Question 1

Differentiation of instruction in mathematics lessons is needed to support and challenge the learning for all students.One statement below is an example of a differentiating process.
A)Identify the mathematics you want each student to know.
B)Identify what thinking will engage students in the mathematical content.
C)Identify what students will show,write or tell to demonstrate learning.
D)Identify the physical environment that will be most conducive for learning.

Accepted Answer

Differentiating the process in instruction involves identifying activities or methods that will engage students in learning the content effectively, catering to their diverse learning styles and needs. Option B focuses on engaging students in the mathematical content, which is a key aspect of differentiating the process of instruction.

Question 2

Asking quality questions are critically important to the potential learning.What question below would solicit higher-level responses from students?
A)Which rectangle would an architect prefer for a dance stage rather than a play stage?
B)How did you find the perimeter?
C)How is the formula for finding the area different from the formula for perimeter?
D)Which rectangle has a matching perimeter and area?

Accepted Answer

Option A encourages students to apply their understanding of rectangles in a real-world context, requiring higher-level thinking to consider the needs of an architect for different types of stages.

Question 3

What statement below would be a method for activating prior knowledge?
A)Analyze problem to anticipate student approaches and misinterpretations.
B)Asking students what they are thinking and ideas they are using to find a solution.
C)Design a worksheet of past problems.
D)Design a warm up to use the vocabulary needed for the task.

Accepted Answer

D

Question 4

When determining the mathematics content and learning goals for a lesson,the teacher should do all of the following EXCEPT:
A)Consult his or her state's curriculum standards.
B)Ask,"What is it my students should be able to do at the end of this lesson?"
C)Plan goals that will take no longer than a day for students to accomplish.
D)Be sure to focus on the mathematics,rather than just the activity.

Accepted Answer

Planning goals that will take no longer than a day for students to accomplish may limit the depth and complexity of the mathematics content taught in a lesson. It is important to have learning goals that are challenging and aligned to state standards, even if they require more than one day to accomplish.

Question 5

Planning a lesson for a classroom where inquiry and problem solving are emphasized requires a shift in the type of lessons being used.What statement below represents this shift in the agenda of a lesson?
A)It is a good idea to stick to one mathematical process that works best for you and your students.
B)It should be derived from your learning goals and require students to work in quiet.
C)It should be a "thought experiment" to consider what might happen.
D)It should not be developed until the teacher has had a chance to see how students perform on practice activities.

Accepted Answer

Inquiry and problem-solving emphasize exploration and experimentation, which aligns with the concept of a "thought experiment" where students consider various outcomes and possibilities. This approach encourages critical thinking and creativity, essential components of inquiry-based learning.

Question 6

Complete this statement,"Parental involvement in students' mathematical development.."
A)Can be positive when parents make derogatory comments about their own math skills and negative feelings about mathematics.
B)Can have a negative impact when teachers help parents understand the ways they can support their students' achievement.
C)Can have a positive or negative effect,regardless of the circumstances.
D)Can be positive when parents provide their children with a quiet workplace and rules about homework completion.

Accepted Answer

Providing a quiet workplace and rules about homework completion can create a positive impact on students' mathematical development by instilling a routine and discipline. Choices A and B have negative impacts, while Choice C is too broad and does not provide a specific context.

Question 7

Selecting,designing or adapting a worthwhile task requires that teacher to ask what important question?
A)Does this task have potential for students to demonstrate Mathematical Practices?
B)Does this task require students to activate prior knowledge?
C)Does the task only require or need the use of one problem solving strategy?
D)Does the task require more than one class period to solve?

Accepted Answer

Asking if a task has potential for students to demonstrate Mathematical Practices is important because it ensures that the task is not just focused on rote memorization and computation, but rather on higher-level thinking and problem-solving skills. This question also aligns with current standards such as the Common Core State Standards for Mathematics, which emphasize the importance of Mathematical Practices. The other options (B, C, and D) may also be important considerations in task selection, but they do not necessarily ensure that the task is worthwhile or aligned with current standards.

Question 8

Learning center and short tasks can be adapted to use the three-phase lesson design.Identify the statement below that would be part of the after portion of a short task.
A)Pose the task at the each center.
B)Pair classmates to discuss strategies.
C)Model what happens at each center.
D)Small groups share and compare strategies.

