Extensions and Enrichment for Fractions and Decimals
· Basic fraction concepts
Teacher’s lesson plans to help students understand fractions as parts of a set - http://illuminations.nctm.org/LessonDetail.aspx?ID=L336 and http://illuminations.nctm.org/LessonDetail.aspx?ID=L337
Teacher’s lesson plans to help students understand fractions as parts of a whole - http://illuminations.nctm.org/LessonDetail.aspx?ID=L343 and http://illuminations.nctm.org/LessonDetail.aspx?ID=L344 (includes interactive tool)
Interactive tool for building fraction concepts and beginning naming fractions - http://nlvm.usu.edu/en/nav/frames_asid_102_g_1_t_1.html?from=topic_t_1.html, then move on to http://nlvm.usu.edu/en/nav/frames_asid_103_g_1_t_1.html?from=topic_t_1.html
Matching game for fractions and pictoral representations - http://www.haelmedia.com/html/mg_m54_001.html
Interactive practice naming fractions based on pictoral representations - http://nlvm.usu.edu/en/nav/frames_asid_104_g_1_t_1.html?from=topic_t_1.html
Interactive practice in identifying fractions - http://visualfractions.com/identify.htm
Fun and interactive game where students must use their knowledge of fractions to complete a task - http://www.learnalberta.ca/content/me3us/flash/lessonLauncher.html?lesson=lessons/10/m3_10_00_x.swf
“Making Manipulatives” Activity (basic concepts, but at an advanced level) – See worksheet embedded in document
“Pattern Block Fractions” uses pattern blocks to give students a hands-on, challenging way to investigate fractional relationships – worksheet embedded
· Equivalent fractions
Equivalent Fractions Online Exploration - http://illuminations.nctm.org/ActivityDetail.aspx?ID=80
Pictoral representations help students understand the concept of common denominator - http://nlvm.usu.edu/en/nav/frames_asid_106_g_2_t_1.html?from=topic_t_1.html
Teacher’s lesson plan to help students conceptualize equivalent fractions - http://illuminations.nctm.org/LessonDetail.aspx?ID=L338
· Comparing and ordering fractions
Comparing fractions using pictoral models - http://visualfractions.com/compare.htm
Fraction Feud Card Game Directions & Cards - http://www.learn-with-math-games.com/support-files/fraction-feud.pdf
“Comparing Fractions” focuses on methods of comparison that do not rely on pictures or common denominators (truly develops fraction concepts!) – worksheet embedded
Teacher’s lesson plan for helping students conceptualize fractions both less than and greater than one - http://illuminations.nctm.org/LessonDetail.aspx?id=L784
· Converting fractions
Online exploration of a variety of fraction models - http://illuminations.nctm.org/ActivityDetail.aspx?ID=11
Concentration game to match fractions, decimals and percentages (note that students will need to select the appropriate game) - http://illuminations.nctm.org/ActivityDetail.aspx?ID=73
· Adding and subtracting fractions
Pictoral representation of adding http://visualfractions.com/add.htm and subtracting http://visualfractions.com/subtract.htm fractions
Interactive use of number lines to combine fractions - http://illuminations.nctm.org/ActivityDetail.aspx?ID=18
Interactive manipulatives take students through the process of finding a common denominator to plotting the sum on a number line - http://nlvm.usu.edu/en/nav/frames_asid_159_g_2_t_1.html?from=topic_t_1.html
· Improper fractions and mixed numbers
Spy Guys Math Lesson (can be done independent of teacher) – “Improper Fractions and Mixed Numbers” http://www.learnalberta.ca/content/mesg/html/math6web/index.html?page=lessons&lesson=m6lessonshell02.swf
Matching game for improper fractions and mixed numbers - http://www.haelmedia.com/html/mg_m54_003.html
· Multiplying fractions
Pictoral representation of multiplying fractions - http://visualfractions.com/multiply.htm
Online manipulatives help students use the area model to understand multiplication of fractions - http://nlvm.usu.edu/en/nav/frames_asid_194_g_2_t_1.html?from=topic_t_1.html
· Dividing fractions
Number line fraction bars (which can be used for a variety of concepts, but the sample illustrates division) help students make sense of the confusing fraction division algorithm - http://nlvm.usu.edu/en/nav/frames_asid_265_g_1_t_1.html?open=activities&from=topic_t_1.html
· Other fraction concepts
Interactive exploration of fractions and ratio, using bike gears - http://illuminations.nctm.org/ActivityDetail.aspx?ID=178
“It’s a Fraction, What Do I Do With It?” activity involves using word problems and pictures to determine operations with fractions – worksheet embedded
“’Fractional’ Thinking” activity asks students to interpret fractional remainders – worksheet embedded
Making Manipulatives
To help develop fraction concepts, you will make two sets of fraction manipulatives. One set will be made from circles and the other from squares. To create these manipulatives, you may not use a protractor or a ruler. (You may use a straight edge to help you draw the lines.)
For the each set (circles and squares):
· Create manipulatives that show 1/2, 1/3, 1/4, 1/5, 1/6, 1/7, 1/8 and 1/9.
