Number theory Essays

In my research paper I will be talking about Marie Sophie Germain, a famous mathematician born and raised in Paris, France. I chose Sophie Germain because I believe that female historical figures deserve the equal amount of recognition that males receive. She also caught my attention because she had no support at all, and because of that would receive education secretly. I believe that Germain has taught us that even though we will encounter obstacles on our path, with determination and perseverance

a whole number is bigger than an improper fraction. When comparing 1 and 4/3 she identified 1 as the bigger number. When Aly was asked for her reasoning she said, "1 group of one number". Aly here doesn't have the understanding that an improper fraction can be turned to a mix number which consist of a whole number and a fraction. For example, 4/3 represents one full group and 1/3 of another group. Another misconception that comes up in the video is when she picks 1/2 as the bigger number than 3/6

upside-down world beyond Alice’s looking glass. No wonder children are confused!” (p. 115). Discovering fractions in a way that enhances a student’s number sense is extremely important before the student begins operations with fractions. The Common Core State Standards for Mathematics in Oregon explain what a child in a certain grade must know concerning number sense and fractions. For example, standards 4.NF.1 and 4.NF.2 state that students in the fourth grade must be able to find, identify, and explain

Pre-Assessment Analysis Before starting my math unit on multiplying and dividing fractions, I had the students complete a short pre-assessment to determine their level of understanding and prior knowledge with the concept of fractions. This assessment consisted of twelve individual questions that ranged from understanding concepts to using mathematical processes. The first four questions determine the student’s understanding of the concept of what fractions represent compared to a whole, how to

Decimals Round to Whole Number: Example: Round to whole number: a. 3.7658 b. 6.2413 If the first decimal number is ≥ 5, round off by adding 1 to the whole number and drop all the numbers after the decimal point. If the first decimal place is ≤ 4, leave the whole number and drop all the numbers after the decimal point. 3.7658 = 4 6.2413 = 6 Round to 1st decimal: Example: Round to whole number: a. 3.7658

compute mathematical operations but explain their reasoning and justify why using certain visual strategies such as number lines, number bonds and tape diagrams, aid in the computation of problems. When encountering mixed numbers, students may choose to use number bonds to decompose the mixed number into two proper fractions. This requires conceptual understanding that a mixed number is a fraction greater than one and can be decomposed into smaller parts. At the beginning of the lesson, students are

1. One of the key things that I learned from Developing Fraction Concepts is how important it is for students to learn and fully comprehend fractions. In this chapter, the author talked about how fractions are important for students to understand more advanced mathematics and how fractions are used across various professions. As I was reading this, I thought about all the nurses who use fractions when calculating dosages and how important it is for them to get the dosages correct. If a nurse messed

combined with reasoning (Knaus, 2013, p.22). The pattern is explained by Macmillan (as cited in Knaus, 2013, p.22) as the search for order that may have a repetition in arrangement of object spaces, numbers and design.

her students multi-digit number comparison, included in comparing prices. For a student to be able to achieve number comparison, several math concepts have to be understood and demonstrated by the student. Comparing multi-digit numbers as well as decimal placement can be very challenging to teach. Not only do students have to recognize the magnitude of the price on the tag, they have to be able to locate the item in the store, and also be able to compare values of numbers. This can all be hard to

Date: 04.03.15 Practicing Out Math Analysis of Learning: Amelia, Erin, and Taz are gaining skill in one to one counting as we count the number of scoops it takes to fill the tube. They are also being exposed to simple math words like, full, half full, and empty as we measure where the sand is up to in the container. Lastly, they are given the opportunity to make comparisons between the tubes and ascertain which tube make the sand come out faster – the broken tube. Observation: Erin, Taz, and

to divide each of the denominators by 2 to get 6.5 and 11.5 respectively. As we can see 7 is greater than 6.5, this means that 7/13 will be to the right of ½ on a number line. 11 is less than 11.5 meaning 11/23 will be to the left of ½ on a number line. We know that the number furthest to the right on a number line is the larger number, so 7/13 is the greater

in barcode numbers. The majority of products that you can buy have a 13-digit number on them, which is scanned to get all the product details, such as the price. This 13-digit number is referred to as the ‘GTIN-13’ where ‘GTIN’ stands for Global Trade Item Number. Error control is used in barcodes because without it, there would be so many errors and people would end up being charged for the wrong products. Sometimes when a barcode is being scanned, the scanner won’t read the number and therefore

 Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 × 7. Children start working with equal groups as a whole instead of counting it individual objects. Students start understanding that are able to group number is according to get a product. Students can solve duplication by understand the relationship between the two number. In third grade it is

daily necessities. Regardless of people’s thought about math, it is everywhere and it is very important in order to succeed in life. However, not everyone will use all the math that were taught about such as finding the angle of a triangle, imaginary number, finding a sequence pattern, or solving for x. These mathematics subject are important and will be taught all over the nation, but not few people will use it. Schools should be teaching students math that everyone will need to know in the future.

Many times we get some situations where a specific block of codes need to be executed repeatedly. When we are calculating factorial of a number say 7, the multiplication continues to happen with the next smaller number (6,5,4..) and the cycle continues until it reaches 1. It will be great if we can write a set of common code for multiplication only once and get it executed repeatedly until the desired value (here 1) is reached. This set of common codes which gets repeated are collectively called

In box number two of students’ drawing paper, they will redraw their model from box number one and add shading in their Earth model, drawing to represent “light and dark” by shading in part of the Earth. After shading, students will be asked “What do you think the shading of dark and light could represent on Earth?” In box number three of students’ drawing paper, they will recreate their drawing from box number two, except they will label their shaded portion

Introduction Place value is one of the cornerstones of our number system. Therefore, developing a robust, conceptual understanding of this topic is vital. If this is not achieved and if focus is placed on short-term performance or procedural knowledge, progress in mathematics is likely to be delayed (Department of Education WA, 2013a). Green (2014) upholds this belief as she describes seeing maths as more than just a list of rules to be memorised. Instead, mathematics should allow children to make

enter two integers, obtains them from the user and prints their sum, product, difference and quotient (division). 5. Write an application that inputs three integers from the user and displays the sum, average, product, smallest and largest of the numbers. 7. Write a Java program that reads a string from the keyboard, and outputs the string twice in a row, first all uppercase and next all lowercase. If, for instance, the string “Hello" is given, the output will be “HELLOhello". 9. Create a class

Leadership [AITSL] (Producer), n.d.-a). Christie's lesson relates well to proficiency strand of understanding; this is because as a teacher, Christie is getting her students to develop their understanding of fractions, decimals, percentages and whole numbers. Christie often uses the appropriate language to communicate explicit learning experiences, and Christie integrates a general literacy capabilities approach to support the numeracy activity (ACARA, n.d.-a). Christie teaches the students how to connect

4.NF.A.1 Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. 21.3–5.ES.2 Essential Concept and/or Skill: Adjust to various roles and responsibilities and understand the need to be flexible to change. Students will: • Recognize like fractions by simplifying, graph