Math - Unit 3: Percent & Proportional Relationships

Focus on Unit 3: Percent & Proportional Relationships, with self-assessment tools such as Stoplight assessments.

a. Fractions, Decimals, and Percent

Understand the relationship between fractions, decimals, and percentages:
- All three represent quantities in different forms.
- They can be converted from one to another through multiplication and division.
Learn how to select the appropriate form for problem-solving based on the context of the problem.

b. Ratios, Unit Rates, and Proportions

Explore how ratios (comparison of two quantities) relate to unit rates (a ratio that compares a quantity to one unit of another quantity) and proportions (an equation that states that two ratios are equal).

c. Constant of Proportionality and Constant Rate

Examine how these constants influence proportional (direct variation) and linear relationships.
- The constant of proportionality is defined as the constant ratio between two directly proportional quantities.
- In linear relationships, the constant rate is the slope of the line, which represents the rate of change.

d. Proportional Relationships

Determine criteria to assess if a relationship is proportional:
- Check if the ratio between two variables remains constant.
- Analyze equivalent fractions, graphs through the origin, and equations in the form $y=kx$.

e. Creating and Comparing Representations

Craft equations, tables, graphs, and real-world contexts to depict relationships.
Compare the visual and numerical representations of the same data to enhance comprehension.

Powers of Ten: A numerical representation of values in the form of $10^n$.
Ratio: A comparison of two quantities, often expressed as a fraction.
Rate: A specific type of ratio that compares different units (e.g., miles per hour).
Unit Rate: A rate in which the second quantity is 1 (e.g., $60$ miles per hour indicates $60$ miles per $1$ hour).
Proportion: An equation that shows two ratios are equivalent, e.g., $a/b = c/d$.
Constant of Proportionality (k): The value of the ratio of any two proportional quantities.
Rate of Change: The ratio that describes how much a quantity changes in relation to the change in another quantity.
Independent Variable: The variable in an equation that represents the input or cause; often denoted as $x$.
Dependent Variable: The variable that represents the output or effect; often designated as $y$.
Equation, Table, Graph: Different forms of data representation used to summarize or analyze relationships.

Proficient calculation with fractions, particularly through multiplication & division.
Ability to find equivalent fractions and convert between fractions, decimals, and percentages.
Understand ratios and graphing on a coordinate plane.

Grade 6 Skills
- Greatest Common Factor
- Least Common Multiple
- Find Equivalent Ratios
- Ratio Tables
- Ratio Table & Graph
Grade 7 Skills
- Practice on the Coordinate Plane:
  - Digital IXL G7: Section O: Percent:
    - Convert between fractions, decimals, and percentages.
    - Estimate Percent.
  - Section L: Ratios, Rates, & Proportions:
    - Finding Percent.
    - Percent Word Problems (answers may vary from the answer key).
    - Percent Change.

Section N: Proportional Relationships
- Focus on equations, tables, and graphs.
Section O: Percent assignments:
- Finding Percent (multiple problems).
- Percent word problems.
- Percent change (several problems).
- Percent change word problem applications.

Engage in conceptual questions related to ratios and proportions to check understanding.

Participate in Ratio Challenges.
Explore additional materials such as 'Percentage extensions.pdf' for further practice.