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Fraction Strips

Fraction Strips
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Contents


Description
Examples
Videos
Customizing the Tool
Sample Files
Features of the Tool Keyboard Shortcuts
PDF supports

Fraction Strips


Use Fraction Strips to represent, compare, order, and operate on fractions. Represent fractions by dragging pieces from the fraction tower into the workspace. Pieces can be placed in a line to form a train. Manipulate the pieces and trains to compare and order fractions or to model fraction operations.

Access a wide variety of Annotation tools Annotation button to communicate thinking.
Insert picturesImport Picture button into the tool.
Work created in a mathies tool can be savedSave File button and openedOpen Button. A saved file can be shared with peers or submitted to a teacher. The file will contain all solution steps from start to finish.

Take a screenshot to use as part of a portfolio, presentation, web page, etc.

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Mathematical Concepts


Create visual representations that aid in mathematical thinking related to:
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Connecting Fundamental Math Concepts with Fraction Strips

Fundamental Concepts and Skills Fraction Strips Connections
Working with numbers:
Understanding and using numbers (e.g., being able to read, represent, count, order, estimate, compare, compose, decompose, and recompose numbers).
Fraction Strips can be used to:
  • recognize that each whole in the fraction tower has been split into equal parts called unit fractions
  • represent unit fractions, proper fractions and improper fractions, as well as mixed numbers
  • identify and count by unit fractions (e.g., one one-seventh, two one-sevenths, etc.)
  • compose and decompose wholes using unit fractions, e.g., show that 9/4 is the same as two wholes and one-fourth
  • demonstrate and explain the concept of equivalent fractions
  • compare and order fractions with like and unlike denominators, including proper fractions, improper fractions and mixed numbers
Recognizing and applying understanding of number properties:
Understanding how numbers behave in operations and drawing on that understanding to master math facts and perform calculations.
Fraction Strips can be used to:
Mastering math facts:
Understanding and recalling math facts, using a variety of strategies.
Fraction Strips can be used to:
  • apply whole number facts as students compute fractional sums and products
  • practise and understand operations with fractions by manipulating visual representations
Developing mental math skills:
Doing calculations in the mind, with little or no use of paper and pencil or calculator.
Using visual tools when learning to perform mathematical operations allows students to draw on these mental models and visualizations to perform mental calculations.

Students will develop their mental math skills with Fraction Strips as they:
  • solve problems involving the addition and subtraction of fractions
  • apply estimation skills to operations with whole numbers and fractions
Developing proficiency with operations:
Performing calculations with ease, precision, and consistency and with a general understanding of number and operations, number properties, and their appropriate application in problem solving.
Fraction Strips can be used to:
  • recognize the inverse relationship between addition and subtraction (e.g., since 1/6 + 1/3 = 1/2, then 1/2 - 1/6 = 1/3).
  • recognize the inverse relationship between multiplication and division (e.g., since 1/2 x 6 = 3, then 3 ÷ 1/2 = 6).
  • demonstrate the relationship between the repeated addition of fractions and the multiplication of that fraction by a whole number
  • solve problems involving fractions

Focusing on the Fundamentals of Math - A Teacher's Guide

Connecting Fundamental Math Concepts with mathies.ca (Draft)

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Examples


Representing


Represent unit fractions, proper fractions, improper fractions, and mixed numbers.
Represent Fractions
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Comparing


Align trains using the built-in snapping feature.
Zoom inZoom In buttonfor more precision.
Rulers, when shown, will illuminate ticks in red if a piece ends exactly in that spot.
Create a vertical comparison bar to track a position between trains.
Comparing
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Exploring Equivalence


The equivalence bar in the tower can be dragged to reveal equivalent fractions in the tower.
The ruler can be shown, with steppers that change the fractional unit (e.g., from thirds to sixths), to assist with renaming fractions.
Equivalence Bar
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Operations


Addition

Place pieces beside or between each other, to combine fractions and perform addition.
Adding Fractions Example
Add Fractions
On desktop, click on the image above to open this file.

