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(^) Copyright © Swun Math Grade 8 Unit 1 Lesson 7 P TE

Estimate Irrational Numbers

Procedural Lesson

Grade 8 · Unit 1 · Lesson 7
MC: 8.NS. 2

Problem of the Day

Objective: I will estimate 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 of two integers; 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

Considerations:

Students may need to look at a list of perfect

squares as a reference. Using a number line will

help students visualize the decimal answer quickly.

Calculators may be used to verify the

reasonableness of their approximations.

Steps:

1. Find the perfect square immediately
   above and below your number.


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


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

Application of MPs:

MP6: How are you estimating the quantities?

I will estimate the quantities by first

___________________.

MP7: How can you use today’s pattern to estimate

a more accurate estimation?

I can use today’s pattern to estimate a more

accurate estimation by

______________________.

MPs

Applied MP

* Embedded MP

1 2 3 4 5 6 7 8

* * * * ^ *

Student Journal Pages

30 - 35