1. Activating Prior Knowledge –
Place the following roots in order on a number line: 8 , 12 , 9 , 14 . Then give a decimal approximation for each. 2 3 8 9 12 14
8 =2.83
9 =3.00
12 =3.46
14 =3.74
Tie to LO

2. Today, we will approximate the decimal expansion of roots of integers
Module 7 LSN 11: The Decimal Expansion of Some Irrational Numbers
Objective –
Today, we will approximate the decimal expansion of roots of integers
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3. Concept Development CFU
Module 7 LSN 11: The Decimal Expansion of Some Irrational Numbers
Module
Pg. 56
Concept Development
Example 1:
Is 3 between 1.2 and 1.3?
If 1.2< 3 <1.3, then <3< 1.3 2
But it isn’t because =1.44 and =1.69 so that estimate would be too low.
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4. Concept Development CFU
Module 7 LSN 11: The Decimal Expansion of Some Irrational Numbers
Module
Pg. 56
Concept Development
Example 1 con’t:
Is 3 between 1.8 and 1.9?
If 1.8< 3 <1.9, then <3< 1.9 2
But it isn’t because =3.24 and =3.81 so that estimate would be too high.
CFU

5. Concept Development CFU
Module 7 LSN 11: The Decimal Expansion of Some Irrational Numbers
Module
Pg. 56
Concept Development
Example 1 con’t:
So what would the correct interval be?
If 1.7< 3 <1.8, then <3< 1.9 2
Since =2.89 and =3.24 this would be the correct interval.
CFU

6. Concept Development CFU
Module 7 LSN 11: The Decimal Expansion of Some Irrational Numbers
Module
Pg. 56
Concept Development
Example 1 con’t:
So we know 1.7< 3 <1.8, can we get and even closer decimal approximation?
Let’s check the interval between 1.72 and If 1.72< 3 <1.73, then we know <3<
=2.96 and =2.99, both are too low, but is pretty close to 3.
Let’s check the interval between 1.73 and If 1.73< 3 <1.74, then we know <3<
=2.99 and =3.03, so, 1.73< 3 <1.74.
This gives us a pretty good decimal approximation to two decimal places for ≈1.73…
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7. Module 7 LSN 11: The Decimal Expansion of Some Irrational Numbers
Pg. 57
Guided Practice
Example 2:
We know that 25<28<36, so 25 < 28 < 36 , 5< 28 <6
How do we determine which interval is correct?
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8. Module 7 LSN 11: The Decimal Expansion of Some Irrational Numbers
Pg. 57
Guided Practice
Example 2 con’t:
Let’s square a few of the tenths.
5.1 2 =26.01
5.2 2 =27.04
5.3 2 =28.09
So 5.2< 28 <5.3. How can we get closer?
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9. Module 7 LSN 11: The Decimal Expansion of Some Irrational Numbers
Pg. 57
Guided Practice
Example 2 con’t:
Let’s square a few of the hundredths. = = = = =
=28.09
So, 5.29< 28 < How can we get closer?
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10. Module 7 LSN 11: The Decimal Expansion of Some Irrational Numbers
Pg. 57
Guided Practice
Example 2 con’t:
Let’s square a few of the thousandths. = = = = =
So, 5.291< 28 <5.292.
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11. Independent Practice (5 min)
Module 7 LSN 11: The Decimal Expansion of Some Irrational Numbers
Module
Pg. 58
Independent Practice (5 min)
Exercise 1:
In which interval of hundredths does lie? Show your work
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12. CFU Module 7 LSN 11: The Decimal Expansion of Some Irrational Numbers
Pg. 59
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13. Closure CFU What did you learn? Why is it important?
Module 7 LSN 11: The Decimal Expansion of Some Irrational Numbers
In your notes
Closure
What did you learn?
Why is it important?
Describe how to approximate the decimal expansion of an irrational number to the hundredths place.
Which interval of hundredths does lie? Show your work.
Homework:
Problem Set 1 – 15 all, pages 59 – 60.
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