Cynthia Lanius

 

Fraction Shapes

- Teachers' Notes

A Pattern-Block Activity

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| No Matter What Shape | Fun Fractions | Drawing Fun Fractions | Designer Fractions |
| Teachers' Notes | Math Forum's Fraction Tour | More Math Lessons |

 
Description:These activities are designed to cause students to think; they are not algorithmic. They do not say, To add fractions, do step one, step two, step three. Students will explore geometric models of fractions and discover relations among them.

Appropriate Grades: 3rd - 6th, maybe. But precocious kindergarteners could do some of it, and middle schoolers needing another look at fractions could appreciate it as well. "Drawing Fun Fractions" would be good for most middle school students.

Lesson Procedures: Students will reinforce their knowledge of fractions by using online pattern block activities. The lessons are designed for students to work independently or with guidance from the teacher. Lessons should be printed so students can draw and color the appropriate shapes.

Mathematics Topics: Identifying fractional values, equivalent fractions, adding and subtracting fractions, ordering fractions, and identifying geometric figures and their properties

Connecting Mathematics:

Materials and media: A computer with Internet access, graphics and printing capabilities. Pattern blocks are helpful. If you don't have access to pattern blocks, you can print these models and color and laminate, if possible. Lessons can be done on- or off-line, but should even be printed for on-line use. If you have a JAVA compatible browser you can explore the shapes online.

Assessment: Questions are included with each section. To further assess learning in the classroom, have students create (and solve) a worksheet of 6-8 more problems like the ones contained in these activities.


Explaining the Math: If you help the students to see the triangle as the basic "counter" in these activities, the problems become much simpler. Here are three examples.

From No Matter What Shape

6. How many are in   ?   1 1/2

Think of the rhombus as two triangles and the trapezoid as three. So you could divide 3 by 2 and get the answer. Or if you have pattern blocks, you could lay 3 triangles on top of the trapezoid, and see that two of them make 1 rhombus and the remaining one makes 1/2 of a rhombus.
10. If    =1,   =___? 2/3
If the trapezoid = 1, then the triangle = 1/3. Now think of the trapezoid as three triangles, or 3/3. The rhombus = two triangles, or 2/3.
 
From Draw Fun Fractions

1. If     +     = 2/3,   what is   1?

Use the triangle again as a counter, so this sum has 4 triangles. Four triangles = 2/3, so 2 triangles = 1/3, and 6 triangles (a hexagon) = 3/3 or one.

| No Matter What Shape | Fun Fractions | Drawing Fun Fractions | Designer Fractions |
| Teachers' Notes | Math Forum's Fraction Tour | More Math Lessons |

Copyright July, 1997-2004 Cynthia Lanius