Area and Surface Area | Junior High General Math, Module 1
One month of a full math curriculum, in which we explore tiling, area of rectangles, triangles, parallelograms, and other polygons, and surface area of polyhedra.
Avrila at Math With Avrila
Average rating:
4.9
Number of reviews:(12)
What's included
12 live meetings
10 in-class hoursHomework
2-4 hours per week. Homework, quizzes, and tests will be delivered through the TeacherMade platform. Some assignments will be scored on a participation basis, while others will be scored for accuracy, and some will be a mix of both kinds of scoring on different problems. Some problems will be previews of upcoming work, in which learners start on a problem before class to have more time to think about strategies; others will be practice of strategies they have already seen in class. Sometimes, learners will need to show their thinking using sentence writing, drawn diagrams, or showing their work. Even in problems that ask for an answer, showing their work is always recommended for better feedback and partial points. Sometimes, to make group meeting time available for interactive activities, learners will be assigned to watch tutorial videos outside of class time.Assessment
Informal formative assessment through discussion comments and homework corrections will be continuous throughout the unit. Shortly after the last meeting, parents will receive a progress report with all scores and a calculated numerical and letter grade. Parents can also get a copy of a draft progress report with work completed up to that point, upon request.Grading
includedClass Experience
US Grade 5 - 7
We will get together in Zoom three times a week for group activities and discussions, and there will be work for learners to do on their own time between sessions. During group activities, learners will work hands-on with GeoGebra and interact with the teacher and each other through slides that are designed to be written on and organize our thinking, not just looked at, in the Explain Everything whiteboard platform. (Learners can either annotate from within Zoom, which will be reset as we move between slides but preserved in the session recording, or request the Explain Everything link, which will let them write directly on the board that will be exported into downloadable class notes. Learners' contributions will be checked for appropriateness, safety, and accuracy before being exported.) Consistent regular attendance is expected. Learners will not be removed from class for missing group activity sessions, but will be responsible for catching up by watching the session video and doing all work. I will be available to help if they find anything tricky. This class is based on a unit from Illustrative Mathematics for 6th Grade, so learners should already be familiar with elementary school arithmetic skills like the four basic operations with whole numbers, decimals, and fractions (with the exception that fraction division is in a later unit and is not expected yet). Needing to refresh their memory, typical of returning to school after the summer slide, is OK!
Learning Goals
Learners will explain the meaning of area.
Learners will explain how to find the area of a figure that is composed of other shapes.
Learners will know what it means for two figures to have the same area.
Learners will use reasoning strategies and what they know about the area of a rectangle to find the area of a parallelogram.
Learners will understand the terms "base" and "height" in the context of parallelograms and identify pairs of base and height of a parallelogram.
Based on their reasoning from the area of a rectangle, learners will develop, write, and explain the formula for the area of a parallelogram.
Learners will use the area formula to find the area of any parallelogram.
Learners will explain the special relationship between a pair of identical triangles and a parallelogram -- that a triangle is half of a parallelogram, and in particular, a right triangle is half of a rectangle.
Learners will use what they know about parallelograms to reason about the area of triangles.
Based on their reasoning from the area of a parallelogram or rectangle, learners will develop, write, and explain the formula for the area of a triangle.
Learners will use the area formula to find the area of any triangle.
Learners will understand the terms “base” and “height” in the context of a triangle and identify pairs of base and corresponding height of a triangle.
When given information about a base of a triangle, learners will identify and draw a corresponding height.
Learners will describe the characteristics of a polygon, including specific polygons (square, rectangle, triangle, parallelogram) using mathematical vocabulary, such as interior, exterior, sides, corners, angles, and parallel.
Learners will reason about the area of any polygon by decomposing and rearranging it, and by using what they know about rectangles, triangles, and possibly other polygons.
Learners will understand surface area of a three-dimensional object.
Learners will describe the features of a polyhedron using mathematical vocabulary, such as vertices, edges, and faces.
Learners will explain the difference between prisms and pyramids.
Learners will understand the relationship between a polyhedron and its net.
