Middle School Math, Logic, and Problem Solving: Similar Shapes, Scale, and Slope
In this five week pre-algebra and middle school math course, learners will identify similar shapes, create scale drawings, and connect existing geometry knowledge to the concept of slope through problem-centered exploration.
Malikai Bass M.A
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5.0
Number of reviews:(316)
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What's included
25 live meetings
20 hrs 50 mins in-class hoursMastery Evaluation
includedAssessment
Students will receive weekly written progress reports.Class Experience
US Grade 7 - 8
Beginner Level
This is the second course in year two of a series of middle school mathematics courses. These courses are taught in small-groups to provide individual instruction and social-learning opportunities aligned with a social constructionist or situated cognition view of learning. This series is based on an accelerated math curriculum that covers three years of content, aligned to Common Core Math Standards, over the course of two school years. It is perfect for students preparing to begin Algebra ahead of time, or those who need review and remedial support. The curriculum is problem-based this means instead of lectures or videos students work together as a small group to solve problems to discover principles and strategies with teacher guidance, as necessary. Therefore, we will spend approximately 90% of each class period working on problems and discussing them as a group. The use of discussion and problem-solving leads to generalized mathematics or proofs. This process prepares students well who may seek advanced mathematics in high-school or beyond. Students will complete a math notebook In the style of a main lesson book to help with recall and long-term retention. In this unit, students gain a conceptual understanding of scale and learn to recognize when pictures and plane figures aren't in scale. They will reason about measurements in scaled copies, interpret and reason with scale drawings, and create their own with and without units. Students will also learn about dilation as they discuss center and scale factor while exploring circles and lines on and off the coordinate plane. They learn what is preserved in a a dilation and compare it to their existing concept of rigid transformations. We then use the developed geometric understanding to explore slope and slope triangles allowing us to generate the equation of a line and reason with equations representing lines.
Learning Goals
Students will understand and use the terms " scaled copy", "to scale", "scale factor", "scale drawing", and "scale".
Students will recognize when two pictures or plane figures are not scale copies of each other.
Students will use tables to reason about measurements in scaled copies.
Students will make, interpret, and reason with scale drawings.
Students will understand dilation and recognize center and scale in this context.
Students will understand how dilation impacts different polygons including line and angle measures.
Students will understand similarity of plan figures using rigid transformations and dilations.
They will use the properties of similarity to make, prove, and disprove claims.
They will learn the terms "slope" and "slope triangle".
They will use similarity to prove they can sue any two distinct points on a straight line to determine the slope.
Syllabus
Standards
Aligned with Common Core State Standards (CCSS)5 Units
25 Lessons
over 5 WeeksUnit 1: Scaled Copies
Lesson 1:
Readiness Assessment
We will begin with a readiness check to understand students existing conception of geometry and algebra ideas that may need to be addressed and inform instruction throughout the unit. 50 mins online live lesson
Lesson 2:
What are scaled copies?
We will explore the idea of a scaled copy and learn to distinguish scaled copies both formally and informally using length and articulate the characteristics of scaled copies quantitatively. 50 mins online live lesson
Lesson 3:
What is a scale factor?
We will focus on developing vocabulary and understanding how to formalize the concepts developed about scaled copies. We will work on describing scaled copies using a scaled factor. We will create scaled copies of simple shapes off a grid and understand the relationship as multiplicative. 50 mins online live lesson
Lesson 4:
How does scale impact the relationship between shapes
We will work on understanding corresponding distances between non-connected points in scaled copies. We will use virtual protractors to explore what happens to angles in scaled copies and reason as to why they are preserved. We will use arguments about angles and lengths to identify scaled copies. We will also work with fractional scale factors to understand how factors greater or smaller than one impact scaled copies. 50 mins online live lesson
Other Details
Learning Needs
This class is designed by an AUDHD/Dysgraphic Educator
- slides and fonts designed to support dyslexia and visual processing
- ability to type and use virtual drawing tools
- communication aids including chat
- ND Affirming classroom
Parental Guidance
Students will need to use Nearpod. They will need to click a link and enter their first name or initial. No other identifying information will be collected.
Pre-Requisites
Students should have good content mastery over elementary math standards and sixth grade math standards. Students should have proficiency (with or without aid) of keyboard and mouse or touch screen devices.
Joined April, 2021
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316reviews
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Teacher expertise and credentials
Professional Experience:
I have been a math tutor for over 12 years and have worked with students from ages 5-25 in small group and academic settings including serving as a primary teacher for home educated learners. I have received training and tutoring certification/awards from nationally recognized organizations. I was a group supplemental instruction leader for math at the collegiate level for four years at ETSU including working with dual enrolled and accelerated learners. I have taught and tutored math up to a graduate level in algebra, geometry, probability, and quantitative reasoning.
Academic Experience:
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Reviews
Live Group Course
$80
weekly or $400 for 25 classes5x per week, 5 weeks
50 min
Completed by 9 learners
Live video meetings
Ages: 11-14
3-6 learners per class
