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Recreational Mathematics

Enrich Your Class... With Recreational Mathematics!

Purpose: Provide discovery, insight, and enrichment to a variety of mathematical concepts, many of which map directly to 4th Grade Standards.

Exploring Lucky 7 Card Trick (A-070)

Standard
NS - Finding the LCM of two numbers

Purpose

Exploring Lucky 7 Card Trick provides a fun, enriching way for finding the LCM of two numbers. This activity allows students to explore the intriguing patterns that arise when a set of cards are manipulated in a magical way. Students discover wonderful geometric patterns that provide the necessary information to find the LCM, blending mathematics and art.

Description

Exploring Lucky 7 Card Trick is a unique blend of mathematics and art. Through card manipulations, this activity provides an exploratory approach to finding the LCM of two numbers (2-9). Beautiful geometrical art is produced as the relationship of two number's multiples is investigated. The LCM is determined by analyzing the characteristics of the art. This activity is introduced with Lucky 7 Card Trick (M-056).

Two numbers are chosen with the goal of finding their LCM. One number is used as the quantity of cards. A set of cards are moved one by one from the top of the deck to the bottom. The quantity of cards moved in a set is determined by the other number. A geometric pattern is drawn as students keep track of each number finishing a cycle (i.e., reaching its next multiple). The LCM becomes the total quantity of cards moved after the two cycles coincide for the first time. The geometric drawing provides all the necessary bookkeeping!

worksheet   |   worksheet answers

extended worksheet   |   extended worksheet answers


Reference(s)

Longe, Bob. The Magical Math Book. New York, NY: Sterling Publishing Co., 1997, pp. 30-31.

Worksheet concept and worksheet original.

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Exploring Handy Times - Multiplication Facts (A-008) 

Standard
NS - General - Place value and Other Bases

Purpose

Handy Times is a handy way to either review multiplication facts or enrich students with a unique finger math technique. Students are typically shown how to use their fingers to produce the multiplication facts of 9. This method can be extended to demonstrate all the basic multiplication facts by using a reduced set of fingers and patterns exhibited in other bases.

Description

The magic show opener Finger Math "6 thru 10" X "6 thru 10" (O-31) is used to demonstrate how the 10 fingers can be used to multiply any number from 6 thru 10 by another number 6 thru 10. Students are then reminded how the multiplication facts of 9 can be produced using their 10 fingers.

Motivated by the magic show event Handy Times - Multiplication Facts (M-037), this activity reveals how different sets of fingers can produce all the multiplication facts.

One finger from a wooden hand set can be removed to show how 9 fingers can be used to create the multiplication facts of 8. This strategy can be repeated until all multiplication facts are shown. A worksheet is available for each finger set to reinforce the place value and number base inherit in the finger set.

This activity can span multiple days, or a single day activity can select a few finger sets of interest (e.g., 9 fingers, 6 fingers, 3 fingers). Another option is to use the worksheets as extra credit to allow more demonstration time. An interesting pattern from finger set to finger set is also discovered and discussed.

worksheet   |   worksheet answers


Reference(s)

Original.

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Exploring the Magic of 142857 - Part 2 (A-069) 

Standard
NS 3.2 (multi-digit) X (2-digit or 3-digit number)

Purpose

This activity provides students with a set of multiplication problems to practice multiplying a multi-digit number (142857) by 2-digit and 3-digit numbers. They are also introduced to the strange behavior of the cyclic number 142857 as the products are rearranged to magically return back to 142857.

Description

This activity is an extension of a 3rd grade activity that introduces students to the cyclic number 142857. The magic trick Magic of 076923 (M-018) motivates this 4th grade activity. Unlike 142857, the number 076923 is a cyclic number involving two numbers: itself and 153846.

In this activity, the cyclic property of 142857 is explored by multiplying 142857 by 2-digit and 3-digit numbers. A worksheet is available to organize this activity. When each product is obtained, it is separated after 6 digits counting from the right.The remianing digits on the left are brought down (right justified) and added to the other 6-digit number. The results are quite surprising. See the worksheet answers for examples. Calculators can also be introduced to explore the behavior when larger numbers are used.

Additionally, students can discover the peculiar results produced when the cyclic number 076923 is multiplied by the numbers 2 through 12 and beyond. If time permits, students can break into groups and continue to play with this amazing property.

worksheet   |   worksheet answers


Reference(s)

Devi, Shakuntala. Figuring - The Joy of Numbers. New Delhi, India: Oriental Paperbacks, 1993, p. 115-118.

Worksheets are original.

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1089 and All That (A-071) 

Standard
General Number Sense

Purpose

This mini-activity is of value in exploring number patterns.

Description

Fun patterns are explored when 1089 is multiplied by 1-9. An interesting follow-up activity of A Smart Trick (M-006).


Reference(s)

Heath, Royal Vale. Math E Magic. New York, NY: Dover Publications, Inc, 1953, p. 36.

 
Exploring 4-Digit Magic and Beyond (A-073) 

Standard
NS 3.1

Purpose

A great way to see how a solid understanding of place value and general number sense can produce instant sums.

Description

Exploring various ways to extend the magic trick 4-Digit Magic and Beyond (M-070) with the aid of worksheets.


Reference(s)

Gardner, Martin. Mathematics Magic and Mystery. New York, NY: Dover Publications, Inc, 1956, pp. 170-172.

Worksheets are original.