(8) Inquiry Lab - Transformations
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This document discusses rigid motions of shapes in a plane, which include rotations, reflections, and translations. Rotations involve turning a shape around a fixed point, reflections involve flipping a shape across a line, and translations involve sliding a shape to a new location without changing its orientation or size. The document provides examples of performing each type of rigid motion on basic shapes like circles, angles, and trapezoids using index cards and tracing paper. It observes that under rigid motions, properties like line segments, angles, and parallel lines are preserved.
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Here are the key points in the example:
1. The triangles ΔCAT and ΔDOG are placed on top of each other so that their vertices coincide or overlap.
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2. This establishes a correspondence between the parts of the two triangles.
3. Since the vertices coincide, the corresponding sides and angles also coincide.
4. Triangles with coinciding corresponding parts are said to be congruent.
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The document provides examples and step-by-step explanations for solving geometry problems involving similar and congruent shapes using transformations and properties of similarity and congruence. In one example, it is determined that two triangles are similar because corresponding angles are congruent. In another example, transformations of a rotation and translation are used to show that two figures are congruent.
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This document provides instruction on determining if two figures are similar using transformations. It includes examples of determining if figures are similar by checking if corresponding angles are congruent and if corresponding sides are proportional. It also covers finding missing measures in similar figures using scale factors and proportions. Determining similarity involves rotations, reflections, translations, and dilations, while congruence only involves rigid motions.
Lesson 7.2
This document contains a lesson on determining congruence between figures using transformations. It provides examples of identifying congruent triangles and determining the transformations needed to map one onto the other. It also gives examples of using congruence to find missing angle measures. The lesson explains that two figures are congruent if their corresponding sides are congruent and corresponding angles are congruent.
Pat05 ppt 0201
This document provides an overview of functions and concepts covered in Chapter 2, including:
- Graphing functions to identify intervals where they are increasing, decreasing, or constant.
- Modeling real-world applications with appropriate functions.
- Graphing functions defined piecewise using different formulas for different parts of the domain.
- Identifying relative maximum and minimum values of functions.
- Defining functions as increasing, decreasing, or constant on intervals.
- Describing the greatest integer function.
Chapter 6
This document provides examples and explanations for describing geometric transformations on a coordinate plane, including translations, reflections, rotations, and dilations. It defines key terms like preimage, image, and scale factor. Examples show how to perform and describe each type of transformation by:
1) Graphing a figure and identifying its vertices with coordinates
2) Performing the transformation by applying the rules for that specific transformation
3) Graphing the transformed image and identifying the new coordinates of its vertices
The document ensures understanding through multiple examples of each transformation type and encourages practicing the skills on additional example problems. It emphasizes that transformations preserve properties like distance and angle measures.
Pat05 ppt 0106
This document discusses solving linear inequalities and compound inequalities. It provides examples of solving various inequalities algebraically and graphing their solution sets. It also gives an example of setting up and solving an inequality to model a real-world situation about payment plans for a house painting job.
Pat05 ppt 0105
This document discusses linear equations and functions. It provides examples of solving linear equations, including special cases where equations have no solution or infinitely many solutions. Applications involving linear models for distance, rate, and time as well as simple interest are presented. The key concepts of zeros of linear functions and finding the zero of a given linear function are also covered.
Chapter 1 Review
- To write fractions as decimals and decimals as fractions, it is helpful to write numbers in different ways. This allows for easier comparisons and calculations.
- Rational numbers can be written as ratios of integers, repeating decimals can be written as fractions, and terminating decimals can be written as fractions.
- Writing numbers in different forms, such as fractions and decimals, allows for easier evaluation of expressions and calculations.
Lesson 1.10 grade 8
This document provides examples and explanations of concepts related to classifying and ordering different types of numbers:
1) It defines rational and irrational numbers, and provides examples of each. Rational numbers can be expressed as ratios of integers, while irrational numbers cannot.
2) Exercises are included for classifying numbers as rational or irrational, comparing irrational numbers on a number line, and ordering sets of numbers from least to greatest.
3) Answering "Why is it helpful to write numbers in different ways?" the document explains that not all numbers can be written the same way, like irrational numbers that cannot be expressed as integers. Being able to classify numbers facilitates understanding and operations involving different types of numbers.
Lesson 1.9 grade 8
This document provides examples for estimating square roots and cube roots of numbers that are not perfect squares or cubes. It shows how to estimate the value by finding the largest perfect square or cube below the number and the smallest perfect square or cube above it. The square or cube roots of these numbers are then used to determine an integer estimate between them. Several step-by-step examples are provided to demonstrate this process. Common Core State Standards addressed in the lesson are also listed.
Lesson 1.7 grade 8
1. The document provides examples of writing numbers in standard form and scientific notation. It also gives examples of performing arithmetic operations such as addition, subtraction, multiplication, and division on numbers expressed in scientific notation.
2. The examples calculate population sizes, planet diameters, and perform other calculations to illustrate how scientific notation makes working with very large and small numbers easier.
