Time for a multiple-choice quiz! Which of the following is the most fully true about the connection between arithmetic and algebra?
A. There is no connection – they’re different branches of mathematics.
B. Sometimes arithmetic is used in algebra, like to solve equations.
C. Six or seven years of arithmetic is necessary in order to do algebra.
D. Algebra is generalized arithmetic.
Let’s discuss each of these:
A. No connection
While arithmetic and algebra are different branches of math, this statement is too strong. There are several significant connections between algebra and arithmetic, which will be discussed below.
B. Arithmetic used sometimes in algebra
Obviously, arithmetic does get used in algebra (and in almost every branch of math). So this statement is true – but it’s not the most fully true statement, because there’s more to this algebra-arithmetic connection.
C. Six years of arithmetic before algebra
This statement is how most people think of algebra and arithmetic – and this is what their own experience has been for most adults. But this is precisely what we have found at Algebra For Kids for the past 20 years: kids DON’T need six years of arithmetic before algebra.
D. Algebra = generalized arithmetic
In arithmetic, we deal with specific exercises like 5 + 3 or 7 • 9. In algebra, we deal with general principles like a + b or 7•x.
In arithmetic, we learn the mental math of 7•(10 + 2). In algebra, we study the general idea of 7•(x + 2).
In arithmetic, students learn about base 10 operations involving “borrowing” and “carrying.” In algebra, students learn how in some ways algebra is easier simply because there is no “borrowing” or “carrying” in the algebra of base x.
In arithmetic, kids learn the relatively complicated two-digit multiplication procedure of (10 + 2)•(10 + 4). In algebra, students practice the comparativelyuncomplicated procedure of (x + 2)•(x + 4).
Are you starting to see how connected algebra and arithmetic are?
This connectedness is why in AFK, for 20 years we have been able to teach substantive algebra to students as young as 3rd grade.
Get the 3rd graders in your life into our summer camp – SAI: the Summer Algebra Institute for Kids.