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LFS DIGITAL > Instructional Unit Topics > Math Unit Topics > Ratios and Proportions  

Ratios and Proportions

LFS-DIGITAL K-U-D for Unit: Ratios and Proportions

 

                                                                                                 Key Learning

(What is the big understanding for this unit?  What will you ultimately want students to understand as a result of the instruction?  This is a “big picture” understanding, based both on the most critical standards and the thematic focus of the unit.)

 

 

Ratios, fractions, differences, and percents can be used to form comparison statements in a given situation and analyzed to solve real world problems

 

 

Unit Essential Question

(What broad question will students be able to answer as a result of the instruction? This question should reflect the most critical standards on which the instruction is based.  This question is the inverse of the Key Learning; the Key Learning would provide an “ideal” response to this question.)

 

 

How can ratios, fractions, differences, and percents  be used to form comparison statements in a given situation and analyzed to solve real world problems?

 

 

Unit Description

(Briefly summarize the focus and content of the unit.)

 

In this unit ratios, fractions, differences, and percents will be used to form comparison

statements in a variety of situations and will be used to analyze and solve real world problems.

 

Grade-Level Standards Addressed in the Unit

(List the critical grade-level standards on which the instruction will be based.  Since many of the standards are recursive, reinforced throughout the year’s instruction, list only those that will be the focus of the instruction and assessments for this unit.)

 

 

CC:  7.RP.1, 7.RP.2, and 7.RP.3

 

 

 

Know

(Factual: nouns or noun phrases related to key concepts; terminology, academic vocabulary, formulas, etc., often found or implied in the language of the grade-level standards.)

Understand

(Conceptual:  key understandings that students will gain as a result of the instruction within the unit, found in the language of the grade-level standards, and generally written in complete sentences. These understandings will contribute to the overall key learning of the unit.)

Do

(Procedural, Extending Thinking:  written as verb phrases, often found or implied in the language of the grade-level standards. These statements provide discreet targets for demonstrating learning.  Often the assessments for the learning will be selected

 from this column.)

 

How to find the unit rate

 

How to express rate

 

How to set up and compute with proportions and ratios

 

How to compare ratios, percents and fractions

 

Effects of scaling up and scaling down ratios

 

 

Ratios, fractions, differences, and percents can be used to form comparison statements in a given situation and analyzed to solve real world problems

7.RP.1. Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units.

7.RP.2. Recognize and represent proportional relationships between quantities.

·         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.

·         Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.

·         Represent proportional relationships by equations. 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.

·         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.

7.RP.3. Use proportional relationships to solve multistep ratio and percent problems.

 

* Integrate a variety of file types to create and illustrate a document or presentation that explains your knowledge of proportional reasoning.  Be sure to use multiple examples that clearly demonstrate your understanding. (1,6)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 Below is a description of LoTi level 3 instructional focus in the classroom. For more information about LoTi and descriptions of higher LoTi levels please follow the link below.
 www.loticonnections.com

 

At a Level 3 (Infusion), the instructional focus emphasizes student higher order thinking (i.e., application, analysis, synthesis, evaluation) and engaged learning. Though specific learning activities may or may not be perceived as authentic by the student, instructional emphasis is, nonetheless, placed on higher levels of cognitive processing and in-depth treatment of the content using a variety of thinking skill strategies (e.g., problem-solving, decision-making, reflective thinking, experimentation, scientific inquiry). Teacher-centered strategies including the concept attainment, inductive thinking, and scientific inquiry models of teaching are the norm and guide the types of products generated by students using the available digital assets.

Digital tools and resources are used by students to carry out teacher-directed tasks that emphasize higher levels of student cognitive processing relating to the content under investigation.

 

Print Resources

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 


 
 
Discovery Education Resources


Videos:

 Rate

Example 1: Speed as a Rate

Example 2: Rate as a Ratio of Changes

Example 3: Calculating with Rates

Defining Ratio and Proportion

Applying Ratios in Word Problems

Ratios

Percents

Solving Problems with Ratios

Fractions: Ratio and Proportion

Math Explanations:

Grades 06-07: Rates: Finding Unit Rate

Grade 07-08: Ratios and Rates: Converting Units in Rates and Comparing

Grade 07-08: Ratios and Rates: Describing Different Ratios from a Diagram

Grade 07-08: Ratios and Rates: Writing Verbal Ratios as Fractions in Simplest Form