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Subtraction

Remove pieces from trains to perform subtraction as take-away.
Align trains to compare fractions, with or without using comparison bars, to find the difference.
Design example
See the Gazette article for more details about representing, ordering, subtracting and adding fractions with Fraction Strips.

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Multiplication

Copy strips or trains to model repeated addition.
Fraction Multiplication

Find a fraction of a fraction.


Fraction Multiplication
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Division

Division of fractions can be a challenging topic. It is useful for students to understand different ways of thinking about division.
One way to approach the division of a fraction by a whole number is to split the fraction into equal pieces as in the example below. Fraction Division
Comparing this division example to the multiplication example above, students may recognize that the action of dividing a quantity by 4 is the same as finding one-fourth of that quantity. This is one illustration of the invert and multiply algorithm.

When dividing one fraction by another fraction, one way to think about the problem is to ask, "how many of the second quantity fits into the first quantity". In the following example, the student is asked to think about how many one-fourth pieces fit into the one-half piece. Fraction Division
Here the answer is 2 which is a whole number. See the Ribbon Problem below for an example where the quotient is not a whole number.

See the Gazette article for more details about multiplying and dividing fractions with Fraction Strips.

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Videos


Comparing Addition of Fractions


Watch a video of the following question being solved by using the Fraction Strips
Fraction Question


Ribbon Problem


The grade 7 class is making decorations. They have 5 meters of ribbon to use. Each decoration takes 2/5 of a meter of ribbon.
How many decorations can they make? (Ribbon Problem Image)

Note: The video below was created with a previous version of the Fraction Strips Tool. Open the ribbon problem in the most recent version of Fraction Strips from the sample files section.


Develop the Fraction Multiplication Algorithm


This video was developed by Dave Petro and Gisele Jobin from Windsor Essex Catholic District School Board.
Thanks for sharing!


Developing the Fraction Division Algorithm Conceptually


This video was developed by Dave Petro and Gisele Jobin from Windsor Essex Catholic District School Board.
Thanks for sharing!

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Customizing the Tool


The image below shows a Fraction Strips workspace with:
The pieces have been made more transparent using the slider Transparency slider accessed from settings Settings button.

The Customize Fraction Tower dialog has been used to: Customize
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Sample Files

To access a sample file:
See the File Operations page for more details.

Sample


Click to open in the tool - desktop only

URL


Type or copy into Open WWW text box, or
save locally by right-clicking or hard-pressing
Adding Fractions
Design example
https://mathies.ca/files/examples/FS_Ex1.xml
Ribbon Problem
Ribbon problem
https://mathies.ca/files/examples/FS_Ex2.xml
Fractions of an Inch
Fractions of an Inch
https://mathies.ca/files/examples/FS_Ex3.xml
Note: These files were designed on a desktop computer and may not open exactly as shown on other devices.

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Features of the Tool

Button Description
Label button

Label

Toggle between showing:
  • no labels
  • the labels in the tower only
  • labels in the tower and in the workspace
Colour button

Customize Fraction TowerColour Settings Dialog

Show the Customize Fraction Tower dialog to:
  • choose a colour palette (Rainbow, Original, or One Colour)
  • include or exclude strips in the tower
  • change the colour of the strips and the related pieces in the workspace
  • restore the tower to its default state
Ruler button

Ruler

Ruler Styles Toggle between
  • not showing rulers
  • showing rulers
  • showing rulers and stepper arrows

Note: Clicking the stepper arrows changes the number of tick marks in a whole.
The ticks are illuminated in red if a piece ends exactly at that position.
Vertical line button

Create a Comparison Bar

comparison bar A comparison bar is a grey, vertical line that is useful to compare fraction strips, especially when the left edges are aligned.
Multiple comparison bars can be created.
The length of a bar, its colour and its thickness can be modified.
English buttonFrench button

English / French

Switch between English and French.
Zoom In buttonZoom Out button

Zoom In / Zoom Out


Use the zoom in buttonZoom In buttonto make the pieces look bigger. This is useful for more precise comparison, especially when working with small fractions.

