Download Discovering The Fibonacci Sequence

Model Mathematics Curriculum
Unit Implementation Plan
UNIT COVER SHEET
Name:
_Jim Clanin________
Unit Title:
Unit 5: Representations of Sequences and Linear Relations
Dates of Instruction:
Grade Level:
Math 1______
December 7, 2015-December 11, 2015
Timeframe (Add days as needed)
Unit Timeframe: 165-220 Hours
Day 1:
Dec. 7, 2015
Lesson/task/assessment:
Pre-assessment
Day 2:
Dec. 8, 2015
Lesson/task/assessment:
Discovering patterns in
sequences
Day 3:
Dec. 9, 2015
Lesson/task/assessment:
Transitioning sequences to
formulas
Day 4:
Dec. 10, 2105
Lesson/task/assessment:
Discovering The Fibonacci
Sequence
Day 5:
Dec. 11, 2015
Lesson/task/assessment:
Toothpick House
Standards Alignment
Content Standards:
F.IF.3 Recognize that sequences are functions, sometimes defined recursively, whose
domain is a subset of the integers. For example, the Fibonacci sequence is defined
recursively by f(0) = f(1), f(n+1) = f(n) + f(n-1) for n ≥ 1.
F.BF.2 Write arithmetic sequences both recursively and with an explicit formula, use
them to model situations and translate between two forms.
A.CED.1 Create equations in one variable and use them to solve problems. Include
equations arising from linear functions.
A.CED.2 Create equations in two or more variables to represent relationships between
quantities; graph equation on coordinate axes with labels and scales.
Standards for Mathematical Practice:
MP2-Reason abstractly and quantitatively
MP3-Construct viable arguments and critique the reasoning of others
MP4- Model with mathematics
MP6- Attend to precision
MP7- Look for and make use of structure
MP8- Look for and express regularity in repeated reasoning
Model Mathematics Curriculum
Unit Implementation Plan
UNIT: ______________5__________________
DAY: _____1_______
DAILY LESSON PLAN
Objectives
Check students’ knowledge of linear functions.
Content
Standards
F.IF.3, F.FB.2, A.REI.10, A.CED.1, A.CED.2, F.LE.1a, F.LE.1b, F.IF.7a
Mathematical
Practices
Materials
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning
of others
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
Unit 5 Pre-Assessment
Preparation
None
Lesson
Activities
None
Assessments
Unit 5 Pre-Assessment
In what ways will you intentionally emphasize the development of student
mathematical practices through this lesson?
Model Mathematics Curriculum
Unit Implementation Plan
UNIT: ______________5__________________
DAY: _____1_______
DAILY LESSON PLAN
Objectives
Introduce discovering patterns and writing them in an notation.
Content
Standards
F.BF.2, F.IF.3
Mathematical
Practices
Materials
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning
of others
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
Discovering Patterns in Sequences worksheet
Preparation
None
Lesson
Activities
Distribute Discovering Patterns in Sequences sheet. Teacher
Notes/Reflections:
As a class, guide the students through the first example –paying particular
attention to an and an+1 notation.
Have students either individually or in pairs, complete the rest of the
worksheet.
Encourage students to come up with as many equations as they can for
#4.
Assessments
Discovering Patterns in Sequences worksheet
In what ways will you intentionally emphasize the development of student
mathematical practices through this lesson?
MP7 and MP 8 will be emphasized when finding common differences so that sequences can
be expressed in an and an+1 notation.
Model Mathematics Curriculum
Unit Implementation Plan
UNIT: ______________5__________________
DAY: _____1_______
DAILY LESSON PLAN
Objectives
Students will take prior knowledge of sequences to create Explicit
Formulas for the sequences.
Content
Standards
F.BF.2, F.IF.3
Mathematical
Practices
3. Construct viable arguments and critique the reasoning of others.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
Materials
Transitioning from Sequences to Formulas worksheet
Preparation
None
Lesson
Activities
Distribute the Transitioning from Sequences to Formulas handout
provided. Teacher Notes/Reflections:
Have students complete the first column of identifying the term values.
Ask students how they determined the values of the different term
numbers.
Demonstrate to the students how to show the “what math did we do to get
here?” and “Can we find a pattern”.
Have students complete the information to the second sequence.
As a class, see if they can determine the pattern for the Explicit Formula,
if not, help the students find the pattern.
Have the students, either in pairs or independently, complete numbers 4,
5, 6, and 7.
Assessments
Transitioning from Sequences to Formulas worksheet
In what ways will you intentionally emphasize the development of student
mathematical practices through this lesson?
MP3 will be emphasized by having students discuss how they developed their formulas for
the given sequences.
Model Mathematics Curriculum
Unit Implementation Plan
UNIT: ______________5__________________
DAY: _____1_______
DAILY LESSON PLAN
Objectives
Students will explore and apply the Fibonacci Sequence
Content
Standards
F.BF.2, F.IF.3
Mathematical
Practices
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
Materials
Discovering the Fibonacci Sequence
Discovering the Fibonacci Sequence Observational Checklist
Choice Menu
Preparation
None
Lesson
Activities
Pass out Discovering the Fibonacci Sequence.
Teacher uses the Discovering the Fibonacci Sequence Observational
Checklist.
Students Jigsaw and share their answers –teacher clarifies any
misunderstandings.
Assign Choice Menu for an assessment.
Assessments
Choice Menu
In what ways will you intentionally emphasize the development of student
mathematical practices through this lesson?
MP7 will be emphasized by ensuring students discover the Fibonacci Sequence.
Model Mathematics Curriculum
Unit Implementation Plan
UNIT: ______________5__________________
DAY: _____1_______
DAILY LESSON PLAN
Objectives
Students will create patterns with toothpicks and find a matching algebraic
pattern. Students will use their graph and equations to predict the number
of toothpicks needed given a number houses. Students will use their
equations to predict the number of houses given a number of toothpicks.
Content
Standards
A.CED.1, A.CED.2
Mathematical
Practices
1 Make sense of problems and persevere in solving them
4 Model with mathematics
6 Attend to precision
Materials
Toothpick Houses
Toothpicks
Preparation
None
Lesson
Activities
Have students work independently or with a partner.
Pass out Toothpick Houses and approx. 50 toothpicks.
Students Jigsaw and share their answers – teacher clarifies any
misunderstandings.
Assessments
None
In what ways will you intentionally emphasize the development of student
mathematical practices through this lesson?
MP6 will be emphasized by requiring students to explain their findings using the proper
mathematical terms and by using expressions applicable to the problem.