Question 1

Order of operations extends working with exponents.What part of the order of operations is a convention?&#10;A)The meaning of the operation.&#10;B)Multiplying before computing the exponent changes the meaning of the problem.&#10;C)Working from left to right,using parenthesis.&#10;D)PEMDAS

Accepted Answer

The decision to work from left to right when using parentheses is a convention, as there is no mathematical reason that mandates this approach. However, it is widely agreed upon and helps to avoid ambiguity in expressions with multiple sets of parentheses.

Question 2

When students begin to work with exponents they often lack conceptual understanding.Identify the method that supports conceptual versus procedural understanding.&#10;A)Explore growing patterns with physical models.&#10;B)Explore with whole numbers before exponents with variables.&#10;C)Instruction on the order of operations.&#10;D)Instruction should focus on exponents as a shortcut for repeated multiplication.

Accepted Answer

Explore with whole numbers before exponents with variables.

Question 3

The contexts below would support learning about very,very large numbers EXCEPT:&#10;A)Distance from the planet Mercury to Mars.&#10;B)Number of cells in the human body.&#10;C)The estimated life span of a Bengal tiger.&#10;D)Population of the European countries in 2011.

Accepted Answer

The estimated life span of a Bengal tiger does not provide any context for learning about very, very large numbers. The other options involve large distances, numbers of cells, and populations, which can help develop an understanding of very large quantities.

Question 4

When students are learning and creating contexts for integer operations.Ask them to consider the following questions EXCEPT:&#10;A)Where am I now?&#10;B)Where am I going?&#10;C)Where did you start?&#10;D)How far did you go?

Accepted Answer

Questions A, C, and D are directly related to understanding and visualizing the movement or transition of values, which is crucial in grasping integer operations. B, "Where am I going?" does not directly contribute to the conceptual understanding of operations with integers as it implies a future state not necessarily related to the operation itself.

Question 5

What is the primary reason to teach and use Scientific Notation?&#10;A)Convenient way to represent very large or small numbers.&#10;B)A number is changed to be the product of a number greater or equal to 1 or less than 10 multiplied by a power of 10.&#10;C)Easiest way to convey the value of numbers in different contexts.&#10;D)To determined by the level of precision appropriate for that situation.

Accepted Answer

Scientific notation is primarily used because it provides a convenient way to represent very large or very small numbers, making them easier to read, write, and work with.

Question 6

For students to be successful in the division of integers they should competence in the following concept?&#10;A)Whole number division.&#10;B)Division of fractions.&#10;C)Relationship between multiplication and division.&#10;D)Rules for dividing negative numbers.

Accepted Answer

Understanding the relationship between multiplication and division is crucial for dividing integers, as it helps students comprehend how division is the inverse operation of multiplication.

Question 7

The term rational numbers relates to all of examples below EXCEPT:&#10;A)Fractions.&#10;B)Decimals and percents.&#10;C)Square roots.&#10;D)Positive and negative integers.

Accepted Answer

Rational numbers are any numbers that can be expressed as a ratio of two integers, such as fractions, decimals and percents, positive and negative integers. Square roots are not rational numbers because they cannot be expressed as a ratio of two integers.

Question 8

Learning about exponents can be problematic.These are common misconceptions EXCEPT:&#10;A)Think of the two values as factors.&#10;B)Hear &#34;five three times&#34; and think multiplication.&#10;C)Write the equation as 5 x 3 rather than 5 x 5 x 5.&#10;D)Use repeated addition versus multiplication.

Accepted Answer

All options except D involve using multiplication, which is the correct operation for exponents. Option D suggests using repeated addition, which is not an accurate way to represent exponents. Therefore, D is the common misconception.

Question 9

The ideas below would guide student understanding of the concept behind scientific notation EXCEPT.&#10;A)Examining patterns that arise when inputting very large and small numbers into a calculator.&#10;B)Researching real-life examples of very large and small numbers.&#10;C)Asking them to perform computation on very large and small numbers that are not in scientific notation,so they can see how difficult it is.&#10;D)Instructing them only on the movement of the decimal point &#34;the exponent with the 10 tells how many places to move the decimal point&#34;.

Accepted Answer

Choice D is the only one that does not guide student understanding of scientific notation. It only provides a definition of how to move the decimal point, but does not help students understand why scientific notation is necessary or how it is applied in real-life situations. A, B, and C all provide examples and scenarios that can help students grasp the concept behind scientific notation.

Question 10

Describe a learning experience that can introduce students to irrational numbers.

Accepted Answer

The answer of Describe a learning experience that can introduce...

Question 11

Discuss the challenges of using number lines and counters to teach about magnitude and direction of integers.

Accepted Answer

The answer of Discuss the challenges of using number lines...

Deck 23: Developing Concepts of Exponents, integers, and Real Numbers