Assignment 2
Teaching Perimeter and Area to Grade 5 Through Hands-on Learning
Abstract
This paper presents my real classroom experience while teaching the topic of Perimeter and Area to Grade 5 students. I used hands-on activities, real-life examples, and group work to make students understand the concept deeply. The experience showed that when learners explore, measure, and discuss on their own, they not only enjoy Mathematics but also develop a strong conceptual foundation.
1. Introduction
Teaching Mathematics to young learners is always a creative challenge. Students often find topics like perimeter and area confusing when taught only through formulas. I wanted my students to understand these ideas in a fun, practical way. So, I decided to design an activity that would help them experience the difference between “boundary” and “space inside” using real objects and materials from their daily life.
2. Classroom Context
This experience took place in my Grade 5 Mathematics class of 30 students. The topic was “Perimeter and Area of Rectangles and Squares.” I had noticed earlier that students easily memorised formulas but mixed up when to use which one. For example, some students calculated the area when the question asked for the perimeter.
To help them, I planned a hands-on learning activity using chart paper, rulers, and graph paper, so that they could measure, calculate, and visualize the concepts themselves.
3. The Experience
I began the lesson by asking:
“If we want to put a fence around our school ground, are we finding the perimeter or the area?”
Students shouted different answers. I didn’t correct them immediately. Instead, I divided the class into groups and distributed rectangular paper sheets and rulers.
Each group had to:
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Measure the length and breadth of their rectangle.
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Find the perimeter by adding all the sides.
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Find the area by multiplying length × breadth.
As they worked, I noticed that some groups got confused, some debated the right formula, and others started comparing their results. I allowed them to explore and make mistakes. After 15 minutes, we discussed their findings on the board.
They were surprised to see that two rectangles could have the same perimeter but different areas. This curiosity led them to understand why both concepts are related but not the same.
Later, I gave them graph paper to draw rectangles and count squares to find the area visually. The visual approach made the idea much clearer.
Finally, I related it to real-life examples:
By the end of the session, most students were confidently using both terms correctly.
4. Reflection and Learning
This experience taught me that students learn better when they explore first and are taught later. Letting them discover through trial and error helped them retain the concept longer.
I also realised that:
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Concrete learning builds strong understanding: Manipulatives and measurements helped students connect abstract formulas to real life.
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Active participation improves memory: Students remembered the formulas better because they found meaning in them.
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Group work encourages learning from peers: Children explained and corrected each other’s mistakes in simple language.
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Mistakes are valuable: Instead of being afraid of errors, students learned through them—making failure truly productive.
5. Conclusion
This classroom experience was a reminder that Mathematics can be joyful when taught through activity and exploration. My students not only learned how to calculate perimeter and area but also understood when and why to use them. As a teacher, I felt proud watching them discover answers on their own. It strengthened my belief that real learning happens when children are allowed to do, think, and reflect.
Assignment 3
Title:
Learning Through Struggle: The Role of Safe Failure in Teaching Measurement
Abstract
This research explores how allowing students to experience productive failure—safe and guided struggle—enhances their understanding of the concept of Measurement. Conducted with Grade 4 students, the study examined how emotional safety and reflection after mistakes improved problem-solving ability, motivation, and confidence. Findings revealed that when students are encouraged to attempt problems before direct teaching, their conceptual clarity and participation increase significantly.
Introduction
Measurement is an important part of mathematics that connects directly to real-life experiences. Yet, many students struggle with unit conversions and practical understanding.
According to Manu Kapur’s theory of Productive Failure, learners develop deeper conceptual understanding when they are allowed to explore, make mistakes, and reflect on them before formal instruction.
This paper demonstrates how creating emotionally safe learning spaces helped students understand and apply conversion rules such as SBD (Smaller to Bigger – Divide) and BSM (Bigger to Smaller – Multiply).
Objectives
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To study the impact of guided struggle on students’ understanding of Measurement.
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To promote emotional safety and reduce fear of mistakes.
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To build problem-solving confidence and resilience among learners.
Methodology
Procedure:
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Students were given practical problems such as estimating the capacity of bottles or comparing object lengths without prior teaching.
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They attempted conversions on their own and made observations.
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Later, I introduced the rules of conversion:
Students practised conversions using real-life examples and reflected on where they went wrong earlier.
Findings
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Students initially confused the direction of conversion but became confident after understanding the SBD and BSM rules.
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Discussions of mistakes made them more alert and motivated.
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Conceptual understanding and test scores improved significantly.
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Students could relate conversions to daily life (e.g., litre–millilitre in kitchen, metre–centimetre in the classroom).
Conclusion
Allowing safe struggle before teaching concepts in Measurement helps students think critically and connect learning with real life. When emotional safety and reflection are part of classroom culture, failure becomes a bridge to understanding rather than a barrier. The use of SBD and BSM rules gave them a clear and simple method to remember conversions.
Assignment 4
Title:
Activating Prior Knowledge: A Key Understanding to Decimals
Abstract
As a mathematics teacher, I have often noticed that students struggle to grasp the concept of Decimals, especially when they fail to see its connection to what they already know—whole numbers and fractions. This research explores how activating students’ prior knowledge before teaching decimals makes learning smoother, more meaningful, and long-lasting. The findings show that when students recall and relate their existing knowledge, they not only understand decimals better but also participate more confidently in class.
