Comparing Division Models with GeoGebra | Grade 4 | Titiknur
This GeoGebra Book helps Grade 4 students understand division by comparing different division models through interactive activities. The book includes: • Introduction to Division • Equal Sharing Model • Grouping (Measurement) Model • Comparing Division Models • Interactive Exploration • Practice Activities • Quiz and Reflection Learning Objectives: Students will be able to: • understand the meaning of division, • compare equal sharing and grouping models, • represent division using visual models, • solve division problems in daily life, • explain their mathematical reasoning. Target learners: Grade 4 Elementary School (9–10 years old).
Table of Contents
- 1. Understanding Division
- Division is Repeated Subtraction
- Understanding the Division Algorithm
- 2. Comparing Division Models
- Dynamic Model for Division
- Division Using an Area Model
- Comparing Division Models
- 3. Practice and Reflection
- Practice with division (whole numbers)
- Division as Equal Sharing and Grouping
Division is Repeated Subtraction
Many students have trouble with division; mostly due to not understanding the concept. Partially, due to not knowing multiplication fully. Many may have been absent from school on the critical day it was explained.[br][br]Division is just counting how many times you can subtract on number ([b]divisor[/b]) from another number ([b]dividend[/b]). The number of times you can subtract is called the [b]quotient[/b] and any number smaller the divisor remaining is called the [b]remainder[/b].[br][br]Click the [b]Start[/b] box to see lesson; click [b]Sub as Add[/b] to see work with negative numbers
While many can understand the subtraction method, the teacher jumps quickly to a short cut. This short cut is based on know you multiplication tables well![br][br]Most teachers feel knowing the time tables though 12 is sufficient; personally, I found knowing them through the 16s lit the concept into my skill set.
Dynamic Model for Division
The model presented is valid for the interpretation of the whole-number quotient of a whole number. For every case of a division “whole-number quotient of a whole number” must be designed a model which helps to interpret the case. Here is chosen the case of partitioning the set of 12 objects into:[br]a) 2 groups of equal shares in each one, symbolically denoted as 12÷2[br]b) 3 groups of equal shares in each one, symbolically denoted as 12÷3[br]c) 4 groups of equal shares in each one, symbolically denoted as 12÷4[br]The 12 objects are represented by 12 blue circles. The respective model for the division interpretation is constructed using GeoGebra software with its effective virtual tools and the excellent periodic properties of the trigonometric functions. The model of this case serves as a demonstrative model for the teachers to use in their classroom, equipped with computers, or in computer laboratories. [br]*** Play with the slider and observe the dynamic of partitioning of the set of 12 objects into 2, 3 and 4 groups, respectively, simultaneously are shown the respective equations of the division.
Dynamic Model for Division
Practice with division (whole numbers)
Practice with division (whole numbers)