Teacher resources and professional development across the curriculum

Teacher professional development and classroom resources across the curriculum

Monthly Update sign up
Mailing List signup
Learning Math Home
Number and Operations Session 5: Divisibility Tests and Factors
Session5 Part A Part B Part C Homework
number Site Map
Session 5 Materials:

Session 5, Part A:
Alpha Math (35 minutes)

"Alpha math" problems, where each letter stands for one digit of a number, can help you identify some of the things you know about the behaviors of particular base ten digits under various operations. Your task is to decode each of the following problems, figuring out what digit each letter represents. Note 1

Problem A1


In the following sums, one letter always represents the same digit in each problem, and no digit is represented by more than one letter. Replace the letters with digits:

Stop!  Do the above problem before you proceed.  Use the tip text to help you solve the problem if you get stuck.
Consider the following:
 What does the sum of a and a in the hundreds column tell you about the value of a?
 Notice that the sum of b and c in the tens column is different from the sum of c and b in the ones column. What does this tell you about the value of b + c?
 Notice that the sum of b and c in the tens column is b. What does this tell you about c?
   Close Tip


Problem A2


Each letter represents a different digit of a number:

Decode the problem to determine the following value:


Problem A3


In these problems, the asterisks represent missing digits (though they do not all represent the same digit, as do the letters in the previous problems). Identify the missing digits in the following multiplication problems:


Problem A4


Each letter represents a different digit of a three-digit number. Decode the problem:

Take it Further

Problem A5


Jen has found a special five-digit number that she calls abcde. If you enter the number 1 and then her number on a calculator and multiply it by 3, the result is the same number with a 1 on the other end:

1abcde • 3 = abcde1

What is her number?


Next > Part B: Divisibility Tests

Learning Math Home | Number Home | Glossary | Map | ©

Session 5: Index | Notes | Solutions | Video


© Annenberg Foundation 2017. All rights reserved. Legal Policy