Simplifying Radicals with Go-Fish

Here is how I am going to attempt to allow my students to discover why and how to rewrite radicals.

Thank you  to https://pumas.gsfc.nasa.gov/files/12_03_06_1.doc for the inspiration.

Simplifying Radicals With Go-Fish

1)      In groups of 3 or 4, take a deck of cards and remove all the jokers and face cards (Jacks, Queens, and Kings) from the deck.  For this activity ignore the suits of the cards.

2)      Deal out all the cards, one at time, to each person.

3)      Fill out the chart as follows:

a.       Write down the square root of the product of all your cards, as an exact number.  (Aces = 1)

b.      Write the decimal approximation, to 2 decimal places

4)      Put your pairs together, and keep the single cards separate.

5)      Fill out the chart as follows:

a.       The product of each pair. (IE if you have 2 3s and 2 4s, you would multiply 3 by 4)

b.      The square root of the product of the single cards, as an exact number.

6)      Multiply the product of the pairs, to the square root of the remaining cards, and round to 2 decimal places.

7)      Repeat for 10 hands.

8)      Answer the questions on the back page.

9)  Explain, why both ways are giving you the same decimal values.

Example:

Jason was dealt a four card hand which consisted of an 8, 3, 5, and another 8.  He filled in the first row and shown.

Hand Number	Square root of the Product	Decimal, to 2 decimal places	Product of the pairs.	Square root of the remaining cards	Product of the pairs and root of the remaining cards
Example		30.98	8		30.98
1
2
3
4
5
6
7
8
9
10