This document provides an overview of a presentation template for a discrete mathematics and probability course for 11th grade. The template includes slides on various mathematical topics like problem-solving strategies, mathematical modeling, and the integration of technology tools in mathematical exploration. It also includes example slides demonstrating concepts, problem-solving approaches, and real-world applications of mathematics.

1. Discrete Mathematics:
Combinatorics and
Probability
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11th Grade

2. Contents of this template
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3. Mathematical
modeling
01
Problem-solving
strategies
Mathematics and
technology
Table of contents
Identifying mathematical
concepts in real-world scenarios
Critical thinking skills and
mathematical reasoning
Analyzing and interpreting
mathematical models
Integration of technology tools
in mathematical exploration
03
02
04
Mathematics in
everyday life

4. Introduction
From mathematical modeling to the
integration of technology tools, these
lessons empower students to
appreciate the versatility and relevance
of mathematics across diverse
contexts. Through this comprehensive
approach, students not only master
mathematical concepts but also
develop essential skills for navigating
the complexities of the modern world
In high school and middle school math
lessons, students delve into various
engaging topics. They explore
problem-solving strategies, honing
critical thinking and logical
reasoning skills. Additionally, at that
age, math lessons focus on the
practical application of mathematics,
revealing its role in everyday life

5. Problem-solving
strategies
01
Apply problem-solving strategies in various contexts

6. How to solve math
problems
In the dynamic landscape of mathematics, honing
effective problem-solving skills is paramount
● Analytical thinking
● Strategic planning
● Effective communication
In cultivating these problem-solving skills, you will
gain not only mathematical proficiency but also tools
for addressing challenges across disciplines

7. Analytical thinking
A systematical and logical approach
to mathematical problems is the
foundation for many disciplines
Cultivate the ability to break down
complex problems into several
manageable parts
Break down
complex problems
Systematic and
logical approach

8. Structure mathematical
reasoning coherently in a
logical sequence
The use of diagrams, graphs,
and charts to supplement
written explanations
Mastering mathematical communication
The importance of
articulating mathematical
ideas with precision
Engage with peers'
mathematical explanations
and provide feedback
Justify mathematical
solutions, providing proof to
validate conclusions
Adapt your communication
style to different audiences
to convey ideas
Clarity and
precision
Logical
organization
Visual
representation
Active
listening
Justification
and proof
Versatile
communication

9. Patterns, precision
and problem-solving

10. Mathematics is the tool that turns curiosity into discovery

11. 123,000
Numbers unfold as a canvas of infinite potential

12. Let’s use some percentages!
25% of the math
curriculum is dedicated
to theoretical knowledge
Theory
50% of the curriculum is
spent creating a solid
understanding of maths
Foundation
75% of the curriculum
cultivates advanced
analytical skills
Exploration
50% 75%
25%

13. Milestones in mathematics
300 BCE
Euclid publishes "Elements"
17th century
The development of calculus
1931
Gödel's Incompleteness Theorem
1994
Proof of Fermat's Last Theorem
01 02 03 04

14. Display concepts visually
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Concept 1
Concept 3
Concept 2
Briefly describe the
concept here
Concept 4
Briefly describe the
concept here
Briefly describe the
concept here
Briefly describe the
concept here

15. Rubric
Criteria Exceptional (4) Proficient (3) Basic (2) Limited (1)
Conceptual
understanding
Deep, insightful
mastery of concepts
Solid understanding
and application
Basic grasp,
occasional struggles
Limited
understanding,
frequent errors
Problem-solving
skills
Exceptional, creative
problem-solving
Strong skills with
various strategies
Basic skills, occasional
struggles
Limited ability,
frequent challenges
Communication of
ideas
Clear, precise
communication
Effective expression of
mathematical ideas
Adequate but may lack
precision
Struggles to
communicate clearly
Accuracy of
calculations
Exceptional accuracy
in computations
High accuracy in
routine calculations
Basic accuracy,
occasional errors
Frequent errors in
calculations

16. Short answer questions
The students should read the following questions and answer them in their paper. These
questions require students to demonstrate their understanding of key concepts
How would you write an algebraic expression for "three times the sum of a
number and 5"?
Can you explain the distinction between the area and perimeter of a
shape? Provide an example for each
What is the result when you add 1/3 and 1/4? Express your answer as a
simplified fraction
01
02
03

17. Budgeting for a trip
Real-life application
Topics
Personal finance
Architectural design
Epidemiology
Divide the class into small groups of 3-5 students. Assign each group a real-life application
for which they will have to use math concepts to solve
Consider transportation,
accommodation, meals and
other activities
Design a floor plan,
calculating the area of each
room with proper proportions
Include expenses like rent,
utilities, groceries and
entertainment
Using statistical methods,
analyze data on infection and
recovery rates
01 02
03 04

18. Mathematical investigation
Students will have to delve into a specific mathematical concept
or problem, explore it in-depth, and present their findings
1. Choose a number sequence: Ask each student to select a
number sequence that interests them
2. Investigate the pattern: Instruct them to explore the
pattern within their chosen number sequence
3. Apply mathematical concepts: They should apply relevant
mathematical concepts to their investigation
4. Solve problems: They have to create and solve problems
related to their chosen sequence
5. Create a portfolio: Instead of a traditional essay, ask them
to compile their findings into a portfolio and present it

19. Conclusions
Recap the main
mathematical concepts
covered during the lesson
Emphasize the practical
relevance of the concepts
and skills of the lesson
Provide a glimpse into the
upcoming lessons for
continuity of learning
Summarize
key concepts
Real-world
applications
Preview
next steps

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