This document discusses using problem based learning to teach functions in a 9th or 10th grade integrated math class. Problem based learning is a student-centered instructional strategy where students work in groups to solve problems based on prior knowledge or research. It allows students to develop problem solving skills and stimulates brain development. Throughout the unit, students will analyze functions using graphs and representations. They will be given word problems about pools filling with water to sketch and interpret graphs showing the relationship between depth and time. The goal is for students to be able to verbally describe functional relationships using mathematical terminology.

1.  
Shelly Gibson
DL 5103 Instructional Models for Digital Learning
September 22, 2013

2.  Problem Based Learning and Mathematics:
• Is an instructional strategy used to enhance learning
• Class is student centered
• Teacher is the facilitator
• Students to work in collaborative groups
• Students will plan a strategy to solve the problem based
upon prior knowledge, asking additional questions or
researching for additional information
• Students devise a plan, share knowledge with others
• They will present their conclusion by a presentation or
just share an answer

3. Problem based learning will allow the teacher to reach many different students with
various levels of abilities. By implementing problem based learning, students will
work through more complex problems and stimulate brain development
(Gasser, 2011)
Universal Design for Learning (UDL), encourages teachers to provide multiple ways
to present materials (CAST, 2011 ). The “what”, “how” and “why” of learning has
become the classroom mantra.
Throughout this unit on Functions, material will be presented in different ways.
Students will be assessed through online quizzes, mini projects and the final unit
test. Giving the students multiple ways to demonstrate their mastery is very
important. Finally, there will be various ways to engage students. One such way is
to have students use a graphing calculator and motion detector (CBR) to match their
movement to a graph. This will allow more kinesthetic or hands on learners to work
experience real-world context.

4.  Unit 2 – Functions
5 days (90 minutes)
 Integrated Math 1 (grade level 9th, 10th)
 CCSS: F-IF.4: Interpret functions that arise in applications
in terms of the context
 CCSS: F-IF.9: Analyze functions using different
representations
 Students will learn more about functions and their graphs
through the experience of problem solving.
 Essential Objectives:
o I can describe the relationship between two quantities by analyzing
a graph
o I can interpret key features and sketch graphs given a verbal
description of the relationship

5.  Two swimming pools are being filled at a constant rate. Cross
sections are shown below.
1. For each pool, write a description of how the depth in meters
of water in the pool varies with the time in minutes from the
moment the empty pool begins to fill.
2. Sketch a graph to show how the depth of the water in each
pool varies with time from the moment the empty pool begins to
fill.

6. Scaffolding Questions:
 How are the pools different?
 Which section of Pool B will fill first?
 What should the graph look like for Pool A? Pool B?
Extension Question:
 Describe a graph that represents the filling of a pool
whose shape is like a trapezoid. Graph the function on
your chart paper.

7.  Create a function (graph) depicting flow of water into a
pool with a student created pool design. Post on the
chart. As a team rotate from poster to poster (gallery
walk). Each team will analyze the graph and draw the
shape of the pool.
 EXAMPLE :
What would the cross section
of the pool resemble?

8.  Throughout the unit, students will practice graphing and
analyzing functions from website:
Click here for graphingstories.com

9. The goal of this unit is for students to be able to describe the relationship with
the domain and range values of a graph and what occurs when it produces a
function. They will be able to describe (verbally) a function using mathematical
terminology.
By providing multiple models for instruction, one being problem based
learning, my students will have a greater possibility of gaining knowledge in this
area of Algebra 1.

10. CAST (2011) Universal Design for learning guidelines version 2.0 Wakefield, MA: Author
Gallow, D. (2005) What is problem based learning? Retrieved from
htttp://www.pbl.uci.edu/whatispbl.html
Gasser, K. W. (2011). Five ideas for 21st century math classrooms. American Secondary
Education, 39(3), 108-116.
Thomas, J.W. (2000) A review of research on PBL. Retrieved from
http://www.bobpearlman.org/estPractices/PBL_Reserach.pdf