Proportional Reasoning/ Proportional Relationships Learning Goal: Students will understand and analyze proportional relationships and use them to solve real-world and mathematical problems. Students will be able to recognize, represent and analyze proportional relationships and use them to solve real-world and mathematical problems. Essential Questions: 1) What kinds of questions can be answered using proportional reasoning? 2) How is proportional reasoning of geometric figures used to solve problems? 3) What kinds of questions can be answered using proportional reasoning? 4) How are comparisons used in proportional reasoning? Higher Order Thinking Questions: 1) How is the unit rate calculated? 2) Can we calculate unit rates when both values in the ratio are fractions? 3) How can finding the unit rate be useful? 4) How can unit rates with fractions be applied in the real world? 5) What relationship do you see between the measurements? 6) What can you predict about an image that has a scale factor of 3? 7) How are comparisons used in proportional reasoning? 8) How can setting up proportions help you determine if figures are similar? 9) What is the relationship between ratios, rates, and proportions? 10) How does a point on a graph represent a proportional relationship? 11) How are the constant of proportionality and the unit rate alike? 12) How do you determine which value is (independent) and which value is (dependent)? 13) What is the structure of proportional relationship equations, and how do we use them? Unit Breakdown: Ratios of Fractions and Their Unit Rates EngageNY Module I: Lesson 11/12 Holt 4-2 Relating Scale Drawings to Rates EngageNY Module I: Lesson 16 Holt 4-8 Using Similar Figures to Find Unknown Measures Holt 4-9 Unit Rate as a Scale Factor EngageNY Module I: Lesson 17 Holt 4-10 Unit Rate as a Scale Factor EngageNY Module I: Lesson 17 Holt 4-10 Computing Actual Lengths from Scale Drawings EngageNY Module I: Lesson 18 Holt 4-10 Unit Rate as the Constant of Proportionality EngageNY Module 1: Lesson 7 (Page 59) Holt 4-2 Building Concepts of Proportions Holt 4-3 Holt 4-4 Representing Proportional Relationships with Equations EngageNY Module 1: Lesson 8/9 (Page 66) Interpreting Graphs of Proportional Relationships Holt 5-3 EngageNY Module 1: Lesson 10 (Page 84) Vocabulary: 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. Rate Unit Rate Rational Numbers Equivalent Ratios Proportions Similar Corresponding Parts/Sides/Angles Indirect Measurement Constant of Proportionality Scale Factor Scale Drawing Rate Unit Rate Proportion Cross Product Proportional Relationship Constant of Proportionality Coordinate Plane X- axis Y- axis Origin Ordered Pair Daily Agenda Monday Aug 18: 1. Bus PowerPoint 2. First Day Check List 3. Student Code of conduct 4. Classroom rules and procedures 5. Evacuation procedures- fire, tornado, lockdown 6. Social Contract Tuesday Aug 19: 1. Continue going over classroom rules and procedures 2. Section 4.1 Ratios Notes: Introduce Ratios (What are they, 3 ways to write them) Wednesday Aug 20: 1. How do you divide a fraction to turn into a decimal 2. Create and compare ratios Thursday Aug 21: 1. Explain unit rate and how to calculate it 2. Practice various unit rate problems (include fractions) 3. Section 4.2 Introduction and Notes on Rates Friday Aug 22: 1. Review unit rate 2. Ratio experiment with Skittles. Monday Aug 25: 1. How to find a proportion 2. Section 4.3 Notes Tuesday Aug 26: 1. Increasing and decreasing fractions to form proportion 2. Section 4.3 Wednesday Aug 27: 1. Section 4.4 2. Notes on solving proportions Thursday Aug 28: 1. Section 4.4 2. Using cross products to find a proportionate amount Friday Aug 29: 1. Review Ratios and Proportions 2. Quiz on Rations and Proportions Monday Sept 1: **Labor Day**No School** Tuesday Sept 2: 1. Notes on proportions and similar figures (what makes figures similar) 3. Explore similar figures 4. Section 4-8 Notes Wednesday Sept 3: 1. Find missing measurements by setting up ratios (cross multiplying) 2. Section 4-9 Notes Thursday Sept. 4: 1. Review of cross products when finding missing measurement of similar shapes. 2. Practice It 4-9 Friday Sept 5: 1. Review 4-9 Practice It 2. Shadow activity to use our shadow to find our true height Monday Sept 8: 1. Review of Similar Shapes 2. Class Work: Apply it 4-9 Tuesday Sept 9: 1. Introduction to scale drawings 2. How do we use models in real life? 3. Section 4-10 Notes Wednesday Sept 10: 1. How are scale drawings useful and how are scale drawings created? What do they have to do with proportions? 2. Clear up any misconceptions with scale drawings 3. Create a scale drawing Thursday Sept 11: 1. Finish Scale drawing 2. HW: Practice It Section 4-10 (Due Friday 9/12) Friday Sept 12: 1. Review of X and Y axis 2. Practice graphing on coordinate plane 3. Learn it Section 5-3 4. Introduction to graphing proportionate relationships Section 5-3 Monday Sept 15: 1. Graphing exercise on white boards 2. How to find if a function is proportionate Tuesday Sept 16: 1. Summarize graphing and clear up any misconceptions 2. HW: Practice It Section 5-3 (Due Wednesday 9/17) Wednesday Sept 17: 1. Review Proportions and Ratios Thursday Sept 18: 1. Review Scale Drawings and Graphing Proportionate Functions Friday Sept 19: 1. Test covering Unit 1 and Unit 2: Proportional Reasoning and Proportional Relationships

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