interconnect. Also important is the concept of rational numbers as fractions, decimals, and real numbers. Teachers need to help ease the transition from whole numbers by clearly explaining the new rules and definitions students are unfamiliar with.

This has proven to be an entertaining, delicious and memorable introduction for my students to the world of fractions. Math can be so much fun!

Literature is a key element for a young child’s learning process. It can be essential in elementary students understanding of mathematics topics. Language arts, social studies, and science instruction commonly uses literature. At times it can be overlooked when teaching or planning lessons for mathematics. Mathematics instruction tends to have a high emphasis on using manipulatives or workbooks. Literature does not tend to be at the top of the resource list (Golden, 2012). While books can be a very useful tool for teachers successfulness in teaching mathematics topics. You can find mathematics in different types of books. For example: recipe, sequential thinking, patterns, and problem solving books (Padula, 2004).

* Denominator – the number below tells how many equal parts the whole is divided.