Whole number computation: understanding multiplication and division through problem types

Whole-Number Computation

Equal-groups math problems can be delineated as word problems where an individual is given a number of equal groups, and then the task is to find the missing number within the problem. In other words, equal-groups are groups that comprise of the similar number of equivalent items.

To simplify the understanding of these questions, a full equal-groups math problem comprises of three different parts including the number of groups, the number of items contained in every group, and the total number in all of the groups. The following formula makes it possible to comprehend how to comprehend these three parts using multiplication:
The number of groups × the number of items in every group = total

The number of groups is one factor, and the “in each” number is the other factor. The total number in all groups is the product. It is imperative to note that in equal-group math problems, one of the numbers is usually missing. Notably, if the total is not provided, then the solution is to conduct the multiplication. On the other hand, if either of the other numbers is not provided, then the solution is to conduct the division (Collins, 2012).

The following examples make it possible to understand equal-group math problems:

Question One:
Fidelis has 12 bottles of soda water. There are 22 ounces of soda water in each of the bottles. How many total ounces of soda water does Fidelis have?
Solution:
Number in every group = 22 ounces of soda water in every bottle
Number of groups = ×12 bottles of soda water
Total 264 ounces of soda water

Question Two

James Arthur coaches the Stevenson High School Football team. The team comprises of 48 football players in total. Each day during practice, Coach James separates the total number of players into 6 different teams with every one of them having the equivalent number of players. How many players are in each team during football practice sessions?
Solution:
This particular math question is an equal-groups problem. To simplify the question, the groups of players in every team are classified into groups. This question can be therefore transformed using the multiplication formula delineated above as follows:
1. Provided is the number of groups in the problem = 6 teams
2. Provided is the total number of football players in the session = 48 players
3. The question being asked is the obtain the number of players contained within every team
Remember the formula provided for equal-groups: The number of groups × the number of items in every group = total
Taking this into consideration, the equation can be re-written as follows:
n football players on every team
× 6 teams in every session
48 football players in total

The missing number is obtained through division (48 / 6) = 8
Therefore, each team during the football session is made up of 8 players

Equal-groups problems are significant in learning math because they enable the student to have a faster understanding towards multiplication and also division. It can be noted that the initial introduction to multiplication for the pupil is as solving math problems regarding equal groups. For instance, basic math can be simplified using this, in the sense that 4 × 5 can be interpreted by the student as 4 groups of 5 and this can also be represented with concrete items such as 4 different groups of 5 objects. This is a significant step in the pupil’s understanding of multiplication. Acknowledging equal-groups and fully comprehending it opens up the student to gaining insight into other mathematical conceptions, such as the area of a rectangle (Victoria State Government, 2018).

References

Collins, A. M. (2012). 50 Leveled Math Problems Level 5. Huntington Beach, CA: Shell Education. 2012b, 50.

Victoria State Government. (2018). Multiplication from Equal Groups to Arrays. Retrieve 4 May 2018 from: http://www.education.vic.gov.au/school/teachers/teachingresources/discipline/maths/continuum/Pages/multarrays.aspx