Middle School Math, Logic, and Problem Solving: Rates, Ratios, and Percentages
This six-week course is part of a math pod for neurodivergent learners ready to begin work on middle school level math. It includes a review of previous topics and uses a problem-based curriculum.
Malikai Bass M.A
Average rating:
5.0
Number of reviews:(316)
Popular
What's included
30 live meetings
25 in-class hoursHomework
1 hour per week. Students may have up to ten minutes of work to wrap up after the end of each session depending on time management during the session. Otherwise, all work will be completed in the session.Assessment
Students will receive a written progress report at the end of the class.Two numerical assessment grades can be provided if requested.Grading
includedClass Experience
US Grade 5 - 8
This is the second course in a micro-pod series for middle school math. Micro-pods are online learning pods which are a hybrid of individualized tutoring and traditional classes. Each section has no more than five learners which provides a foundation for strong relationships, social-emotional learning, and truly individualized instruction. This series is based on an accelerated math curriculum which covers three years of content, aligned to Common Core Math Standards, over the course of two school years. It is perfect for students beginning middle school and students who need to catch-up. 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 lead 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 found in Waldorf and Steiner education philosophies to help with recall and long-term retention. Course B is a six weeklong study of ratios, rates, and percentages which reinforces fraction and decimal based multiplication, area and volume, and unit conversion skills traditionally developed in the last years of elementary school while also encouraging students critical thinking and problem-solving skills through real world application. In week 1, learners work with mixtures and diagrams to develop an understanding of ratios as a mathematical relationship between two quantities. They then begin to identify equivalent ratios using existing fraction knowledge and are introduced to the double number line strategy. In week 2, learners continue working with double number line diagrams to explore ratios and begin to work with unit ratios and the specific “per each” language. They then expand their ability to use ratios to compare situations. As they gain comfort with ratios, students begin using tables to organize information about ratios. In week 3, students work with equivalent ratios on tables and begin working on part-whole problems. We also focus on problem-solving skills as we prepare for our mid-unit assessment. In week 4, students apply their knowledge to real-world problems through studying the Burj Khalifa as an example of ratios. Students take their mid-unit assessment and then apply ratios to solve problems based on unit conversions within imperial and metric systems. In week 5, students begin working more explicitly with rates including speeds and prices. They work on interpreting and comparing rates. They also learn that equivalent ratio have the same unit rate and use this to solve real-world problems comparing sales and deals in a grocery store setting. In week 6, students expand their knowledge of rates, ratios, and fractions to work with percentages using double number lines and tape diagrams. Students learn and implement benchmark percentages, and work on finding the percentage in real-world problems. In week 7, students tackle the real-world problem of calculating the time and money it would cost to paint a room based on a detailed floor plan. They generate a supply list and compare fictional deals to determine the best deal. We will have a review day and notebook check to prepare for our final assessment.
Learning Goals
This course aligns with the following "I can" statements:
I can draw a diagram that represents a ratio and explain what the diagram means.
I include labels when I draw a diagram representing a ratio, so that the meaning of
the diagram is clear.
I can explain the meaning of equivalent ratios using examples.
If I have a ratio, I can create a new ratio that is equivalent to it.
If I have two ratios, I can decide whether they are equivalent to each other.
I can label a double number line diagram to represent batches of a recipe or color
mixture.
When I have a double number line that represents a situation, I can explain what it
means.
I can create a double number line diagram and correctly place and label tick marks to
represent equivalent ratios.
I can explain what the word per means.
I can choose and create diagrams to help me reason about constant speed.
If I know the price of multiple things, I can find the price per thing.
I can decide whether or not two situations are happening at the same rate.
I can explain what it means when two situations happen at the same rate.
I know some examples of situations where things can happen at the same rate.
If I am looking at a table of values, I know where the rows are and where the columns
are.
When I see a table representing a set of equivalent ratios, I can come up with
numbers to make a new row.
When I see a table representing a set of equivalent ratios, I can explain what the
numbers mean.
I can solve problems about situations happening at the same rate by using a table
and finding a “1” row.
I can use a table of equivalent ratios to solve problems about unit price.
I can decide what information I need to know to be able to solve problems about
situations happening at the same rate.
I can explain my reasoning using diagrams that I choose.
I can create tape diagrams to help me reason about problems involving a ratio and a
total amount.
I can solve problems when I know a ratio and a total amount.
I can choose and create diagrams to help think through my solution.
I can solve all kinds of problems about equivalent ratios.
I can use diagrams to help someone else understand why my solution makes sense.
I can see that thinking about “how much for 1” is useful for solving different types of
problems.
When I know a measurement in one unit, I can decide whether it takes more or less
of a different unit to measure the same quantity.
I can convert measurements from one unit to another, using double number lines,
tables, or by thinking about “how much for 1.”
I know that when we measure things in two different units, the pairs of
measurements are equivalent ratios.
I understand that if two ratios have the same rate per 1, they are equivalent ratios.
When measurements are expressed in different units, I can decide who is traveling
faster or which item is the better deal by comparing “how much for 1” of the same
unit
I can choose which unit rate to use based on how I plan to solve the problem.
When I have a ratio, I can calculate its two unit rates and explain what each of them
means in the situation
I can give an example of two equivalent ratios and show that they have the same unit
rates.
I can multiply or divide by the unit rate to calculate missing values in a table of
equivalent ratios.
I can choose how to use unit rates to solve problems.
I can use double number line diagrams to solve different problems like “What is 40%
of 60?” or “60 is 40% of what number?”
I can use tape diagrams to solve different problems like “What is 40% of 60?” or “60 is
40% of what number?”
When I read or hear that something is 10%, 25%, 50%, or 75% of an amount, I know
what fraction of that amount they are referring to.
I can choose and create diagrams to help me solve problems about percentages.
I can solve different problems like “What is 40% of 60?” by dividing and multiplying.
I can solve different problems like “60 is what percentage of 40?” by dividing and
multiplying.
I can apply what I have learned about unit rates and percentages to predict how long
it will take and how much it will cost to paint all the walls in a room.
Other Details
Supply List
Graph Paper Pencil Colored Pencils Ruler Scissors Whiteboard Index Cards Markers Worksheets and printed materials provided in the Outschool classroom.
Language of Instruction
English
External Resources
In addition to the Outschool classroom, this class uses:
Joined April, 2021
5.0
316reviews
Popular
Teacher expertise and credentials
I have been completed three college-level courses on common-core math instruction. I have worked as a math instructor for middle school students in a private school setting. I have ten years of experience as a math tutor including working with students from ages 5 (kindergarten) to 25 (Graduate Readiness Exam). Reviews
Live Group Class
$425
for 30 classes5x per week, 6 weeks
50 min
Completed by 10 learners
Live video meetings
Ages: 10-12
3-6 learners per class
