8th grade Instructional Unit

Unit 2 – Exponents & Square Roots Review
Unit 3 – Pythagorean Theorem Instructional Unit

by
Nancy Perzel

Day 1 - Squares and Square Roots Review

Warm-Up:

1) Using one rubber band, make a square on your geoboard.  What is the length of the side?  What is the area? 

2) Find the square on your geoboard with the smallest area.   What is the length of the side?  What is the area?

3) Find the square on your geoboard with the next smallest area. What is the length of the side?  What is the area? 

4) Find the square on your geoboard with the largest area.  What is the length of the side?  What is the area? 

5) Can you predict the size of the next largest square? What would be the length of the side?  What would be the area? 

 

This can be done in a variety of ways:

1)   Using actual geoboards

2)   With dot paper or graph paper

3)   Using the ÒGridÓ or ÒDotted GridÓ feature on GSP

4)   Using an Interactive Geoboard found on the website for the National Library of Virtual Manipulatives (http://nlvm.usu.edu/en/nav/vlibrary.html)

 

Once students have been given enough time to complete this activity, bring the class back together for a whole-group discussion.  Do you see any patterns?  What is the relationship between the side length and the area? Can you come up with a rule? (Exponent, perfect square)  Is there an inverse relationship?  What can you do to the area to get the resulting side length?  Can you come up with a rule? (Square root, radical, rational number)  *Be sure to review these key vocabulary terms in your discussion!

 

Activity 1:

Use GSP to construct a square and drag a vertex of the square to create the following side lengths, manipulating the area.  Complete the missing measurements in the following table.

 

** The directions for this construction are included on the GSP file for students to use. Square Root Lab

 

AREA: 1 cm2

LENGTH = ___________  cm

AREA: 4 cm2

LENGTH = ___________  cm

AREA: 9 cm2

LENGTH = ___________  cm

AREA: 16 cm2

LENGTH = ___________  cm

AREA: 25 cm2

LENGTH = ___________  cm

AREA: 36 cm2

LENGTH = ___________  cm

AREA: 49 cm2

LENGTH = ___________  cm

AREA: 64 cm2

LENGTH = ___________  cm

AREA: 81 cm2

LENGTH = ___________  cm

AREA: 100 cm2

LENGTH = ___________  cm

AREA: 121 cm2

LENGTH = ___________  cm

AREA: 144 cm2

LENGTH = ___________  cm

AREA: 169 cm2

LENGTH = ___________  cm

AREA: 196 cm2

LENGTH = ___________  cm

AREA: 225 cm2

LENGTH = ___________  cm

 

What is the relationship between the area of the square and the length of the side of the square?  Describe in your own words the definition of a square root.

 

* For additional practice you can play the ÒI Have... Who HasÉ?Ó game

 

Instructions:

 

 

Examples of cards:

 

 

   

Activity 2:

What would happen if I presented you with a square with an area of 50 cm2?  (Insert any non-perfect square here.)  Is the number 50 a perfect square?  How could you determine the length of the side of the square?  SoÉ when you take the square root of 50, what type of number would you get?  A whole number/ fraction/ decimal?  (Decimal expansion) Would this be a rational or irrational number?  Why? What if you had to come up with an answer without using any technology?  Can you estimate your answer?  YES!  

 

Encourage the students to use the table aboveÉ what two perfect squares does the area of 50 cm2 fit between? A: 49 cm2  and 64 cm2.   Since the Ã49 = 7 and the Ã64 = 8, that means the Ã50 is between 7 and 8.

 

To check your estimation – use the GSP construction, manipulating the area of the square until you get 50 cm2.  (You could also incorporate the use of calculators here.)  What is the corresponding side length?  What do you know about the relationship between these two numbers?

 

LetÕs try a few moreÉ Use the estimation strategy first, and then check your answer in GSP or by using a calculator.

Ã90 =

Ã114 =

Ã42 =

Give students some time to create a few non-perfect squares on their ownÉ

 

Activity 3:

Students can explore the CCGPS Task below, in groups or individually.

 

Extra Practice/ Homework:

1)   LetÕs say that Mrs. Perzel wants to sew a fringe on the edges of a square tablecloth with an area of 500 cm2.  What is the length of each side of the tablecloth?  How much fringe would I need to buy?  Please solve this problem first using estimation and show your work.  Then check using a calculator, Graphing Calculator or by creating a sketch on GSP. 

 

Additional Technology Resources:

-       http://www.brainpop.com/math/numbersandoperations/squareroots/preview.weml

-       http://www.brainpop.com/math/numbersandoperations/rationalandirrationalnumbers/preview.weml

   

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