15.2 - Make a List

Links and useful resources

• gr7's Prealgebra Course Outline START HERE<<<
• AoPS Online Textbook
• IXL Grade 7 index
• IXL Grade 8 index
• AoPS Alcumus
• IXL prealgebra practice index
• OpenSTAX Prealgebra-1 textbook

Concept summary and lesson

• In problems where there are a bunch of constraints that whittle away possible answers, it's sometimes handy to just write them down and cross them off.
• Sometimes there just aren't that many possible answers. That's another time when writing them down and filtering them out is fast and convenient.
• When you're going to make a list, try to start with the most restrictive property because it will give you the smallest set of things at the beginning.

Remember: Getting the correct answer is the goal here, not proving you can do hard work. If you have a clever way to get it done, just use it (as long as it's actually you doing the work, not just looking up the answer or asking AI...).

Guided practice

• Elizabeth spent exactly $\mathrm{\$}7$ for some $15$-cent stamps and some $31$-cent stamps. How many $15$-cent stamps did she buy?
• Find a two-digit positive integer with all these properties:
  • the tens digit is larger than the ones digit (units digit),
  • the difference between the digits is greater than 3,
  • the sum of the digits is greater than 10, and
  • the integer is a multiple of 12.
• A partition of a positive integer $n$ is a way of writing $n$ as the sum of positive integers in which the order of the numbers in the sum doesn’t matter. For example, the partitions of 3 are 3, $2+1$, and $1+1+1$. We consider $2+1$ and $1+2$ to be the same, so there are 3 partitions of 3. How many partitions of 6 are there?

Homework

• #hw (math) (gr7) 15.2 Make a List (p. 552) 2025-05-14