Translations
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The document discusses translations, which are horizontal and/or vertical slides that move a shape to a new position without changing its size or shape. Translations are determined by a rule that specifies the change in x- and y-coordinates from the original figure to the translated image. Examples are given of translating shapes right, left, up, and down according to translation rules.
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The document discusses scientific notation, which is a way to write very large or small numbers in a more compact form using two factors - a number between 1 and 10 multiplied by a power of 10. It provides examples of converting numbers between standard form and scientific notation, such as 2.3 x 103 representing 2300. The Andromeda Galaxy contains at least 200 billion stars, which can be written more concisely in scientific notation as 2 x 1011 stars.
Volume of Prisms
Rectangular and triangular prisms have formulas to calculate their volume (V).
For a rectangular prism, V = (bh)h, where b is the width, h is the height, and the product bh gives the area of the rectangular base.
For a triangular prism, V = (1/2)bh, where b is the base, h is the height. The area of the triangular base is calculated as (1/2)bh.
Both formulas multiply the area of the base by the height to determine the volume of the entire prism.
Circles
This document provides information about calculating the circumference and area of circles. It defines key terms like diameter, radius, circumference, and area. Formulas are provided to calculate circumference using either the diameter or radius. The circumference formula is C=πd or C=2πr. The area formula is A=πr^2. Examples are worked through to find the circumference or area given values for diameter or radius. Readers are prompted to try sample problems applying the formulas.
Area of triangles and trapezoids
The document discusses formulas for calculating the areas of triangles and trapezoids. For triangles, the area formula is 1/2 base × height. For trapezoids, the area formula is 1/2 × (sum of the two bases) × height. Several examples are provided to demonstrate calculating areas using these formulas.
Area and perimeter of parallelograms
This document discusses finding the perimeter and area of squares, rectangles, and parallelograms using formulas. It instructs the reader to look at a formula chart to find the appropriate formulas rather than memorizing them. It provides examples of calculating the perimeter and area of different shapes using the side lengths provided and the correct formulas from the chart. The base and height of any shape always form a right angle within the shape.
Reflections
This document contains instructions for reflecting geometric shapes across various lines. It discusses reflecting a pentagon across the x-axis, a triangle across the y-axis, and other shapes across the lines x=3 and y=-2. The final reflection is of an unknown shape across the y-axis.
Data Representations
This document provides a tutorial on statistics and data displays. It includes definitions and examples of key statistical concepts like measures of central tendency, measures of spread, and types of data and variables. It also describes commonly used data displays like line plots, bar graphs, circle graphs, and stem-and-leaf plots. For each display, it explains what they consist of, when they work best, and includes examples. Questions to consider when analyzing each display are also provided. The tutorial is intended to refresh teachers' knowledge but can also be used by students.
Warm-Ups for January 14-18, 2013
The document provides the daily objectives and agenda for a math class over the course of a week. Each day's objective is to model equations to find solutions. The daily agenda includes warm-up problems, homework review, and new vocabulary or concepts. Warm-up problems involve writing algebraic expressions, modeling equations, and defining math terms. Quotes of the day are also provided for inspiration.
Warm-Ups for January 7-11
The document provides daily lesson plans and objectives for a math class over the course of a week. Each day's plan includes: welcoming students, listing objectives and activities for the day, providing a daily quote, and presenting word problems or sequences for students to work on as a warm-up. The weeklong plans focus on using words and symbols to describe arithmetic sequences and using different strategies to solve problems.
Modeling 2 Step Equations
1) The document discusses using algebra tiles to model and solve two-step equations.
2) It provides an example of modeling and solving the equation 2y + 4 = 10 using algebra tiles.
3) The key steps are to first group like terms on each side, then remove common terms from both sides to simplify the equation before solving for the variable.
Modeling one step equations
This document contains symbols and formatting that do not convey clear meaning. It includes white circles, bullet points, and dashes but no discernible words, sentences, or paragraphs that can be succinctly summarized in 3 sentences or less. The content and essential information is unclear from the symbols and characters provided.
Expression Notes
A variable is a symbol that represents a number, while an expression consists of numbers, variables, and operations. Key words in word problems indicate whether to add, subtract, multiply, or divide. Expressions can be written as mathematical statements, and evaluated by substituting values for variables.
Percent Bars
Here are the steps to solve problems like these:
1. Identify the "is", "of", and "%" amounts given in the problem
2. Set up a proportion relating the amounts:
is/of = %/100
3. Solve the proportion algebraically for the missing value
Be sure to show the proportion and substitution steps to arrive at the solution. Drawing a percent bar can also help visualize the relationship between the amounts. Practice these types of problems until you feel comfortable setting up and solving the proportions. Let me know if any specific problems give you trouble.
Sales Tax and Total Cost
Sales tax is a percentage tax added to the original price of an item or service. The total cost is the original price plus the calculated sales tax rounded to the nearest cent. This document provides formulas and examples to calculate sales tax and total cost. It defines key terms like original cost, tax rate, and total cost. Several examples demonstrate applying the formulas to find the sales tax and total cost for different prices and tax rates.
Discount and Sale Price
This document shows examples of calculating sale prices after applying various percentage discounts to original prices. Each example shows the original price, discount percentage, calculation of the discounted amount, and final sale price. Discounts ranged from 10-50% and were applied to original prices between $12-$1,200. The final example also calculates a 9% sales tax on the sale price to determine the final cost.
October 9 12, 2012
The document outlines the daily agenda and objectives for a classroom, including assignments on operations with decimals, independent study time, a math test, and converting fractions, decimals, and percents. Each day's agenda is introduced with a quote of the day and includes warm-up problems or assignments related to the objective.
Warm-ups Week of October 5, 2012
The document appears to be notes from a math class, listing the daily objectives and math problems for students on different levels. It provides the dates from Monday, October 1st to Friday, October 5th and includes the learning objectives for comparing, ordering, and performing calculations with decimals each day. Motivational quotes are also included at the bottom of each page.
Order of Operations
1. The document discusses the order of operations and why it is important for getting the correct answer to math problems.
2. It explains that the order of operations (PEMDAS) is an agreed upon procedure, not a mathematical fact, to ensure consistency.
3. Examples are provided to demonstrate solving problems using the proper order of operations and to illustrate how the order matters.
Order of Operations
1. The document discusses the order of operations and why it is important for getting the correct answer to math problems.
2. It explains that the order of operations (PEMDAS) is an agreed upon procedure, not a mathematical fact, to ensure consistency.
3. Examples are provided to demonstrate solving problems using the proper order of operations and to illustrate that the order matters.
More from bujols (20)
Translations
- 1. y x
- 2. y A translation is a horizontal and/or a vertical slide. B C x A D B C Square ABCD is the original shape. The A D new shape, Square A’B’C’D’ is called the “image”.
- 3. y Draw an arrow from yellow triangle to the blue triangle to show the direction of the slide and then give the distance. How did the x- and y-coordinates x change? How did the x- and y-coordinates change?
- 4. y Translations are determined by a rule. The rule looks like this: (x, y) (x +/-#, y +/- #) x A B C D Translate the figure 4 to the right and 3 up. This rule would be written as: (x, y) (x + 4, y + 3)
- 5. Translate the figure 4 to the y left and 3 down A x C B What is the rule for this translation? (x, y) (x - 4, y – 3)
- 6. y What is the rule for this translation? A x C B Translate the figure 3 down and 2 to the right. (x, y) (x + 2, y – 3)
- 7. 1. Translate the triangle right 3 units, then 7 units down.