Math Quick Tips | Solve in under 1 min | Slope | Functions | Proportions | Kathleen Jasper

Kathleen Jasper
12 Feb 202114:06
EducationalLearning
32 Likes 10 Comments

TLDRKathleen Jasper's video script focuses on solving math problems quickly, a skill essential for standardized math exams like the ACT. She emphasizes the importance of solving problems in under a minute on average. The script covers four types of math problems: word problems involving proportions, probability questions, function evaluation, and calculating slope. Kathleen uses practical examples to demonstrate how to approach each problem efficiently. She also shares a trick for finding the slope without memorizing the traditional formula. The video is designed to help students gain confidence and speed in tackling various math problems, preparing them for exams. Kathleen invites viewers to join her for live math sessions on Tuesdays at 5 p.m. EST on YouTube and Facebook, where she works through an hour of math problems.

Takeaways
  • ⏱️ Time Efficiency: Kathleen emphasizes the importance of solving math problems quickly, ideally under a minute, to perform well on standardized tests like the ACT.
  • 🔍 Answer Choices First: She suggests looking at the answer choices before diving into the problem to understand what is being asked and to set up the correct equation.
  • 📝 Proportions: Kathleen demonstrates how to solve a word problem involving proportions by setting up a ratio and using the 'matchy-matchy' principle to find the solution.
  • 🎲 Probability: She explains the concept of probability using the example of drawing bills from a wallet, and how to calculate it by dividing the number of desired outcomes by the total number of outcomes.
  • 📐 Functions: Kathleen simplifies the process of finding the value of a function by substituting the given variable with the value provided and carefully following the order of operations (PEMDAS).
  • 📈 Slope Calculation: She offers a trick for finding the slope of a line by stacking and subtracting the coordinates, then calculating the rise over run, and reducing the fraction if necessary.
  • 🧮 PEMDAS: Kathleen stresses the importance of following the correct order of operations, especially when dealing with parentheses, to avoid common mistakes.
  • 📖 Word Problems: She encourages students to approach word problems by working backwards, starting from the answer choices and working up to the problem statement.
  • 🤝 Equation Setup: Kathleen highlights the need to first set up the correct equation for a problem rather than jumping straight into solving, which can save time and prevent confusion.
  • 📉 Fraction Reduction: She points out the importance of reducing fractions to their simplest form, especially when dealing with probability problems.
  • 🔢 Negative Numbers: Kathleen cautions about being careful with negative numbers, especially when subtracting, as this can be a common source of errors in math problems.
Q & A

  • What is the main goal of Kathleen Jasper's video?

    -The main goal of Kathleen Jasper's video is to demonstrate how to solve various math problems quickly, aiming to help viewers improve their performance on standardized math exams like the ACT.

  • What is the average time expected to solve a math problem on a standardized test?

    -The average time expected to solve a math problem on a standardized test is about a minute or less.

  • What is the first step Kathleen Jasper suggests when approaching a word problem on a standardized test?

    -Kathleen Jasper suggests starting from the bottom and looking at the answer choices first when approaching a word problem on a standardized test.

  • How does Kathleen solve the proportion problem involving Marcus's casserole recipe?

    -Kathleen sets up a proportion by matching the number of eggs to the number of servings, then cross-multiplies and solves for 'x' to find the number of servings made with five eggs.

  • What is the probability calculation for the bill drawn from the wallet being a twenty-dollar bill?

    -The probability is calculated by dividing the number of twenty-dollar bills (8) by the total number of bills in the wallet (20), which simplifies to two-fifths (2/5).

  • How does Kathleen approach the function problem involving f(x)?

    -Kathleen approaches the function problem by substituting the given value (3) for x in the function's expression and carefully following the order of operations (PEMDAS) to solve it.

  • What is Kathleen's trick for finding the slope of a line given two points?

    -Kathleen's trick involves stacking the coordinates, subtracting each corresponding pair, and then calculating the 'rise over run' to find the slope, simplifying the process without using the traditional slope formula.

