# Questions tagged [algebra]

Algebra is the part of mathematics in which letters and other general symbols are used to represent numbers and quantities in formulae and equations.

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### How can you elicit the $\log x = {\log} \cdot x$ error?

You know the error, when you're watching a student work through an algebraic calculation to solve for a variable trapped in the argument of a function, usually $\log$ or a trig function, and you watch ...
1 vote
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### Is there a College Algebra book that was written by a world-class mathematician? [duplicate]

I have taught College Algebra several times and will teach it again in the next semester. College Algebra, according to the catalogue of my college, is described as follows: This course provides ...
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### What's the best ratio for algebra tiles?

A good model for algebra are Algebra Tiles. See: https://calculate.org.au/wp-content/uploads/sites/15/2019/03/lesson-sequence-for-algebra-tiles.pdf In this presentation they recommend an aspect ratio ...
140 views

### Teaching Solving Linear Equations before teaching evaluating expressions

Traditionally, I have always taught evaluating expressions before teaching linear equations. But, I was recently given a remedial class of students that have to cover the bare minimums (and we have ...
87 views

### What is Algebra 1 "Number and quantity; Interpreting Data"?

My sister received her scores for "End-of-Course Examination Program" test results. There is a section "Algebra 1" and underneath a table with rows: Algebra Functions Numbers and ...
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### Why the fear of polynomial long division?

Why do people think long division of polynomials is complicated ? I heard this expressed recently and it seems like an odd sentiment. For me, synthetic division is complicated and totally adhoc ...
237 views

### How to train facility with numbers?

I have a student (age 14) who is valiantly striving to improve his algebra. He knows the "rules", and he more-or-less manages to apply them correctly, and hence is generally able to tackle ...
85 views

### Is the AC Method of Factoring polynomials more popular and used by teachers than others methods of factoring polynomials?

This is an example of the AC Method: $x^2 + 16x +63$ (1) $x² + 7x$ (2) $9x + 63$ (1) $x(x + 7)$ (2) $9(x + 7)$ so we have: $x(x + 7)+ 9(x + 7)$ (1) with (2) The Result is: $(x+9)(x+7)$ I have more ...
189 views

### How to create an equation of a given form with integer coefficients and variables

A math textbook gives the following problem: What is the solution of 3(2x-1) – 2(3x+4) = 11x. The solution is an integer. Using Excel to choose some numbers at random and compute the remaining numbers,...
1 vote
460 views

### Why is highschool math so unrigorous?

I am an highschool student (I'm starting soon the italian equivalent of 12th grade) and I have many problems with the way hs math education works. I don't understand why everything is explained only ...
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### What is the expected fluency with fractions at UK key stage 3?

I have recently started some summer tuition for a student who has failed in mathematics at UK key stage 3 (age 14), and trying to plumb the depths of his knowledge. Having engaged him in some simple ...
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### How can maths assistants at a college be extra helpful for professors?

I am a maths graduate student. A little background: In the coming semester, I will be assisting a prof whom I admire and whom I also want to thank a lot, and I actually will have a lot of free time. ...
175 views

### A linear equation -- my approach

Here is an example of a lesson I did on linear equations where my objective was to show that they are equations of first degree. The reason I do it this way is because I tend to find that students ...
134 views

### Arithmetical Progression

I recently came across a very old Algebra textbook from the 1860s, and on the chapter discussing "arithmetical progression", it says there are "20 cases for arithmetical progression&...
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### Why do we write $x$ instead of $1x$?

I am currently student teaching for an Integrated Math 1 class (which is similar to Algebra 1) that consists of 9th graders. I have been teaching my students how to solve linear systems using ...
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### Geometric and Graphical perspective on completing the square

I just read an interesting article that helps to understand completing the square, and prove the quadratic equation from a geomterical perspective. My question is how do I understand the graphical ...
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### Multiplying the square roots of negative numbers before we calculate a result using $i$ [closed]

To evaluate $\sqrt{-1}$ $\times$ $\sqrt{-1}$ we cannot use $\sqrt{A}$ $\times$ $\sqrt{B}$ = $\sqrt{AB}$ as the result would be 1. I know (?) that we must first respect that the initial numbers ...
392 views

### Do my students know elementary algebra; do they just use online calculators or external help; and is this ok?

Background I know the question in the title is very broad so I will try to explain it as succinctly as I can. Half my time is spent on as a researcher on didactics, while the other half is devoted to ...
304 views

### Looking for a rigorous middle school self-study math course

My son is in 5th grade (US) and since he is doing remote learning, we have been doing a lot of topics in pre-algebra just using worksheets. I'd like to start him on a formal middle school curriculum, ...
567 views

### What is the motivation for teaching Factoring by Grouping?

This seems like such a niche trick to teach students when factoring polynomials. Like, the polynomials I've seen textbooks ask students to factor by grouping seem so cherry picked that I can't imagine ...
1 vote
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### I'm in 8th grade and just finished Algebra 2. What math would I do for the next 4 years? [closed]

I'm in 8th grade and just finished Algebra 2. What math would I do for the next 2 years? In what order would math I would do in 9th, 10th, 11th, and 12th grade. Thanks!
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### Why is isolating for $x$ taught before factoring?

I'm currently working on some precalculus packages for students who need review. For inspiration, I'm looking at some prealgebra books and I'm wondering why isolating for $x$ is taught before ... 169 views

### How do I teach my kid [closed]

I am struggling with teaching my 9th grade kid to solve math problems that are just outside of routine. For e.g., An example problem given by math teacher at school. x, y, z are in geometric ...
1 vote
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### Exercises for explaning homothety, homothetic center, similarity on line and plane, free vector and vector space

I need the collection of exercises for such topics as: maps and transformations, composition of maps homothety, rotation homothety, homothetic center similarities of the line and the plane free ...
1 vote
276 views

### Practical case for solving with system of 2 equations

When I teach basic math I want to emphasize on it's power (algebraic part for starters) as a tool for solving certain problems you cannot solve with naked brain, so that one models a problem with ...
729 views

### When does thinking $(-8)^{1/3} = -2$ result in problems for an undergraduates?

In high school we learn that the cube root of $-8$ is $-2$. Much later some of us learn about the single valued natural logarithm of a complex number, and that $w^z = e^{z\cdot Lz(w)}$ when $w$ and $z$...
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### What topics are considered to be part of pre-algebra?

I know pre-algebra is like a terminology thrown around to really basic stuff that are taught before high school algebra. Some stuff taught there are already considered as part of algebra in some ...
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### How can I introduce the idea of eigenvectors and matrix decompositions to a general audience in an engaging manner?

So I'm doing a freelance writing job, writing a script for a YouTube video about eigenvectors/values. It took me a while to decide what the focus was going to be, but I finally settled on focusing on ...