Use the zoom out buttonZoom Out buttonto see more of the workspace. The fraction pieces will look smaller.

Note: If using a mouse use the mouse wheel to zoom in and out.
If pieces are selected the zooming will be centered around the selected pieces.
On touch screen devices use the pinch-to-zoom gesture on an empty space to zoom in and out.
Zoom to Fit

Zoom To Fit

Zoom the workspace so that all the fraction pieces are visible.
Pieces may be resized and/or repositioned as a result.
Scroll Bar

Scroll Workspace

On desktop, use the scroll bars.
On touch screen devices, use a two finger slide gesture on an empty space.
Equivalence Bar

Equivalence Bar

Drag to highlight equivalent fractions in the tower.
To move the tower, drag it by the dark blue area at the very top.
Double-headed arrow

Change Tower Height

Drag to adjust the height of the tower.
If the tower is made too small, a scroll bar will be displayed, allowing hidden strips to be revealed.
Button Annotation

Annotation Tool

Make notes or highlight various features of the representation. More details.
Import Picture

Insert Image Button

Insert images into the tool. More details.

Undo Redo

Undo / Redo

Step backward or forward through the actions with the tool.
This feature is not only useful for backtracking when a misstep is made, it enables a student to demonstrate their work from the start to the finish. The student can press Undo until they are at the start of their solution and then press Redo repeatedly, explaining each step.

Note: Undo / Redo is not available for annotation objects.
Button Reset

Reset

Return the tool to its original state.
All objects in the workspace will be deleted and the settings will be restored to their defaults.
Button Info

Information

Shows a dialog with a link to this support page, a feedback form as well as copyright details and version number.

Information dialogue
Settings button

Settings

Show the Settings dialog to:
  • open a previously saved Fraction Strips file (work will be centered and fitted to the window automatically)
  • save work in a file (see File Operations for more details)
  • restore Defaults to retain the objects in the workspace, while restoring the settings to their defaults
    including labels, rulers, and colours
Button Recycle

Recycle

Click to clear selected objects. If nothing is selected, the entire workspace will be cleared.
Alternatively, drag objects to the recycle bin to remove them.
Copy Button

Copy

Make a copy of the selected objects.


Other Functionality

Selected Objects

Multiple Select

To select fraction pieces draw a marquee rectangle around them.
Hold down the SHIFT key when drawing a marquee rectangle to add to the previous selection.

Click a fraction piece to add or remove it from the selection.

Selected fraction pieces can be moved, copied, or recycled as a group.

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Keyboard Shortcuts


On the desktop version of this tool, the standard Keyboard Shortcuts have been implemented.

Specific keyboard shortcuts for the Fraction Strips tool are as follows:
- Zoom out to see more of the workspace.
+ Zoom in on the workspace.
F Zoom to fit to re-orient the workspace.)

PDF supports


mathies Fraction Strips Learning Tool Tip Sheet

Gazette Articles
September 2017 - Representing, Comparing and Ordering Fractions, Equivalent Fractions, Addition and Subtraction of Fractions using the Fraction Strips Tool
December 2017 - Multiplication and Division of Fractions using the Fraction Strips Tool

Connecting to Fundamentals
Focusing on the Fundamentals of Math - A Teacher's Guide
Connecting Fundamental Math Concepts with mathies.ca (Draft)

Other Resources
A Fraction Strips Story: Reflections on a Student’s Mathematical Exploration (Draft)

Fraction Strips and Fraction Towers
(Source - EduGAINS | Ministry Developed Resources | Mathematics | Lessons & Supports | Manipulatives)

Visit EduGAINS for additional Manipulative Sheets.

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