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| Seventh Grade - Find unit rates associated with ratios of fractions, areas, and other quantities in like or different units
- Decide whether two quantities are proportional using ratio tables and graphs
- Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions
- Represent proportional relationships with equations
- Explain what a point (x,y) means on a proportional graph in context, particularly (0,0) and (1,r), where r is the unit rate
- Use proportionality to solve ratio problems
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| Ratios & Proportional Relationships 7.RP.A. Analyze proportional relationships and use them to solve real-world and mathematical problems. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction ½ / ¼ miles per hour, equivalently 2 miles per hour. 7.RP.A.2. Recognize and represent proportional relationships between quantities. 7.RP.A.2a. Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin. 7.RP.A.2b. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn. 7.RP.A.2d. Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error. © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved. | Students will have opportunities to: - SMP1 - Make sense of problems and persevere in solving them
- SMP2 - Reason abstractly and quantitatively
- SMP3 - Construct viable arguments and critique the reasoning of others
- SMP4 - Model with Mathematics
- SMP5 - Use appropriate tools strategically
- SMP6 - Attend to precision
- SMP7 - Look for and make use of structure
- SMP8 - Look for and express regularity in reasoning
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| Fifth Grade - Generate numerical patterns given rules, identify the relationship, and form ordered pairs
- Plot points in the first quadrant of the coordinate plane
- Convert standard measurement units within a measurement system
Sixth Grade - Graph ordered pairs in all four quadrants of the coordinate plane
- Understand ratios and describe ratio relationships
- Compare ratios using tables
- Use ratio reasoning to convert measurement units
- Understand rates and unit rates
| Eighth Grade - Use similar triangles to explain why the slope is the same between any two points on a line
- Graph proportional relationships, interpreting the unit rate as the slope
- Compare proportional relationships represented in different ways.
- Derive y=mx and y=mx + b
- Interpret the rate of change and initial value of a function
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| Teacher Edition Vocabulary: Unit Rate, Proportion, Equivalent, Cross Product Property, Equivalent, Rate of Change, Slope, Direct Variation, Ratio Table, Ordered Pairs Other Vocabulary: Communication Satellite, Orbit, Pay Rate, lap vs. length
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| The following lesson plan sequence is obtained from Big Ideas Learning (2015). Each lesson is aligned with a learning objective to inform the teachers on what students should be able to do at the end of the lesson. The student objective informs the students of their learning goals for the day and it should be reviewed before, during and at the end of the lesson. Each lesson includes a mathematics task that should be implemented to meet the learning objectives. Teachers can select from the practice opportunities to reinforce the learning goals of the day |
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| The use of sentence stems as a language support are beneficial to all students, including English Language Learners. The use of sentence stems encourages the learning of mathematics in a language rich environment which has an impact on other learning as well. The sentence stems are a beginning place for supporting students' use of academic language and encourage discussion and writing as students learn content. |
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