· Describe strategies you used when making the manipulatives.
· Pretend you are talking to someone who missed class today. Explain how to make 1/3 and 1/5.
Which fractions were difficult to create?
What made them more difficult?
What did you learn from making the fraction manipulatives?
Take a minute to jot down any questions you still have about fractions. Find a time to discuss these questions with your teacher.
Imagine that you have met an alien from the planet Zonga-Zonga. He has just landed on our planet and is trying to learn math and would like to understand the terms fraction, numerator and denominator. The alien speaks English, but does not know much “math language.” How would you explain these terms to him? (You need to be specific enough to help him understand the concepts.)
Read the following statements, made by other students. Are they correct or incorrect? If they are incorrect, where are the mistakes or misconceptions?
Making 1/5 was easy because it is halfway between 1/4 and 1/6.
Once I made 1/4, it was easy to make 1/8. I just made the 1/4 again and then folded it in half.
Adapted from:
Bassarear, Tom (2001). Mathematics for Elementary School Teachers. Houghton Mifflin: New York.
Comparing Fractions
You will be using your understanding of fractions and your reasoning ability to put fractions in order. You will not be finding common denominators or using calculators. The goal is more that getting the right answer. In this exploration, you are expected to apply basic fraction concepts. When you justify your answer, you must do more than draw a picture (because pictures are not always accurate and could lead you to an incorrect answer).
Here are some examples of strategies that may help you:
7/8 is greater than 4/5 because both are missing one “piece of the pie,” but the pieces in the 7/8 pie are smaller so less is missing.
7/12 is greater than 6/13 because 7/12 is more than half and 6/13 is less than half.
2/5 is less than 2/4 because each “pie” has two pieces, but the pieces of the 2/5 pie are smaller.
Fraction / >, < or = / Fraction / Justification3/5 / 3/8
5/6 / 7/8
3/5 / 5/12
1/2 / 8/17
3/8 / 3/9
2/4 / 3/7
5/8 / 10/16
3/8 / 4/10
9/11 / 7/9
Before continuing with this exploration, find time to discuss your answers and justifications with your teacher.
Next, you will try to create some rules. These rules should always work when comparing fractions. For example:
“When both numerators are one less than the denominators, the fraction with the larger denominator is smaller.”
Based on your work comparing fractions, discussion with your teacher and rules you created, you will put fractions in order. Be prepared to explain your reasoning.
3/10 2/3 7/12 4/5 3/7
1/3 4/7 2/5 7/8 5/16
Adapted from:
Bassarear, Tom (2001). Mathematics for Elementary School Teachers. Houghton Mifflin: New York.
It’s a Fraction...
What do I do with It?!
For each of the following problems, you will begin by drawing a representation. Then, you will try to determine what operation best fits and why. Here is a guideline to the four operations:
+ combine, increase
- take-away, comparison
x repeated addition, area
¸ repeated subtraction, partitioning
After you have determined the operation, explain to a partner why you feel it best fits.
Here is an example:
A patient requires ¾ of an ounce of medicine each day. IF the bottle contains 12 ounces, how many days’ supply does the patient have?
To solve this problem, I looked at how many ¾ ounces I could take away until I ran out of medicine. When I realized this was repeated subtraction, I knew the operation must be division.
Problems:
1) The label on a bottle of juice says that ¾ of the bottle consists of apple juice, 1/6 of the bottle consists of cherry juice, and the rest is water. What fraction of the bottle is juice?
2) Freida had 12 inches of wire and cut pieces that were each ¾ of an inch long. How many pieces does she have now?
3) Jake had 12 cookies and ate ¾ of them. How many cookies did he eat?
4) Kareem had 12 gallons of ice cream in the freezer for his party. Last night Brad and Mary ate ¾ of a gallon. How much ice cream is left?
5) The Bassarear family is driving from home to a friend’s house, and Emily and Josh are restless. They ask, “How far do we have to go?” Their father replies that they have gone 12 miles and that they are ¾ of the way there. What is the distance from home to the friend’s house?
6) Karla has ¾ of an acre of land for her garden. She has divided this garden into 12 equal regions. What is the size of each region?
“Fractional” Thinking
What?!?! Can you explain this?
Marvin, the tailor, has 11 yards of cloth which he will use to make costumes for a children’s play. Each costume requires 1 ½ yards of fabric.
1) Draw a diagram to represent this problem.
2) Work this problem out using the equations you have been taught.
WHY do these two methods produce different answers?
(Jot down your ideas, discuss with a partner or draw a different diagram to help you understand this concept.)
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Are you stuck? Here is a similar problem that may help you.
At the pharmacy, they have 31 ounces of amoxicillin. Each does is 4 ounces. How may doses can be made? (Use the diagram and equation, just as you did before.)
o We can write the answer as 7 ¾ or as 7 R3. What does the ¾ mean? What does the remainder of 3 mean?
o Once you understand the meaning of the fraction and the remainder, you should be able to apply this idea to the “tailor” problem.
Want to keep going?
Create similar problems of your own and jot down an explanation as to the meaning of the fractional answers.