Exam 14: Developing Aspects of Proportional Reasoning: Ratio, Proportion, and Percent

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A ratio is a mathematical expression tha...

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A) $20.16
B) $8.40
C) $19.60
D) $7.84

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To create a design with blue pieces repr...

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A) part-whole sense
B) part-part sense
C) ratio as a rate
D) probability relationships

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A) 250%
B) 50%
C) 300%
D) 200%

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D

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Percent and percentage are two terms that are often used interchangeably, but they actually have slightly different meanings. Percent is a term that is used to describe a proportion out of 100. For example, if you have 50 out of 100, you would say that you have 50 percent. Percentage, on the other hand, is the actual calculation or expression of a proportion out of 100. So, if you want to calculate the percentage of a number, you would divide that number by 100 and then multiply by the proportion you are interested in. In summary, percent is the concept of a proportion out of 100, while percentage is the actual calculation or expression of that proportion.

A) they must have a thorough understanding of fractions before percents are introduced.
B) they should always work with fractional denominators of 100.
C) they must have mastery of decimals before percents are introduced.
D) they should have a thorough understanding of learning aids such as base-ten materials used to introduce fractions and decimals.

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One model that could help the teacher cl...

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A) 12
B) 6
C) 8⅙
D) 6⅛

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A) the ratio of the diameter to the radius in a circle.
B) the ratio of the circumference to diameter in a circle.
C) the ratio of the circumference to the radius in a circle.
D) the ratio of the radius to the diameter in a circle.

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A) 300/25 or 12 miles per gallon
B) 25/300 or 0.08 gallons per mile
C) 300/25 or 60 miles per 5 gallons
D) any of these answers apply

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A) common fractions do not require labels for each of their parts like ratios do.
B) neither common fractions nor ratios can have zeros in the denominator (common fraction) or second position (ratio) .
C) ratios can have parts added to them such as when the ratio of boys to girls in a class changes when new students add the class; common fractions cannot.
D) ratios are not independent numerical expressions and must be understood in the context of the relationships they represent; common fractions are independent of context.

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A) proportions are common fraction relationships.
B) any problem solved using a rate table can be solved using a proportion.
C) proportions can be explained in terms of equivalent fractions.
D) proportions are equalities between two ratios.

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Ratios and fractions are mathematical co...

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A) concrete level of thinking.
B) semi-concrete level of thinking.
C) abstract level of thinking.
D) semi-abstract level of thinking.

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A) using a multiples table
B) using a unit rate
C) using unitizing
D) using the cross-product algorithm

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To answer this question, we need to understand the composition of a tangram set. A tangram is a Chinese geometric puzzle consisting of seven pieces, called tans, which are used to create various shapes, including a square. The seven pieces are: 1. Two large right triangles 2. One medium right triangle 3. Two small right triangles 4. One square 5. One parallelogram If the entire square made with all seven tangram pieces is considered to be 1/2 (or 50%), we can determine the size of each piece relative to the whole. The traditional tangram set has the following size relationships: - The two large right triangles together are half the area of the square. - The medium right triangle is half the area of one large right triangle. - The two small right triangles together are half the area of the medium right triangle. - The square is the same area as one of the small right triangles. - The parallelogram is the same area as one of the small right triangles. Given these relationships, we can calculate the size of each piece as a fraction of the whole square: 1. Each large right triangle is 1/4 of the whole square (since both together are 1/2). 2. The medium right triangle is 1/8 of the whole square (since it is half the area of one large right triangle). 3. Each small right triangle is 1/16 of the whole square (since both together are 1/8, which is half the area of the medium right triangle). 4. The square is 1/16 of the whole square (since it is the same area as one small right triangle). 5. The parallelogram is 1/16 of the whole square (since it is the same area as one small right triangle). Now, let's convert these fractions to decimal fractions and percentages: 1. Large right triangle: 1/4 = 0.25 (or 25% of the whole square) 2. Medium right triangle: 1/8 = 0.125 (or 12.5% of the whole square) 3. Small right triangle: 1/16 = 0.0625 (or 6.25% of the whole square) 4. Square: 1/16 = 0.0625 (or 6.25% of the whole square) 5. Parallelogram: 1/16 = 0.0625 (or 6.25% of the whole square) Remember, these percentages are relative to the whole tangram square being considered as 1/2 (or 50%). If the whole tangram square were considered as a full unit (100%), the percentages would be doubled.