G8

Copyright © Swun Math Grade 8 Unit 1 Lesson 6 C TE

Estimate Irrational Numbers

Conceptual Lesson

Grade 8 · Unit 1 · Lesson 6
MC: 8 .NS. 2

Problem of the Day

Objective: I will use estimation to approximate the value of an irrational square root.

Vocabulary Teacher Resources

Square Numbers (Perfect Square): the result after

multiplying an integer by itself

Irrational Numbers: the set of all numbers that

cannot be written as a ratio; it cannot be written

as a simple fraction because the decimal is non-

terminating and non-repeating

0.101101110... , �^23 ,π,√ 10 ,√1.6,−√ 123

Square Root: the square root of a number is a

value that, when multiplied by itself, gives the

number

√ 16 = 4

Considerations:

Use an area model to determine if the number is a

perfect square. If not, use the number line to

approximate and use the list of perfect squares as a

reference. Calculators may be used to verify the

reasonableness of their approximations.

Steps:

1. Determine if the number is a perfect square.


2. If not, find the perfect square immediately
   above and below the number.


3. The answer will be between the square roots
   of these two numbers.


4. Estimate the decimal based on how close your
   number is to each of the squares.

Application of MPs:

MP5: What approach are you considering trying

first?

I am going to first try _____________________.

MP6: How are you estimating the quantities?

I estimate the quantities by first,

_________________________________________.

MPs

Applied MP

* Embedded MP

1 2 3 4 5 6 7 8

* ^ ^ *

√ 16 √^25 √^36

4 5 6

√^29

Student Journal Pages

26 - 29