Question 1

All of the statements below relate students' understanding of the equal sign EXCEPT:
A)Understanding or confusion with the equal sign does not usually cause difficulties understanding the process of solving equations.
B)Because of their early experiences,many students tend to believe the equal sign represents "and the answer is".
C)The equal sign is one of the principle methods of representing important relationships within the number system.
D)The equal function can be represented concretely by a number balance scale,which can lead to deeper conceptual understanding.

Accepted Answer

This statement focuses on the relationship between understanding the equal sign and solving equations, rather than on students' understanding of the equal sign itself.

Answer: B
 This statement addresses a common misconception among students about the meaning of the equal sign.

Answer: C
 This statement emphasizes the importance of the equal sign in representing relationships within the number system.

Answer: D
 This statement highlights one way in which the equal sign can be represented concretely, which can help deepen students' conceptual understanding.

Question 2

What is an early misconception about variables?
A)A constant value.
B)A symbol of relationships.
C)A placeholder for one exact number.
D)A quantity that varies.

Accepted Answer

An early misconception about variables is that they are only placeholders for one exact number. However, variables can represent a range of values, not just one specific number.

Question 3

Identify the true statement for all proportional relationships.
A)They can only be represented accurately with an equation.
B)They will always show in a graph as a straight line that passes through the origin.
C)They will always have a positive slope.
D)They are more challenging for students to generalize than a non-proportional one.

Accepted Answer

A

Question 4

Complete this statement,"The use of a two-pan balance scale or semi-concrete drawings of a balance help develop a strong understanding of..".
A)Pattern identification.
B)Function patterns.
C)Abstract concept of equality.
D)Conjecture.

Accepted Answer

The use of a two-pan balance scale or semi-concrete drawings of a balance help develop a strong understanding of the abstract concept of equality by visually demonstrating the balance of weight on both sides. This concept is foundational in understanding mathematics and problem-solving skills. Pattern identification, function patterns, and conjecture are not directly related to the use of balance scales.

Question 5

These patterns are technically referred to as sequences and they involve a step-to-step progression.
A)Recursive.
B)Covariational.
C)Correspondence.
D)Linear.

Accepted Answer

Recursive sequences involve a step-to-step progression where the next term is derived from the operations performed on the previous term(s).

Question 6

What is a reason for students to create graphs of functions?
A)They are representing them in the manner that makes it the hardest to visualize relationships between patterns.
B)They should be provided to them with examples within a real-life context.
C)They should place the independent variable (step number)along the vertical axis.
D)They should always be given specific data,equations,or numbers.

Accepted Answer

Creating graphs of functions helps students to understand how mathematical concepts can be applied in real-life situations, which can help to engage them and make the material more relevant and interesting. Additionally, seeing the relationship between the graphed function and real-world phenomena can aid in visualizing the concepts and understanding how they work in practice.

Question 7

The ________ property is central to learning multiplication basic facts and the algorithms for the operation.
A)Associative.
B)Multiplicative identity.
C)Distributive.
D)Inverse relationship of addition and subtraction.

Accepted Answer

The distributive property is central to learning multiplication basic facts and the algorithms for the operation because it allows for the breaking down of complex multiplication problems into simpler ones by distributing the multiplication over addition or subtraction within parentheses.

Question 8

A tool called __________________,is normally thought of as teaching numeration but can help students to connect place value and algebraic thinking.
A)Open number line.
B)Grid paper.
C)Calculator.
D)Hundreds chart.

Accepted Answer

A hundreds chart can help students not only understand numeration but also connect place value to algebraic thinking as they can see patterns and relationships between numbers. It also allows for easier visualization of adding and subtracting multiples of 10 and 100, which is important in understanding place value.

Question 9

Three of these are the strands of algebraic thinking described by Blanton and Kaput.Which one is not considered a strand by itself?
A)Structures in the number system.
B)Meaningful use of symbols.
C)Mathematical modeling.
D)Patterns,relations and functions.

Accepted Answer

The answer of Three of these are the strands of...

Question 10

All of the following are examples of algebraic thinking a young student would demonstrate in kindergarten EXCEPT:
A)Acting out a situation.
B)Recognizing patterns in sounds (clapping).
C)Applying properties of addition.
D)Adding and subtracting with fingers.

Accepted Answer

Applying properties of addition, such as the commutative or associative property, is more advanced than the other options and typically not expected of kindergarten students. The other choices (acting out situations, recognizing patterns, and using fingers for basic arithmetic) are more aligned with the developmental stage of young learners.

Question 11

This method of recording can help students think about how two quantities vary from step to step.
A)Grid paper.
B)Hundreds chart.
C)Table.
D)Open number line.

Accepted Answer

Tables can show how two (or more) quantities vary from step to step by organizing the information in a clear and easy-to-read format. They allow students to write down each step and see a pattern in how the quantities change. While the other options (grid paper, hundreds chart, and open number line) can also be useful tools for recording data, they may not be as effective in showing the relationship between two quantities.

Question 12

Patterns are found in all areas of mathematics.Below are examples of repeating patterns EXCEPT:
A)Patterns that have core the repeats.
B)Patterns in number i.e.place value.
C)Patterns in seasons,days,music.
D)Patterns in skip counting.

Accepted Answer

The answer of Patterns are found in all areas of...