Learners will match polyhedra to their nets and explain how they know.
Given a prism, a pyramid, or a net of a prism or a pyramid, learners will be able to calculate its surface area.
Given a prism or a pyramid, learners will be able to draw its net.
Learners will write and explain the formula for the volume of a cube, including the meaning of the exponent.
Learners will develop, write, and explain the formula for the surface area of a cube.
When learners know the edge length of a cube, they will be able to find the volume and surface area, and express them using appropriate units.
Learners will apply what they know about the area of polygons to find the surface area of three-dimensional objects.
Learners will use surface area to reason about real-world objects.
Learners will be familiar with modeling shapes in GeoGebra.
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adapted from Open Up Resources Illustrated Math, Accelerated 6th Grade Unit 1, CC-BY
Syllabus
12 Lessons
over 4 WeeksLesson 1:
Tiling the Plane
50 mins online live lesson
Lesson 2:
Decomposing and Rearranging
50 mins online live lesson
Lesson 3:
Puzzling Areas
50 mins online live lesson
Lesson 4:
Parallelograms
50 mins online live lesson
Other Details
Parental Guidance
GeoGebra Classroom is a free site running the open-source GeoGebra dynamic geometry software in such a way as to sync to the cloud and allow the teacher to view learners' work. Accounts which allow learners to sign back in with full access to previous work are offered, but not required. Learners need to give a name either when entering the class code or when setting up their accounts so that I can find their work in the teacher interface; if they wish, such as for added privacy, a nickname or pseudonym is OK.
Explain Everything is a shared whiteboard, similar to Google Jamboard but more flexible. Learners do not need an account and can access the board to write on it through a link. Learners who do not specifically want to write on the board don’t need to access Explain Everything at all – I will share the screen in Zoom and they can watch.
TeacherMade is a site designed for school use which allows learners to access and complete worksheets, tutorials, and practice problems. If they wish, such as for added privacy, learners can sign in using a nickname or pseudonym.
External Resources
In addition to the Outschool classroom, this class uses:
- GeoGebra Classroom
- Explain Everything
- TeacherMade
Sources
Illustrative Mathematics, Accelerated Grade 6, Unit 1, including teacher guide -- accessed at im.kendallhunt.com
Joined May, 2021
4.9
12reviews
Teacher expertise and credentials
Master's Degree in Mathematics from Western Governors University
Hello mathematicians, puzzlers, and other curious people!
I'm a homeschool graduate, math professor, textile/sewing enthusiast, literary hobbyist, and general curious individual, here to share all of the above with the next generation. Math classes that are helpful and understandable, instead of just trying to figure it out for yourself from a book, are my main focus — I believe deep, confident understanding of math is for everybody.
I'm in US Central Time but flexible as to time zones. If you need a class offered at an international friendly time, just ask!
Want to start class already knowing a classmate? Or, do you just like getting deals? With my Bring-a-Friend discount, you can tell a friend to sign up and tell me who sent them, and you'll both get 25% off (processed manually through the refund system). You can bring more than one friend and get more than one discount — if you bring four friends, you get the class for free!
A few testimonials, in my students' own words:
I needed some help to knock out a 6 week Summer Business Calc class after not doing any math for over 20 years. Avrila worked with my schedule and demonstrated expert level knowledge of the subject matter in every lesson. Whether helping me construct equations from cryptic setups, develop test strategies, or just review the standard limit or calculus rules to complete problems, Avrila always knew what was required and gave me just enough information to figure things out for myself. I can not recommend her highly enough!
She explains things so well and walks you through topics step by step. She is extremely patient and super nice!
Avrila is awesome! She is extremely knowledgeable and flexible with my busy schedule. She explains these concepts in a super simple way making it much easier to understand. She helped me get through the majority of my semester, helping me improve my GPA more than I ever had hoped. I highly recommend her for any of your tutoring needs regarding stats.Reviews
Live Group Course
$57
weekly or $225 for 12 classes3x per week, 4 weeks
50 min
Live video meetings
Ages: 10-13
1-9 learners per class
