Difference Between Proportional and Non-Proportional Variables Introduction
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This learning activity provided by:
Author:
YVETTE AKRIDGE
System: Andalusia City School: Andalusia City Board Of Education
General Activity Information
Activity ID:
2884
Title: Difference Between Proportional and Non-Proportional Variables Introduction
Digital Tool/Resource: Difference Between Proportional and Non-Proportional Variables Introduction Google Doc
Web Address – URL:
Overview: In this learning activity, students will be introduced to the differences between proportional and non-proportional situations or relationships. The lesson includes dialogue, teaching material, and re-teaching material. To get the most from this activity, students should know that linear relationships can be represented as words, tables, graphs, and equations.
This learning activity can be used as a stand-alone activity or a Before/Engage Activity, the During and After activities can be found in the Notes or Recommendations section.
Associated Standards and Objectives
Content Standard(s):
Mathematics 4. Determine whether a relationship between two variables is proportional or non-proportional. [Grade 8, 7]
Unpacked Content
Evidence Of Student Attainment:
Students:
Describe a given relationship as proportional or non-proportional when given in various contexts. Teacher Vocabulary:
Ratio
Proportion
Proportional
Independent variable
Dependent variable Knowledge:
Students know:
How to use rates and scale factors
to find equivalent ratios.
What a unit rate is and how to find
it when needed. Skills:
Students are able to:
Recognize whether ratios are in a proportional relationship using tables and verbal descriptions. Understanding:
Students understand that:
a proportion is a relationship of equality between quantities. Diverse Learning Needs:
Mathematics 7. Determine whether a relationship between two variables is proportional or non-proportional.
Unpacked Content
Evidence Of Student Attainment:
Students:
Describe a given relationship as proportional or non-proportional when given in various contexts. Teacher Vocabulary:
Ratio
Proportion
Proportional
Independent variable
Dependent variable Knowledge:
Students know:
how to use rates and scale factors to find equivalent ratios.
What a unit rate is and how to find
it when needed. Skills:
Students are able to:
Recognize whether ratios are in a proportional relationship using tables and verbal descriptions. Understanding:
Students understand that:
a proportion is a relationship of equality between quantities. Diverse Learning Needs:
Essential Skills:
Learning Objectives: M.8.7.1: Define proportional, independent variable, dependent variable, unit rate.
M.8.7.2: Recall equivalent ratios and origin on a coordinate (Cartesian) plane.
M.8.7.3: Recall how to write a ratio of two quantities as a fraction.
M.8.7.4: Identify the unit rate of two quantities.
M.8.7.5: Recall that for a relationship to be proportional, both variables must start at zero.
Prior Knowledge Skills:
Define unit rate, proportion, and rate.
Create a ratio or proportion from a given word problem.
Calculate unit rate by using ratios or proportions.
Write a ratio as a fraction.
Define ratio, rate, proportion, percent, equivalent, input, output, ordered pairs, diagram, unit rate, and table.
Create a ratio or proportion from a given word problem, diagram, table, or equation.
Calculate unit rate or rate by using ratios or proportions with or without a calculator.
Restate real-world problems or mathematical problems.
Construct a graph from a set of ordered pairs given in the table of equivalent ratios.
Calculate missing input and/or output values in a table with or without a calculator.
Draw and label a table of equivalent ratios from given information.
Identify the parts of a table of equivalent ratios (input, output, etc.).
Compute the unit rate, unit price, and constant speed with or without a calculator.
Create a proportion or ratio from a given word problem.
Learning Objectives: The students will determine whether a relationship between two variables is proportional or non-proportional.
Strategies, Preparations and Variations
Phase: Before/Engage
Activity:
This activity will be used to introduce the differences between proportional and non-proportional situations or relationships.
The teacher will use the Difference Between Proportional and Non-Proportional Introduction to introduce the lesson objective.
The lesson should be taught whole group and it includes an Essential Question, Methods, and Review to help the student understand the concept.
The teacher will begin the lesson by using the Essential Question to check to see what the students already know about proportional and non-proportional relationships.
Next, the teacher will use the Methods section of the lesson to teach the students about the different ways to determine if a relationship is proportional or non-proportional.
In conclusion, the teacher will use the Review section of the activity: If a relationship is nonlinear, it is nonproportional. If it is linear, it may be either proportional or nonproportional. When the graph of the linear relationship contains the origin, the relationship is proportional.
The teacher should circulate the room while using the Difference Between Proportional and Non-Proportional Introduction to check for understanding.
Assessment Strategies: The student responses during the class discussion will be used as a formative assessment.
Advanced Preparation:
Students should know that two variables show direct variation if y = kx and k is not equal to zero. k represents the constant of proportionality.
The teacher should review the Difference Between Proportional and Non-Proportional Introduction slides prior to using the activity.
The teacher will need to decide on how he/she will display the Google Slide presentation prior to using the activity.
Variation Tips (optional):
Teachers may modify the slides and examples to fit their needs.
Teachers may substitute the chosen text for those that they feel are more suitable to their students, or those that align with a unit in their classes.
Notes or Recommendations (optional):
Keywords and Search Tags
Keywords and Search Tags:
constant, direct variation, nonproportional, proportional, ratio, ykx
