For parents desiring to homeschool children, parents who want a general idea of what they’re babies should know already, or adults curious about when they were probably exposed to certain math-related concepts, here’s a broad look at when those concepts are usually introduced or revisited.
Sometimes, it’s hard to know at what time in a person’s development one should be introduced to specific skills. This list is not intended to be comprehensive. With hope, this list of 11 math classes adds a bit of clarity. Somewhere down the line, more specific information will be added.
1. General Math (Kindergarten – Grade 5)
What is it?
Counting and coordinality, operations and algebraic thinking, fractions, numbers and operations in base ten, measurement and data, and geometry
Who uses it in real life?
Everyone! Everyone uses these basic math concepts. Sure, the wording makes it seem as if folks’ itty bitty children are poised to take engineering worlds by storm, but that’s not the case. In another post, I’ll explain exactly what these terms mean, but–rest assured–these concepts are basic, and we use them on daily bases. For example, if you buy an eight-pack of oranges, take the pack home, open it, count the contents, then realize there are only seven good oranges in the pack (one is moldy), then you’ve engaged in “operations and algebraic thinking”. If you see the numeric representation, you understand what the number represents–seven items–that’s “counting and coordinality”.
You get the picture. Now, although almost all concepts are introduced in each grade, the level of complexity increases each year.
For example, using the example about the purchase of oranges (which is representative of kindergarten-level expectations). Well, by fifth grade, students should be able to be able to write expressions that represent that scenario, such as 8 – 1.
Let’s get busy getting you over your academic, professional, or personal hurdles.
2. General Math, Continued (Grades 6 – 8)
What is it?
The study of concepts including ratios and proportional relationships, the number system, expressions and equations, geometry, statistics and probability, and functions.
Who uses it?
Again, we all do. Let’s use the example from Kindergarten – Grade 5, which is representative of expressions. After Grade 5, we’re capable of changing that expression to an equation; 8 – 1 (an expression) becomes 8-1 = x (an equation). We also understand why having -$17 is worse than having $2.
3. Pre-Algebra (Grades 7 and 8)
What is it?
Pre-algebra is a segue between basic math and algebra–an introduction to variables, expressions, factors, equations, integers, fractions, square roots, exponents, lines, properties, inequalities, ratio, proportion, probability, percents, linear functions, polynomials, area, perimeter, volume, and angle relationships and transformations.
At what grade is it usually taken?
As noted above, usually, this course is taken in middle school/junior high school.
Who uses it?
Scientists, artists (whether or not they realize it), architects, social planners, event planners, project managers
By the way, if you’ve if you’ve had to increase or decrease ingredients in a recipe to make greater or fewer portions, or if you’ve accurately figured a bill on a restaurant (including tax) you–Mr., Ms., or Miss Joe or Jane Q. Public–have used pre-algebra.
4. Algebra (Grade 9)
What is it?
Algebra involves solving problems based on patterns or groupings associated with variables and numbers.
The course may be broken into two parts (i.e., Algebra 1 and Algebra 2). Topics include rules and terminology related to solving problems, as well as roots, exponents, linear equations, graphing, absolute values, unit conversions, systems of equations, trigonometry, functions, logarithms, and word problems.
At what grade is it usually taken?
Again, algebra’s usually taken in high school, during the first year. If a school or district splits the course into two parts, Algebra 1 and Algebra 2, Algebra 1 is usually offered in Grade 9, and Algebra 2 is usually offered in Grade 11. Geometry is taken in Grade 10 (between the time the two algebra courses are taken).
Who uses it?
Everybody uses it. If the cost of an item that appears on a grocery store receipt has been smudged beyond recognition, but you need to know what that number is, and you’ve figured it out, you’ve used algebra.
Generally, though, scientists, city designers, amusement park designers, and machinists are among the folks who use algebra in their line of work.
5. Algebra 1 (Grade 9)
What is it?
Using a variety of methods to solve problems related to equations, functions, and inequalities. Vocabulary and basic rules related to algebra are covered, as are roots, exponents, linear equations, linear graphs, inequalities, quadratics, absolute values, unit of conversions, systems of equations, functions, sequences, and word problems.
At what grade is it usually taken?
Usually, Algebra 1 is taken in Grade 9.
Who uses it?
See Number 4.
6. Algebra 2 (Grade 9)
What is it?
Topics covered in Algebra 1 may be reviewed before the following are covered: complex numbers, polynomials, rational exponents, transforming functions, trigonometry, logarithms, and modeling.
At what grade is it usually taken?
Algebra 2, usually, is taken in Grade 11.
Who uses it?
See Number 4.
7. Statistics (Grade 11)
What are they?
The interpretation and presentation of data after it’s been collected, organized, and analyzed.
The study of sampling, experimental design, designing a sampling plan, graphical methods for describing data, numerical methods of describing data, summarizing bivariate data, probability, random variables and probability distributions, sampling variability, sampling distributions, estimation using samples, hypothesis testing using samples, comparing populations, comparing treatments, the analysis of categorical data and goodness-of-fit tests, and simple linear regression and correlation.
At what grade is it usually taken?
If the course is offered, statistics are usually studied in Grades 11 or 12.
Who uses them?
Data scientists, advertisers, and sociologists are some of the folks who use statistics.
With hope, you or someone you know are familiar with correct methods of using statistics to help make determinations such as where to live, what impact your purchases will make, or what profession to choose.
8. Geometry (Grade 10)
What is it?
The study of shapes, including perimeter, area, surface area, volume, parallelism, congruence, lines, planes, angles, measurements, and relationships to each other; theorems, probability, and proofs.
At what grade is it usually taken?
High school students (usually, freshpersons [9th graders], sophomores [10th graders], and juniors [11th graders])
Who uses it?
Architects, carpenters, engineers, plumbers, machinists, are among those who use geometry to get their jobs done.
9.Trigonometry (Grade 11 or 12)
What is it?
The study of triangles, including ratios, reciprocal ratios, graphs of ratios, modeling of ratios, radians, inverses, identities, and functions
At what grade is it usually taken?
High school students (usually, sophomores [10th graders] and juniors [11th graders])
Who uses it?
You probably have. If you’ve needed to figure out the shortest route from a given point on a city block or rectangular field, you could’ve used trigonometry to help you.
Professionally, though, air traffic controllers, radiologists, astronomers, and architects are among those who use trigonometry at work.
10. Precalculus (Grade 11)
What is it?
In preparation for calculus, a combination of coordinate geometry, trigonometry, and algebra are reviewed. Covered topics include functions and their graphs, polynomial and rational functions, exponential and logarithmic functions, systems of equations, systems of inequalities, matrices and determinants, sequences, series, and probability.
At what grade is it usually taken?
Precalc is usually taken during the junior, or 11th, year.
Who uses it?
I’ll need to come back and answer this one.
11. Calculus (Grade 12)
What is it?
The study of how things change (from a mathematical perspective). Includes learning about velocity, circular motion, derivatives, the chain rule, integrals, differential equations, limits, continuity, and functions, polar coordinates, complex numbers, infinite series, vectors, and matrices.
At what grade is it usually taken?
Usually, calculus is taken during the senior year of high school.
Who uses it?
Aerospace engineers, computer scientists, and meteorologists are some of the folks who use calculus at work.
Again, this list isn’t comprehensive. There are courses offered by some schools that aren’t offered by others. This list is meant to give an idea of when common math classes are offered in either elementary school, middle school, or high school.