this lesson, students will attempt to find a three-digit house number
that meets certain criteria. Review some examples of three-digit
numbers which would be familiar to students.
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 house number could be placed.
Hold up the Numeral Cards for 3, 0, and 1.
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 4
Ask students if there is another way to get a sum of 4 using any of the numeral cards. Students may suggest the following:
Ask students how they know when they've listed all of the possible
number combinations. Be sure to point out the combinations where the
digits are all different.
Present the following problem to students:
- The house number has three different digits.
- The sum of the three digits is 6.
- The number does not begin with 0.
- What could the house number be? List all possible numbers.
Distribute the Create a House Number Activity Sheet.
Create a House Number Activity Sheet
Have students cut the digits from the bottom of the activity
sheet. They will use these tiles to physically generate the three-digit
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
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 six) 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 house numbers.
Solutions to the Create a House Number Activity Sheet are as follows.
There are 14 house numbers that meet the given criteria:
Note: Students who finish this lesson early may complete one of the Extension activities, as described below.
Marcy Cook. "IDEAS: Possible Solution Sets" The Arithmetic Teacher Vol.36, No.5 (January, 1989) pp. 19 -24.