Reflective Reading Response 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). Prior to reading the chapter, I had no idea that the strategies students use to solve fractions had names. Such strategies include: additive coordination, ratio, repeating halves, etc.. I always referred to other strategies as inventive strategies or the common “other way” to get the solution.
Students will be able to read story problems that include division problems and read vocabulary words that pertain to the lesson.
The teacher selects five cards to demonstrate to the class how to place the fractions cards in the boxes correctly. The teacher thinks out-loud to model to students how can they choose the appropriate box to place the first card. Then the teacher repeats with the second card.
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
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.
Through the Rational Number Interview I was able to gain insight into Adams mathematical understanding of fractions, decimals and percentages. As a student in year 5, Adam was able to make connections using various mathematical strategies. Adam has an understanding of infinite numbers, for example, when asked how many decimals are there between each rational number (0.1 and 0.11), he answered promptly with “many numbers”. Adam was able to acknowledge that a fraction can be shown as a division problem, “divide the pizza into fifths and each get 3 pieces”. He was able to calculate by partitioning the pizza, and by dividing each pizza into the amount of people (5). Adam shows residual thinking when building up to the whole
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
Many students get confused when learning about fractions. At our grade level we teach about parts of a whole, equal shares, and partitioning.
Chapter 5 is yet again another huge step involving fractions. It seems that each grade gets more and more complicated. For 5th grade students will learn representation of decimals in the thousands and comparing decimals in the thousands. It also expands on adding and subtracting of fractions, interpreting them as implied division, multiplying and dividing fractions as well.
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
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)/
Research shows that parents’ engagement in dialogic reading (i.e., using extratextual talk about the story as it is being read; Opel et al. 2009) promotes children’s comprehension of stories (Lauricella et al. 2014; Parish-Morris et al. 2013; Hindman et al. 2008). Specifically, research suggests that children whose parents engage in dialogic reading during storybook reading are predicted to have better comprehension (Han, J., & Neuharth-Pritchett, S., 2014). In our study, we examined the relationship between one measure of dialogic reading, conversational turns between parents and children during storybook reading, and children’s comprehension of the story’s content. We predicted that more conversational turns during parent-child storybook reading is related to better content comprehension in children. To test our hypothesis, we recruited parents and children, aged 48-to-60 months (N=6) to
I would with one students on how to make equivalent fractions, She was very confused and did not know how. So I demonstrated the example that was written on the board. I wrote 3/6 and then wrote the division character by the numerator and denominator and then wrote 3. So then I said 3/3=1 and 6/3=2, then wrote 1/2. Then we tried to reduce 25/100, so I said, “What can you divide by 25 and 100.” She said 5 so she followed the example that I had written. So I said, what’s 100/5, she said, 20. So we knew the denominator was 20. Then I said whats 25/5, she said 5. So then I said the equivalent fraction is 5/20. She wrote done all that we had discussed above as we were finding the answer. I still think she was a little confused after, but it was time for discussion. For next time, I think I would try multiplying as another example, which I think could help the student see both. what I would have done was try multiplying instead of
“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).
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.
Writing has always been something I dread. It’s weird because I love talking and telling stories, but the moment I have to write it all down on paper, I become frantic. It’s almost as if a horse race just begun in my mind, with hundreds of horses, or words, running through my mind, unable to place them in chronological order. Because I struggle to form satisfying sentence structure, it takes me hours, sometimes even days, to write one paper. It’s not that I think I’m a “bad writer,” I just get discouraged easily. Needless to say, I don’t think highly of my writing skills. When I was little I loved to both read and write. I read just about any book I could get my hands on, and my journal was my go to for my daily adventures. Although it’s