# Free Math Prep Wednesdays | Hot Topics Math [FTCE, TExES, Praxis, & MTTC] - July 31, 2024

TLDRDr. Ray and math specialist Amy Sink host a Wednesday math session for educators preparing for certification exams. They cover a range of math problems from K-12, aiming to build confidence and clear testing confusion. Amy provides strategies for solving equations, ratios, and geometry, emphasizing the importance of understanding multi-step problems and the Pythagorean theorem. The session also includes a special offer for comprehensive exam preparation courses with a discount code for attendees.

### Takeaways

- ๐ The session is a math preparation webinar hosted by Dr. Ray and Amy Sink from the Learning Lions, focusing on various math levels from kindergarten through high school.
- ๐ Amy has prepared a set of approximately 10 practice math questions covering a wide range of grade levels to build confidence and tackle different types of problems.
- ๐ The main objective of the Learning Lions is to clear up testing confusion and provide support for exam preparation, emphasizing the importance of understanding each step in solving math problems.
- ๐ Amy demonstrates how to solve a multi-step equation, emphasizing the importance of understanding the process rather than just the final answer.
- ๐๏ธ Amy shares personal anecdotes to make the math session more relatable and engaging, discussing favorite dinners and relaxing aspects of teaching math.
- ๐ The session includes a problem-solving approach that involves eliminating impossible answer choices based on logical reasoning before diving into calculations.
- ๐ Amy explains the Pythagorean theorem and its application in solving for the hypotenuse of a right triangle, highlighting common mistakes to avoid.
- ๐ A detailed walkthrough of factoring a quadratic equation is provided, including tips on recognizing when to factor by grouping and simplifying the equation.
- ๐ The difference between prisms and pyramids is clarified, with an emphasis on understanding the number of faces, vertices, and edges for each geometric solid.
- ๐ Amy discusses strategies for identifying the vertex of a parabola, both when the equation is in vertex form and when it requires calculation using the formula.
- ๐ A special offer is presented for attendees of the live session, providing a discount code (SYNC35) for comprehensive exam preparation courses available on the Learning Lions' website.

### Q & A

### What is the main purpose of the Wednesday evening math sessions hosted by the Learning Lions?

-The main purpose of the Wednesday evening math sessions is to help attendees build confidence and provide them with different ways to look at math problems, as well as to clear up testing confusion and give them the support they need to succeed in their exams.

### Who are the hosts of the Wednesday evening math sessions?

-The hosts of the Wednesday evening math sessions are Dr. Ray, the founder of Learning Lions, and Amy Sink, a math specialist at Learning Lions.

### What range of math levels is covered in the sessions?

-The sessions cover a wide range of math levels, from kindergarten all the way through 12th-grade high school math.

### How can attendees access the practice questions discussed during the sessions?

-Attendees can download the practice questions as a PDF, which will be made available during the session through a message on the screen.

### What is the significance of the 'numerator jail' analogy used by Amy during the math problem-solving?

-The 'numerator jail' analogy is used by Amy to explain the process of eliminating fractions in equations by multiplying both sides by the denominator, which in this context is 5x, to simplify the equation and continue solving for x.

### What is the strategy Amy suggests for solving equations with multiple steps?

-Amy suggests breaking down the problem into single steps and solving each step individually, focusing on undoing the operations performed on the variables, such as addition, subtraction, multiplication, and division.

### How does Amy approach the problem of finding the number of children at a playground given a ratio of children to adults?

-Amy first eliminates impossible answer choices based on the ratio provided, then uses cross-multiplication to solve for the number of children, by setting up the ratio of children to total people and comparing it to the given total number of people at the park.

### What is the error Amy points out that people commonly make when distributing a negative number in an equation?

-The common error is not distributing the negative sign through the entire expression, which can lead to incorrect calculations and ultimately the wrong solution.

### What is the method Amy uses to solve the problem involving the hypotenuse of a right triangle?

-Amy uses the Pythagorean theorem, setting up the equation as a^2 + b^2 = c^2, where a and b are the legs of the triangle and c is the hypotenuse. She then simplifies and factors the equation to find the value of x, which represents the length of one leg of the triangle.

### Why does Amy disregard the solution x = -3 when finding the length of the hypotenuse?

-Amy disregards x = -3 because lengths cannot be negative, and in the context of the problem, the hypotenuse represents a distance or length.

### How does Amy differentiate between a prism and a pyramid when discussing geometric solids?

-Amy explains that a prism has two identical bases and rectangles surrounding it, with the number of vertices being double the amount of the base's vertices. A pyramid, on the other hand, has one base and triangles connecting the base to a single vertex at the top, with the number of vertices being the base vertices plus one.

### What is the key to identifying the number of vertices and faces in a geometric solid based on its base shape?

-For a prism, the number of vertices is double the vertices of the base, and the number of faces is two bases plus the number of rectangles that match the number of sides of the base. For a pyramid, the number of vertices is the base vertices plus one, and the number of faces is one base plus the number of triangles that match the number of sides of the base.

### How does Amy determine the vertex of the given parabola?

-Amy uses the formula h = -b/(2a) to find the x-coordinate of the vertex, and then substitutes this value back into the original equation to find the y-coordinate, thus identifying the vertex as a point (h, k).

### What is the significance of the Y-intercept in the context of the parabolas discussed in the script?

-The Y-intercept is the point where the parabola crosses the Y-axis, which occurs when x = 0. In the context of the script, all the given parabolas have the same Y-intercept, which is a key characteristic used to identify them.

