Is there anything better than a themed math puzzle? We think not! As we enter into the season of fall festivities, it can be fun to give students an opportunity to do some problem solving and mathematical reasoning outside of our usual content area. Whether you’re looking for a way to fill the 25 minute class period on the half-day of Halloween or you just need a break from the usual routine, we’ve got just what you need to put a delightful autumn spin on your math class.

Today we’ll share with you three different fall-themed puzzles that can be used in any high school math class.

##### These puzzles are great for:

Developing the mathematical practices (especially

__MP1__,__MP2__, and__MP7__)Fostering collaboration (they’re too challenging to do individually!)

Reviewing essential mathematical concepts (like proportional reasoning)

Honoring diverse ways of thinking (many possible solution approaches)

Having students work on VNPS (vertical, non-permanent surfaces)

Preserving your own sanity with a zero-prep lesson plan (self-explanatory 😀)

## Activity 1: The Pumpkin Spice Latte Problem

#### Proportional Reasoning

Students get a recipe for a 16 oz PSL and use proportional reasoning to answer a series of questions based on the recipe. If your students are not already familiar with the double number line (aka the __Swiss Army Knife of math__), the debrief of the PSL problem provides an excellent opportunity to introduce it. The activity also emphasizes the importance of units!

#### Download Answer Key

Special shout out to our executive director of the __Math Medic Foundation__, Pete Grostic, who LOVES a PSL and inspired this activity!

## Activity 2: The Candy Corn Puzzle

#### Spatial Reasoning

In this adaptation of the classic chessboard problem, students will place candy corn pieces on an 8x8 grid so that no two candy corn pieces are on the same line, vertical, horizontal, or diagonal. If you want to embrace the fall theme, you will need candy corn for all of your students (8 pieces per person). Another option is to use bingo chips or counters. Alternatively, you could put the grid in a plastic sleeve so students can write with a whiteboard marker or have students work directly on whiteboards. The important thing is that students can easily move the pieces as this activity requires a lot of trial and error.

Be aware! This puzzle is harder than it looks!

#### Download

## Activity 3: The Pumpkin Sale

#### Algebraic Reasoning

In this activity, students receive information about the cost of small, medium, and large pumpkins and a single purchase of pumpkins from Ms. Jones who is decorating for the fall festival. The task is to figure out how many pumpkins of each size she purchased. This activity would work great in an Algebra 2 or Precalculus class but no formal methods for solving systems of equations in more than 2 variables are needed! Since the number of pumpkins has to be a whole number, non-solutions can be eliminated using number sense and knowledge of factors and multiples!

There are actually two solutions to this problem, which comes up in Jamirea’s wondering in the second half of the task. This means that students might differ in what solution they come up with in part 1 of the task. There is room for rich discussion on why both solutions are valid, so we suggest taking some time to have students share out their strategies and solutions in a whole-class debrief. If you are having students work on vertical non-permanent surfaces, you could travel to different boards in the debrief and point out unique features of each solution. We recommend choosing some ideas to highlight while you are monitoring students’ progress during the task.

While writing this activity, I became curious about how the selection of numbers (for the prices of the pumpkins and the total quantity of pumpkins Ms. Jones purchased) contributed to the number of solutions. This led me to write two extensions to the problem that students could work on if they finish early and are ready for a challenge. The extensions are written on the second page of the task, but you may wish to only print page 1 and give the extensions verbally instead.

**Extension 1:** Change only the numbers in the problem and nothing else so that there is exactly one solution. Can you do it by changing the fewest numbers possible?

**Extension 2:** Change only the numbers in the problem and nothing else so that there are more than two solutions.