To use this document please select FILE → MAKE A COPY
Unit Plan
Grade: 7 | Content Area: Math | Course Name: Pre Algebra |
Unit: 4 | Description of Course: During this unit students will use proportional relationships to solve real world problems. | Approximate Time Needed: 15-20 Days |
Learning Targets | Assessments | Instructional Considerations | Instructional Approach | Resources |
4.1 I can identify proportional relationships including inversely proportional ones. 4.2 I can identify and use direct variation. 4.3 I can show a proportional relationship through multiple representations. 4.4 I can translate from one representation to another. 4.5 I can identify and use equivalent rates. 4.6 I can identify and find the slope of a line. | Pre-Assessments: (none) Formative Assessments: Practice Exercises in lessons Benchmark Assessment: (none) | Student Background Knowledge: Students must have a basic understanding that a ratio can be represented as a fraction, as either part-to-part or part-to-whole. Essential Questions: 1. How can ratios be used to make decisions and solve problems? 2. How is writing and solving ratios, proportions and unit rates helpful when solving real-life problems? 3. What is the difference between direct and indirect variation and how are both represented? 4. What is slope and how can it be used in real-world situations? 5. How can proportional relationships be shown as equations, functions, graphs, and tables? Academic Language: compare compute determine display function identify interpret relation Content Specific Language: Listed Below | Cross-Content Integration: agriculture social studies science economics physical fitness | Web Resources: Research: ck12 Technology Resources: Khan Academy Math Playground James Sousa ck12 Community Resources: (none) |
Content Specific Language:
Coefficient- In an equation that represents a line, the coefficient of represents the slope. The coefficient of a term is the numerical part of the term.
Constant of Proportionality- The constant of proportionality is the constant value of the ratio of two proportional quantities x- and y; usually written y = kx, where k is the factor of proportionality
Constant of Variation- The constant of variation in a direct variation is the constant (unchanged) ratio of two variables quantities.
Direct Variation- Direct variation is when one variable changes the other changes in proportion to the first.
Directly Proportional- Directly proportional relationships are in the form y=kx. The x and y values increase or decrease together.
Equivalent Ratio- Equivalent ratios are two ratios that are equal.
Inversely Proportional- Inversely proportional relationships are in the form y=k/x. As the one of the values increases, the other decreases.
Linear Equation- A linear equation is an equation that represents a line.
Linear Graphs- A linear graph is a graph of a straight line or lines.
Negative Slope- A line that slants down from left to right has a negative slope.
Per- Per signals us that we are talking about a rate, such as $6 per pound of turkey.
Positive Slope- A line that slants up from left to right has a positive slope.
Proportion- A proportion is a statement in which two ratios are equal: .
Proportional Reasoning- Proportional reasoning is when we figure out a missing value in a proportion by thinking about the relationship between the numbers in the two ratios.
Proportional Relationship- A proportional relationship between two quantities is one in which the two quantities vary directly with one and other. If one item is doubled, the other, related item is also doubled.
Rate- A rate is a special kind of ratio. It compares two different types of units, such as dollars and pounds.
Rate of Change- The rate of change is the change in the y-value divided by the change in the x-value for two points on a graph.
Ratio- A ratio represents a comparison between two quantities. We can write ratios in fraction form, using a colon or using the word "to."
Rise- The rise is the number of units that you move up or down from one point on a graph to another point.
Run- The run is the number of units that you move left or right to get to the next point on the line.
Slope- The slope of a line describes the steepness of a line. It is described as the rise over the run.
Unit Rate- A unit rate has a denominator of 1, meaning that it is the measure for one of whatever you are talking about: 1 mile, 1 pound, 1 foot, etc.