Connections

Books:

Van De Walle, J.A., Karp, K., & Bay-Williams, J.M. (2010). Elementary and Middle School Mathematics: Teaching developmentally, 7th ed. Bostson: Pearson.

•       Chapter 17 (pages 328-347) focuses on helping to teach students how to connect fractions, decimals, and percents.  Examples of activities to do with students using base ten blocks and hundredth wheels are presented including key questions to help guide students’ thinking from connecting fractions to decimals, to the role of place value and the decimal point, to defining percents in terms of hundredths, and finally how to operate on the various notations.
• You can find this book on Amazon by clicking here if you're interested in purchasing it or would like more information.

Links to Lessons and Teaching Activities:

Number Line Teaser this is the number line teaser game that was mentioned on slide 22 of the Connections learning block.

Representing Hundredths:
This pdf package has several pages of lesson ideas and printable materials (including a hundredth wheel and hundredth grids) to help students see and connect different ways of representing hundredths.
http://www.eworkshop.on.ca/edu/pdf/Mod27_representing_hundredths.pdf

Teaching Activities:
Hundredth Grid Interaction:

On slide 19 a link is provided to an interactive hundredth grid that you can use to illustrate the relationship between multiple representations of values, like fractions, decimals, and percents.  Use the interactive hundredth grid to:

• Show different representations (different names) for the same value.

         Select which representations you want to use by dragging and dropping each one from the    menu at the top of the screen.  To link them up to one another touch each interaction to the green box below the representation you would like to connect.  A video tutorial on how to do this will be available soon.

• Illustrate how renaming fractions works.  

The segmentation of the red grid into 4 quartiles of 25 as well as 100 individual blue squares shows that 25/100=1/4. 

The green segmentation tool will show students that 50 of the 100 blue squares, or 0.50, is the  5 green tens.  

• Show the relative values of fractions, decimals, and percentages to one another.  

After selecting the number line tool, click on the grey box to the right of the number line to set which values are displayed and to modify the increments and the beginning/end points you wish to use.

Hundredth Wheels:
On slides 16 and 17 we mention that you can use a hundredth wheel to help students connect fractions, decimals, and percents.  Here is how you make a hundredth wheel:

1. Print 2 hundredth wheels for each student.  You'll need to print each of the two wheels on different colors of paper. 

         If you don't already have a hundredth wheel template you can find one on page 7 of this pdf
         http://www.eworkshop.on.ca/edu/pdf/Mod27_representing_hundredths.pdf

2.  Cut each circle out and cut along the dotted line to the center of each circle.

3.  Fit the circles together to make one circle by sliding the cut dotted lines together.

4. You have a hundredth wheel that you can rotate to show various fractions, decimals, and percents.

5.  Have your students spin the wheel around to show various values like 0.90.  

What's great about hundredth wheels is they provide students with a great visual representation of decimal values that is easy to relate to familiar visual representations of fractions, like 0.25 and 1/4.

Challenge students by asking them questions like those mentioned on slide 17.