Grades 06-07: Ratios: Comparing Two Ratios

Grades 06-07: Ratios: Comparing Three or More Ratios

Grades 07-08: Percents, Decimals, and Fractions: Comparing Percents of Shaded Parts in Different Figures

Grades 07-08: Percents, Decimals, and Fractions: Identifying Easier Ways to Compare Numbers

Open Resources

 


Resource 1: Ratios and proportions - Video and ebook
Media type: video, ebook
Description: A short video that introduces proportions, ratios, the rule or proportions, and cross-multiplication and an ebook with more detailed explanations as well as many practice problems including word problems.
Level: Intermediate

Credit: K12 Handhelds
License: CC BY

Notes/activity suggestions:
Tags: grade7, math, ratios, proportions, rule of proportions, cross-multiplication

 


Resource 2: Solving proportions, Simplifying ratios, Three ways to solve a proportion
Media type: video
Description: Short videos with a teacher explaining how to solve proportions and simplify ratios
Level: Intermediate

Credit: Duane Habecker, www.nextvista.org
License: custom

Notes/activity suggestions:
Tags: grade7, math, ratios, proportions, cross-multiplication

 

 

Resource 3: Ratios and proportions

Media type: textbook
Description: A chapter of a textbook on ratios and proportions, including word problems
Level: Intermediate

Credit: Anne Gloag, Andrew Gloag, CK12
License: CC BY SA

Notes/activity suggestions:
Tags: grade7, math, geometry, similiarity, ratios, proportions

 

 

Resource 4: Unit on Proportional Reasoning, Rates, Ratios and Percents
Media type: Text
Description: An entire unit of activities for proportional reasoning (including percents). The approach mixes direct instruction with guided inquiry and real-life applications. Includes a comprehensive student packet as well as PowerPoints and other resources.
Level: Intermediate

Credit: Kevin Hall
License: CC BY SA

Notes/activity suggestions:
Tags: grade7, math, grade8, math, proportional reasoning, ratios, percents

 

 


Resource 5: Similarity
Media type: textbook
Description: A chapter of a textbook on similiarity, ratios, and proportions
Level: Intermediate

Credit: Jim Sconyers, CK12
License: CC BY SA

Notes/activity suggestions:
Tags: grade7, math, geometry, similiarity, ratios, proportions

 


Resource 6: Ratios and proportions
Media type: text
Description: An explanation of ratios and proportions with many practice worksheets
Level:

Credit: HelpingWithMath.com
License: CC BY SA

Notes/activity suggestions:
Tags: grade7, math, ratios, proportions

 


Resource 7: Ratios and proportions
Media type: text
Description: A textbook chapter on ratios, proportions, and solving proportions using cross products
Level: Advanced

Credit: Anne Gloag, Andrew Gloag (CK12)
License: CC BY SA

Notes/activity suggestions:
Tags: grade7, math, ratios, proportions, cross-products, cross-multiplying

 


Resource 8: Animation tutor - Dimensional thinking (requires a download)
Media type: interactive
Description: An interactive tutorial taking users through a variety of real-world problems involving proportions and rations
Level: Intermediate, Advanced

Credit: San Diego State University
License: CC BY NC ND

Notes/activity suggestions:
Tags: grade7, math, ratios, proportions, word problems

 

Resource 9: Khan Academy videos:  Introduction to ratios, Ratio problem with basic algebraScale and indirect measurement
Media type: video
Description: Short talking chalkboard explanations of math concepts
Level: Intermediate

Credit: Sal Khan
License: CC BY SA

Notes/activity suggestions:
Tags: grade7, math, ratios, proportions

 

 

Media type: interactive
Description: SMART Board notebooks for learning about direct proportion and solving ratio problems and for learning about direct proportion and solving ratio problems
Level: Intermediate

Credit: SMART Technologies
License: CC BY

Notes/activity suggestions:

Tags: grade7, math, ratios, proportions, SMART

 

 
* new Resource 11: Solving Proportions and Percents (downloadable versions not in YouTube available here)
Media type: video
Description: Explanatory video with learning goals, explanations and examples, guided practice, and self-checks.
Level: Advanced

Credit: Karl Fisch
License: CC BY SA 

Notes/activity suggestions:

Tags: grade7, math, ratios, proportions, percents, percentages

Last modified at 7/20/2011 11:19 AM  by SEAFORD\jwwhite