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Question
Although many teachers worry that multiple representations of the same problem will confuse students, research shows that, if students are shown a variety of methods from the beginning, they gain flexibility in their problem-solving strategy use and, consequently, enhanced learning.Answer
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Parental involvement in students' mathematical development
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Q:
Which is NOT an illustration of the relationships between the various area formulas?
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b) A rectangle can be cut in half to produce two congruent triangles. Therefore, the formula for a triangle is like that for a rectangle, but the product of the base length and height must be cut in half.
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b) Asking students to reduce the amount of each ingredient that is needed for a recipe that is divided in half to accommodate a small family
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Which of the following is NOT an example of a connection between proportional reasoning and another strand of mathematics?
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b) The negative slope of the line on the graph represents the fact that, for every 30 miles the car travels, it burns one gallon of gas.
c) The triangle has been enlarged by a scale factor of 2. How wide is the new triangle if its original width is 4 inches?
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Which of the following is an example of teaching throughproblem solving?
a) Providing students with a list of area formulas and asking them to find the area of a given rectangle
b) After students have conceptual understanding of the area of a rectangle, asking them to find the area of a triangle that was constructed by cutting a given rectangle in half and then to generalize their process to how they might find the area of any given triangle
c) Teaching students the algorithm for fraction division and then asking them to find out how many servings of 1/3 pizza could be made from 3-2/3 pizzas
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All of the following are features a problem should have EXCEPT
a) Its design must take into consideration the students' current level of understanding.
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c) It must require some kind of justification for methods and answers.
d) It must be at a level that would make a student unable to solve it alone.
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When comparing ratios to fractions keep in mind that
a) Conceptually, they are exactly the same thing.
b) They have the same meaning when a ratio is of the part-to-whole type.
c) They both have a fraction bar that causes students to mistakenly think they are related in some way.
d) Operations can be done with fractions while they can"t be done with ratios.
Q:
Which of the following is a true statement regarding the practice of exposing students to multiple approaches to solving problems?
a) The most useful aspect of the strategy is that students should see a variety of inferior methods so that they can better appreciate the one best method to solve a problem.
b) Class discussions are not a valuable way for students to investigate alternative problem-solving strategies and make connections between mathematical ideas.
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To set up an environment for "doing" mathematics, teachers need to
a) Develop and demonstrate rules.
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d) Allow students to make engage in "productive struggle."
Q:
Which of the following is an example of a statement spoken in the language of doing mathematics?
a) "Memorize these steps."
b) "Compute this answer."
c) "Explain how you solved the problem."
d) "Copy down these steps into your notebooks."
Q:
Which of the following is NOT a common misconception about fraction computation?
a) Multiplying always results in a bigger number, while dividing always make a number smaller.
b) Fractions have to have a common denominator for all computation.
c) Procedures developed from conceptual understanding are usually easier than the standard algorithms.
d) Estimation is not important.
Q:
In this ever-changing world, those who love mathematics will likely survive the ups and downs of the economy. Which of the following is NOT a contributing factor to this fact?
a) Society is becoming more reliant on technology and the data it produces.
b) There are countless jobs in which people do simple computation.
c) Teachers are currently preparing students for jobs that don"t yet exist, and they will likely need to be skilled at approaching problems in different ways.
d) The world is surrounded by algorithms that help make predictions.
Q:
Estimation of fractions can result in estimates that are not close to the actual computed answer and should be avoided.