3. Writing numbers in scientific notation allows for easier operations like multiplication and division of very large and small quantities, as well as comparing the relative sizes of numbers like population and distances in the solar system.
Lesson 1.7 grade 8
1) The document provides examples of writing numbers in standard form and scientific notation. It also gives examples of performing arithmetic operations such as addition, subtraction, multiplication, and division on numbers expressed in scientific notation.
2) The examples illustrate how writing very large or very small numbers in scientific notation makes it easier to perform operations with them. It also allows for estimating quantities that would otherwise be difficult to comprehend in standard form.
3) Understanding scientific notation helps to compare quantities that differ vastly in magnitude, such as populations and diameters of astronomical objects. It enables estimating ratios and relative sizes in a straightforward manner.
Lesson 1.6 (8)
Here are the steps to write a number between 0 and 1 in scientific notation with an example:
1. Write the number in decimal form. For example, 0.000375.
2. Count the number of decimal places in the number. In this example there are 4 decimal places.
3. Move the decimal point to the left by that number of places. This gives 3.75.
4. Write the number as a coefficient and exponent of 10. Since we moved the decimal point 4 places to the left, the exponent is -4.
So, 0.000375 written in scientific notation is 3.75 × 10-4.
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(8) Inquiry Lab - Transformations
- 1. WHAT are some rigid motions of the plane? Course 3, Inquiry Lab before Lesson 6-1 Geometry
- 2. • 8.G.1 Verify experimentally the properties of rotations, reflections, and translations: • 8.G.1a Lines are taken to lines, and line segments to line segments of the same length. • 8.G.1b Angles are taken to angles of the same measure. • 8.G.1c Parallel lines are taken to parallel lines. Mathematical Practices 1 Make sense of problems and persevere in solving them. 3 Construct viable arguments and critique the reasoning of others. Course 3, Inquiry Lab before Lesson 6-1 Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved. Geometry
- 3. Course 3, Inquiry Lab before Lesson 6-1 Activity 1 continued Geometry Animated movies are created using frames. Each frame changes slightly from the previous one to create the impression of movement. In this Activity, you will make animation frames using index cards. Arrange ten index cards in a pile. On the top card, draw a circle at the top right hand corner.
- 4. Course 3, Inquiry Lab before Lesson 6-1 Activity 1 continued Geometry Animated movies are created using frames. Each frame changes slightly from the previous one to create the impression of movement. In this Activity, you will make animation frames using index cards. On the next card, draw the same circle slightly down and to the left.
- 5. Course 3, Inquiry Lab before Lesson 6-1 Activity 1 continued Geometry Animated movies are created using frames. Each frame changes slightly from the previous one to create the impression of movement. In this Activity, you will make animation frames using index cards. Repeat this for three of four more cards until your circle is at the bottom of the card. Use the remainder of the cards to draw the circle up and to the left
- 6. Course 3, Inquiry Lab before Lesson 6-1 Geometry Animated movies are created using frames. Each frame changes slightly from the previous one to create the impression of movement. In this Activity, you will make animation frames using index cards. Place a rubber band around the stack, hold the stack at the rubber band, and flip the cards from front to back. Describe what you see when you flip the cards from front to back. ___________________________________________________________ Look at the circles on the first and second cards and then the second and third cards. How would you describe the change in the position of the circle from one card to the next?______________________________________ ___________________________________________________________ Did the shape or size of the circle change when you moved it? If yes, describe the change.___________________________________________
- 7. Course 3, Inquiry Lab before Lesson 6-1 Activity 2 continued Geometry Draw right angle XYZ on a piece of tracing paper. Place a dashed line on the paper as shown.
- 8. Course 3, Inquiry Lab before Lesson 6-1 Geometry Fold the paper along the dashed line. Trace the angle onto the folded portion of the paper. Unfold and label the angle ABC so that A matches up with X, B matches up with Y, and C matches up with Z. tape the paper to your book. andXYZ ABC Use a protractor to find the measure of . Did the measure of the angle change after the flip? _____________________ Use a centimeter ruler to measure the shortest distance from X and A to the dashed line. Repeat for Y and B and for Z and C. What do you notice? ___________________________________________________ _________________________________________________________ _________________________________________________________
- 9. Course 3, Inquiry Lab before Lesson 6-1 Activity 3 continued Geometry Place a piece of tracing paper over the trapezoid shown. Copy the trapezoid. Draw points A, B, and C. Draw .AB
- 10. Course 3, Inquiry Lab before Lesson 6-1 Geometry Place the eraser end of your pencil on A. Turn the tracing paper until passes through C. Tape the paper to your book. Did the shape of the trapezoid change when you moved it? If yes, describe the change._________________________ ________________________________ AB Did the size of the trapezoid change when you moved it? If yes, describe the change. _______________________________________
- 11. Course 3, Inquiry Lab before Lesson 6-1 WHAT are some rigid motions of the plane? Geometry