Math Methods Chapter 18

15) The statements below represent illustrations of various relationships between the area formulas? Identify the one that is NOT represented correctly. 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, h/2 (b1 +b2).

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.

12) What language supports the idea that the area of a rectangle is not just measuring sides? A) Height and base B) Length and width C) Width and Rows D) Number of square units

A) Height and base

8) Young learners do not immediately understand length measurement. Identify the statement below that would NOT represent a misconception about measuring length. A) Measuring attribute with the wrong measurement tool. B) Using wrong end of the ruler C) Counting hash marks rather than spaces. D) Misaligning objects when comparing.

A) Measuring attribute with the wrong measurement tool.

2) Identify the statement that is NOT a part of the sequence of experiences for measurement instruction. A) Using measurement formulas. B) Using physical models. C) Using measuring instruments. D) Using comparisons of attributes.

A) Using measurement formulas.

7) All of these statements are true about reasons for including estimation in measurement activities EXCEPT: A) Helps focus on the attribute being measured. B) Helps provide an extrinsic motivation for measurement activities. C) Helps develop familiarity with the unit. D) Helps promote multiplicative reasoning.

B) Helps provide an extrinsic motivation for measurement activities.

11) As students move to thinking about formulas it supports their conceptual knowledge of how the perimeter of rectangles can be put into general form. What formula below displays a common student error for finding the perimeter? A) P = l + w + l + w B) P = l + w C) P = 2l + 2w D) P = 2(l + w)

B) P = l + w

14) Volume and capacity are both terms for measures of the "size" of three-dimensional regions. What statement is true of volume but not of capacity? A) Refers to the amount a container will hold. B) Refers to the amount of space of occupied by three-dimensional region. C) Refers to the measure of only liquids. D) Refers to the measure of surface area.

B) Refers to the amount of space of occupied by three-dimensional region.

17) Identify the attribute of an angle measurement. A) Base and height. B) Spread of angle rays. C) Unit angle. D) Degrees.

B) Spread of angle rays.

4) When using a nonstandard unit to measure an object, what is it called when you use many copies of the unit as needed to fill or match the attribute? A) Iterating. B) Tiling. C) Comparing. D) Matching.

B) Tiling.

9) The concept of conversion can be confusing for students. Identify the statement that is the primary reason for this confusion. A) Basic idea if the measure is the same as the unit it is equal. B) Basic idea that if the measure is larger the unit is longer. C) Basic idea that if the measure is larger the unit is shorter. D) Basic idea that if the measure is shorter the unit is shorter.

C) Basic idea that if the measure is larger the unit is shorter.

5) There are three broad goals to teaching standard units of measure. Identify the one that is generally NOT a key goal. A) Familiarity with the unit. B) Knowledge of relationships between units. C) Estimation with standard and nonstandard units. D) Ability to select and appropriate unit.

C) Estimation with standard and nonstandard units.

16) What is the most conceptual method for comparing weights of two objects? A) Place objects in two pans of a balance. B) Place objects on a spring balance and compare. C) Place objects on extended arms and experience the pull on each. D) Place objects on digital scale and compare.

C) Place objects on extended arms and experience the pull on each.

10) Comparing area is more of a conceptual challenge for students than comparing length measures. Identify the statement that represents one reason for this confusion. A) Area is a measure of two-dimensional space inside a region. B) Direct comparison of two areas is not always possible. C) Rearranging areas into different shapes does not affect the amount of area. D) Area and perimeter formulas are often used interchangeably.

C) Rearranging areas into different shapes does not affect the amount of area.

13) 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. D) Converting between metric and customary units.

D) Converting between metric and customary units.

19) All of these are ideas and skills for money that students should be aware of in elementary grades EXCEPT: A) Making change. B) Solving word problems involving money. C) Values of coins. D) Solving problems of primary interest.

D) Solving problems of primary interest.

6) The Common Core State Standards and the National Council of Teachers of Mathematics agree on the importance of what measurement topic? A) Students focus on customary units of measurement. B) Students focus on formulas versus actual measurements .C) Students focus on conversions of standard to metric. D) Students focus on metric unit of measurement as well as customary units.

D) Students focus on metric unit of measurement as well as customary units.

18) Steps for teaching students to understand and read analog clocks include all of the following EXCEPT: A) Begin with a one-handed clock. B) Discuss what happens with the big hand as the little hand goes from one hour to the next. C) Predict the reading on a digital clock when shown an analog clock. D) Teach time after the hour in one-minute intervals.

D) Teach time after the hour in one-minute intervals.

3) All of the ideas below support the reasoning behind starting measurement experiences with nonstandard units EXCEPT: A) They focus directly on the attribute being measured. B) Avoids conflicting objectives of the lesson on area or centimeters. C) Provides good rational for using standard units. D) Understanding of how measurement tools work.

D) Understanding of how measurement tools work.

1) When a teacher assigns an object to be measured students have to make all of these decisions EXCEPT: A) What attribute to measure? B) What unit they can use to measure that attribute? C) How to compare the unit to the attribute? D) What formulas they should use to find the measurement?

D) What formulas they should use to find the measurement?