Lesson Title: F.BF.1 Lesson Quadratic Pattern (Bears)
Date: _____________ Teacher(s): ____________________
Course: Algebra I, Unit 4
Start/end times: _________________________
Lesson Objective(s): What mathematical skill(s) and understanding(s) will be developed?
F.BF.1 Write a quadratic function that describes a relationship between two quantities.
a. Determine an explicit expression, a recursive process, or steps for calculation from a context.
Lesson Launch Notes: Exactly how will you use the
first five minutes of the lesson?
Examine each table of values. Describe the pattern and
find the next term.
3
4
5
6
x
40
34
28
22
y
x
y
2
32
3
128
4
512
5
2048
x
y
1
4
2
8
3
14
4
22
Lesson Closure Notes: Exactly what summary activity,
questions, and discussion will close the lesson and provide
a foreshadowing of tomorrow? List the questions.
It is customary for athletes to shake the hands of opposing
players at the end of a game.
a. How many handshakes would take place between
an 8-player team and a 9-player team?
b. How many handshakes would take place between
a 12-player team and a 13-player team?
c. Write an equation for the number of handshakes
between a team with n players and a team with n –
1 players.
Emphasize that the third table does not have a common
difference or constant ratio and discuss the idea of
finite differences.
Lesson Tasks, Problems, and Activities (attach resource sheets): What specific activities, investigations,
problems, questions, or tasks will students be working on during the lesson?
Activity: The Bears Problem
1. Distribute “The Bear Problem” resource sheet. Say, “In a particular circus act there are six bears lined up on a
mat with seven squares. In this act, the Black Bears switch places with the Brown Bears following the given
rules:
 Bears may move by sliding.
 Bears may move by jumping one bear.
 Brown Bears must move only from right to left.
 Black Bears must move only from left to right.”
2. Students will work in groups to answer the following questions:
a. Determine how this act is accomplished. Be sure to explain your thinking. What moves are made?
How many moves are required to complete this trick?
b. How many moves would be required if there were 20 Black Bears and 20 Brown Bears on a mat with 41
squares? Explain how you determined your answer.
3. Groups will present their solutions and their strategies. (If you choose to have students complete and submit as a
project, have students complete a self-assessment prior to submitting.)
HCPSS Secondary Mathematics Office (v2); adapted from: Leinwand, S. (2009). Accessible mathematics: 10 instructional shifts that raise student
achievement. Portsmouth, NH: Heinemann.
Lesson Title: F.BF.1 Lesson Quadratic Pattern (Bears)
Course: Algebra I, Unit 4
Date: _____________ Teacher(s): ____________________
Start/end times: _________________________
Evidence of Success: What exactly do I expect students to be able to do by the end of the lesson, and how will I
measure student mastery? That is, deliberate consideration of what performances will convince you (and any outside
observer) that your students have developed a deepened (and conceptual) understanding.
Students will use the recursive pattern to generate a table and use finite differences to recognize that the pattern is
quadratic. Students will also write an explicit equation to model the quadratic relationship. Evidence of success will
be measured through the group presentations.
Notes and Nuances: Vocabulary, connections, common mistakes, typical misconceptions, etc.



This activity could also be completed as an out-of-class project. A rubric is attached.
Students have the opportunity to create a table or graph to help determine the equation. Students should not use
quadratic regression on the calculator to develop the relationship.
There is an optional applet at http://www.hellam.net/maths2000/frogs.html, but it uses frogs instead of bears.
Resources: What materials or resources are essential
for students to successfully complete the lesson tasks or
activities?
Homework: Exactly what follow-up homework tasks,
problems, and/or exercises will be assigned upon the
completion of the lesson?
“The Bears Problem” Resource Sheet (attached)
“The Bears Problem” Resource Sheet—Key (attached)
“The Bears Problem” Rubric (attached)
Markers or Teddy Grahams to represent the bears
Graphing calculator
Chart Paper
Finding Patterns and Graphing resource sheet (either
version)
(http://education.ti.com/calculators/downloads/US/Activiti
es/Detail?id=5753)
Lesson Reflections: What questions, connected to the lesson objectives and evidence of success, will you use to
reflect on the effectiveness of this lesson?
Can students recognize and use a recursive process to generate a table of data?
Can students use finite differences and the recursive pattern to develop a quadratic equation?
HCPSS Secondary Mathematics Office (v2); adapted from: Leinwand, S. (2009). Accessible mathematics: 10 instructional shifts that raise student
achievement. Portsmouth, NH: Heinemann.
Lesson Title: F.BF.1 Lesson Quadratic Pattern (Bears)
Date: _____________ Teacher(s): ____________________
Course: Algebra I, Unit 4
Start/end times: _________________________
HCPSS Secondary Mathematics Office (v2); adapted from: Leinwand, S. (2009). Accessible mathematics: 10 instructional shifts that raise student
achievement. Portsmouth, NH: Heinemann.
Lesson Title: F.BF.1 Lesson Quadratic Pattern (Bears)
Date: _____________ Teacher(s): ____________________
Course: Algebra I, Unit 4
Start/end times: _________________________
THE BEARS PROBLEM KEY
3 BROWN BEARS AND 3 BLACK BEARS
X
X
X
X
X
X
O
O
O
O
O
O
O
O
O
X
X
X
X
X
X
X
X
X
X
X
O
O
O
X
O
O
X
X
X
O
O
O
O
O
O
O
O
O
O
X
X
X
X
X
X
O
O
O
O
O
O
O
O
O
O
X
X
X
O
O
X
O
O
O
X
X
X
X
X
X
X
X
X
X
X
O
O
O
O
O
O
O
O
O
X
X
X
X
X
X
TOTAL MOVES = 15
TOTAL NUMBER OF EACH COLOR
1
2
3
4
5
n
MINIMUM NUMBER OF MOVES
3
8
15
24
35
2
n  2n
HCPSS Secondary Mathematics Office (v2); adapted from: Leinwand, S. (2009). Accessible mathematics: 10 instructional shifts that raise student
achievement. Portsmouth, NH: Heinemann.
Lesson Title: F.BF.1 Lesson Quadratic Pattern (Bears)
Date: _____________ Teacher(s): ____________________
Course: Algebra I, Unit 4
Start/end times: _________________________
The Bears Problem
Rubric
Item
Points Possible
The title page is neat and colorful.
2
The title page includes the title, your name,
date, and class.
3
The project is typed and neat.
5
The number of moves for switching 3 bears
on each side is given correctly.
The description of the steps required to
switch the bears is clear and correct.
A clear explanation of the logic involved in
selecting the appropriate moves is given.
The number of moves for switching 20
black bears and 20 brown bears is correctly
given.
A clear explanation or demonstration of
how the answer was determined is given.
Self Evaluation
Teacher
Evaluation
5
10
5
10
10
The self-evaluation was completed.
5
Total Points Possible
50
HCPSS Secondary Mathematics Office (v2); adapted from: Leinwand, S. (2009). Accessible mathematics: 10 instructional shifts that raise student
achievement. Portsmouth, NH: Heinemann.