Model: minsuas/Misconceptions__1
Author: minsuas
Pipeline: sentence-similarity
Library: sentence-transformers
Tags: sentence-transformers, safetensors, bert, sentence-similarity, feature-extraction, generated_from_trainer, dataset_size:17405, loss:CachedMultipleNegativesRankingLoss, arxiv:1908.10084, arxiv:2101.06983, text-embeddings-inference, endpoints_compatible, region:us
Card metadata: tags: sentence-transformers, sentence-similarity, feature-extraction, generated_from_trainer, dataset_size:17405, loss:CachedMultipleNegativesRankingLoss
widget: source_sentence: Subject: Range and Interquartile Range from a List of Data
Construct: Calculate the range from a list of data
Question: What is the range of the following numbers?
\[
1,5,5,17,-6
\]
Incorrect Answer: \( 5 \)
sentences: To find the range adds the biggest and smallest number rather than subtract
The passage is clarifying a common misunderstanding about how to calculate the range of a set of numbers. The misconception here is that someone might think the range is found by adding the largest number to the smallest number in the dataset. However, this is incorrect. The correct method to find the range is to subtract the smallest number from the largest number in the dataset. This subtraction gives the difference, which represents how spread out the numbers are., Finds the mode rather than the range
The passage is indicating a common mistake made in solving math problems, particularly those involving statistics. The misconception lies in a confusion between two statistical concepts: the mode and the range.

- **Mode**: This is the value that appears most frequently in a set of data. It helps to identify the most typical or common value.
- **Range**: This is the difference between the highest and lowest values in a set of data. It gives an idea about the spread or dispersion of the values.

The misconception described here suggests that a student might calculate the mode when asked to find the range, or simply mix up these two concepts. The important distinction is that while the mode tells you about the frequency of the most common value, the range informs you about the span of the data., Believes a cubic expression should have three terms
The misconception described here is that someone might think a cubic expression, which is a polynomial of degree three, should consist of exactly three terms. This is a misunderstanding because a cubic expression can have any number of terms, but the highest power of the variable must be three. 

For example, both \( x^3 + 2x + 1 \) and \( 4x^3 - 3x^2 + x - 7 \) are cubic expressions, even though they have different numbers of terms. The defining characteristic is that the highest power of the variable (x in these examples) is three. So, a cubic expression can have fewer or more than three terms, as long as the degree (the highest power) of the expression is three., source_sentence: Subject: Reflection
Construct: Reflect an object or a point in a diagonal line with the line of reflection drawn, where the line of reflection lies on the edge or outside the object
Question: The triangle is reflected in the dashed line
What are the new coordinates of point \( \mathrm{P} \) ? ![Four quadrant, coordinate grid with the reflection line y=-x drawn and a triangle. The triangle has coordinates: (-2,3) (-2,6) and (0,5). The point P is the coordinate (0,5)]()
Incorrect Answer: \( (-4,5) \)
sentences: Reflects horizontally or vertically instead of across a diagonal line of symmetry
The passage is discussing a common mistake made in geometry, particularly when dealing with reflections of shapes. The misconception is that students might incorrectly think that the reflection is happening horizontally or vertically (i.e., across a line that is either parallel to the x-axis or y-axis). In reality, the reflection might be across a diagonal line of symmetry, which means the line that serves as the mirror could be at an angle, such as a 45-degree line from one corner of a square or rectangle to the opposite corner.

To correct this misconception, it's important to emphasize the actual direction and axis of reflection, understanding that a line of symmetry can be oriented in any direction, not just horizontal or vertical. Visual aids and examples that include diagonal lines of symmetry can help in grasping this concept better., Fails to reflect across mirror line
The passage is discussing a common misconception in geometry, specifically in relation to reflecting shapes or points across a line, often referred to as a "mirror line." This reflection involves creating a mirror image of a given figure on the other side of the mirror line, maintaining the same distance from the line as the original figure.

