Overview: This lesson is to help students develop an ...
Abstract for Comparing Fractions Mentally
Developed by Martin Meyer (Lake Center Christian School) and Debbie Capper (Emmanuel Christian Academy) in association with Akron Math Community Web Project.
Subject: Mathematics
Grade: 6-7
Strands: Numbers and number relations. Estimation.
Objectives: Students will develop a mental method of comparing fractions to 1/2. They will use the TI-73 calculator to check their answers. Students also have the opportunity to discuss their mental methods, as well as attempt higher level comparisons.
Materials Worksheet (included)
TI-73 calculator
Overhead projector (optional)
Manipulatives for fraction review (optional)
Time: One 40 minute period.
Comparing Fractions Mentally
developed by Martin Meyer (Lake Center Christian School) and Debbie Capper (Emmanuel Christian Academy) in association with Akron Math Community Web Project
OVERVIEW: This lesson is designed to help sixth and seventh grade students develop
an understanding of fractions and be able to compare fractions that are
greater than one half and less than one half using mental math skills and
calculator skills.
CONCEPTS: Using mental math to compare fractions.
Using calculator test operations to check mental answers.
Using mental math and calculators for problem solving.
OBJECTIVES: Students will determine whether fractions are greater than or less than
1/2 using mental math, calculators, and problem solving.
Proficiency Outcomes:
Grade 6 # 4. Identify needed and given information in a problem
situation, as well as irrelevant information.
5. Validate and/or generalize solutions and problem-solving
strategies.
6. Compute with whole numbers, fractions, and decimals.
9. Order combinations of whole numbers, fractions, and decimals by
using the symbols , and = and/or by placing them on a
number line
Grade 9 #1 Compute with whole numbers,
fractions, and decimals.
2. Compare, order, and determine equivalence of fractions, decimals, percents, whole numbers, and integers.
LEARNING
STRATEGIES: 1. A. Introduction: The teacher should review the concept of a number divided by 2 equals 1/2 of a number (6 divided by 2 = 1/2 of 6 = 3).
B. The teacher should use manipulatives if necessary to review concept in 1a (crayons, paper clips, etc…).
2. Worksheet Part I: Preparing to use worksheet, students can work
with a partner or work independently. On part I of the worksheet,
students will look at the numerators of the fractions and determine
whether they are more or less than one half of the denominator. At
this point the teacher should discuss students' answers to make sure
they are understanding the concept of one half before moving on to
part II.
3. Worksheet Part II: Students will actually compare fractions to 1/2
using the greater than/less than signs. If the numerator is greater
than 1/2 the denominator, then the fraction will be greater than
1/2; whereas, if the numerator is less than 1/2 the denominator,
then the fraction will be less than 1/2
.
4. Worksheet Part III: Students will check their answers in part II of the worksheet using the test operations on their TI-73 calculators.
Students will probably enjoy checking their answers on this
calculator because the test operations uses a true/false method.
*Please see note at bottom about using test operations.
5. Worksheet Part IV: Students will have a chance to explain their mental methods for parts I and II in writing. After they have written out the methods they used, the class will have a short discussion on the different methods the students tried. Students are also given the opportunity to find new mental methods if their first methods did not work (through the discussion or asking a peer).
5. Worksheet Part V: Students will now use successful mental math strategies to compare two unlike fractions and determine which one is greater than 1/2 and which one is less than 1/2, thus determining the greater of the two fractions. Students will again check their answers using the TI-73 calculator.
6. Worksheet Part VI: Students will use their comprehension of comparing fractions to 1/2 and calculator skills by applying what they have learned to solving word problems.
7. Extension Exercises: Students who are up to the challenge can
try to solve problems that have an odd number in the denominator, and also try estimating sums and differences of fraction problems.
8. Conclusion: Teacher will collect the worksheets when thelesson is finished. Students should have made all necessary corrections since they self-checked their answers with the calculator and participated in the class discussion.
ASSESSMENT: Student- using calculator to check answers (Type I)
Teacher- grading written worksheet (Type II)
Teacher- observing discussion participation (Type II)
TOOLS/RESOURCES: -Comparing Fractions Mentally Worksheet
-overhead of worksheet (optional)
-TI-73 calculator
-manipulatives for review (optional)
MANAGEMENT: If the teacher is using the overhead, the transparency should be ready
to use when the review is finished. Students should work individually
or in groups of two. Teacher should act as facilitator throughout
entire lesson, allowing students to discover concept techniques and
apply knowledge to evaluation and problem solving.
DO AND HOW: Students will compare fractions by using mental math. Students will
check mental answers by using the test operations feature on the TI-73
calculator. Students will write about mental methods and discuss
which methods work and which methods need improvement. Students
will apply what they have learned by comparing more fractions,
problem solving, and even extension activities the students can try.
SHARING: After the students have attempted to compare fractions mentally and have
checked their answers with the calculator, the class will have the opportunity to write about the mental methods they used then share their methods with others in a class discussion.
RESULTS: Students will turn in completed, corrected worksheets to teacher.
*Note on using the TI-73 test operations: To compare fractions on the TI-73, enter the first fraction using the [b/c] key (example 2[b/c]3). Move out of the fraction with the right arrow key. To insert the test operator, choose the text menu (2nd Math) and use the arrow keys to choose the appropriate sign and press [enter]. Use the arrow keys once again to choose done and press [enter]. Enter the second fraction. Press [enter] to obtain your result. A "1" means the statement is true and a "0" means the statement is false.
Comparing Fractions Mentally Worksheet
I. Look at each numerator and tell whether it is more or less than half the denominator (write more or less on the line provided).
a. [pic]_______ b. [pic]_______ c. [pic]_______ d. [pic]_______
[pic][pic]
II. Use this strategy to mentally compare each fraction to one half using .
a. [pic] [pic] b. [pic] [pic] c. [pic] [pic] d. [pic] [pic]
e. [pic] [pic] f. [pic] [pic] g. [pic] [pic] h. [pic] [pic]
III. Use the test operations () on the TI-73 to check and correct your answers to part II.
IV. In the space provided describe your mental method for comparing the fractions in parts I and II.
If your method did not work, how can you find a new method that will work?
V. Use mental math to compare the following fractions (hint: compare each fraction to one half). Check your answers with the TI-73.
a. [pic] . [pic] b. [pic] [pic] c. [pic] [pic] d. [pic] [pic]
VI. Use what you have learned to solve each of the following:
a. Antonio ate [pic] of his sandwich, Paula ate [pic] of her sandwich. Which person ate more of their sandwich?
b. Debbie’s stock went up [pic] and Marty’s stock went up [pic]. Whose stock went up more?
c. Mary Jo walked [pic] of a mile to Betty Lou’s house. The two then walked [pic] of a mile to the park. Did Mary Jo walk farther with Betty Lou or alone?
d. Tom’s stock went up [pic], Becca’s stock went down [pic]. Whose stock had the greater change?
e. When gas cost $1.25 per gallon, our old care used [pic] of a tank of gas to go to Granny’s house. Now gas costs $1.85 per gallon and our new car uses [pic] of a tank of gas to go to Granny’s house. Does the new car use more or less than [pic] tank of gas to go to Granny’s house?
Extension: Compare the following mentally.
a. [pic] [pic] b. [pic] [pic] c. [pic] [pic] d. [pic] [pic]
Use this idea to estimate the sum or difference. (Hint: round all fractions to 0, [pic], or 1.)
a. [pic] b. [pic] c. [pic] d. [pic]
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