Prior Knowledge: Students should have a good idea of what a fraction is. Students should also know how to divide a whole and a collection into fractional parts.
Lesson Objective: By the end of this lesson you will be able to draw pictures that represent fractions that are close to 0, 1/2 and 1.
Materials: You will need paper, crayons and a stencil if you have one!
Ready to Draw!
Step 1: Draw three identical polygons and number them 1, 2 and 3. For example, I could draw three triangles that are the same shape and size (use a stencil if you need to).
Step 2: In polygon #1, shade in an amount that would represent a fraction that is very close to 0. In polygon #2, shade in an amount that would represent the fraction 1/2. In polygon #3, shade in an amount that would represent a fraction that is very close to 1. These are your benchmark pictures that we will use for the rest of the activity.
Step 3: Look at the following fractions. Draw any polygons you want and shade in the amount that you think would represent the fraction. DO NOT separate your polygons into fractional pieces. For example, for the fraction 6/7, do not draw a rectangle and divide it up into 7 pieces and then shade in 6. Simply shade in the rectangle to the amount that you think would equal that particular fraction. Finally, place each picture under the benchmark picture you think it goes with, is it closest to 0, 1/2 or 1?
Here is your list of fractions:
1/10, 3/18, 19/20, 10/50, 5/10
3/12, 98/100, 4/12, 8/10, 8/15
2/7, 3/4, 12/20, 9/18, 21/50
Thinking Behind the Lesson:
Estimating fractions is a concept that is over looked far too often in textbooks, curriculums and even standards. However, this concept is so important for helping students develop a fractional number sense. Van de Walle states in his book Elementary and Middle School Mathematics: Teaching Developmentally, that students need to be able to know "about" how small or big a specific fraction is. The most important benchmarks for helping students acheive this goal are 0, 1/2 and 1 (Van de Walle p. 251).
This activity pushes students to think "about" how small or big a particular fraction is. It also reinforces these benchmarks which will help them in their development of a solid fractional number sense. While other activities may use manipulatives, such as Cuisinaire Rods, I designed an activity that would provide students with the opportunity to draw and create. It is important to include student choice as well as art into our lessons. My hope was that this activity would fulfill both of these important aspects.
Reflection:
*The above activity is helpful in pushing students to think critically about how small or big specific fractions are and where they land on the spectrum between 0 and 1. While this may be a great place for your child to start thinking about this concept, to make this activity more accessible for more struggling learners, you may want to help them draw their benchmark pictures. It may also be helpful for them to use fraction strips
*For students who are catching on quickly and mastering this concept, push them with more challenging fractions. Another way to challenge your student is to ask them to use mental math instead of drawing a picture. Make sure they justify their answer with a detailed explanation of how they placed their fraction on the spectrum between 0 and 1. You may also want to ask them follow-up questions after they state that their fraction is close to 1/2, for example. Ask them, is it more than 1/2 or less than 1/2. Ask them is it close to 1/4 or 3/4. These questions will push your students to think more critically.
References:
Van de Walle, J.A. (2004). Elementary and middle school mathematics: Teaching developmentally. Boston: Pearson.
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