In this lesson, students will attempt to find a three-digit address number that meets certain criteria.
You may wish to draw a house, similar to the one shown below, on the board or overhead projector. Be sure that the house has three slots where the digits of the address number could be placed.
Hold up the Numeral Cards for 6, 0, and 2.
Ask students what they notice about the three-digit number formed by those digits. They may notice that:
- the digits are different
- the sum of the digits is 8
- the digits form the number 602.
Ask students if there is another way to get a sum of 8 using any of the numeral cards. However, the digits must be different and the number formed by the three digits must be greater than 600. Students may need time to think about the various possibilities. A class discussion should yield only one other possible solution: 701.
Students will solve a similar problem in today’s lesson. However, there will be multiple solutions possible. Present the following problem to students:
- The house number has three different digits.
- The sum of the three digits is 12.
- The number is greater than 480.
- What could the address number be? List all possible numbers.
Distribute one copy of the Create an Address Number Activity Sheet to each student.
Create an Address Number Activity Sheet
Have students cut the number tiles from the bottom of the activity sheet to use as digits.
Allow students some time to work on the problem individually. Then, allow students to work with a partner to discuss their answers. In particular, they should attempt to create a complete list, which may be accomplished by combining the answers they attained individually. Students should compare their lists, noting any "repeats" or missing number combinations.
Lead a discussion to arrive at a conclusion. The discussion should include the need for keeping an organized list, so that students can be sure when they have found all possibilities. Students should also discuss how house numbers were found. For example, they might mention that they tried to find a set of three numbers that met one criteria (for instance, the set had a sum of twelve) but then removed those sets that did not meet the other criteria (for example, remove sets with digits repeated). Continue the discussion until students are convinced that they have found all possible address numbers.
After the discussion, you may wish to ask students the questions listed in the Extensions section.
Cook, Marcy. "IDEAS: Possible Solution Sets" The Arithmetic Teacher Vol.36, No.5 (January, 1989) pp. 19 -24.
Collect students' Create an Address Number Activity Sheets to verify if they found all 24 different address numbers. The solutions are as follows:
- How many address numbers can be formed if the problem is the same except that the three digits need not be different?
[Six more addresses can be formed: 822, 660, 606, 633, 552, 525.]
- How many address numbers can be formed if the problem is the same except that the number need not be greater than 480?
[54 more addresses can be found (30 more than the original answer) if the digits must be different; 66 if the digits can be the same.]
- Experiment with numbers to find all possible ways to add three different digits to obtain a given sum (for example, 12).
- Explore the ways three digits can be placed together to form different three-digit numbers greater than a given number (for example, 480).
NCTM Standards and Expectations
- Understand the place-value structure of the base-ten number system and be able to represent and compare whole numbers and decimals.
- Develop fluency with basic number combinations for multiplication and division and use these combinations to mentally compute related problems, such as 30x50.
Common Core State Standards – Mathematics
Grade 4, Num & Ops Base Ten
Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700 ÷ 70 = 10 by applying concepts of place value and division.
Grade 4, Num & Ops Base Ten
Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and <. symbols to record the results of comparisons.
Grade 5, Num & Ops Base Ten
Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left.
Common Core State Standards – Practice
Reason abstractly and quantitatively.