Cynthia Lanius No Matter What Shape Your Fractions are In . | Exploring the Shapes 1. Can you name the 4 geometric fig
Views 131 Downloads 8 File size 198KB
Cynthia Lanius
No Matter What Shape Your Fractions are In . |
Exploring the Shapes 1. Can you name the 4 geometric figures? 2. What fun! Experiment online with the shapes. (If you have a JAVAcapable browser). This will open a new window and you can move back and forth between the problems below and the online pattern blocks. 3. Print, color, and cut out these shapes to explore their various relations. 4. Print this page and color the four shapes on the triangle grid.
Determining the Relations Use the figures you colored to answer the following questions. 1. How many
are in
2. How many
are in
3. How many
? ?
are in
4. How many
?
are in
?
5. How many
are in
?
6. How many
are in
?
Based on these relations,
7. If
= 1,
8. If
= 1,
9. If
= 1,
10. If
= 1,
= ___ . = ___ .
Check your answers.
[email protected] June 1997-2004 by Cynthia Lanius
= ___ . = ___ .
More Fun Fractions . | Let's do some really fun ones.
1. If
+
2. If
+
3. If
+
= 1, what is
?
= 1, what is
= 1, what is
4. If
+
= 1, what is
5. If
-
= 1, what is
+
?
+
?
?
+
?
Drawing Fun Fractions .
Print this page, and on the grid below, draw your answers as polygons. Warning! These are a challenge, but fun to figure out! Here's an extra piece of grid paper if you need to experiment more. Or if you have a JAVA capable browser you can explore online. 1. If
+
= 2/3, what is 1?
2. If 3. If
+ +
= 4/5, what is 2/5? = 3/4, what is 1/2?
4. If
+
= 5/8, what is 3/4?
5. If
-
= 1 1/3, what is 2/3 ?
Check Your Answers
New Internet Project Make up your own fractions problem using the shapes, email me the problem and the answer, and I will post it here for others to try. See the responses. [email protected]
| No Matter What Shape | Fun Fractions | Drawing Fun Fractions | Designer Fractions | | Teachers' Notes | Math Forum's Fraction Tour | More Math Lessons |
[email protected] Copyright June 1997-2004 by Cynthia Lanius
Designer Fractions .
Multiple Choice 1. What fraction of the design is blue? A. 4/24 = 2/12 = 1/6 B. 6/24 = 3/12 = 1/4 C. 8/24 = 4/12 = 1/3 2. What fraction of the design is red? A. 4/24 = 2/12 = 1/6 B. 6/24 = 3/12 = 1/4 C. 8/24 = 4/12 = 1/3 3. What fraction of the design is yellow? A. 4/24 = 2/12 = 1/6 B. 6/24 = 3/12 = 1/4 C. 8/24 = 4/12 = 1/3 4. What fraction of the design is green? A. 4/24 = 2/12 = 1/6 B. 6/24 = 3/12 = 1/4 C. 8/24 = 4/12 = 1/3
You Be the Designer Use the four shapes and their colors to design a figure on the triangle grid below. Calculate the fractional part of each color. If you can color it electronically with your computer, email it to me and I will post it here.
Investigate Line Symmetry . It can save you work!
| [email protected] Copyright June 1997-2004 by Cynthia Lanius
Cynthia Lanius
Fraction Shapes - Teachers' Notes A Pattern-Block Activity . | 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:
Connects math, art, writing, and technology Connects arithmetic and geometry
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 offline, 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