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Below are links to different textbook series, grade level curriculum and the resources that have been put together to help you be successful in math this year!

(6-8 Math)

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U1 , U2 , U3 , U4 , U5 , U6 , U7 , U8

7th Grade Resources

8th Grade Resources

Preparation for High School Algebra or Integrated Math 1

University High School Summer Bridge Course

High School Mathematics

Algebra 1 Resources

U1 , U2 , U3 , U4 , U5, U6, U7, U8, U9

Open Up Resources 6-8 Math is based on IM® 6–8 Math, which was originally developed by Open Up Resources and authored by Illustrative Mathematics®, copyright 2017-2019 by Open Up Resources. It is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0) . OUR's 6–8 Math Curriculum is available at https://openupresources.org/math-curriculum/ . Adaptations and updates to IM 6–8 Math are copyright 2019 by Illustrative Mathematics , and are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0) . IM® 6-8 Math is available at IM.Kendall Hunt .

Mr. Morgan's Math Help is an independent educational resource and is not affiliated with, endorsed by, or officially associated with Illustrative Mathematics in any way. The Illustrative Mathematics® name and logo are registered trademarks of Illustrative Mathematics and not subject to the Creative Commons license.

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Master Math 7 with Morgan's Homework Help

Updated on Dec 26,2023

Master Math 7 with Morgan's Homework Help

Table of Contents :

Introduction

Understanding scale factor.

Multiplying Lengths by Scale Factor
Drawing Scaled Copies on GRID Paper

Adding versus Multiplying in Scale Copy

Example 1: adding vs multiplying, example 2: adding gaps in scaled copies, example 3: multiplying for scaled copies.

The Difference between Multiplying and Adding
Understanding the Scale Factor
Why Adding Units Does Not Work
Multiplying Units for Scaled Copies

Example 1: 3-4-5 Triangle

Example 2: equilateral triangle, using patty paper for accuracy, scale factors for enlargement and reduction, understanding perimeter in scaled copies, finding the scale factor from perimeter, making scaled copies: understanding scale factor and creating accurate scaled copies.

In the field of mathematics, the concept of scale and proportion plays a crucial role. When it comes to creating scaled copies of shapes and figures, it becomes essential to understand scale factor and its implications. In this article, we will Delve into the process of making scaled copies, examine the relationship between scale factor and proportion, and explore different techniques for accurately drawing scaled copies on grid paper. By the end of this article, You will have a firm grasp on the intricacies of creating scaled copies and be armed with the knowledge to tackle a variety of mathematical scenarios.

Before delving into the process of creating scaled copies, let's first establish what scale factor means and its significance in the realm of geometry. Scale factor can be defined as the ratio of the lengths of corresponding sides of two similar shapes. It describes the relationship between the original object and its scaled copy. In simple terms, scale factor determines how much the Dimensions of a Shape need to be increased or decreased to Create an accurate copy.

To create scaled copies, one must master the skill of multiplying lengths by the scale factor. By multiplying each length of a shape by the scale factor, the dimensions of the scaled copy can be determined. For instance, if the scale factor is 2, it means that each length in the original shape must be multiplied by 2 to obtain the corresponding length in the scaled copy.

Creating Scaled Copies

Drawing scaled copies requires Attention to Detail and precision. To ensure accurate representations, it is often helpful to use grid paper. Grid paper provides a structured framework that aids in maintaining the proportions of the original shape. By following a step-by-step process, one can successfully create scaled copies that closely Resemble their originals.

To begin, place the shape on the grid paper and Outline its boundaries. Next, multiply each length of the shape by the scale factor. For example, if a length is 3 units and the scale factor is 2, the corresponding length in the scaled copy will be 6 units. Repeat this process for all lengths of the shape. Connect the corresponding points to complete the scaled copy.

Drawing Scaled Copies on Grid Paper

Grid paper proves to be a valuable tool when faced with the challenge of drawing scaled copies. Its defined lines aid in maintaining accuracy and proportionality. By following the step-by-step process outlined earlier, one can create scaled copies that are true to the original shape.

In the realm of mathematics, the distinction between addition and multiplication plays a critical role in determining the feasibility of creating scaled copies. Addition may seem like a viable option at first glance, but it falls short in accurately replicating the proportions of the original shape. Multiplication, on the other HAND , proves to be the appropriate operation for achieving accurate scaled copies.

Examples of Adding and Multiplying

To illustrate the disparity between adding and multiplying in creating scaled copies, let's examine a few examples.

Consider two individuals, Diego and Jayden, attempting to create scaled copies of the same shape. Diego opts for adding while Jayden chooses multiplication. Diego subtracts 10 units from each length, hoping to create an accurate scaled copy. However, due to the inherent differences between adding and multiplying, Diego's copy presents a noticeable gap, indicating a lack of accuracy. Jayden, on the other hand, multiplies each length by a third, accurately replicating the proportions of the original shape. Jayden's copy emerges as a true scaled copy, reinforcing the importance of multiplication over addition.

Andre ponders whether adding four units to the lengths of all segments would result in a scaled copy. However, upon closer examination, it becomes evident that the addition operation does not facilitate accurate scaling. While adding four units may increase the overall size of the figure, it fails to maintain the proportional relationships between the lengths. This observation highlights the necessity of multiplication in creating scaled copies.

