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Question
Name at least two examples of a tool that could help students to do mathematics and gain relational understanding of a concept. Describe a specific example of a way each tool could help develop this understanding.Answer
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Related questions
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To make teaching more culturally relevant, teachers should
a) Simplify the mathematics into isolated sets of skills.
b) Ignore students' background knowledge, as it's frequently irrelevant to the math.
c) Incorporate students' identities.
d) Assign leadership positions only to those students they believe to be the most capable.
Q:
Common features across RTI tiers include all of the following EXCEPT
a) Explicit instruction
b) Research-based practices
c) Strategies that are specific to the context of the school, classroom, and student needs
d) Decisions that are based on data
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Because construction of a circle graph requires working with percentages, it is an inappropriate task for younger students.
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One of the earliest forms of displaying ____________kids encounter is bar graphs or tally charts.
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It is not enough for a teacher to have the desire to be equitable. He/she must be familiar with specific strategies that accommodate each type of learner.
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The undeniable truth is that, for the most part, what teachers grade is what students determine to be the most valuable.
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Which of the following is NOT a good source from which to draw ideas for data collection?
a) The students' favorite things
b) Analysis of characteristics between the students in different classrooms
c) Science class
d) Any context that students can"t relate to
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Which of the following statements about tessellations is true?
a) A regular tessellation consists of 5 different shapes.
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Quadrilaterals provide good models for bringing concepts of line segments, angles, and symmetry together.
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Performance indicators are usually written in terms of the number of correct answers out of the total number of problems attempted.
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Performance-based tasks
a) Are used primarily to assess students' ability to compute answers.
b) Should be constructed in a way that allows every student in the room to demonstrate knowledge, skills, or understanding.
c) Do not have much assessment value when students are required to explain their thought process behind completing them.
d) Usually don"t have enhanced value when strategies for approaching them are discussed as a whole class.
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Steps for teaching students to understand and read analog clocks include all of the following EXCEPT a) Begin with a one-handed clock.
b) Teach time after the hour in one-minute intervals.
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One source of confusion regarding angle measurement isa) Students' belief that angles with different side lengths sometimes have the same degree measurement.b) Degrees are very small units.c) The way that a student reads a protractor depends on the direction in which the angle opens.d) That the Core Content State Standards don"t mention angles.
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Parental involvement in students' mathematical development
a) Can be positive when parents provide their children with a quiet workplace and rules about homework completion.
b) Can be positive when parents make derogatory comments about their own math skills and negative feelings about mathematics.
c) Can have a negative impact when teachers help parents understand the ways they can support their students' achievement.
d) Has little positive or negative effect, regardless of the circumstances.
Q:
Which is NOT an illustration of the relationships between the various area formulas?
a) A rectangle can be cut along a diagonal line and rearranged to form a non-rectangular parallelogram. Therefore the two shapes have the same formula.
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.
c) The area of a shape made up of several polygons (a compound figure) is found by adding the sum of the areas of each polygon.
d) Two congruent trapezoids placed together always form a parallelogram with the same height and a base that has a length equal to the sum of the trapezoid bases. Therefore, the area of a trapezoid is equal to half the area of that giant parallelogram, 1/2h(b1+b2).
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Challenges with students' use of rulers include all EXCEPT
a) Deciding whether to measure an item beginning with the end of the ruler
b) Deciding how to measure an object that is longer than the ruler
c) Properly using fractional parts of inches and centimeters
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Which of the following is an important principle of iterating units of length?
a) They must always be standard measurement units.
b) There must be no overlapping or gaps between the units.
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d) Rulers are the best tool to measure any length.
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Describe at least 4 ways that teaching through problem solving helps ensure equity in the classroom.
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According to the NCTM position statement on the metric system, it is important that schools equip students to deal with diverse situations in both metric and customary systems while developing their ability to solve problems in either system.
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Which of the following is the weakest example of providing students with relevant contexts for problems?
a) Using a piece of children's literature to introduce a situation that requires some kind of solution
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
c) Asking a student to explain how he chose to divide the numerator and denominator of a fraction by 2 in order to simplify it
d) Asking students to determine, given the area and population of two countries, which would be less crowded
Q:
Which of the following is NOT an example of a connection between proportional reasoning and another strand of mathematics?
a) The area of a rectangle is 8 square units and the length is four units long. How long is the width?
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?
d) Sandy ate 1/4 of her Halloween candy and her sister ate of it. What fraction of her candy was left?
Q:
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
d) Having students develop their own word problems that use a recently learned algorithm
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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.
b) It should have an engaging context.
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.
Q:
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.
c) The strategy is not very useful for very simple mathematical ideas, such as basic computation facts.
d) Exposure to multiple approaches and the subsequent connections that develop can help students to recall the steps to complete mathematical processes.
Q:
To set up an environment for "doing" mathematics, teachers need to
a) Develop and demonstrate rules.
b) Efficiently manage time and materials.
c) Quickly provide corrected answers, so students are not embarrassed by mistakes.
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.