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Read the 4 post below and provide a 1 paragraph substantiated reply whether you agree or disagree and why?

1.What is the difference between solving a problem with direct modeling and solving a problem with an invented strategy? What is the traditional algorithm? Direct modeling is the developmental step that usually precedes invented strategies. Direct modeling uses manipulatives or drawings along with counting to represent directly the meaning of an operation or story problem. While invented strategies become mental methods after the ideas have been explored, used, and understood. Traditional algorithm is a set of rules for solving a problem in a finite number of steps, as for finding the greatest common divisor. How is computational estimation different from other types of estimation? Measurement estimation determines an approximate measure without making an exact measurement. Quantity estimation approximates the number of items in collection. Computational estimation determine a number that is an approximation of a computation that we cannot or do not wish to determine exactly. Computational estimation is different from the other estimations meanly because with computational estimation you are estimating with facts. How can the calculator be used to practice estimation strategies? The calculator is not only a good source of estimation activities but also one of the reasons estimation is so important. The calculator as an estimation teaching tool lets students work independently or in parts in a challenging, fun way without fear of embarrassment. I really think the calculator is a great tool even though some people don’t like the fact of students using the calculator. The students should be taught how to make problems out manually as well as on the calculator. I also think that students should be able to use them on test just make it to were the students have to show their work on paper to go along with the test. Distinguish between the two uses of a variable. Give examples. Variables used as unknown values expressions or equations with variables are a means for expressing patterns and generations. Variables can be used as unique unknown values or as quantities that vary. In the open sentence exploration, the box is a precursor of a variable used in this way. Even in the primary grades, you can use letters instead of a box in your sentences, such as an n standing for the missing number. Rather than ask students what number goes in the box, ask what number the letter could be to make the sentence true. Initial work with finding the value of the variable that makes the sentence true solving the equation should rely on relational thinking. Variables used as quantities that vary. When there are different variables in a single equation, each variable can represent many, even infinite, numbers. This shift from the variable as an unknown representing a single value to a variable representing a relationship can be difficult for students. The number line is an important model in developing the concept of variables. Finding where variables are in relation to numbers and in relation to other variables helps to build meaning. Example of unknown values 3+_=6, _- 2=7, 5+5=_

2.What is the difference between solving a problem with direct modeling and solving a problem with an invented strategy? What is the traditional algorithm?
Solving a problem with direct modeling is when the use of manipulatives or drawings along with counting to represent directly the means of an operation or story problem. Student invented strategies is referred to any strategy other than the standard algorithm or that does not involve the use of physical materials or counting by ones. Traditional algorithms is referred to as a method of computation which is conventionally taught for solving particular math problems. The problem with standard algorithm is that it varies from culture to culture, even more family to family. What may be the proper way for a student to learn something, their family could have taught them another way which would make it difficult for the teacher to try and teach and help the student understand the concept.
How is computational estimation different from other types of estimation?
The difference between computational estimation and other types of estimation is that computational estimation is to be able to flexibly and quickly produce an approximate result that will work for the situation and give a sense of reasonableness. With other types of estimations such as measurement estimation and quantity estimation; measurements involves determining an approximately measure without making an exact measurement. Quantity involves approximating the number of items in a collection.
How can the calculator be used to practice estimation strategies?
The calculator as an estimate teaching tool lets students work independently or in pairs in a challenging, fun way without the fear that they got an answer wrong. Calculator can also be used because for checking an answer. If a student is making an estimation and wants clarification: they can use the calculators to check to see if the answer is correct.
Distinguish between the two uses of a variable. Give examples.
In chapter 14, it talks about the variable used as unknown values and variable used as quantities that vary. The variable used as unknown values when a teacher is teaching algebraic functions and in equations the teacher uses a letter to represent the value of what needs to be solved in the equation. For example 2x+1=7, the variable represents the x which is the unknown. Variable used as quantities that vary is when there are different variables in a single equation, each variable can represent many, even infinite number. For example, y=3x+5, whereas the y and x are the variables used in this one equation.

3. Topic: Select any grade between 2 and 6, and discuss what you feel is an appropriate skill level for whole-number computation at that grade. Should these skills be taught at that grade or earlier?
I would select the 2nd grade because I believe that each student is a unique individual who needs a secure, caring, and stimulating atmosphere in which to grow emotionally, intellectually, physically, and socially. It is my desire as a future educator to be able to help students meet their fullest potential in these areas by providing an environment that is safe, supporting, risk-taking, while inviting them to their share ideas. When the teacher’s role is to guide, providing access to information rather than acting as the primary source of information, the students’ search for knowledge that is met as they learn to find answers to their questions. With that being said the teacher should always push the students to work at least a grade level ahead so that they will be prepared for whatever is thrown at them. In order for students to construct knowledge, they need the opportunity to discover for themselves and practice skills in authentic situations. Providing student’s access to hands-on activities and allowing a reasonable amount of time and space to use materials that leads the lesson being studied creates an opportunity for the students discovery and construction of knowledge to be learned. It’s also important that having the opportunity to study things that are meaningful and relevant to the students life and interests. Creating a curriculum around student interests fosters intrinsic motivation and stimulates the passion to learn. Helping students to develop a love and respect for themselves and others which occurs through an openly sharing of ideas and self-discipline is my biggest goal.

4.Topic: Select any grade between 2 and 6, and discuss what you feel is an appropriate skill level for whole-number computation at that grade. Should these skills be taught at that grade or earlier?
Selecting 3rd grade, I feel that whole number computation is vital at this age due to it being the first year they will take standard state testing that will include alot of whole number computations. Chapter 12 talks about appropriate skills for 3rd graders to learn whole number computations by giving 3 computational instructional strategies that will assist students in learning whole number computations. Teachers should implement the direct modeling from counting by ones to using based ten models. Teachers should also implement standard algorithm and student invented strategies that are supported by written recordings and mental methods. With standard algorithm, teachers should use based ten materials to model the steps and prove that it produces correct answers through understanding. I feel that students should have an understanding of basic counting by ones before reaching this grade as well as an understanding of basic math skills, so that when the teacher is teaching base ten models, students will already have an understanding of addition and subtraction base ten.

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