Hi there. I talk about multiplication and division as foundation topics for young students. I think I might have done this topic before. If I did sorry. When I write my posts it is mostly from scratch. I save drafts in RStudio offline as most of my posts takes days to write up. It is rare for me to write a post all in one sitting.
Build A Solid Foundation
This idea of building a solid foundation is not just in mathematics education or in education in general. It is important for a house or building to have a solid foundation so it can stand strong. People in general should have a solid foundation in a lot of aspects in their lives. A solid foundation in finances, health, knowledge, wisdom, healthy sceptisim, relationships, friends and family helps a lot.
In the mathematics framework I think that multiplication and division are important foundational topics. These two topics are taught as early as grade two or three and are heavily used in higher level topics. Multiplication and division are major part of calculations and in algebra.
Multiplication Examples
Multiplication is a form of repeated addition that deals with mainly groups. Four times three can be viewed as four groups with three items in each group. As repeated addition this 4 x 3 = 4 + 4 + 4 = 12.
One dozen is a group of twelve. Three dozens would be 3 x 12 = 36. In repeated addition form it would be 12 + 12 + 12 = 36.
Multiplication also applies to calendars and days of the week. One week is 7 days. Five weeks would be five groups of seven days. This would be 5 x 7 = 35.
On a chess board there are 8 rows of 8 spaces. Eight times eight would be 64 making it 64 squares on a chessboard.
Division Examples
Division deals with making groups. How many groups of a number can be made from another number. Answers from division may have a remainder or not.
From 20 students there would be 5 groups of four that can be made.
From 21 students there would be 5 groups of four that can be made with one student not in a group. This one student would be a remainder from division.
One dozen contains 12 items. Sixty donuts can be regrouped as five dozens (60 ÷ 12 = 5).
A set of ramen noodles are sold in five packs. This set of noodles costs five dollars. As five packs costs 5 dollars, this means that one pack costs one dollar each.
Multiplication & Division As Foundations For Algebra
For educators this may be obvious but it is a good idea to state the importance of multiplication and division for young students. Multiplication and division is not just a prerequisite for higher level topics. The applications for multiplication and division are important for a lot of daily tasks. Not knowing multiplication and division would make it hard to know if a sale or price is good or not while shopping.
Some careers like business, finance, cooking, engineering use some form of mathematics in the workplace. If it is not a super technical job then university level math is not really needed.
Bigger Picture Note
Mathematics may not seem important to some youths when they are young. The thing is that some form of mathematics is everywhere. For everyday life you do not really need mathematics past the high school level. It would be mostly multiplication, division and percents.
Those who wish to study in natural sciences (physics, chemistry, biology), medical school, pharmacy, mathematics, computer science or engineering you do need high school mathematics. Multiplication and division plus a bunch of other math topics are needed as requirements to study STEM (Science, Technology, Engineering, Mathematics) topics past high school.
Thank you for reading.