Review+Questions+3

**Review Question #3 **
====**1. What are the five different representations of functions? What are the important ideas students should understand about these representations and about the connections among them? (Chapter 14) **====
 * ====__The pattern itself, or context__: Students should understand the concept of the problem in order to be able to come up with a formula and understand more explicit information. ====
 * ====__The table__: This helps the students clearly see possible patterns by using only the numbers or figures and makes it easier to make a formula for the problem. ====
 * ====__The verbal description__: This is important so that students connect the formula’s symbols to the word problem itself and understand how to explain the formula verbally. ====
 * ====__The symbolic equation__: Students should understand that letters can represent things, or objects, in a word problem. ====
 * ====__The graph__: Works as a visual to demonstrate how the problem looks by using a formula and seeing the pattern. ====

====**2. List three equivalent fractions for 2/3. How did you generate this list of fractions? How could you prove that they are equivalent using an area model, a length model, and a set model? What are some teaching points to keep in mind when helping students develop understanding of equivalent fractions? (Chapter 15) **====

==== The three equivalent fractions I came up with are: 4/6, 8/12, and 16/24. I made them by multiplying 2 to both the numerator and denominator. For the area model, I can use circular pieces and use a different color for each circle in order to easily see that the same area is colored only the numbers of the fraction change. For the length model, I choose to use folded paper strips by folding the numerator part, yet having all the strips the same length to show the denominator. Finally for the set model, I can use objects like pencils and erasers to show the various fractions. For example, 2 groups with 2 erasers each and 1 group with 2 pencils. Out of the 3 groups, there are 2 groups with erasers (2/3), and there are a total of 4 erasers out of 6 total objects (4/6). To begin a lesson on fractions, a teacher should let the students know what they are and how they are a part of life by using real-life examples (food and/or chances in life that can be compared to fractions). I also think that one important point to keep in mind would be to use a wide variety of models, because it is easier for the students to compare equivalent fractions when you can see them alongside each other. Another point is to insist on using vocabulary so that students can get familiar with specific math language that is used to be able to verbally explain a fraction. ====

====**3. Briefly explain and give an example of each of the four guidelines you should keep in mind as you help students develop computational strategies for fractions. Which of these guidelines will be the easiest and which will be the hardest for you to implement and why? (Chapter 16) **====
 * ====__Begin with simple contextual tasks__: Letting students use word problems so that they understand what the operation means and the fractions being used. (Example) The teacher bought a pizza for the class to celebrate her students’ perfect attendance. There was a total of 8 slices(whole) and only 6 slices(part) were eaten. What fraction represents what was eaten from the pizza? ====
 * ====__Connect the meaning of fraction computation with whole-number computation__: Providing example of fractions and whole-number operations to students while explaining what is diverse and what is the same. (Example) What does 3 ½ x ¼ mean? Follow with these questions: What does 3 x 1 mean? What does 3 x 1 ½ mean? ====
 * ====__Let estimation and informal methods play a big role in the development of strategies__: Guide the students when they try to develop their own ways of solving a problem because this helps create a foundation to better understand how a formula or strategy functions. (Example) Which fraction is closest to being a whole: 2/3 or 2/5? An informal method can consist of multiplying numbers to get the same denominator and then compare the two fractions. ====
 * ====__Explore each of the operations using models__: Showing and explaining many different types of models benefit the students by letting them play around with actual manipulatives or just on paper and can prepare them to solve problems in the future. (Example) Show 2/3 + 1/4 with the help of a model. ====

==== The easiest guideline for me to implement will be “exploring each of the operations using models” because I, myself, usually find it easier to work out problems by using models. It help me see and understand if my answer makes sense or not. The hardest guideline for me to implement is “connect the meaning of fraction computation with whole-number computation” because this takes me a longer time to explain and I feel that the students would get lost with my explanation rather than understand the concept. ====