Introduction
While teaching decimals in Grade 5, I realized that many children find it abstract and confusing. They often mix up tenths and hundredths or fail to understand the value of digits after the decimal point. I understood that instead of directly teaching the topic, it was more effective to begin by activating their prior knowledge—the understanding they already had about place value, fractions, and real-life examples like money or measurements.
This approach is supported by Manu Kapur’s concept of Productive Failure, where students are encouraged to explore and make sense of new concepts through their existing understanding, even if it includes initial errors.
Objectives
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To connect the topic of decimals with students’ prior understanding of whole numbers and fractions.
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To make learning more meaningful by linking it to real-life examples.
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To help students gain confidence and actively participate through discussion and reflection.
Methodology
Before introducing the topic, I started with a simple discussion:
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Have you seen prices like ₹25.50 or marks like 8.25 out of 10?
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What do you think the dot (.) means?
Students began sharing examples from shopping, fuel prices, and scorecards. I then asked them to relate these to fractions (e.g., 0.5 as ½ or 0.25 as ¼).
This discussion helped me assess what they already knew and identify misconceptions.
After this, I formally introduced decimals—explaining tenths, hundredths, and thousandths using a place value chart and real-life examples like money and measurements.
Students practised writing decimals, converting them into fractions, and representing them on number lines.
We ended with a reflection where students wrote what new ideas they had formed and what they already knew before.
Findings
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Students were able to connect decimals with familiar contexts like money and fractions.
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Misconceptions such as “0.05 is greater than 0.5” reduced significantly.
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Participation increased because the lesson started with what they already understood.
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The class became more interactive, and students showed more confidence in expressing their thoughts.
Teacher’s Reflection
This activity reminded me how important it is to start where the learner is. When I allowed students to recall their previous knowledge and share experiences, they became more involved and curious.
Activating prior knowledge not only helped in understanding decimals but also developed their reasoning and problem-solving skills.
As a teacher, I learned that connecting lessons to students’ lived experiences and past learning is the foundation of meaningful teaching.
Conclusion
Activating prior knowledge transforms the classroom into an engaging and thinking space. In the topic Decimals, it made students feel capable and confident, reducing their fear of mistakes.
Learning became more than memorising—it became connecting, reflecting, and discovering.
As a teacher, I realised that before introducing any new concept, it is essential to unlock what students already know.
Assignment 5
Title:
Task Design Matters: Enhancing Collaboration and Discussion in Simplification
Abstract
As a mathematics teacher, I observed that while students in Class 5 could perform basic operations, they often got confused while solving mixed-operation problems in the chapter Simplification. This research explores how thoughtful task design and collaborative discussion can improve understanding. Inspired by Manu Kapur’s concept of Productive Failure, I redesigned activities to encourage exploration, peer discussion, and self-correction before formal explanation. The results showed a significant increase in student engagement, conceptual understanding, and confidence.
Introduction
In traditional math classes, students are often given direct exercises for Simplification, like:
25 + 5 × 2 − 10 ÷ 5,
without being encouraged to think why they must follow the order of operations (BODMAS).
I noticed that students applied rules mechanically without truly understanding them.
To address this, I implemented task-based learning where students explored simplification problems through collaboration and guided struggle.
As Manu Kapur suggests, when students are allowed to face initial confusion and collaborate to solve challenging tasks, their eventual understanding becomes deeper and more meaningful.
Objectives
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To improve students’ understanding of the BODMAS rule through well-designed collaborative tasks.
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To enhance group discussion, reasoning, and explanation during problem-solving.
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To analyse how productive struggle supports learning in Simplification.
Methodology
Procedure:
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I began by giving students a real-life situation:“Ravi has ₹25, buys 3 pencils costing ₹5 each, and then gives ₹10 to his friend. How much money is left?”Students were asked to write and solve this as a mathematical expression.
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Most students wrote different expressions and got varying answers. I did not correct them immediately.
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In groups of 4, they discussed their reasoning, compared answers, and tried to find out why results were different.
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After the discussion, I guided them towards the correct approach using BODMAS, connecting it to their earlier work.
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Students then solved a set of progressively challenging problems (task ladder)—from simple mixed operations to multi-step word problems.
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Finally, students reflected on what they learned through group work and self-discovery.
Findings
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Initially, only 30% of students could solve mixed-operation problems correctly.
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After collaborative discussion and teacher facilitation, accuracy improved to 85%.
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Students began explaining why multiplication or division must come before addition or subtraction.
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They became more confident and curious about the logic behind the rule rather than just memorising it.
Teacher’s Reflection
I realised that the key to learning Simplification was not in repetition, but in how tasks were designed. When problems were real, slightly challenging, and open for discussion, students naturally collaborated and thought critically.
Allowing them to first struggle and debate helped them internalize the logic of BODMAS. I shifted from being an instructor to a facilitator—guiding reflection rather than giving answers.
Conclusion
This study reaffirmed that Task Design Matters. When students engage in collaborative exploration before instruction, they construct knowledge meaningfully.
Through productive struggle and peer discussion, learning becomes active, deep, and joyful.
In the context of Simplification, this approach transformed confusion into clarity and hesitation into confidence.
Sunbeam School Indiranagar
