##### Ralleia Experimental Primary Schools

Math Lessons with Operations: Euclidean Division

Teacher: Kotsiolis John - Petraki Evangelia

Class: F2 (ST2)

Objectives

1. To learn how to divide natural numbers

2. To learn and to distinguish when a division is perfect or incomplete.

3. To learn that division is the inverse arithmetic operation of multiplication.

4. 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.

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.

Step 2

Initial Assessment Rubric

Below there are the questions and the answers (number of students) of the initial assessment rubric:

1rst Scratch Lesson

Question 1: What is Euclidean division?

Highest score                Moderate score                Lowest score

13                                      9                                           4

Question 2: What is called “quotient”?

Highest score                Moderate score                Lowest score

16                                      7                                          4

Question 3: What is called “division remainder”?

Highest score                Moderate score                Lowest score

20                                      4                                          3

Question 4: What are “multiples of a number”?

Highest score                Moderate score                Lowest score

13                                      7                                          7

Question 5: Do you know that division functions as an inverse operation of multiplication?

Highest score                Moderate score                Lowest score

15                                      5                                          7

Question 6: What is called “the divisor” of a number?

Highest score                Moderate score                Lowest score

17                                      4                                          6

Question 7: What is called «the dividend” of a number?

Highest score                Moderate score                Lowest score

17                                      3                                          7

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.