Deck 14: Algebraic Thinking, equations, and Functions

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.

Answer 1

Understanding or confusion with the equal sign does not usually cause difficulties understanding the process of solving equations.

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.

Answer 2

A placeholder for one exact 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.

Answer 3

They can only be represented accurately with an equation.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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

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.

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.

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".

Question 21

Describe three different ways algebra can be connected to other areas of the mathematics curriculum.

Question 22

Describe two different ways you could determine whether a function is linear.Describe how these two methods relate to one another,and a possible classroom activity that would help students to see this connection.