Mathematics, Fractions and Decimals
Students do not always learn axiomatically, by nature, they ought to learn inductively. It is professional for an instructor to first provide examples when introducing a concept before going forth to proofing. The following guiding questions should always guide the instructor before introducing a concept; what learning opportunities and experiences should I provide to enhance learning of the outcomes and allow learners to demonstrate their learning? What teaching strategies and resources should I use? How will I meet the diverse learning needs of my students?
Fractions and Decimals
Fractions is the most critical concept that should be taken into consideration when introducing it to a new learner, this is because of its technical nature;
Illustration 1; a manipulative resource
What does equivalent fractions and investigating a square object has in common? Take consideration of the term; equivalent fractions and explain to them using examples e.g. ½, 2/4, 4/8 and much more. Begin the process by folding thepiece of paper in half; shade one half of the paper with a marker. Ask one of the students to explain what fractions represents the shaded part/area; ½. Take another piece of paper and fold it in half, repeat the process twice, this will create fourths, shade two sides i.e.2/4 with a marker, pick one student and to determine what fraction is represented in the shaded area, answer; 2/4. Discuss and explain to students what the two fractions have in common.
Clearly explain to the students that, they can write an equivalent fraction by taking the numerator and multiplying it by the same number. Note: in renaming fractions that are not on their lowest possible terms, find greatest common factor, then divide the numerator and denominator by itself. More so, in order for the students to understand more on this, advise them to carry out more research on folding the papers and naming equivalent fractions to match the facts.
In assessing skills, test whether the students are using the original fraction to multiply the denominator and numerator randomly to get equivalent fractions. Also, check whether the students are dividing the numerator by the denominator to the lowest possible terms, confirm if the division is random or greatest common factor is being used.
According to Davis, S. (2002), fractions and decimals is a day-to-day activity; in his printed example, he explained how a piece of an orange can be split into quadrants, i.e. ¼. ¼. ¼. ¼.He explained that once the piece of orange is split into four, pass it to students and ask each of them to state and explain the size from the original piece that each of them own, if its anything less or more than ¼., take the pieces of oranges and explain to the students the aspect of equivalent fractions and how the piece of orange came to be quadrants. He further stated that, for the students to understand the aspect of equivalent fractions fully then they should practice more often with the oranges.
Illustration 2; print source
Vance, J. (1990) states that; before introducing a new material, consider different ways to assess and build on the student’s knowledge and skills related to fractions. For example; describe two everyday examples of where we use fractions? Sort out the following diagrams into those that represent equal parts and those that do not, and explain your sorting;
Draw a diagram to represent the fraction ¾. Given the following diagram; write the fraction shown by the shaded areaof the diagram? Write the fraction shown by the unshaded area of the diagram?
Explain the meaning of the numerator and denominator in the fraction 2/3 and use a model to illustrate what you mean; if a student appears to have difficulty with these tasks, consider further individual assessment, such as a structured interview to determine the student’s level of skill and understanding.
|Not Quite there||Ready to Apply|
|“Sort the following diagrams into those that represent equal parts and those that do not, and explain your sorting.”
Show the student the following diagrams:
|· Thinks that aand c show equal parts but not the other diagrams but can’t quite explain why.
· Thinks that only a and c show equal parts because you could fold them to show it.
· Thinks that only a, c and f show equal parts because the parts are the same size and shape
|· Thinks that a, c, e and f show equal parts because they all show that they are the same size. The parts in e are the same size because you cut the rectangle in half and then cut each of the halves in half to get the quaters|
|“Given the following diagram:
(Show the student the diagram.)”
a. Write the fraction shown by the shaded part of the diagram.
b. Write the fraction show by the un-shaded part of the diagram.”
|· Mixes up the shaded and unshaded parts of the diagram.
· Writes the fraction with the incorrect numerator and/or denominator.
|· Writes ¼ for the shaded part and ¾ for the unshaded part.|
|“Explain the meaning of the numerator and denominator in the fraction 2/3 and use a model to illustrate what you mean.”
(Show the student the fraction symbol.)
|· Draws a diagram of a region and shades 2 of 3 unequal parts with no explanation.
· Draws a diagram of a region and shades 2 of 3 equal parts with no explanation.
· Draws a diagram of a region and shades 2 of 3 equal parts and explains that the whole is divided into 3 parts but does not specify equal parts, or if equal parts are mentioned then the meaning of equal is unclear.
|· Draws a diagram of a region and shades 2 or 3 equal parts with a clear explanation of the meaning of the numerator and the denominator; e.g., the denominator is 3 and divides the whole into 3 equal parts that are all the same size and the numerator is 2 which counts 2 of these equal parts.|
Illustration 3; Use of ICT resources for teaching
|Technology||Match with formal teaching||Match with math standards|
|Calculators||· Uses calculators to solve fraction problems.
· Uses calculators to check answers
|· Uses calculators proficiently andeffectively.
· Demonstrates the understanding of the math problem.
· Is able to judge when calculator use is appropriate and efficient
|Computers||· Understands the mathematical skills, concepts and relationship behind the purpose of the tools
· Uses electronic tools to extend comprehension, reasoning, and problem-solving skills beyond what is possible with traditional resources
|· Canoperate effectively avariety of machines
· Recognizes a computer as a tool for improving learning productivity and performance.
· Can assess and fix minor problems
These may include:
b) Interactive whiteboards
c) Flash games
d) Resources created by teachers
f) Database programs
|· Is familiar with the purpose and function of a variety of general software and from them prudently
· Uses databases to store, organize and access information
· Keys in information to spreadsheets, produces graphs and compiles statistics.
· Uses technology to express mathematical ideas precisely
|· Uses a variety of appropriate, available software packages to assist and enhance learning
· Can import and export images and text between applications
· Is able to enhance work with paint and draw programs
· Can scan and edit pictures and text.
|Digital resources||· Exchanges ideas and tests hypotheses with a wide audience
· Recognizes and applies mathematics in contexts outside of mathematics
|· Conducts research through the stages of information management
· Evaluates information gathered
· Uses information to create new knowledge
· Is able to use digital imaging equipment to download and edit images
|Multimedia||· Communicates mathematical thinking on fractions coherently and clearly through presentation media||· Identifies a variety of resources tocollect information including people, technology, the web, electronic encyclopedias and databases, places and print.
· Presents what they have learntthrough various modes.
Cathcart, W., George, Y., & James, H.(1997). Learning Mathematics in Elementary and Middle Schools; Fractions and Decimals, 2, 75-92.
Davis, S. K. (2002). Mathematics in the Junior Level: Fractions and Decimals, 3, 16-21..
Zebedee, F. K. $ Branson, L. (1994). Mathematics and its Dynamics: Fractions, 5, 141-182.
Vance,J. (1990). Rational Number Sense: Development and Assessment, 28, 23-27.
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