### Outlines

### ๐ Introduction to Wednesday Math Sessions

Dr. Ray, the founder of Learning Lions, introduces Wednesday evening math sessions led by math specialist Amy Sink. The session covers a range of practice questions from kindergarten through 12th-grade math. The purpose is to provide support and build confidence in problem-solving, aiming to clear testing confusion. Attendees are encouraged to download practice questions as a PDF and participate by asking questions. The session is part of a series, and attendees are assured of ongoing support.

### ๐ฃ๏ธ Engaging with the Learning Community

Amy Sink greets the attendees and expresses her enthusiasm for the Wednesday night math sessions. She encourages interaction by asking participants to share their location, the exam they are preparing for, and their favorite dinner. Amy also shares her own favorite dinners, creating a personal connection with the audience. She acknowledges the importance of the session and invites questions and comments from the participants.

### ๐ Solving a Complex Math Equation

Amy demonstrates how to solve a multi-step algebraic equation, emphasizing the importance of understanding each step for those preparing for exams. She uses the strategy of eliminating fractions by multiplying both sides of the equation by the denominator. Amy also highlights common mistakes to avoid, such as incorrect distribution of negative signs, and encourages participants to engage with the material and ask questions.

### ๐ข Ratios and Proportions at the Playground

The session continues with a word problem involving ratios at a playground. Amy explains how to approach the problem both conceptually and mathematically, emphasizing the need to compare like terms when setting up ratios. She illustrates the process of elimination for answer choices that do not make sense and then proceeds to solve the problem using cross-multiplication, showing the importance of basic computation skills.

### ๐ The Pythagorean Theorem in a Right Triangle

Amy introduces a problem involving the Pythagorean theorem, a fundamental concept in geometry. She explains the theorem and how to apply it to find the missing side of a right triangle. The problem is solved by setting up an equation based on the theorem and then factoring and simplifying to find the value of x, which represents the length of the side in question.

### ๐ Geometric Solids with Seven Faces, Vertices, and Edges

This paragraph delves into the properties of geometric solids, specifically prisms and pyramids. Amy clarifies the difference between the two, explaining the relationship between the number of faces, vertices, and the base shape of each solid. She then solves a problem about identifying a solid with seven faces, vertices, and edges, concluding that a hexagonal pyramid fits the description.

### ๐ Parabolas with the Same Y-Intercept

Amy addresses a question about parabolas and their Y-intercepts. She explains that the Y-intercept is the point where the graph crosses the Y-axis, which occurs when X is zero. By examining the given equations, she identifies that all have a Y-intercept of -3, thus they share the same Y-intercept when graphed.

### ๐ Finding the Vertex of a Parabola

The session includes a discussion on finding the vertex of a parabola, which is a key point on its graph. Amy demonstrates how to calculate the vertex's X-coordinate using the formula h = -B/(2A) and then finds the Y-coordinate by substituting the X-coordinate back into the original equation. She solves the example and identifies the correct vertex coordinates from the given answer choices.

### ๐ Closing Remarks and Special Offer

In the closing segment, Dr. Ray returns to offer a special discount code 'SYNC35' for attendees to use on the Learning Lions' website for exam preparation courses. He emphasizes the comprehensive nature of the courses, which include practice, lessons, and content review with Amy as the math specialist. The goal is to provide a complete study package to help attendees pass their exams with confidence.

### Mindmap

### Keywords

### ๐กMath Specialist

### ๐กPractice Questions

### ๐กTesting Confusion

### ๐กElementary Math

### ๐กHigh School Math

### ๐กMulti-Step Problems

### ๐กRatio

### ๐กHypotenuse

### ๐กQuadratic Equation

### ๐กVertex

### ๐กY-Intercept

### Highlights

Dr. Ray introduces the Wednesday evening math sessions, which are designed to help attendees build confidence and tackle math problems across various grade levels.

Amy Sink, the math specialist, presents a set of 10 practice questions that cover a range of math topics from kindergarten through high school.

The session aims to clear up testing confusion and provide support for attendees preparing for various math exams, such as FTCE, TExES, Praxis, and MTTC.

Amy explains the importance of understanding each step in solving multi-step math problems, especially for those preparing for K-6 exams.

A detailed walkthrough of solving a complex equation, emphasizing the method of undoing operations to simplify the problem.

Amy engages with the audience by asking about their test preparation and shares her favorite dinners, creating a relaxed and interactive learning environment.

The transcript showcases a problem-solving approach for a ratio question involving children and adults at a playground, with a focus on critical thinking and elimination of impossible answers.

Amy demonstrates how to use the Pythagorean theorem to find the hypotenuse of a right triangle, with a step-by-step explanation suitable for various skill levels.

A geometric solids problem is tackled, differentiating between prisms and pyramids, and identifying the correct solid with seven faces, seven vertices, and 12 edges.

The session includes a discussion on the characteristics of parabolas, focusing on finding the Y-intercept and the vertex of a given parabola.

Amy provides a coupon code 'SYNC35' for a 35% discount on prep courses, encouraging attendees to take advantage of comprehensive study materials.

The importance of practicing no-calculator problems is highlighted, as it prepares attendees for exams where calculators may not be allowed.

Amy invites feedback and requests for specific topics to be covered in upcoming sessions, emphasizing the session's adaptability to audience needs.

A summary of the session's goals is provided, reiterating the mission to support attendees in passing their certification exams with confidence.

The session concludes with a reminder of the ongoing support provided by the Learning Lions community, and an invitation to join future sessions.