Consider a triangle, Triangle A, with side lengths of 6, 9, 9, and 12 units. Tim claims that Triangle B, with side lengths of 2, 3, 3, and 4 units, is a scaled copy of Triangle A. To verify this claim, we must analyze the scale factor between the two triangles. By comparing the corresponding side lengths, we can ascertain whether multiplication or addition was involved in creating the scaled copy. It turns out that Triangle B is indeed a scaled copy with a scale factor of a third, reinforcing the significance of multiplication in accurately replicating shapes.

Can Different Operations be Used for Scale Copies?

As we have established, multiplication is the preferred operation when creating scaled copies. Attempting to use addition to determine scale copies would yield inaccurate results. This distinction between the two operations is pivotal in understanding the intricacies of creating scaled copies.

Andre's Question on Adding Units for Scaled Copies

Andre raises an interesting query regarding whether adding four units to the lengths of all segments would result in a scaled copy. While it may seem logical to assume that adding units would facilitate scaling, this assumption is erroneous. The key lies in recognizing that scaling requires multiplication, not addition. By multiplying the lengths, the proportionality of the shape can be accurately maintained. Addition, however, disrupts the proportionality, leading to distorted scaled copies. Therefore, Andre's Notion of adding units is not viable for creating accurate scaled copies.

Exploring Different Types of Triangles for Scaled Copies

Different types of triangles pose unique challenges and considerations when creating scaled copies. Let's examine two examples to gain a deeper understanding.

A 3-4-5 triangle serves as an excellent example to highlight the implications of scale factor. In this triangle, the ratio of the side lengths is 3:4:5. When creating a scaled copy, it is crucial to maintain this ratio.

Equilateral triangles present another fascinating Scenario . With equal side lengths, the scale factor remains uniform across the shape. Maintaining proportionality is relatively straightforward, as each length must be multiplied by the scale factor.

Creating Scaled Copies of Polygons

Creating scaled copies of polygons requires meticulous attention to detail and accuracy. Utilizing tools such as patty paper can enhance precision during the process. By employing a step-by-step approach and multiplying each length by the scale factor, one can successfully generate scaled copies that accurately replicate the original shape.

Patty paper proves to be a valuable aid in ensuring accuracy during the creation of scaled copies. By tracing the original shape onto the patty paper, one can work on determining and multiplying the lengths according to the scale factor. This meticulous approach guarantees the creation of precise scaled copies.

Scale factors play a crucial role in determining whether a scaled copy is a reduction or an enlargement. By analyzing the scale factor, one can identify the magnitude of the change in size. For example, a scale factor greater than 1 indicates an enlargement, while a scale factor less than 1 signifies a reduction in size.

Perimeter of Scaled Copies

Determining the perimeter of scaled copies involves understanding the relationship between the scale factor and the original perimeter. Multiplying the original perimeter by the scale factor provides the new perimeter. By grasping this concept, one can accurately calculate the perimeter of scaled copies.

The perimeter of a shape refers to the sum of all its sides. In the Context of scaled copies, multiplying the perimeter of the original shape by the scale factor yields the new perimeter of the scaled copy. This relationship between scale factor and perimeter is crucial in accurately determining the proportions of scaled copies.

When provided with the perimeter of a scaled copy and asked to determine the scale factor, one must reverse engineer the process. By dividing the perimeter of the scaled copy by the perimeter of the original shape, one can ascertain the scale factor. This approach helps in understanding the relationship between scale factor and perimeter.

Creating scaled copies requires a comprehensive understanding of scale factor and its implications on shape proportions. By multiplying each length of an original shape by the scale factor, accurate scaled copies can be generated. Understanding the distinction between adding and multiplying is essential in maintaining proportionality. Additionally, examining the angle measurements and the Type of shape aids in creating precise scaled copies. With the knowledge gained from this article, you are equipped to confidently embark on the Journey of making scaled copies, unlocking new possibilities in the realm of geometry.

Highlights:

Understanding scale factor and its role in creating accurate scaled copies.
Using grid paper to maintain proportionality and precision in drawing scaled copies.
The distinction between adding and multiplying in the context of scaling shapes.
Examples illustrating the implications of adding and multiplying in scaled copies.
Exploring different types of triangles and the implications for scaled copies.
Utilizing patty paper and meticulous measurements in creating precise scaled copies of polygons.
Determining the perimeter and finding the scale factor in scaled copies.

Q: What is a scale factor?

A: A scale factor is the ratio of the lengths of corresponding sides of two similar shapes. It determines how much the dimensions of a shape need to be increased or decreased to create an accurate copy.

Q: Can addition be used to create scaled copies?

A: No, addition is not suitable for creating accurate scaled copies. Multiplication is the preferred operation as it maintains the proportionality of the original shape.

Q: How can grid paper help in drawing scaled copies?

A: Grid paper provides a structured framework that aids in maintaining accuracy and proportionality when creating scaled copies. It helps ensure the correct placement of points and the consistency of lengths.

Q: What should be considered when making scaled copies of polygons?

A: When making scaled copies of polygons, it is crucial to determine the scale factor and multiply each length accordingly. The use of patty paper can increase accuracy and precision in the process.

Q: How can the perimeter of scaled copies be determined?

A: The perimeter of a scaled copy can be calculated by multiplying the scale factor by the perimeter of the original shape. This relationship allows for accurate determination of the proportions in scaled copies.

The above is a brief introduction to Master Math 7 with Morgan's Homework Help

Let's move on to the first section of Master Math 7 with Morgan's Homework Help

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