This document discusses using mathematical modelling in early grades to develop 21st century skills. It suggests providing students opportunities to solve authentic real-world problems from their own experiences. Examples of student work include generating problems and data, quantifying information, representing solutions, and communicating results. The document provides examples of turning word problems into mathematical equations and using real-world contexts to bring meaning to operations and concepts. It advocates for using a mathematics laboratory for students to explore ideas through games and puzzles in a low-stakes environment. Critical thinking, communication, collaboration, and creative problem solving are skills that can be developed through posing problems based on real phenomena and evaluating models and solutions. An example problem and approach is provided for planning a family vacation trip

1. MATHEMATICAL MODELLING IN
EARLY GRADES

2. Development of 21st Century
Skills
Mathematics involved in the real world requires:
 Recognising where mathematics is applicable,
 Translating practical problems into
mathematical problems,
 And interpreting and evaluating the outcomes.
Developing these essential skills to solve problems
can be nurtured as early as elementary grades, by
providing students with opportunities to engage in
solving authentic real – world problems within
their world.

3. Associated Student Work
 Generating problems
 Generating data
 Quantifying information
 Representing solution
 Communicating results.

4. Make a Real- Life Problem
60 X 7

5. Make a Real- Life Problem
3¼÷½

6. Take some thing (chapatti, land,
cookies, etc.) and divide equally
among two people?

7. So what about this one?
3¼÷ 2

8. Division by a Fraction
Two meanings of division - share and quotient [e.g. 20
divided by 4]
Two types of questioning
So what would it mean when I say 3 divided by 1/2
Change in number system has changed the meanings of the
operation

9. How to understand division by
a fraction?
Two meanings of division - share and quotient [e.g. 20
divided by 4]
Two types of questioning
So what would it mean when I say 3 divided by 1/2
Change in number system has changed the meanings of the
operation

10. Real Contexts Role in
Mathematics
O Bring meanings to
operation, entities
and rules [e.g.
BODMAS]
O We have been
hearing that Math
let us understand
reality better, but
also reality makes
us understand
math better!

11. What is the area of this figure?

12. What is the area of this new
assembled figure?

13. Change in Area
• How did the area increase?
• Is that possible, can we
increase the area if we make
some cuts within a shape?

18. Mathematics Laboratory
O A place to explore
mathematics ideas
through games and
puzzles.
O NOT as a tool for
assessment, rather an
aid in
learning/exploring.
O The materials can be
used by students as
well as by teachers.
MATHS LAB

19. Mathematics Laboratory

20. Homi Bhabha Centre for Science Education: http://
www.hbcse.tifr.res.in
 MathEdu@HBCSE: https://mathedu.hbcse.tifr.res.in
 Vigyan Pratibha Learning Units:
https://vigyanpratibha.in/ index.php/learning-
units/#9th-mathematics
 Vigyan Pratibha Learning Bytes:
https://drive.google.com/
drive/u/2/folders/1hmf9OQr57lSisLsK_Qt5u1XA8F5
7gAvS
 Mathematics Teachers’ Association (India): https://
www.mtai.org.in/

21. https://mathedu.hbcse.tifr.res.in

22. What Can We Develop
 Mathematical modelling is “a process
that uses mathematics to represent,
analyse, make predictions or
otherwise provide insight into the
real-world phenomena”
 A grade wise activity that involves
mathematising reality.

23. Critical Thinking
Communication
Collaboration
Creative
Problem Solving
Pose a problem
based on a real
phenomenon
Evaluate the
model/solution
based on the
real
Analyse and
revise if
necessary
Gather
information,
make
assumptions and
define variables
Build a Model
/Solution.

24. Example Work by a Teacher
 Your family is going on vacation this summer.
What is the best way to get your family to visit
city in only one day. Constraints given to the
students were a Rs. 2500 family budget,
timeline of one day from 6:30 a.m. to 11:59
p.m., the chosen city must be within a the
state they live in or nearby state area, they
must see three different tourist sites, and must
eat at least two meals.

25. How to use the Scenario to
develop 21st Century Skills?
1) Defining the task by posting a
mathematics problem;
2) Considering the variables;
3) Building a solution;
4) Creating a generalised model;
5) Evaluating the “best” trip

26. (1)Defining the task by posting
a Mathematics Problem
What is our budget?
What mode of transportation can we use
to get there?
What mode of transportation can we use
while we are there?
What sites do we want to see in this city?
What sites can we skip while there?

27. (2) Considering the
Variables
Figure out the price of food depending on how
much people eat that led to the question of :
 What is the relation between the price of
food and the number of people eating the
food?
Figure out the price of transportation
depending on the time of year and place, that
led to the question of:
 What is the best way to get to the
destination? Considering choices between
driving a car, taking a train, subway, or
plane. How will traffic be accounted for?
 Considering how weather could be a factor
when planning a trip.

28. (3) Building a solution
 Does our answer/solution make sense?
 How does our answer compare to the
problem?
 Is there another solution we could look at?
 What are the strengths of or model?
Where could our model use some
improvements?
 Are there any factor or ideas we haven’t
considered.

29. (4) Creating generalised
The teacher in this class, used this
opportunity to introduce Excel Sheet
to 4th Graders.

30. (5) Critiquing and Defending
their best Trip
In defending their best trip, students had an
opportunity to offer their rationale for why
their trip was the best. Some cited that their
trip was the best because it was
 the most economical and fun,
 the closest and fun,
 the most entertaining for all age groups,
These criteria led to a great discussion with
the teacher.

31. Work for Today
Individual task
1) Solve the city tour problem yourself-
Give responses for each of the five
stages.
2) Design one math game- that bridges
math and reality gap.
Group Task
1) Design one scenario for your students.
Write details for each stage.