Accepted Answer

Small groups sharing and comparing strategies would be part of the after portion of a short task, as it allows for reflection and discussion on the strategies used during the task. A) is part of the before portion, as it introduces the task. B) is part of the during portion, as students are actively discussing strategies. C) could be either part of before or during, as it involves modeling what happens at each center, but it is not specifically part of the after portion.

Question 9

What statement below can inadvertently shut down student thinking and possibly affect their self-esteem?
A)How easy was this problem?
B)How did you solve the problem?
C)Can you tell me more about your strategy?
D)Can you tell me how your picture connects to your equation?

Accepted Answer

The answer of What statement below can inadvertently shut down...

Question 10

What is the purpose of establishing clear expectations for a lesson before the lesson transpires?
A)Allow students to embrace the struggle.
B)Guide students on the products they need to prepare.
C)Allow students to finish quickly and have free time
D)Guide students on the assessment they will need to complete

Accepted Answer

Establishing clear expectations before a lesson helps guide students on the products they need to prepare. This can include providing specific instructions on assignments or projects, outlining the intended learning outcomes, and setting expectations for behavior and participation. By giving students a clear understanding of what is expected of them, they are more likely to be engaged and successful in the lesson.

Question 11

A three-phase lesson format provides a structure for students to have inquiry on a topic,engage in the content through action and discussion and time to reflect and make connections.What statement below demonstrates the Beforerelated agendas?
A)Be sure the task is understood.
B)Let go.
C)Provide extensions.
D)Identify future problems.

Accepted Answer

The "Before" phase in a three-phase lesson format focuses on preparing students for the lesson, which includes ensuring they understand the task at hand. This sets the foundation for effective inquiry and engagement with the content.

Question 12

Tiered lessons and Parallel Tasks are examples of strategies that teachers can use to differentiate mathematical instruction.Which problem below would provide students with choice?
A)Find the product of 675 and 43.
B)What are the factors of 36?
C)Represent one of numbers in the list at least four different ways.
D)Can you estimate the difference between 479 and 216?

Accepted Answer

Option C allows students to choose their own number from a given list and represent it in at least four different ways. This provides students with a choice and allows them to work at their own pace and level of understanding. Options A, B, and D do not offer any choice and only have one correct answer.

Question 13

Parents may be concerned when their child struggles with a single mathematics problem.Often parents see "fast" as successful.What is a reason that fast does not mean smarter?
A)Students should be using inventive strategies.
B)Students should have productive struggle to help them with making connections.
C)Students should be practicing more of the same problems.
D)Students should just learn the standard algorithm

Accepted Answer

Productive struggle helps students develop a deeper understanding and make connections, which is more beneficial for learning than simply solving problems quickly.

Question 14

21st Century teachers need to support students and parents in understanding the way mathematics is taught and learned.Identify the question below that a teacher should address about their pedagogy before it is asked by a parent.
A)Is my child doing their own work when they are in groups?
B)Is my child learning basic facts?
C)Is my child going to need help with homework?
D)Is my child learning mathematics or just doing activities?

Accepted Answer

The answer of 21st Century teachers need to support students...

Question 15

What is the most critical aspect of the After phase of the lesson?
A)Potential to engage students in problem solving.
B)Prepare for the assessment.
C)Make sure all students are participating.
D)Make the main ideas of the lesson visible to others through drawings,notations and writing.

Accepted Answer

Making the main ideas of the lesson visible through various forms such as drawings, notations, and writing helps in reinforcing the concepts taught, aids in retention, and allows for a visual summary of the lesson's key points, which is crucial for effective learning and understanding.

Question 16

What statement represents how a teacher listens without evaluation?
A)That strategy worked for you,but will it work for others?
B)You only used one representation and one equation is that right?
C)Do others agree with Caroline's strategy?
D)Why did you solve the problem without any models?

Accepted Answer

In option C, the teacher is not evaluating the strategy used by Caroline but is seeking agreement from other students. This indicates that the teacher is listening without making any judgments or evaluations. The other options, A, B, and D, contain evaluative statements that either question the effectiveness of the strategy or suggest that the student's approach was not ideal.

