Mathematical and Proportional Reasoning

Books:

The 2002 NCTM Yearbook: Making Sense of Fractions, Ratios, and Proportions.
This book has many helpful strategies and provides a wealth of student examples. There is also a Classroom Activities companion book that provides classroom ready activities for students of all ages.  Click here if you'd like to purchase this book.


Links to Lessons and Teaching Activities:

UC Irvine Proportional Reasoning Wiki has more background information about proportional reasoning and has ready made worksheets you can download as well as links to online tools that help students develop proportional reasoning skills.
https://wiki.eee.uci.edu/index.php/Proportional_Reasoning

Games:
There are several games available online that will help students develop proportional reasoning skills all while having fun!

Lemonade Stand is a game on Cool Math where students have a lemonade stand.  They buy lemons, sugar, cups, and ice in various increments each day and try to make a profit.  They can adjust the proportions of lemon, ice, and sugar to make their own recipe.

Concentration is a game from NCTM Illuminations.  This game is similar to memory where students uncover various representations of numbers and have to match the pairs or sets with the same value.

Do You Know Blue? has students experiment with mixing different proportions of red, green, and blue to make various colors.

Teaching Activities:
There are plenty of quick tasks you can use in your classroom to encourage students to use proportional reasoning.
One of these tasks is to ask students to add up all of the numbers between 1 and 100.

• Have students share their strategies for adding all of these numbers quickly.
• Encourage them to find patterns such as 1 + 99 = 100, 2 + 98 = 100, 3 + 97 = 100  that will allow them to find an answer without having to add each number individually.