Rational Number Interview

From birth, it is important for practitioners to support the early years’ mathematical development. Children learn emergent maths which is a “term used to describe children construct mathematics from birth” (Geist, 2010). The Early Years Statuary Frameworks (EYFS) (Department of Education) states that maths is one of the specific areas.

The real number system consists of five subsets of numbers (Blitzer, 2013). The first subset is natural numbers; natural numbers consist of positive counting numbers not including zero. The second subset is whole numbers; whole numbers consist of zero and natural numbers. The third subset is integers; integers are positive and negative whole numbers, as well as zero. The fourth subset is rational numbers; rational numbers are numbers that can be written in fraction form. The fifth and last subset is irrational numbers; irrational numbers are numbers that are not a perfect square, do not have a repeating or terminating decimal, and are not included in the whole numbers subset (Blitzer, 2013). Rational and irrational numbers are often the most difficult to understand out of these 5 subsets of real numbers. Simply put, rational numbers are any numbers that can be re-written as a simple fraction, and if a number cannot be defined as rational then it is defined as irrational. For example, the number 7 is a rational number because it can be re-written as , which is a simple fraction. The number 2.5 is also defined as rational because it can be re-written as , which, again, is a simple fraction. However, if the number π were defined, it would have to be irrational since it has neither a repeating decimal nor a terminating decimal, and cannot be written as a simple fraction.

Van De Walle, Karp, & Bay-Williams (2013) discuss the importance of Iterating and partitioning in building conceptual understanding of fractions and the way they assist students to understand the meaning of fractions, particularly numerators and denominators and the relationship between the part and the whole. Partitioning involves sectioning shapes into equal-sized parts. Area, length and set models are particularly useful in partitioning. Iterating involves counting fractional parts and assists students to understand the relationship between the parts and the whole or the numerator and the denominator (pg 355). Although Iterating applies to all of the models it is mostly connected with length models as

Numeracy development is important for all children as maths is an important part of everyday life. The way in which maths is taught has changed greatly over the years. When I was at school we were taught one method to reach one answer. Now, particularly in early primary phase, children are taught different methods to reach an answer, which includes different methods of working out and which also develops their investigation skills. For example, by the time children reach year six, the different methods they would have been taught for addition would be number lines,

He can convert improper fractions to a mixed number with 57% accuracy and convert mixed numbers to improper fractions with 80% accuracy. John can simplify a fraction with 92% accuracy. However, he does not always simplify his answer, instead he stops with his answer rather than seeing if it can be simplified. He can add and subtract fractions with 88% accuracy. He can multiply a fraction by a fraction with 14% accuracy and by a whole number with 90% accuracy. He can divide a fraction by a whole number and a whole number by a fraction with 89% accuracy. He needs to be able to simplify fractions when computing with fractions. He needs to be able to add, subtract, multiply, and divide fractions. He needs to identify the correct operation to solve a word problem. He needs to be able to solve one-step and multi-step word problems involving all 4 operations (addition, subtraction, multiplication, and division) of whole numbers and fractions. John’s weaknesses in math impact his ability to solve multi-step word problems, which is expected in 5th

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).

In a fifth-grade math classroom, the standard of the lesson of the day was 5NF 1 because the lesson covered the learning of addition and subtraction fractions. In the lesson, students learned to add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. (a/b + c/d= (ad + bc)/

I would start with a visual representation of the topic. To try an engage a visual learning style I would present the subject with some pie. I would start by having 2 pies each cut into eight pieces. We would talk about how each pie is composed of eight pieces and so one piece would be 1/8. We would then compare the following that 1 pie is the same as 8/8. We would then add in the second pie. We would have 2 whole pies and we would then link in that if 1 pie is 8/8 then 2 pies would be 8/8 + 8/8, and thus 2 pies = 16/8. Once this concept is grasped I would take away half a pie. Like she described in her interview we would start by describing our situation as a compound fraction. We would now have 1 and ½ pies. With that we would then count the number of slices we have, remembering that each slice is 1/8th of a whole. So we would have 8/8 + 4/8 = 12/8th. This is an improper fraction. I would hold off for now on simplifying the

This report will explore the similarities and differences between numeracy and mathematics, and address the importance of its development across the curriculum.

Educators are required to interpret students’ responses to mathematical questions. The purpose of this report was to provide an opportunity to examine the step by step approach to answering problems, interrogate the results and recognise mathematical concepts. There are six questions in total from the Australian Curriculum Assessment Reporting Authority [ACARA], (2012) NAPLAN year nine numeracy non-calculator test. The six questions mentioned in the report are question 12, 14, 16, 18, 22 and 23. Each issue is set out in the report in numerical order with a screen shot of the methods used to solve the question followed by a reflection. The reflection describes my feelings, confidence and approach towards each question along with the type of mathematics used, the year level suitable for each question according to the ACARA (2015) and alternative ideas for solving the six questions.

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

This multi-phase learning project is intended to provide incremental instruction in various aspects of numeracy for students who possess the fundamentally capabilities associated with their educational functioning but are innumerate when attempting to apply these fundamental abilities to the dominion of fractions, decimals, ratios and proportions. Goals of the learning project include but are not limited to the following:

Multiplicative thinking, fractions and decimals are important aspects of mathematics required for a deep conceptual understanding. The following portfolio will discuss the key ideas of each and the strategies to enable positive teaching. It will highlight certain difficulties and misconceptions that children face and discuss resources and activities to help alleviate these. It will also acknowledge the connections between the areas of mathematics and discuss the need for succinct teaching instead of an isolated approach.

Norton & Irvin (2007) found that a considerable number of students who have difficulties understanding fractions, negative numbers and ratios also struggle with solving algebraic problems.

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