  • What is the correct answer for the slope of the line through the points (-2, 1) and (-1, -5)?

    -The correct answer for the slope is negative three over two (-3/2), after simplifying the 'rise over run' calculation from the coordinates.

  • How can viewers join Kathleen Jasper for live math problem-solving sessions?

    -Viewers can join Kathleen Jasper for live math problem-solving sessions every Tuesday at 5 p.m. Eastern Standard Time on YouTube and Facebook.

  • What social media platform is Kathleen Jasper trying out for speed math?

    -Kathleen Jasper is trying out speed math on the social media platform TikTok.

  • Where can viewers find the replay of the live math problem-solving sessions if they miss the live broadcast?

    -Viewers can find the replay of the live math problem-solving sessions on YouTube or on the Facebook page.

  • What is the name of Kathleen Jasper's TikTok account for those interested in speed math?

    -Kathleen Jasper's TikTok account for speed math is @kathleen_jasper.

Outlines
00:00
📚 Quick Math Problem Solving Techniques

Kathleen Jasper introduces the video by expressing her enthusiasm for solving math problems quickly. She emphasizes the importance of speed in standardized math exams like the ACT, where problems are expected to be solved within a minute. Kathleen provides a strategy for approaching word problems by starting from the answer choices and working upwards, which is particularly useful for standardized assessments. She demonstrates this with an ACT math problem involving proportions, showing how to set up a proportion and solve it using the matchy-matchy principle and cross-multiplication.

05:02
🎲 Understanding Probability in Math Problems

The second paragraph focuses on probability, a concept that can be challenging for many. Kathleen explains how to calculate the probability of drawing a twenty-dollar bill from a wallet containing different denominations of bills. She shows the process of finding the reduced fraction to represent the probability and addresses a common mistake of not reducing fractions. Kathleen also extends the example to a scenario where a second draw is made after the first, altering the total number of bills and thus the probability of the subsequent draw.

10:05
🔢 Solving Functions and Evaluating Expressions

In this part, Kathleen tackles functions, which can be daunting for some students. She simplifies the process by demonstrating how to evaluate a given function f(x) by substituting x with a specific value, in this case, 3. Kathleen carefully follows the order of operations (PEMDAS) and warns against common mistakes, such as incorrectly distributing numbers within expressions. She successfully solves the function and finds the correct answer.

📈 Calculating the Slope of a Line

The final paragraph deals with calculating the slope of a line, a topic that can cause anxiety for those not well-versed in it. Kathleen shares a trick to find the slope without using the traditional formula (y2 - y1) / (x2 - x1). Instead, she advises stacking the coordinates and subtracting each column, being cautious with negative numbers. After finding the rise and run, she demonstrates how to express the slope as a fraction and reduce it if possible. Kathleen successfully calculates the slope and selects the correct answer from the provided choices.

