Meaning Of Fractions, An Understanding Of Wholes

I enjoyed reading your post. You provided a lot of good examples of fractions and decimals according to our reading for this week. Fractions, like you had mentioned, are “part of a whole” (“Definition of Fraction,” 2014).

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

Today we will be learning about place value. When we divide numbers with three and four digits by a one digit number, the quotient doesn’t always go about the first number in the dividend like we saw yesterday. This is important to know because if you had to split $100 with your sister and you divided $100 by 2 and placed the 5 above the 1, then added two zeros, you would have to pay your sister $500. That’s not dividing, or fair. Remember we need to know how to divide so you can evenly split something, like money.”

My goal is to assess student’s prior knowledge of division and to teach students how division can be modeled by using place-value blocks so students can see that division consists of arranging items into equal groups. My goal for day one is to help students develop and understanding of division through the use of manipulatives and drawings so when they transfer that knowledge to day two, students will have a better sense that division consists of dividing a large number into equal groups. By using place-value blocks I also want students to visually see what a remainder looks like so they can better understand what a remainder represents. Sometimes students can’t understand the definition of a remainder which is the part that is left over after

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

5. Please outline in your own words, one other new thing you learned this week in the course. How does it apply to your life?

I was expecting for the student to have a few difficulties solving the harder fraction problems. Angel, however, was having a very difficult time answering addition problems. He continuously solved addition and subtraction problems different ways. There were moments he added numbers starting from the left and other times he started at the right. In the end, Angel almost never got a question correct and when he did, his explanation showed that he did not understand the problem correctly.

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).

For the Kidwatching Project Part 1, I found myself interviewing a few students on the concept of multiplication and division. According to Merriam-Webster Dictionary, multiplication is defined as the process of adding a number to itself a certain number of times: the act or process of multiplying numbers. Merriam-Webster Dictionary also defines Division to be the act or process of dividing something into parts: the way that something is divided (Merriam-Webster, 2015). Multiplication and Division is a subject that many different students in early ages can grasp or struggle with because the concept of using different ways to approach these particular problems. Many kindergarten children can solve simple multiplication and division problems

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)/

The aim of the essay is to critically discuss the pedagogical uses, and the implications for learning, of core domain (and some of non-core domain) knowledge and conceptions of aggregates in the teacher-learner exchanges aimed at the teaching and learning of the notion of halving evident in the video records of the two Grade 1

“He knew this informal experience with the distributive property would be important in subsequent lessons and the student writing would provide him with some insight into whether his students understood that quantities could be decomposed as a strategy in solving multiplication problems.” (Ex. Lines 81-83 provides evidence of Elicit and use evidence of student thinking).

Formal: Each student will complete a worksheet with 15 questions on comparing fraction on it. This will assess their ability to compare fractions with like denominators and like numerators. The students need to receive a score of 11 out of 15 to show an 83% mastery of the skill. The first three questions will be bonus questions dealing with to assess higher learning connections. The last three questions will deal with musical notation to assess what the students have learned in regards to notation and fraction similarities.

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.

Teaching students effectively in areas of multiplicative thinking, fractions and decimals requires teachers to have a true understanding of the concepts and best ways to develop students understanding. It is also vital that teachers understand the importance of conceptual understanding and the success this often provides for many students opposed to just being taught the procedures (Reys et al., ch. 12.1). It will be further looked at the important factors to remember when developing a solid conceptual understanding and connection to multiplicative thinking, fractions and decimals.