## Address Number Combinations

- Lesson

This lesson focuses on forming numbers which meet specific requirements. Careful reading of information and understanding of mathematical language are important to finding appropriate solutions. Using the problem-solving strategies of looking for patterns and establishing an organized list will aid students in finding all the possible solution sets.

### Activity: Create a House Number

Explain to students that they will be forming a three-digit house number using the digits 0‑9.

Distribute one copy of the Create a House Number Activity Sheet to each student. Give students number tiles 0 through 9, or have them cut the digits from the bottom of the activity sheet.

Create a House Number Activity Sheet

Review the problem by reading it to the students. Then, give them some time to explore the problem. Lead a discussion to arrive at a conclusion.

After the discussion, ask students to consider how many more numbers could be formed with a product of 24 if the digits do not have to be different. That is, what happens if a digit can be used more than once in a house number?

### Activity: Create a Mailbox Number

Explain to students that they will be forming a five-digit mailbox number using the digits 0‑9.

Distribute one copy of the Create a Mailbox Number Activity Sheet to each student.

Create a Mailbox Number Activity Sheet

Give students number tiles 0 through 9, or have them cut the digits from the bottom of the activity sheet.

Review the problem by reading it to the students. Then, give them some time to explore the problem. Lead a discussion to arrive at a conclusion.

### Reference

Cook, Marcy. "IDEAS: Possible Solution Sets" The Arithmetic Teacher Vol.36, No.5 (January, 1989) pp. 19 -24.

**Assessment Options**

1. Note student participation during the class discussion. At the end of the lesson, collect student work on the Create a House Number Activity Sheet. 21 different house numbers can be formed:

831 813

641 614

622

461 416

423 432

381 318

342 324

262 226

243 234

183 138

164 146

2. Collect the Create a Mailbox Number Activity Sheet from each student. Solutions are as follows:

[Sixty possible numbers could be formed: the six possible two-digit numbers are 16, 25, 36, 49, 64, or 81; those numbers can be combined with the three-digit numbers: 100, 121, 144, 169, 196, 225, 256, 289, 324, and 361 (6 x 10 = 60).]

**Extensions**

1. *Activity: Create a House Number*— How many house numbers can be formed if the product of the digits in a four-digit address is 24?

[64 house numbers can be formed with the various combinations of 6221, 6141, 2431, 1831, and 2223.]

2. *Activity: Create a Mailbox Number*— How many five-digit address numbers can be formed if the first two digits form a two-digit cube number and the last three digits form a three-digit cube number less than 400?

[6 mailbox numbers can be formed: 27125, 27216, 27343, 64125, 64216, and 64343.]

### Learning Objectives

Students will:

- Experiment with numbers to find all possible ways to multiply three digits and get a product of 24.
- Explore the ways three digits can be placed together to form different three-digit numbers.
- Experiment with numbers to find all possible ways to combine a two-digit square number with a three-digits square to form a five-digit address number.

### NCTM Standards and Expectations

- Use the associative and commutative properties of addition and multiplication and the distributive property of multiplication over addition to simplify computations with integers, fractions, and decimals.