Question 13

Using expressions and variables in elementary classrooms should be evident with all of the following EXCEPT:
A)Involve situation with a specific unknown.
B)Express it in symbols.
C)Use letters in place of an open box.
D)Use specific data,numbers and equations.

Accepted Answer

Option D suggests the use of specific data, numbers, and equations, which may not be suitable for all elementary students. Instead, elementary students should be introduced to expressions and variables through real-life situations involving a specific unknown (option A), representing it through symbols (option B), and using letters in place of an open box (option C).

Question 14

The term algebraic thinking is used instead of the term algebra because algebraic thinking goes beyond the topics that are typically found in an algebra course.All of the ideas below could be used as "algebraified" activity EXCEPT:
A)Familiar formulas for measuring a geometric shape.
B)Data from census reports and survey.
C)Experiments that look for functional relations.
D)Strategies for model-based problems.

Accepted Answer

The answer of The term algebraic thinking is used instead...

Question 15

What is one method that students can use to show that they are generalizing properties?
A)Symbols.
B)Written examples.
C)Equations with numbers.
D)Model with manipulatives.

Accepted Answer

Symbols are a method students can use to generalize properties because they allow for the representation of any number or variable, making the property applicable in a general sense.

Question 16

Students need to be familiar and use the language to describe functions of graphs.All of vocabulary below will support the knowledge of functions EXCEPT:
A)Discrete are isolated or selected values.
B)Covariational is the input generated by the output
C)Range is the corresponding possible values for the dependent variable.
D)Domain is the possible values of the independent variable.

Accepted Answer

Covariational is not a term related to functions or graphs. The other three terms are essential vocabulary when describing functions of graphs.

Question 17

The statements below are students' views of equations EXCEPT.
A)Relational-structural view
B)Relational-computational view
C)Correspondence-relational view
D)Operational view

Accepted Answer

The other options - Relational-structural view, Relational-computational view, and Operational view - all describe valid perspectives on equations, but the "Correspondence-relational view" is not a commonly recognized perspective on equations.

Question 18

Mathematical modeling is one of the eight Standards for Mathematical Practice.Three of the statements reference the true meaning of mathematical modeling.Identify the one that is often mistaken for modeling.
A)Links classroom mathematics to everyday life.
B)Process of choosing appropriate mathematics for situations.
C)Visual models,such as manipulatives and drawings of pattern.
D)Analyzing empirical situations to better understand.

Accepted Answer

Visual models, such as manipulatives and drawings of patterns, are often mistaken for modeling because they can be a tool used in the modeling process, but they do not necessarily encompass the entire modeling process. The other choices all reference different aspects of mathematical modeling, such as connecting math to real-world situations and analyzing empirical data.

Question 19

Growing patterns can be represented in multiple ways.Identify the representation below that actually illustrates covariation.
A)A table.
B)Symbols.
C)Physical model.
D)Graph.

Accepted Answer

A graph is the best representation for illustrating covariation because it shows the relationship between two variables on a coordinate plane, with each point representing a pair of values. This allows for easy visual interpretation of how the variables relate to each other over time or as other factors change.

Question 20

Making sense of properties of the operations is a part of learning about generalizations.Identify the statement below that a student might use to explain the associative property of addition.
A)" When you add three number you can add the first two and then add the third or add the second and third and then the first.Either way you get the same answer".
B)" When you add two number in any order you will get the same answer".
C)" When you have a subtraction problem you can think addition by using the inverse".
D)"When you add zero to any number you get the number you started with".

Accepted Answer

The associative property of addition states that the way we group addends does not change the sum. This is exactly what is stated in option A.

Quiz 14: Algebraic Thinking, equations, and Functions

All of the statements below relate students' understanding of the equal sign EXCEPT:

What is an early misconception about variables?

Identify the true statement for all proportional relationships.

Complete this statement,"The use of a two-pan balance scale or semi-concrete drawings of a balance help develop a strong understanding of..".

These patterns are technically referred to as sequences and they involve a step-to-step progression.

What is a reason for students to create graphs of functions?

The ________ property is central to learning multiplication basic facts and the algorithms for the operation.

A tool called __________________,is normally thought of as teaching numeration but can help students to connect place value and algebraic thinking.

Three of these are the strands of algebraic thinking described by Blanton and Kaput.Which one is not considered a strand by itself?

All of the following are examples of algebraic thinking a young student would demonstrate in kindergarten EXCEPT:

This method of recording can help students think about how two quantities vary from step to step.

Patterns are found in all areas of mathematics.Below are examples of repeating patterns EXCEPT:

Using expressions and variables in elementary classrooms should be evident with all of the following EXCEPT:

The term algebraic thinking is used instead of the term algebra because algebraic thinking goes beyond the topics that are typically found in an algebra course.All of the ideas below could be used as "algebraified" activity EXCEPT:

What is one method that students can use to show that they are generalizing properties?

Students need to be familiar and use the language to describe functions of graphs.All of vocabulary below will support the knowledge of functions EXCEPT:

The statements below are students' views of equations EXCEPT.

Mathematical modeling is one of the eight Standards for Mathematical Practice.Three of the statements reference the true meaning of mathematical modeling.Identify the one that is often mistaken for modeling.

Growing patterns can be represented in multiple ways.Identify the representation below that actually illustrates covariation.

Making sense of properties of the operations is a part of learning about generalizations.Identify the statement below that a student might use to explain the associative property of addition.