Questions tagged [middle-school]

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21
votes
15answers
6k views

Explaining why (or whether) zero and one are prime, composite or neither to younger children

There are lots of discussions out there about whether $1$ is a prime number (such as this one) and even about zero (such as this question, though note zero does generate a prime ideal in $\mathbb{Z}$ ...
17
votes
8answers
5k views

Prisoner's dilemma formulation for children

I am preparing an introductory course on Game Theory for children (between 10 and 17 years old). In the course description, I want to include a prisoner's dilemma in order to catch children's ...
-2
votes
4answers
253 views

Inefficient methods

I see many teachers use slow methods to solve a given problem where there's another faster methods that doesn't demand much more effort. I'm not looking for mistakes like saying that $a$ is the slope ...
3
votes
3answers
187 views

How to explain to pupils that “$\frac n{100}$ OF $a$” is equivalent to “$a$ TIMES $\frac{n}{100}$”?

How to explain to pupils that "$\frac n{100}$ OF $a$" is equivalent to "$\frac{n}{100}\times a$"? There is some difficulty in explaining that the first sentence, containing "OF" (which could suggest ...
9
votes
4answers
593 views

Is the constant term a coefficient?

I'm a baby boomer who was taught that the constant term of a polynomial is a coefficient, being the constant factor for the x^0 term. That's not what's taught today. Current text books are vague on ...
7
votes
6answers
163 views

Simple Number Theory Task

I am doing exercises with middle grade students and looking at their capacities to create arguments for simple number theory conjectures. I want three tasks, and I have two so far: 1. The sum of three ...
5
votes
2answers
363 views

How to Teach Middle School Students to Read Square Roots?

This exact quote from my standard American Algebra 1 textbook states when first introducing rational square roots: $\sqrt{49} = 7$ is read "The positive square root of $49$ equals $7$." $-\...
18
votes
10answers
2k views

How to Write Steps of Solving Equations?

This is a common way to write the steps during solving equations: But in GeoGebra the steps are shown this way (the highlighted part): I'm going to use GeoGebra to teach equations. Is it OK to let ...
8
votes
5answers
460 views

Exponents with Negative Base; with or without Parentheses

How can I convincingly and mathematically explain the reason behind difference between $(-1)^2$ and $-1^2$? I used to add "negation" to the order of operations, in the same row as multiplication and ...
2
votes
4answers
239 views

Might it be helpful for students to have different symbols for subtraction (-) and negation ( _ )?

Might it be helpful for students to have two different symbols for subtraction (-) and negation ( _ )? Subtraction, after all is a binary operation (with 2 operands). Negation is a unary operation (...
3
votes
1answer
138 views

“Seeing” GCD and LCM in Word Problems

Last year, I taught GCD and LCM and then gave my students word problem relating to these concepts ("Two runners with given different speeds; when will they meet again?", "Having three kinds of flowers ...
6
votes
4answers
308 views

Am I too formal teaching this middle school student?

Solve for $x$ the equation below, writing the universe set and the solution set: $$\frac{a}{b}+\frac{b}{a}-\bigg(\frac{a^2}{bx}+\frac{b^2}{ax}\bigg)=1$$ Let's choose $U=\{x\in \mathbb R;x\neq 0\}...
4
votes
1answer
223 views

how to prove my 6th grade son knows algebra 1?

My son is taking pre-algebra in 6th grade. He mastered algebra 1 in detail more than what school can teach. How to prove to school that he mastered Algebra 1? He wants to start Algebra 2 in 7th grade. ...
0
votes
1answer
100 views

Using Substitution in place of the balance model

How does substitution work as an alternative to the balance model in introducing solving equations? My biggest worry is that, lacking a concrete representation, is too abstract for middle schoolers. ...
7
votes
3answers
156 views

Mathematical Task with Various Solutions

I need to come up with a mathematical task for middle school (9th grade), which involves either algebra, functions, probability or statistics (anything but geometry actually). My problem is, that the ...