The misconception "Fails to reflect across mirror line" means that someone might not correctly understand or apply the rules of reflection in their work. They might draw the reflected image incorrectly, perhaps by not maintaining the same distance from the mirror line, or by not placing it directly opposite the original shape with respect to the line.

In essence, the misconception stems from a misunderstanding of how reflection works in geometry, leading to errors in the placement or orientation of the reflected figure. Correcting this involves ensuring that each point of the original shape is equidistant from the mirror line to its corresponding point on the reflected side., Believes that dividing by 100 gives 10%
The misconception described here is that someone might think dividing a number by 100 results in getting 10% of that number. This is incorrect. Dividing a number by 100 gives 1% of that number, not 10%. To get 10% of a number, you should divide the number by 10. For example, if you have the number 200, dividing it by 100 gives 2, which is 1% of 200. To get 10%, you would divide 200 by 10, giving 20., source_sentence: Subject: Time
Construct: Solve problems involving subtracting a period of time from a given end time
Question: What time is \( 30 \) minutes before midnight?
Incorrect Answer: 11:30 am
sentences: Thinks that times just before midnight are "am" times
The passage is discussing a common misconception about the timing just before midnight. The misconception is that someone might incorrectly believe these times are denoted as "am" (ante meridiem), when in fact, times just before midnight are part of the "pm" (post meridiem) period. Midnight marks the transition from "pm" to "am" — the period from midnight to noon is designated as "am", and from noon to midnight, it is "pm". Therefore, the correct understanding is that the times just before midnight are "pm" times, not "am"., Answers as if there are 100 minutes in an hour
The passage is indicating a common mistake where individuals incorrectly assume there are 100 minutes in an hour, rather than the correct 60 minutes. This misconception could arise in problems that require calculations involving time, leading to inaccurate results. It's important to remember there are 60 minutes in an hour to perform calculations correctly., Thinks measures of area must end in squared
The misconception described here is that some people believe the units of measurement for area must always end in "squared," such as square meters, square feet, etc. While it is true that area measurements are often expressed using squared units (like square meters, m²), this is a specific case when the measurements are taken in units like meters, feet, etc.

However, depending on the context and the system of measurement, area can be expressed in units that do not explicitly end in "squared." For example, when measuring land, units like acres or hectares are used, which are not expressed as squared units but represent a specific area. An acre, for instance, is a unit of area commonly used in English-speaking countries, and it equals 43,560 square feet.

In summary, while squared units are a common way to express area, it is incorrect to assume that all units measuring area must end in "squared.", source_sentence: Subject: Quadratic Equations
Construct: Solve quadratic equations using factorisation in the form x(x + b)
Question: Solve this equation, giving all solutions:
\[
k^{2}=4 k
\]
Incorrect Answer: \( k=4 \)
sentences: Believes they can divide by a variable without checking whether it could equal zero
The misconception described here pertains to the process of solving algebraic equations, particularly when dividing both sides of an equation by a variable. The misconception is that one can divide by a variable without considering whether that variable could potentially be zero.

In algebra, dividing both sides of an equation by a variable (let's say \(x\)) is generally valid only if \(x \neq 0\). If \(x\) could be zero, then dividing by \(x\) is not allowed because division by zero is undefined in mathematics. This oversight can lead to losing a solution (specifically, \(x = 0\)) or deriving incorrect conclusions.

For example, consider the equation \(x^2 = 3x\). If one incorrectly divides both sides by \(x\) without checking whether \(x\) can be zero, they might reduce it to \(x = 3\), thereby missing the solution \(x = 0\).

