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Rational approximations of irrational numbers 8.NS.A.2

Rational approximations of irrational numbers 8.NS.A.2 preview
Rational approximations of irrational numbers 8.NS.A.2 preview
Rational approximations of irrational numbers 8.NS.A.2 preview 2
Rational approximations of irrational numbers 8.NS.A.2 preview 3
Rational approximations of irrational numbers 8.NS.A.2 preview 4
Rational approximations of irrational numbers 8.NS.A.2 preview 5
Rational approximations of irrational numbers 8.NS.A.2 preview 6

Look Inside · 9 pages

Title slide: rational approximations of irrational numbers, showing the standard code CCSS.Math.Content.8.NS.A.2
Opening slide that names the standard
Irrational numbers review: slide says they have infinitely many non-repeating decimals and are sometimes estimated
Quick recap before the estimating lesson
Estimating square root of 3 by trial and error: squares of 1.5, 1.7 and 1.8 show the answer begins with 1.7
Worked example to model guess and check
Square root of 3 estimate continued: 1.75 squared is 3.0625, then 1.7 is marked on a number line from 0 to 3
Shows how to place the estimate on a number line
Square roots by hand: a note on the pen-and-paper algorithm used before calculators, with a link to read more
Optional extension for interested students
Number pi: slide on how many digits are needed, noting NASA uses 15 digits and giving pi as about 3.14159265
Discussion starter on how precise estimates must be
Case pi squared: squares of 3.1, 3.14, 3.141, 3.1416 and 3.14159 compared with the calculator value 9.8696044
Example for comparing estimate accuracy by decimals
Accuracy takeaway: no exact rule for how many decimals are needed, as both factors carry the same rounding error
Wrap-up point after the pi squared case
References: two web links, one on the most calculated digits of pi and one from NASA on how many pi digits we need
Source list for the pi facts
Attributes
Subject

Math, Algebra

Grades

Grade 8

Types

Teacher Tools, Lesson Plans

File

Microsoft PowerPoint

Editable
Yes
Author
TheBrightestKid
Rating
Add To Collection
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About This Product

This PowerPoint explains how to approximate irrational numbers and place irrational numbers on the number line. 8.NS.A.2.

What's Included

1 PPT 9 slides

Resource Tags

Irrational numbers Approximation Number pi estimating by trial and error approximating irrational numbers

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