Review+Questions+2

**Review Questions #2**
===1. What are the differences between invented strategies and the traditional algorithms for whole-number computation? Give an example of each difference. (Chapter 12) ===

====Invented strategies are personal, even unique, ways that students come up with on their own in order to solve mathematical problems. Children do the calculations in their head by moving around the numbers in a way that they understand, rather than using a way that they were taught. Invented strategies work a lot better with the use of a paper and pencil because they are able to write down the process of their work and show it to their classmates. They can start a discussion about each of their invented strategies and compare the one they understand the best. For example, when solving 53 x 8, first multiply 50 x 8 is 400, and then 3 x 8 is 24. So, the total of the sum of ==== ====400 + 24 is 424. Therefore, the final answer for 53 x 8 is 424. Traditional algorithms consist of the teacher modeling to the students how to solve a problem with the use of manipulatives, or instructional material. Once the problem solving strategy has been modeled, the students are able to repeat the process and apply it to other similar algorithms. Technology, such as calculators or computers, can also be used to teach problem solving techniques. By using traditional algorithms, students can not come up with solutions easily. They require a more step-by-step guidance approach when teaching. For example, traditional algorithm can be beneficial when trying to solve 2,355 x 8,174. These type of problems are not as easy to solve in your head and involve using more manipulatives. I think it is crucial to use the invented strategy approach, because students are sure to understand their personal way to solve mathematical problems. Also, by having them explain to the class how they solve it can help others find an easier way to be able to use in the future. ====

===2. What are five general principles you need to keep in mind as you work with children to develop their estimation skills? Give an example for each principle. (Chapter 13) ===


 * ====__Use Real Examples of Estimation__: Encouraging a connection to their lives outside of school is a great way to get the students involved in math. A real life example that can be used when teaching proportions is using cut-outs of donuts, pizzas, or tortillas (it is even better if they are real). Using these things can call their attention by demonstrating the proportions of favorite foods. ====
 * ====__Use the Language of Estimation__: Words like close to, about, or more/less than can help students understand that we are not going to achieve a specific number. For example, ¾ (or 0.75) is about 1.====
 * ====__Use Context to Help with Estimates__: By offering students examples of the numbers that are being estimated, they are more likely to find an answer. For example, “How many students are in the school?” 10, 1,000, or 100,000? They will be sure that the total amount of students is definitely not 10 and 100,000 can be way too much. ====
 * ====__Accept a Range of Estimates__: Every answer given by a student should be followed by an explanation. That way, students learn to estimate instead of simply guessing. For example, if a student were to respond to the question in the previous principle by saying 1,000 the next step would be to ask for an explanation as to how he/she got there. Saying that there are more than 10 students in the school, so there can not be 10 in the whole school. Also, 100,000 is enough to fill a stadium and so that would be too much. ====
 * ====__Focus on Flexible Methods, Not Answers__: Letting the students express the strategy they use to solve helps them be open to different ways. Not only is it important to have students explain their work, but having the rest of the class listen to it can have advantages. Children will see that there are various ways to working out a problem. ====