Ralleia Experimental Primary Schools
Math Lessons with Operations: Euclidean Division
Teacher: Kotsiolis John - Petraki Evangelia
Class: F2 (ST2)
Objectives
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To learn how to divide natural numbers
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To learn and to distinguish when a division is perfect or incomplete.
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To learn that division is the inverse arithmetic operation of multiplication.
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To learn to calculate the quotient and the Euclidean division remainder of two integers.
Initial Situation in October 2016
(Why we decided to teach the specific subject)
Step 1
The choice of this particular subject is due to the fact that some students in F2 class have difficulty in finding the dividend as well as in understanding that division is the the inverse operation, the multiplication.
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What more is needed for the students to understand the specific subject?
A) A better enhancement of their cognitive abilities.
B) Study of the division of numbers that can be divided only by themselves and number 1.
C) Better understanding that division functions as an inverse operation of multiplication.
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Step 2
Initial Assessment Rubric
Below there are the questions and the answers (number of students) of the initial assessment rubric:
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1rst Scratch Lesson
Question 1: What is Euclidean division?
Highest score Moderate score Lowest score
13 9 4
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Question 2: What is called “quotient”?
Highest score Moderate score Lowest score
16 7 4
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Question 3: What is called “division remainder”?
Highest score Moderate score Lowest score
20 4 3
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Question 4: What are “multiples of a number”?
Highest score Moderate score Lowest score
13 7 7
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Question 5: Do you know that division functions as an inverse operation of multiplication?
Highest score Moderate score Lowest score
15 5 7
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Question 6: What is called “the divisor” of a number?
Highest score Moderate score Lowest score
17 4 6
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Question 7: What is called «the dividend” of a number?
Highest score Moderate score Lowest score
17 3 7
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2nd Scratch Lesson
Conclusions
a) Students increased their ability to recognize when a division is perfect or not (incomplete).
b) Students understood that division is the inverse operation of multiplication.
c) They learned to calculate the quotient and the remainder of the Euclidean division of two integers.
As a conclusion, scratch helped students to better understand mathematical concepts which were difficult for them.
Students' Scratch Projects
In the ICT school subject students created their own math quizes with scratch and practiced with Euclidean division. Though this procedure they got familiar with basic programming structures and concepts like if-then-else structure, lists, variables etc.