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Lorraine Baron's Math Site:

proportional reasoning

Ratios, Ratios ... Everywhere


It has been argued that proportional reasoning is one of those important building blocks in Middle School.  This page includes activities to help connect Middle and High School topics that draw on students' proportional understanding. 

Why we can cross-multiply

Picture
Cross-multiplying is also one of those procedures that students do incorrectly too often.  This first activity aims to get at that understanding through context and multiple ways of representing ratios.
baron_-_understanding_ratio.pdf
File Size: 171 kb
File Type: pdf
Download File

baron_-_understanding_ratio_-_key.pdf
File Size: 295 kb
File Type: pdf
Download File


Trigonometric Ratios

Picture
Many students see a larger triangle of the same shape (a similar triangle) as having "bigger" angles. This may be because they have not mastered the use of a protractor to measure angles. Before proceeding to this activity, it may be important to check to see if students can measure angles.
baron_-_trigonometric_ratios.pdf
File Size: 75 kb
File Type: pdf
Download File

baron_-_trigonometric_ratios_-_key.pdf
File Size: 295 kb
File Type: pdf
Download File


Slope and Ratios

Picture
This activity gets to the student's personal "gut-understanding" of what slope means.
baron_-_slope_and_ratio.pdf
File Size: 178 kb
File Type: pdf
Download File

baron_-_slope_and_ratio_-_key.pdf
File Size: 410 kb
File Type: pdf
Download File


Slope as a Graph

Picture
Slope is also important in graphing lines and other functions.
baron_-_slope_as_a_graph.pdf
File Size: 181 kb
File Type: pdf
Download File

baron_-_slope_as_a_graph_-_key.pdf
File Size: 423 kb
File Type: pdf
Download File


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Photos used under Creative Commons from Didriks, Arenamontanus, JessyeAnne, comedy_nose Tatters ❀
  • Home
  • Basics
    • Building Blocks 1 - Factoring
    • Building Blocks 2 - Factors & Multiples
    • Building Blocks 3 - Fractions, Decimals, Percents
    • Building Blocks 4 - Why Exponent Laws?
    • Building Blocks 5 - Perfect Squares and Square Roots
    • Building Blocks 6 - Multiplying and Dividing Fractions using Area Model
    • Building Blocks 7 - Adding Fractions
  • Algebra Basics
    • Multiples of x
    • Equivalent Rational Expressions
    • FOIL with and without Algebra
    • Linear Relationships
  • High School Curriculum
    • Basics - Proportional Reasoning
    • Arithmetic Sequences and Linear Functions
    • BC Teaching Notes
  • Applets and Video
    • Arithmetic Sequences
    • Introduction to Polynomial Functions
    • Intro to Graphing Quadratics
    • Translations of Quadratic Functions
    • Expansions and Compressions of Quadratic Functions
    • General and Vertex Forms & Algebra Tiles
    • Applications of Quadratic Functions
    • Review of Quadratics
  • Manipulatives
    • Sourcing Algebra Tiles
    • Alternative to Hands-On
  • About me
    • Videos and Songs
    • Publications and Teaching Notes
  • Blog
  • MY FAVE WEBSITES