Created on: August 24, 2009

Website Address: https://library.curriki.org/oer/21--26-Unit-on-Proportional-Reasoning-Rates-Ratios-and-Percents

TABLE OF CONTENTS

- Cluster - MA.8.CCSS.Math.Content.8.NS The Number System
- Curriki Project Based Geometry
- Cluster - MA.8.CCSS.Math.Content.8.EE Expressions and Equations
- Cluster - MA.8.CCSS.Math.Content.8.F Functions
- Cluster - MA.8.CCSS.Math.Content.8.G Geometry
- Cluster - MA.8.CCSS.Math.Content.8.SP Statistics and Probability

- Quiz - 8.NS The Number System Cluster: Know that there are numbers that are not rational, and approximate them by rational numbers. Standards: 8.NS.1, 8.NS.2
- 8.NS.1 Know that numbers that are not rational are called irrational.
- 8.NS.2 Use rational approximations of irrational numbers to compare the size of irrational numbers.

- Quiz - 8.EE Expressions and Equations Cluster: Work with radicals and integer exponents. Standards: 8.EE.1, 8.EE.2, 8.EE.3, 8.EE.4
- Quiz: 8.EE Expressions and Equations: Understand the connections between proportional relationships, lines, and linear equations Standards: 8.EE.5, 8.EE.6
- Quiz - 8.EE Expressions and Equations: Understand the connections between proportional relationships, lines, and linear equations Standards: 8.EE.7a, 8.EE.7b, 8.EE.8a, 8.EE.8b, 8.EE.8c
- 8.EE.1 Know and apply the properties of integer exponents to generate equivalent numerical expressions.
- 8.EE.2 Use square root and cube root symbols to represent solutions to equations of the form x^2 = p and x^3 = p, where p is a positive rational number.
- 8.EE.3 Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities
- 8.EE.4 Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used.
- 8.EE.5 Understand the connections between proportional relationships: Graph proportional relationships, interpreting the unit rate as the slope of the graph.
- 8.EE.6 Understand the connections between proportional relationships: Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line
- 8.EE.7.a Analyze and solve linear equations and pairs of simultaneous linear equations: Solve linear equations in one variable
- 8.EE.7.b Analyze and solve linear equations and pairs of simultaneous linear equations: Solve linear equations with rational number coefficients
- 8.EE.8.a Analyze and solve linear equations and pairs of simultaneous linear equations: Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs
- 8.EE.8.b Analyze and solve linear equations and pairs of simultaneous linear equations: Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations.
- 8.EE.8.c Analyze and solve linear equations and pairs of simultaneous linear equations: Solve real-world and mathematical problems leading to two linear equations in two variables.

- 8.EE.5 Curriculum Unit
- Proportional Relationships
- Pythagorean Theorem and Similar Triangles: Karlie Turner- Lesson Plan 3
- 2.1 - 2.6: Unit on Proportional Reasoning, Rates, Ratios and Percents

- Institute for Education Sciences principles for instructional design
- 2.1-2.6 Complete Student Packet
- 2.1 Introduction to Proportions and Percents--Sample Lesson
- 2.1 Powerpoint
- 2.1 Supplementary Resources
- 2.2 Proportions (continued) and Intro to Unit Rate
- 2.2 Powerpoint
- 2.2 Supplementary Resources
- 2.3 Unit Rates and Proportions (Making Connections)
- 2.3 Powerpoint
- 2.3 Supplementary Resources
- 2.4 Rates: Applications and Multiple Representations
- 2.4 Supplementary Resources
- 2.5 Mastery of Percent Applications
- 2.5 Supplementary Resources
- 2.6 Rates, Graphs, and Linear Equations
- Open Format Copies of Materials

IN COLLECTION

An entire unit of activities for proportional reasoning (including percents). Designed for classes that need to re-teach a lot of middle school content while also meeting high school Algebra I objectives. Also a great resource for middle school teachers. The approach mixes direct instruction with guided inquiry and real-life applications. Students won't get lost, but they will construct some of the concepts themselves and see how the material applies to their lives.

This research summary on organizing instruction introduces the design principles underlying the Implementing Algebra project. Citation: Pashler, H., Bain, P., Bottge, B., Graesser, A., Koedinger, K., McDaniel, M., and Metcalfe, J. (2007). Organizing Instruction and Study to Improve Student Learning (NCER 2007-2004). Washington, DC: National Center for Education Research, Institute of Education Sciences, U.S. Department of Education. Retrieved from http://ncer.ed.gov.

Packets for Lessons 2.1-2.6, in a single MS Word file.

Introduces proportions and percents through a pictorial model, building up to the Equivalent Fractions method of solving proportions. Comes with a companion PowerPoint presentation to help implement the lesson. Fully editable. A mix of direct instruction and small-group inquiry.

Companion Powerpoint to accompany Lesson 2.1. The Powerpoint is designed to help the teacher quickly and easily draw diagrams that aid student understanding. It also frees the teacher to wander among the students while they work and discuss...let the computer stay in the front of the room and do the writing for you when you need direct instruction.

Bellwork, extension activity, flashcards (important), and related materials.

In teaching proportions, this lesson shifts students from 2.1's pictorial approach to 2.2's computational approach of equivalent fractions. With deeper comprehension, students move from the concrete (pictures) to the abstract (an algorithm). After some differentiated drill practice, the lesson introduces the concept of Unit Rates. A mix of direct instruction and small-group inquiry.

Companion Powerpoint to accompany Lesson 2.2. Differentiated drill practice displays several questions at once, in increasing order of difficulty, allowing students to work at their own pace through the problems that are right for them. With a remote mouse clicker, the teacher can wander the room as students work, praising and prompting students, while gradually displaying the correct solutions with simple clicks of the mouse. This Powerpoint also includes notes on unit rate and division.

Extra materials for Lesson 2.2

In 2.2, we introduced what Unit Rates mean and how to calculate them. In 2.3, we apply Unit Rates to solve problems and then investigate how the same problems could be solved with proportions. The lesson begins with a pictorial model of applying unit rates (concrete) and moves to a computational method (abstract). A mix of whole-class practice and small-group collaboration.

A companion Powerpoint to Lesson 2.3. The presentation allows the teacher to quickly and easily display diagrams step-by-step to model problem-solving with pictures. The presentation also allows for efficient interleaving of worked examples and practice problems. Worked examples can be displayed with a few clicks of the mouse, leaving more time for class discussion and reflection on the examples.

Supplements (e.g., Bellwork) for Lesson 2.3

Begins with an intro to Cross-Multiplying (including a clear presentation of why it works). Then builds fluency with rates. Teaches how to set up rate problems quickly so the proper units cancel. Applies this concept to percent questions, laying the groundwork for Lesson 2.5. A mix of whole-class discussion and small-group practice.

Extra stuff for Lesson 2.4

Integrates 3 ways of understanding percents: proportions, rates, and percent equations. In a percent equation, "45% of x" is translated into (0.45)(x). Lessons 2.1-2.4 are prerequisite. This lesson requires students to make connections between all the different was of representing percent questions. Making connections leads to deeper understanding and better retention. A mix of whole-class and small-group instruction.

Bellwork, etc. for Lesson 2.5

Teach slope-intercept form now, while rates of change are fresh in their minds. This early focus on slope-intercept form gives students months to master the main ideas. Later, in your unit on linear functions, they'll have a solid foundation for your teaching of standard and point-slope form. This lesson builds smoothly on 2.3-2.5 and uses real-world problems to help students make meaning from the symbols. A companion PowerPoint is being created.

These are the same materials in open formats such as ODF