Estimating with Rational Numbers
6683
Introduction
In this activity, students will round fractions and mixed numbers, and then
use their rounding skills to estimate sums, differences, products, and quotients.
Grades 6-8
NCTM Number and Operations Standards
• Compute fluently and make reasonable estimates
• Develop and use strategies to estimate the results of rational-number computations and judge the reasonableness
of the results
Files/Materials Needed
PART 1
Estimate.act, Sum_Difference.act, Multiply and Divide.edc
PART 1 FINDING BENCHMARKS
PART 2 ESTIMATING SUMS AND
1
DIFFERENCES
a.
Launch2TI-Navigator™ on the computer and start
PART
the session.
b. Have each student log into NavNet on their
calculator.
PART
3
3
PART
2
4
2
PART
2
4
2
2
4
4
2
2
3
2
4
4
423
3
4
7
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a. Load the Sum_Difference.act activity settings file
into Activity Center. This sets up the Activity Center
PART
so that4students will have a number line (from –9 to
9) on their calculator.
b. Call out the sum or difference of two fractions (proper
2 40 PART
3
55 6
4 4 3 62 3 12 1 34 77
1
1
3
6
6
4
or
+ 1 73 , 4and
students
5 100
8 mixed),
8
5 such
5 as
2 5 3 74 12
412instruct
122
2
3
3
3
1
7
to estimate the value of the sum or difference
using the benchmarks used in Part I. For example,
1
3
6
6
4
2 40
3
5
6
4 3 6 3 1 1 4 7
students
be encouraged
to
as 4,7 4 12 12
3
3
3
1
7should
5 100
8
8
5 think
5 of5 3 7 12
2 4 2 2 3 24 7 321 721 1 3 1 67 36 1 64 1 62 3 40
4 6 2 3 640 5 4 36 2 540
4
4 2 3 and
4 4 1 32 2as 1
442 , giving
233 2a4
3 sum
3 32of 5
31 2 . Have
37 3 15students
3100
7 3 5 8 11008 7 85 5 8100
5
mark and send this location as they did in Part I.
c. Depending on the ability level of your students, you
may want to work with signed numbers as well. You
times (clear the activity
5
6 can
4 redo
3 6 this
3 activity
1 1 several
4 7
time)
variety of proper and mixed
8
5 data
5 5each
7 12
7 using
4 12a 12
fractions.
a. Load the Estimate.act activity settings file into
Activity Center. This sets up the Activity Center
PART
2
3 line 7(from1 –4
so that5students will4have2 a number
2
4
3
4
2
2
4
to 4) on their calculator. You may choose to click
2
Configure and type a number that will appear as
a prompt on the student calculators. You can also
change the length of the number line as you see fit
as well as the step size.
3
7
1
1
3
6
6
4
2 40
b. Call
as 1 38 ,
4 out
2 a fraction
2
3 (proper
3
3or mixed),
1
7 such
5 100
and instruct students to estimate the fraction’s value
2
3
7
1
1
3
6
6
4
2 40
5
instruct
to
this 38
3to the4 nearest
2
2 . Then
3
3
3 them
1
7 mark
5 100
8
location just above the number line.
c. Once all students have marked their position,
instruct them to send it. Discuss the results and use
this opportunity to let students know that rounding
4
2
2
3
7
1
1
3
6
6
4
2 40
2 fractions
4
3to the4 nearest
2
2 can
3 help
3 them
3 estimate
1
7
5 100
operations on fractions.
d. You can redo this activity several times (clear the
activity data each time) using a variety of proper and
mixed fractions.
32 Texas Instruments
6683.indd 32
3
6
5
3
8
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5
5
8
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6 3 1
7 12 7
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1 4 7
4 12 12
6 3 1
7 12 7
1 4 7
4 12 12
Getting Started with the TI-Navigator™ System: Middle Grades
4/9/06 7:20:19 PM
Estimating with Rational Numbers
PART 1
PART 2
PART 3 ESTIMATING PRODUCTS AND
QUOTIENTS
4
PART 4
Tell students that it is usually helpful to round fractions
to the nearest whole number before multiplying and
3
7
1 PART
1
3 5 6 46
4
2
22 40 3 3 7 5 1 6 1 4 33 6 6 3 61 14 4 2 7 40
6 4 can
4
2
2 dividing.
3
3 For 3example,
21
7
4 4 53 •100
8 2 be
8 2thought
5 3 5 of35 7 3 12 17 47 125 12100
as 4 • 7 = 28. In division, students may need to find
compatible numbers that are close to the rounded
1 3 3 6 66 6 4 42 240 40 3 3 5 5 6 6 4 43 6
3 36 13 1 14 7
4 7
numbers.
can
3 3 3 3 31 1 7
75 100
5 For
100 8example,
8 8 8 5 395 5 ÷55 5 7
5 12
7 12
7be4
7 rounded
12
4 12 12
to 40 ÷ 6, but the result is a fraction. However, the
problem can be rewritten as 40 ÷ 5, giving an estimated
quotient of 8.
3
8
5
8
6
5
4
5
3
5
6 3 1
7 12 7
1 4 7
4 12 12
5
Send students the LearningCheck™ file Multiply and
Divide.edc. They will have five products and five
quotients to estimate. Collect their answers and use
Class Analysis to review the results and provide
additional clarification.
Getting Started with the TI-Navigator™ System: Middle Grades
6683.indd 33
Texas Instruments 33
4/9/06 7:20:20 PM