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Chapter 4: Planning in the Problem-Based Classroom
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or
answers the question.
1) 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.
2) 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.
3) 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 Before related agendas?
A) Be sure the task is understood.
B) Let go.
C) Provide extensions.
D) Identify future problems.
4) 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.
Answer: D
5) 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.
6) The During phase of the lesson the teacher has to ask this question when determining what
students need.
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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?
7) 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?
8) 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.
9) 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?
10) 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.
11) 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?
12) What is an example of the type of assessment question that is used in the During phase 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?
13) Asking quality questions are critically important to the potential learning. What question
below would solicit higher-level responses from students?
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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?
14) Learning centers 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.
15) 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.
16) 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?
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.
18) 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?
19) Parents may be concerned when their child struggles with a single mathematics problem.
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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.
20) 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.
Essay. Write your answer in the space provided or on a separate sheet of paper.
21) Identify three strategies that teachers can use to build strong rapport with all families to
support the learning of mathematics.
6. Put homework on your webpage
22) What are two advantages of flexible grouping related to differentiation of instruction?
