Louise Boucher

When the denominator is the same he is able to partition and see what fraction is needed to make the whole. When comparing fraction pairs, Adam is using gap thinking of the fractions 5/6 and 7/8 “both need 1 of their fraction to make a whole” understanding that each numerator needs one more part to make it a whole. In saying that, when comparing ¾ to 7/9 that have more than 1 to the whole, Adam said ¾ is larger, “1 more ¼ to make 1. 2 more 9ths to make a whole” He tried to apply gap thinking, incorrectly not understanding the unit of fractions. Adam has limitations surrounding improper fractions, not recognizing that 4/2 is larger than 1 whole and is equal to 2. He has misconceptions when comparing fractions with proportional reasoning is limited. When asked to draw a fraction he automatically swaps the numerator and denominator (6/3 to 3/6) when the numerator is larger than the denominator, when considering improper fractions, rather than converting to a mixed number fraction or whole number.. This displays Adams misconceptions of the understanding of the

spread. But with fame came even heavier tasks as she caught the attention of the

Through her trailblazing personality and a camera, Margaret Bourke White was able to forge her own path to go and encapsulate the tragic state of affairs that was consuming America. Margaret Bourke-White was born on June 14, 1904 to Joseph White, an engineer, and Minnie White, a stenographer. With two other siblings, she was brought up in a strict household,that favored determination and perseverance (Margaret Bourke-White). These core values instilled in her the courage that was required to break free of the societal norm and follow her passion into photography. White attended Plainfield high school where she first discovered her passion for the arts, being yearbook editor, and competing in literature competitions. She later attended Columbia

I had a great opportunity of interviewing a former teacher I had, and a teacher I was familiar with, but was never in her class. Shirley Norris is a middle school Quest teacher. “QUEST” is an acronym for Quality Utilization and Enrichment of Student Talents. The “QUEST Program is designed to meet the needs of identified gifted students who have demonstrated above-average ability in the following two areas of giftedness as defined by the Texas State Plan for the Gifted: 1) high general-intellectual ability at the 95th percentile; and, 2) creative and productive thinking.” (Leander Isd). Mrs. Norris is in charge of 6-8 graders. Shawna Queen is a high school math teacher. She in charge of the math department for her school. Mrs. Queen teaches

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.

CCSS.MATH.CONTENT.7.NS.A.2.B Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then -(p/q) = (-p)/q = p/(-q). Interpret quotients of rational numbers by describing real-world contexts.

The focus of this class is on applying fractions to solve real world problems. Students

Susan Bordo an author who writes about how the American culture has always shown and used women's bodies throughout our history and to most is considered completely normal. In the print “Beauty Rediscovers the Male Body” Bordo states “naked female body became an object of mainstream consumption”(Bordo 168). She explains that the female body was completely normal for people to look at while on the other hand showing a naked male body was considered a taboo that most people were afraid to break. Over the history of time mainstream perceptions of masculinity have changed dramatically! Everything from ads, movies, fashion, character, and what is socially acceptable in todays world has changed since Bordo’s writings. When men started to show

Constructs in fractions extend many of the principles encountered in multiplicative thinking. It has been observed language and a variety of models improve understanding of these constructs (Reys et al, 2012). Therefore, these models should be scaffolded to develop student skills and knowledge for manipulating fractions with operations. The underpinning principle is the part-whole construct (Charalambous & Pitta-Pantazi, 2005). The subconstructs for fractions that build on this construct are quotient, ratio, measure and operator (Charalamous & Pitta-Pantazi, 2005; Clarke, Roche & Mitchell, 2008). As with multiplicative thinking there is a loose sequence to learning these constructs which overlaps. Their instruction during the primary years is important because a fifth-grader’s fractional knowledge can predict later outcomes in mathematics (Dooren & Vershaffel, 2015).

The purpose of this lesson is to introduce the students to the concept of division. This will be somewhat of a review for the students who have had practice with division in past grade levels. It has been a long time since the students have had any practice with division, so this lesson will serve an introduction to the meaning of division, division vocabulary, as well as its relationship to multiplication. Students will be introduced to fact families as a way to show the connection between multiplication and division. The students will be able to see the relationship between a concept they have had a lot of practice with (multiplication), to a concept that might be new to them (division).

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.

As students continue to grow on the quest of computational fluency, it is important that teachers continue to create challenges that expose students to build on patterns and number sense. Division is no exception; students should be able to make connections to place value, patterns, and previously used strategies to solve division problems. Therefore, once students reach a certain point of fact fluency they must develop new methods to perform divisions. As explained in the Inside Division video, (Laureate, 2013) when solving division problems with higher dividends some strategies are no longer practical. The count on strategy should be replaced by other effective methods that provide flexibility and accuracy. Through this paper, I will investigate and describe various models that can help students acquire proficiency with long division.

2.1 Solve problems involving addition, subtraction, multiplication, and division of positive fractions and explain why a particular operation was used for a given situation.

Christie Kawalsky from St Albans East primary school is observed teaching a year 3/4 class the mathematical concepts of whole numbers, percentages, fractions and decimals (Australian Institute for teaching and school leadership {AITSL} (n.d.a). At the start of the lesson (Christie’s lesson) she uses written and visual strategies by using a picture of a whole chocolate bar and writing the various different ways of representing a whole in fractions, decimals and percentages. During Christie’s lesson the use of manipulatives (chocolate bars) are used to help students apply and interpret proportional reasoning of fractions, decimals, percentages and whole numbers as stated in the content descriptor ACMNA058 (Australian Curriculum and Assessment Reporting Authority {ACARA}, nd., ACMNA058). The use of manipulatives help the students gain a better understanding of how to model and represent unit fractions as they are able to cut the

Sam is able to synthesise fractions using a number of different models and approaches. He is able to benchmark, use residual thinking and proportional reasoning when approaching fractions, and was able to articulate his thinking clearly when prompted for a response on his problem solving approaches. When presented with models, such as the pattern blocks or images of pizza, he still did his visualizing in his head, rather than using the models or writing it on paper. In the fraction pairs questions, he knew immediately which was larger, applied a number of different thinking strategies and could explain to me straight away and in a concise manner exactly why he had reached that conclusion.