Questions tagged [middle-school]
The middle-school tag has no usage guidance.
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How to motivate $x^n−y^n ≡ (x−y)(x^{n−1}+x^{n−2}y+...+xy^{n−2}+y^{n−1})$, to 13 year olds?
You can safely presuppose that 13 year old (y.o.) students learned the Difference of Squares and of Cubes identities, before tackling this Difference of Powers Identity ($x^n – y^n$).
The glut of ...
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How to explain why we can’t factor $x^n + y^n$ for all natural numbers n, to 13 year olds?
Michael Spivak, Calculus (4th edn 2008), p 13. I know this monograph is aimed at undergraduates (not middle schoolers), but this kind of multiple-part question resurfaces on standardized tests for 13 ...
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Does the "Middle School Mathematics domains" refer to (I) through (V) topics?
Does the "Middle School Mathematics domains" on page 3 of https://www.ets.org/content/dam/ets-org/pdfs/praxis/5164.pdf refer to the the following 5 topics/categories?
(I) Numbers and ...
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Do any middle-school texts indicate that irrationality requires proof?
I believe that most middle-school math curricula have at least a brief section about irrational numbers, in which students are taught (among other things) that $\sqrt{2}$ is irrational and $\pi$ is ...
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Resources for teaching decimal numbers
I am currently teaching special classes to students whose ages range from 11 to 15 and there is quite a wide spectrum in their levels of maths. The lessons are given in English and we do not have a ...
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Law of large numbers as a middle school topic?
My daughter (a biologist) is presently teaching also math at a middle school (9th grade, so about 14 years olds). Now the topic in probability seems to be the law of large numbers! More and more I ...
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Why do we explicitly state the equality of two things when we know they're equal
Recently my brother in high school and I were talking about some math when he said
If we know two things are the same i.e. equal why do we need to state
that they're the same? What he was trying to ...
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1
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Help needed to find 7th & 8th grade completed math samples
I am trying to find samples of completed homework, class work and tests for 7th and 8th grade math in the US. I can find a million blank workbooks but not copies that students have completed with ...
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What value is there in requiring students to declare the dimensions of an answer when it is already clear from context?
When I was in late primary and middle school (east coast US, early 1990's), we were assigned a lot of word problems of the following general form:
Mary has eight self-sealing stem bolts. She sells ...
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Middle school math games for the parking lot
I'm looking for math games that a group of students in grades 5 to 10 (ages 11 to 15, say) could play in a gym or parking lot. My school has a STEM Day each year and I get tasked with cooking up some ...
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Word problems written in past tense, present tense, or future tense
Does anyone have extensive classroom experience regarding the best verb tense to use when writing word problems at an elementary or middle school level? I have been writing some lessons recently and I ...
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Why is my 8th grade Algebra 1 tutoring student learning mean absolute deviation and standard deviation?
I’m tutoring an 8th grade student in Algebra 1, and he showed me that their class learned how to find standard deviation and mean absolute deviation using the following formulas:
$SD=\sqrt{\...
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Is there an agreed upon difference between how we represent $\frac{a}{b}$ and $a \cdot \frac{1}{b}$?
When teaching addition and multiplication of fractions, I seem to recall some advice on this site that one should first treat the cases
$a \cdot \frac{c}{d}$ and $a + \frac{c}{d}$ before moving on to ...
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Are these fraction problems different enough to warrant individual consideration?
Consider the following problems:
A) You have 20 problems for your math homework this week, and you want to do 1/5 of them today. How many problems do you need to do today?
B) You need to read a 20 ...
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2
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The value of making students copy your derivations exactly
I have a hypothesis that I have not yet implemented, and am seeking guidance before I do. I have always taught algebra (and above) in such a way that the students understand the derivations. I check ...
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Teaching words with multiple meanings in Mathematics and English
We want to teach about words that have multiple meanings, in mathematics and
English for middle school children (e.g., function, root, or, volume, angle, constant). This is for students who are ...
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Why do we introduce the notion that triangles are "congruent" instead of just saying that they are "the same" or "equal"?
The assumed age of the students is 10-15 years old.
What is the danger in saying that two triangles are "the same" or "equal" instead of saying that they are congruent? It seems to ...
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When working with 12-16 year olds, how should I graph functions when the domain technically isn't $\mathbb{R}$?
Let us assume that I want to graph any of the functions below.
A) A can of soda costs $\$1$. Draw a graph depicting the total cost as a function of the number of cans you buy.
Comment: One cannot ...
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What is the preferred way to denote the Pythagorean theorem equation?
I am teaching 12-16 year olds.
How should I write down the Pythagorean theorem equation?
Some alternatives:
$a^2 + b^2 = c^2$
$\text{leg}^2 + \text{leg}^2 = \text{hypotenuse}^2$
$\text{leg}_1^2 + \...
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Is there a virtue to learning how to compute by hand?
I have been professionally tutoring a wide range of students (from elementary school through graduate school) for many years. Most of them are from the United States. I generally focus on helping my ...
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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, ...
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Resources for Unit Rates
I am currently mentoring my little brother in mathematics. There is an issue with the pedagogy of unit rates. For example when given the following concept " 11.00 U.S. Dollars to 20 Planet X ...
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Ramanujan results for middle school?
Pls I wonder what Ramanujan's results could be explained to middle school level audience, ie without using integral etc that is up to university curriculum?
For example Ramanujan's infinite radicals ...
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What are the resources to learn prerequisite knowledge to latter High school and undergrad prep textbooks?
I use textbook study and am planning on studying Spivak's Calculus, Mathematics It's Content, Methods, and Meaning, How to Prove it by Velleman, etc. However, I'm worried I lack the prerequisite ...
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Logic and proofs in secondary school
Inspired by the question When do college students learn rigorous proofs?, I became curious when pupils in secondary schools learn about proofs, what kinds of proofs they are, how rigorously they are ...
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Teaching Approach at primary, middle and higher level
I would like to have a comparison or a big picture of how and why the approach for teaching math varies from primary (or pre
primary) to middle to higher classes.
I understand at every level one ...
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I find high school math very hard compared to middle school? [closed]
i hope i can get some help on how to get better at high school maths i find them very difficult compared to middle school.
Whats the big difference so i can work on it ?
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Patterns that unexpectedly fall apart at large $n$
I am constructing a learning sequence for middle grade students designed to convince them that empirical arguments (arguments by example) are not sufficient in mathematics. To motivate this, I am ...
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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 $\mathbb{Z}$ ...
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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 ...
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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 ...
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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 ...
user12116
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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 ...
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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 ...
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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 $7$."
$-...
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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 ...
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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 ...
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4
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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 (...
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"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 ...
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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 $U=\{x\in \mathbb R;x\neq 0\}$ as ...
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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. ...
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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. ...
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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 ...
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