Question 17

Flexible grouping means that the size and makeup of the small group vary in a purposeful and strategic manner.Below are examples of considerations teachers must make in putting together mixed-ability groups.What statement reflects the shared responsibility?
A)Whether groups stay the same for a full unit.
B)Whether groups must understand that each individual must be able to explain the content,process and product.
C)Whether group members participate in team building activities to set the standard for collaboration.
D)Whether groups present oral reports to the whole class.

Accepted Answer

The answer of Flexible grouping means that the size and...

Question 18

The Duringphase of the lesson the teacher has to ask this question when determining what students need.
A)Do the students have enough information to get started?
B)Does the task connect to students' experiences?
C)Does my action lead to deeper-thinking or is taking away the thinking?
D)Do they know the products they will need for the discussion?

Accepted Answer

The answer of The Duringphase of the lesson the teacher...

Question 19

The focus of an inquiry lesson should be start with what method?
A)Fun and engaging mathematical task.
B)Mathematical content and Mathematical practices.
C)Exposure to an isolated,but needed skill.
D)Exposure to multiple methods of solving problems.

Accepted Answer

The focus of an inquiry lesson should be on both the mathematical content and the mathematical practices. This approach encourages students to not only learn the mathematical concept but also to engage in problem-solving and critical thinking. A fun and engaging mathematical task is important, but it should not be the sole focus of the inquiry lesson. The focus should not be on exposing students to isolated skills or multiple methods, but rather on providing a deeper understanding of the mathematical concept at hand.

Question 20

What is an example of the type of assessment question that is used in the Duringphase of the lesson?
A)What strategies did your group use to find the area of the rectangle?
B)What is the relationship between area and perimeter of that rectangle?
C)How did you figure out the area of that rectangle?
D)How did the vocabulary help you to solve this problem?

Accepted Answer

This question asks students to reflect on the specific process they used to solve a problem or complete a task. This is an example of a formative assessment question during the During phase of a lesson, as it allows the teacher to gauge student understanding as they are actively engaged in the learning process. Option A also asks about strategies, but it is more focused on group work rather than individual understanding. Option B is more focused on the relationship between concepts rather than the specific process of solving a problem. Option D asks about the role of vocabulary in problem-solving, which is important, but may not be as directly related to the content of the lesson at hand.

Quiz 4: Planning in the Problem-Based Classroom

Differentiation of instruction in mathematics lessons is needed to support and challenge the learning for all students.One statement below is an example of a differentiating process.

Asking quality questions are critically important to the potential learning.What question below would solicit higher-level responses from students?

What statement below would be a method for activating prior knowledge?

When determining the mathematics content and learning goals for a lesson,the teacher should do all of the following EXCEPT:

Planning a lesson for a classroom where inquiry and problem solving are emphasized requires a shift in the type of lessons being used.What statement below represents this shift in the agenda of a lesson?

Complete this statement,"Parental involvement in students' mathematical development.."

Selecting,designing or adapting a worthwhile task requires that teacher to ask what important question?

Learning center and short tasks can be adapted to use the three-phase lesson design.Identify the statement below that would be part of the after portion of a short task.

What statement below can inadvertently shut down student thinking and possibly affect their self-esteem?

What is the purpose of establishing clear expectations for a lesson before the lesson transpires?

A three-phase lesson format provides a structure for students to have inquiry on a topic,engage in the content through action and discussion and time to reflect and make connections.What statement below demonstrates the Beforerelated agendas?

Tiered lessons and Parallel Tasks are examples of strategies that teachers can use to differentiate mathematical instruction.Which problem below would provide students with choice?

Parents may be concerned when their child struggles with a single mathematics problem.Often parents see "fast" as successful.What is a reason that fast does not mean smarter?

21st Century teachers need to support students and parents in understanding the way mathematics is taught and learned.Identify the question below that a teacher should address about their pedagogy before it is asked by a parent.

What is the most critical aspect of the After phase of the lesson?

What statement represents how a teacher listens without evaluation?

Flexible grouping means that the size and makeup of the small group vary in a purposeful and strategic manner.Below are examples of considerations teachers must make in putting together mixed-ability groups.What statement reflects the shared responsibility?

The Duringphase of the lesson the teacher has to ask this question when determining what students need.

The focus of an inquiry lesson should be start with what method?

What is an example of the type of assessment question that is used in the Duringphase of the lesson?