DP pilot unit planner 1
Teacher(s) Melanie Parker
Course Unit 5: Mathematics
part and
topic
Subject group and course TOK
SL or HL/Year 1 or 2 1
Unit description and texts
DP assessment(s) for unit
Mathematics is explored through the knowledge framework and
the construction of knowledge. Students will evaluate
knowledge claims and counter claims.
Mini Essay
Dates 7-8 weeks
INQUIRY: establishing the purpose of the unit
Transfer goals
List here one to three big, overarching, long-term goals for this unit. Transfer goals are the major goals that ask students to “transfer” or apply,
their knowledge, skills, and concepts at the end of the unit under new/different circumstances, and on their own without scaffolding from the
teacher.
Students will make connections between a critical approach to the construction of knowledge, the academic disciplines, and the wider world.
Students will examine how academic disciplines/areas of knowledge generate and shape knowledge.
Students will explore the links between knowledge claims, knowledge questions, ways of knowing, and areas of knowledge.
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ACTION: teaching and learning through inquiry
Content/skills/concepts—essential understandings
Learning process
Check the boxes for any pedagogical approaches used
during the unit. Aim for a variety of approaches to help
facilitate learning.
Students will know the following content:
Knowledge Framework
Learning experiences and strategies/planning for selfsupporting learning:
Axioms
Lecture
Euclid’s Model of Reasoning
Socratic seminar
Nature of Propositions
Small group/pair work
Views of Mathematical Knowledge
PowerPoint lecture/notes
Individual presentations
Students will develop the following skills:
Group presentations
Stating and defending knowledge claims and counter-claims
Student lecture/leading
Writing the TOK essay
Interdisciplinary learning
Other/s:
Students will grasp the following concepts:
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Details: See Lesson Plans
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Alternative Geometries
Formative assessment:
Math vs. Applied Math
Bellringers
Math in Art and Nature
Group Assignments
Math as a Language
Journals
Beauty in Math
Further Reading
Visible Thinking Strategies
Summative assessment:
Mini-essay
Differentiation:
Affirm identity—build self-esteem
Value prior knowledge
Scaffold learning
Extend learning
Details:
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Students access prior knowledge from maths classes.
Scaffolded instruction for essay in claims and counterclaims. Extend understanding of mathematics through
ways of knowing and group research.
Approaches to learning (ATL)
Learner Profile
Check the boxes for any explicit approaches to learning connections
made during the unit. For more information on ATL, please see the
guide.
Thinking
Inquirers
Social
Knowledgeable
Communication
Thinkers
Self-management
Communicators
Research
Principled
Details:
Open-minded
Critical Thinking Skills: Gather and organize relevant information to
formulate an argument. Evaluate evidence and arguments. Develop
contrary or opposing arguments.
Communication Skills: Read critically and for comprehension.
Structure information in summaries, essays and reports.
Caring
Risk-Takers
Balanced
Reflective
Details:
Knowledgeable
TOK students strive to be knowledgeable about the nature of
knowledge. This means becoming knowledgeable about the methods
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of inquiry of a variety of subject areas, from a number of perspectives.
Students are encouraged to explore the processes by which
individuals arrive at their own knowledge and understanding of the
world and the presuppositions that underpin this understanding.
Language and learning
TOK connections
CAS connections
Check the boxes for any explicit language and
learning connections made during the unit. For
more information on the IB’s approach to
language and learning, please see the guide.
Check the boxes for any explicit TOK
connections made during the unit
Check the boxes for any explicit CAS
connections. If you check any of the boxes,
provide a brief note in the “details” section
explaining how students engaged in CAS for
this unit.