Mindmap
Keywords
💡Standardized Math Assessments
Standardized Math Assessments refer to tests that are administered and scored in a consistent manner. They are designed to measure a student's knowledge and skills in mathematics against a set of established criteria or standards. In the video, Kathleen Jasper emphasizes the importance of solving problems quickly on these assessments, as they often have strict time limits, which is a common feature of tests like the ACT Math.
💡Proportion
A proportion in mathematics is an equation that states that two ratios are equal. It is often expressed as 'a:b = c:d', where 'a' and 'b' are the terms of one ratio, and 'c' and 'd' are the terms of another ratio. In the context of the video, Kathleen uses the concept of proportion to solve a word problem involving a recipe that has been modified, illustrating how to set up and solve a proportion to find the number of servings the modified recipe will make.
💡Probability
Probability is a branch of mathematics that deals with calculating the likelihood of a particular event occurring. It is quantified as a number between 0 and 1, where 0 indicates impossibility and 1 indicates certainty. In the video, Kathleen discusses how to calculate the probability of drawing a twenty-dollar bill from a wallet containing various denominations of bills, demonstrating the use of fractions to express and solve probability problems.
💡Function
In mathematics, a function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. An example of a function used in the video is 'f(x)', where 'x' is an independent variable and 'f(x)' represents the dependent variable. Kathleen shows how to evaluate a function by substituting a specific value for 'x' and following the order of operations (PEMDAS) to find the result.
💡Slope
Slope is a measure of the steepness of a line, indicating how much the 'y' value changes for a given change in the 'x' value. It is calculated using the formula 'rise over run' or 'change in y over change in x'. In the video, Kathleen simplifies the process of finding the slope by stacking coordinates and subtracting them directly, avoiding the need to remember the traditional slope formula, and then applying 'rise over run' to find the answer.
💡Word Problem
A word problem is a type of mathematical problem that is presented in a verbal or narrative form, often requiring the solver to translate the narrative into a mathematical equation or set of equations. Kathleen addresses the common anxiety around word problems and demonstrates a methodical approach to solving them, starting by identifying key information and setting up the appropriate mathematical relationships.
💡Matchy-Matchy Principle
The 'matchy-matchy' principle, as mentioned in the video, is a technique used to set up proportions or equations that have corresponding parts. Kathleen uses this principle to help solve the recipe modification problem by ensuring that the ratios of eggs to servings are set up correctly, allowing her to cross-multiply and solve for the unknown number of servings.
💡Order of Operations (PEMDAS)
PEMDAS is a mnemonic used to remember the order of operations in arithmetic and algebra: Parentheses, Exponents (including square roots and other roots), Multiplication and Division (from left to right), Addition and Subtraction (from left to right). Kathleen emphasizes the importance of following PEMDAS when evaluating expressions, particularly when dealing with functions and parentheses in the given script.
💡Reduced Fraction
A reduced fraction is a fraction in which the numerator and denominator have no common factors other than 1, meaning they are in their simplest form. In the context of the video, Kathleen shows how to reduce the fraction 8/20 to 2/5 by dividing both the numerator and the denominator by their greatest common divisor, which is 4, to simplify the probability calculation.
💡Coordinates
Coordinates are pairs of numbers that define a point's location on a graph or coordinate plane. They are typically written as an ordered pair (x, y), where 'x' represents the horizontal position and 'y' represents the vertical position. Kathleen uses coordinates to discuss the concept of slope, showing how to calculate it by considering the change in 'y' over the change in 'x' between two points.
💡Rise Over Run
Rise over run is a method used to calculate the slope of a line, where 'rise' refers to the vertical change in 'y' and 'run' refers to the horizontal change in 'x'. Kathleen explains that by stacking the coordinates, subtracting the respective 'x' and 'y' values, and then dividing the change in 'y' (rise) by the change in 'x' (run), one can find the slope of a line without memorizing the slope formula.
Highlights

Kathleen Jasper demonstrates how to solve math problems quickly for standardized tests like the ACT

She emphasizes the importance of solving problems in under a minute on average

Kathleen shares a method for solving word problems by working backwards from the answer choices

She shows how to set up a proportion to solve a recipe modification problem

Kathleen explains the matchy-matchy principle for setting up equations

She solves the recipe problem by cross-multiplying and dividing to find the answer is 10 servings

For probability problems, Kathleen shows how to find the whole and the part to calculate likelihood

She calculates the probability of drawing a $20 bill as 2/5 by reducing fractions

Kathleen explains how to handle conditional probability when one outcome has already occurred

She simplifies function problems by substituting the given input directly into the function

Kathleen emphasizes the importance of following PEMDAS when evaluating expressions

She solves a function problem by carefully applying the order of operations to get the answer -60

For slope problems, Kathleen shares a trick to avoid using the traditional formula

She demonstrates calculating slope by stacking and subtracting coordinates, then rise over run

Kathleen shows how to handle negative numbers carefully when finding slope

She solves the slope problem by reducing the fraction to get the answer -3/2

Kathleen invites viewers to join her for live math problem solving sessions on Tuesdays at 5pm EST

She also has a TikTok account @kathleen_jasper where she posts one minute math problems

Kathleen encourages viewers to subscribe and enable notifications to stay updated on new content

Transcripts

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