Reflections* is a monthly column for teachers, by teachers on topics of interest to mathematics educators: reflections on classroom experiences, professional development opportunities, resource reviews, and more. If you are interested in sharing your own ideas with mathematics educators in the province (and beyond), consider contributing to this column! Contact us at thevariable@smts.ca.*

**Foundations 20 Introduction Tasks – Linear Inequalities and Statistical Reasoning**

*Sharon Harvey*

I’ve taught Foundations of Mathematics 20 a few times, and each time I have found myself struggling with the disconnect between topics. At times, it feels as though the course is a dumping ground for concepts students should know, but that didn’t really fit anywhere else. And I notice that students struggle to remember concepts from the beginning of the course (that we do not use again after the unit) when it comes time to prepare for the final exam.

So I decided to look for opening tasks for units that would help introduce the main topic, perhaps shake up a little prior knowledge, and create memorable experiences that I could relate to when reviewing for the final exam. Collaborating with Amanda Culver and Andrea Klassen, we came up with activities that we felt would work well. Today, I’m going to share two of my favorites with you.

**Unit: Linear Inequalities
Activity: Zombie Apocalypse Now
Time: 1 class**

*Purpose:
*Students use the Zombie apocalypse scenario to review graphing linear functions using a table of values and the slope-point method. Each linear function has a direction (NESW) associated with it, which I use later to introduce the idea of inequalities.

*Materials:*

- double-sided activity sheet (one per person; see below, or download PDF here)

*Procedure:
*

- Pair students (I randomly pair them using Triptico).

- Give each student a handout and have them move into their pairs. In the story, I always use the names of 6 students in the story, 5 of which are killed by the zombies and 1 whom will survive and save the class—they find this amusing.

- Tell them that the safe house and other cabins need to be identified and submitted by the end of class. (I have them hand in their worksheet and quickly check to see how it went and to know what to remind them of, such as what to do when the y-intercept is off the graph, during our lesson the next day.)

*Follow-up:*

The next day, I project the map and go through the first set of directions with them. I ask how they knew to cross out the cabin above the line—they say because that’s north. Then, I ask about how we tell directions in math: If I wanted them to go above the line, what symbol would that be? How would they know they were right? We agree on which cabin is the safe house, then move on to the Cartesian plane and using mathematical symbols for inequalities.

**Unit: Statistical Reasoning
Activity: Skittles Lab
Time: 1 class**

*Purpose:
*Students access prior knowledge related to data management and statistics. This introduction activity allows for discussion about how to use a set of data to make predictions and what precautions need to be taken.

*Materials: *

- 1 bag of Skittles for each group of 3 or 4
- 1 extra bag of Skittles
- mini whiteboards
- markers
- erasers
- napkins

*Procedure: *

- Give each group of three or four students a bag of skittles, a napkin, a whiteboard, a marker, and an eraser.

- Ask each group to open the Skittles, pour them onto the napkin, then record as much data as possible about their bag of Skittles onto their whiteboard (typically, all of the groups will count the number of each colour, the unique/not round/deformed Skittles, and Skittles missing the ‘S’ marking; some groups will go further and calculate the weight of a Skittle, the number of calories per Skittle, etc.).

- Collect the data from each group and put it onto the classroom whiteboard. I collect the numbers of the different colours and the number of “unique” Skittles only. It looks similar to the following table:

Yellow | Red | Orange | Purple | Green | Unique | |

Group 1 | 15 | 22 | 16 | 12 | 15 | 1 |

Group 2 | 18 | 21 | 17 | 11 | 19 | 0 |

Group 3 | 12 | 16 | 24 | 8 | 27 | 2 |

Group 4 | 24 | 25 | 25 | 19 | 10 | 1 |

Group 5 | 16 | 24 | 18 | 15 | 17 | 3 |

Group 6 | 17 | 28 | 25 | 16 | 16 | 1 |

Group 7 | 18 | 21 | 19 | 14 | 23 | 2 |

Group 8 | 18 | 20 | 21 | 12 | 24 | 4 |

- Let the students eat the Skittles.

- Ask them to use the data to predict how many Skittles of each color and in total will be in the last unopened bag, and how many unique Skittles there will be. Tell them that they need to be ready to defend their predictions.

- Discuss the This is where the fun really begins. In all the times that I have done this activity, there have been groups that use the mean, the median, and the mode to make their predictions. There is also always a group that just guesses. Of course, they don’t often use these words, but then I ask for the “math words” that are associated with their methods and they usually come up with the vocabulary. This part of the task generally opens up a discussion about outliers. (For example, should they be using that 24 count in yellow if they’re finding the average?) Often, we also take time to chat about the difference between the range and the interval.

- Reveal the numbers.

- On their boards, ask students to give each prediction a +/- score. So, if there were 17 yellow Skittles in the last bag and they predicted 16, that would be a -1 (they under-guessed by 1). If they predicted 18, that would be a +3. If they predicted the exact number of Skittles, they would score a 0.

- Compile the results into the chart on the board (I just erase their old data and fill the chart with +/- numbers).

- Ask what they notice and wonder. What colour were they best at predicting, and how do they know?

*Follow-up*:

The next day, we have a formal lesson on the concepts of measures of central tendency, range, outliers, and dispersion. Throughout the unit, I am able to reference parts of the Skittles activity, and when it comes time for final review, I add Skittles next to the title and it helps them to remember the relevant concepts. I also start with this unit, so it’s a great chance to chat with students and establish a collaborative atmosphere in the room.

If you have any questions about the above activities, please contact me at derrick.sharon@gmail.com. And stay tuned for future editions, where I will share more introduction activities for Foundations of Mathematics 20.

*Sharon Harvey has been a teacher within the Saskatoon Public School Division for eight years. She has taught all secondary levels of mathematics, as well as within the resource program. She strives to create an inclusive and safe environment for her students.*