Activating background knowledge
Personal and shared knowledge
Creativity
Scaffolding for new learning
Ways of knowing
Activity
Acquisition of new learning through practice
Areas of knowledge
Service
Demonstrating proficiency
The knowledge framework
Details:
Details:
Background Knowledge: students’ knowledge of
mathematics
Introduction, definition, and practice
Details:
Scaffolding: building knowledge claims and
knowledge questions and counter claims
New Learning: group presentation assignments
Resources
List and attach (if applicable) any resources used in this unit
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See http://qaktok.weebly.com/unit-5-references.html
Lesson Plans
Week
Content
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Knowledge Framework—1
1. Bellringer—3-2-1
2. What is the knowledge framework? Peeling the fruit diagram—skin (class display, students can add post-its throughout
unit)
3. Group Activity—Distribute knowledge framework templates and the explanations. Each group is responsible for 1 of the
key features of the knowledge framework. As a group, they should research and prepare a 5 minute presentation on this
key feature.
Assignment—work on group presentation
Knowledge Framework—2
1. Bellringer--Division
2. Research and prepare
Assignment—complete group presentation
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Knowledge Framework—3
1. Bellringer—Under the Skin
2. Presentations—Students take notes on the Knowledge Framework template
3. TPS—Headlines (17 vt)/peeling the fruit--getting under the skin—Think about all we have been talking about today in
class. If you were to write a newspaper headline for this topic right now, what would that headline be? Share your
headline with your neighbor. Who heard a headline from someone else that they thought was particularly good at
getting to the core of things? Someone record responses.
Assignment: Work on Unit 3 Tasks
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Intro to Maths
1. Bellringer—Questionnaire
2. What is Maths?
3. Maths Scavenger Hunt—take students outside to find math. Students will have cameras to take pictures of x examples of
maths. Give no further instructions. Students return to classroom and prepare simple slideshow with a one sentence
explanation for each picture—how it is math. Share with teacher by airdrop.
Assignment: Work on Unit 5 Tasks
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Axioms
1. Bellringer—View slideshows on class website and complete handout.
2. Invent a game—groups: 1s, 2s, 3s, 4s
a. brainstorm ideas for a game that makes use of the three objects given to them or selected by them.
b. write clear rules for their game.
3. Share/Discuss—What were your rules? Why are rules important?
4. Phase 2—new groups: 1 + 2 + 3 + 4
a. Play a game using the common objects, but follow the rules your original group created.
5. Share/Discuss—What happened? Why? What about the rules? What does this tell us about rules?
6. Axioms
7. How did this activity parallel the nature of axioms?
Assignment: Work on Unit 5 Tasks Make a list of “axiomatic” truths. Does not have to be related to math.
Euclid’s Model of Reasoning
1. Bellringer—Axiomatic Truths
2. Euclid’s Model of Reasoning
3. Geometries Research
Assignment:
Complete/practice presentation.
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Justifying Mathematic Knowledge Claims
1. Bellringer—Presentation Prep
2. Presentations
3. Justifying Knowledge Claims
Assignment: Work on Unit 5 Tasks. Find out answers to Goldbach’s conjecture
Is Math Certain?
1. Bellringer—Math and Faith
2. Nature of Propositions
3. 3 Views of Mathematical Knowledge
4. Is math invented or discovered?
Assignment: Prepare for debate. Work on Unit 5 Tasks.
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Invented or Discovered?
1. Bellringer—Prepare for debate
2. Debate
Assignment: Work on Unit 5 Tasks
More Math
1. Bellringer--Solve and show work.
2. Research and prepare presentation on pure math vs applied math, math in art and nature, math as a language, beauty in
math
Assignment: Prepare for presentation. Work on Unit 5 Tasks
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Presentations
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Essay Prep
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Essay Prep
Assignment: Essay due next class
Stage 3: Reflection—considering the planning, process and impact of the inquiry
What worked well
What didn’t work well
Notes/changes/suggestions:
List the portions of the unit (content,
assessment, planning) that were successful
List the portions of the unit (content,
assessment, planning) that were not as
successful
List any notes, suggestions, or considerations
for the future teaching of this unit
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