6th Grade Math Textbook, Fundamentals

Chapter 2 51

More Enrichment Topics

Use different starting numbers. Describe the results.
Then use algebra to explain how the trick works.

1. a.Choose any whole number.
   b.Add the next greater whole number to it.
   c.Add 9 to that sum.
   d.Divide the new sum by 2.
   e.Subtract the number you chose.

2.Discuss and Write Make up a magic number trick of your own. Test it to

see that it works. Then ask a friend to try it.

pages 53–54 for exercise sets.

Here is another trick. Try it and see what result you get.

Steps of Trick 2: a.Start with your age in years.

b.Multiply it by 2.

c.Add 10.

d.Multiply the sum by 5.

e.Add the number of siblings you have.

f.Subtract 50.

You now have a three-digit number. The first two digits are your age, and the

last digit tells how many siblings you have.

To understand how this trick works, you first have to know that any one- or

two-digit number can be written as 10tu, where tis the tens digit and uis

the units digit. For example, 34 can be written as 10 • 3 4, and 8 can be

written as 10 • 0 8.

No matter what age you start with, the number you end with will have the

tens digit, t, of your age in the hundreds place, the units digit, u, of your age

in the tens place, and the number of siblings, s, in the ones place (assuming

you have fewer than 10 siblings).

Steps of Trick With Age 12 and 2 Siblings With Any Age and sSiblings

a. Start with your age in years. 12

10 tu, where tis the tens digit

and uis the ones digit

b.Multiply it by 2. (^24) 2(10tu)  20 t 2 u
c. Add 10. 34 20 t 2 u 10
d. Multiply the sum by 5. 170 5(20t^2 u10) 
100 t 10 u 50
e. Add the number of siblings. 172
100 t 10 u 50 s, where sis
the number of siblings
f. Subtract 50. 122
100 t 10 u 50 s 50 
100 t 10 us