The correct approach would be to rearrange the equation to \(x^2 - 3x = 0\), factor it to \(x(x - 3) = 0\), and then conclude that \(x = 0\) or \(x = 3\), thus ensuring no solutions are lost., Thinks tables of values are symmetrical about (0,0)
The misconception described here pertains to the assumption that all tables of values representing a mathematical function or a set of data points are symmetrical about the origin, which is the point (0,0) on the coordinate plane. This means someone might incorrectly believe that for every value of \(x\), the corresponding \(y\) value would be mirrored on the opposite side of the origin, like in the case of the function \(y = x^3\), which is symmetrical about the origin.

However, not all tables of values are symmetrical about (0,0). Symmetry about the origin is a specific property that only applies to certain types of functions, particularly odd functions, where \(f(-x) = -f(x)\) for all \(x\) in the domain of \(f\). Many other functions and sets of data points do not exhibit this symmetry. For example, a parabola \(y = x^2\) is symmetrical, but not about the origin; it is symmetrical along the y-axis. A linear function \(y = mx + b\), unless it passes through (0,0) with \(b=0\), would not be symmetrical about the origin either.

Thus, one should not assume symmetry about (0,0) for any given set of data or function without proper analysis or evidence that confirms this symmetry., When solving an equation, multiplies instead of dividing
The passage is highlighting a common mistake made when solving mathematical equations, where a student might mistakenly multiply when they should be dividing. This can happen in various contexts, such as solving for a variable in an equation or converting units. For example, if a problem requires you to divide both sides of an equation by a number to isolate the variable, mistakenly multiplying instead would lead to an incorrect solution. 

The key here is to carefully read the problem, understand the operations needed, and apply the correct mathematical operations to solve the equation accurately., source_sentence: Subject: Construct Triangle
Construct: Construct a triangle using Side-Side-Side
Question: Tom and Katie are arguing about constructing triangles.

Tom says you can construct a triangle with lengths \( 11 \mathrm{~cm}, 10 \mathrm{~cm} \) and \( 2 \mathrm{~cm} \).

Katie says you can construct a triangle with lengths \( 8 \mathrm{~cm}, 5 \mathrm{~cm} \) and \( 3 \mathrm{~cm} \).

Who is correct?
Incorrect Answer: Neither is correct
sentences: Does not realise that the sum of the two shorter sides must be greater than the third side for it to be a possible triangle
The passage is discussing a common misconception about the properties required to form a triangle. The misconception is that one might think any three given side lengths can form a triangle. However, for three lengths to actually form a triangle, they must satisfy the triangle inequality theorem. This theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the remaining side. This rule must hold true for all three combinations of added side lengths. 

To apply this to the misconception: one does not realize that the sum of the lengths of the two shorter sides must be greater than the length of the longest side to form a possible triangle. This ensures that the sides can actually meet to form a closed figure with three angles., Does not know that a single letter labels a vertex
The passage is indicating a common misconception in geometry or graph theory, where students or individuals may not understand that a single letter can be used to label or identify a vertex (a corner or a point where lines or edges meet) in a geometric shape or a graph.

Explanation: In mathematics, particularly in geometry and graph theory, vertices (plural of vertex) are often labeled with single letters (like A, B, C, etc.) to easily identify and discuss them. This labeling helps in referring to specific points when describing shapes, calculating angles, distances, or when analyzing the structure of graphs. The misconception arises when someone does not recognize or utilize this convention, potentially leading to difficulties in understanding problems or communicating solutions effectively., Draws both angles at the same end of the line when constructing a triangle
The misconception described refers to a common error in geometry when students are constructing a triangle based on given angles and a line segment. The mistake is to draw both given angles at the same end of the given line segment. This is incorrect because in a triangle, each angle is located at a different vertex, and each vertex connects two sides. To correctly construct the triangle, each given angle should be drawn at different ends of the line segment (if constructing based on one line segment and two angles) or at vertices defined by the construction steps (if additional sides are given). This ensures that the three angles are positioned to form the corners of the triangle, with each angle at a distinct vertex, thereby creating a proper triangle.
pipeline_tag: sentence-similarity
library_name: sentence-transformers
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Created: 2025-01-05 09:20:52