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:
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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