Tayo Olowoniyi
Strategy Overview
A system is a method for doing things systematically. A systematic list is a method of organizing possibilities to make sure that no solutions are repeated or missed. When we look over the list, you can also see patterns or discover shortcuts to help you solve the problem. The objective of learning a systematic list is to learn how to create organized lists to solve problems, improve mathematical thinking, organize problem-solving methods, and pay attention to detail.
Let’s cite an example of how a systematic list is applicable in our daily lives: Imagine you have 2 shirts (red and blue) and 2 pairs of shorts (black and gray). You want to find all the different ways to wear your outfits. Instead of guessing, you can make a list of different ways to wear the outfits, that is, making a systematic list:
- Red shirt + Black shorts
- Red shirt + Gray shorts
- Blue shirt + Black shorts
- Blue shirt + Gray shorts
By making this list in order, you know you have all four outfits without missing any.
The goal of using a systematic list is to help you solve problems one step at a time. It helps you stay organized, think carefully, find all the possible answers, and avoid repeating or forgetting any solution.
For what types of problems is this strategy helpful?
- Make a systematic list can be used for analyzing information, for example, finding the combinations that are possible.
- When you need to solve a puzzle-type problem that requires testing different possibilities
- To determine how to make a certain amount of money using different coins
- Identifying favorable outcomes and total outcomes
- Compare and sort data
When is it NOT very useful?
- Make a Systematic List might not be useful for geometry problems
- Make a Systematic List might not be useful to measure temperature over time
Common mistakes or misconceptions to watch out for:
- You might list the same combinations of numbers without realizing.
- You might assume that all possibilities have been attempted, not knowing that there are still more solutions to identify
- You might not understand the question, so you make a list that doesn’t answer the question
How does this strategy help students become better mathematical thinkers?
- Systematic lists teach learners how to organize problems instead of guessing, learn how to find patterns in a given problem, and become better problem solvers. You’ll also become proficient at explaining your reasoning, which is a very valuable skill, and at becoming a successful learner.
Example Problems
Problem 1:
Frisbin
On a famous episode of Star Trek, Captain Kirk and the gang played a card game called Phisbin. This problem is about another game, called Frisbin. The object of Frisbin is to throw three Frisbees at three different-sized bins that are set up on the ground about 20 feet away from the player. If a Frisbee lands in the largest bin, the player scores 1 point. If a Frisbee lands in the medium-sized bin, the player scores 5 points. If a Frisbee lands in the smallest bin, the player scores 10 points. Kirk McCoy is playing the game. If all three of his Frisbees land in bins, how many different total scores can he make? Make a systematic list for this problem. (Johnson & Herr, 2001, p. 36))
Problem 2:
choose a snack and drink
Three friends James, Mia and Amanda they are choosing a snack and a drink. They can choose one snack: Apple, Cookies Or Popcorn. They can choose one drink: Water Or Juice. How many different snack-and-drink combinations are possible? Use a systematic list to prove that you found them all.
Worked Examples + Think-Aloud
Problem 1:
What do we know?
- The object frisbee is to be thrown three times
- The bin contains three different sizes
- Each size represents a point
What is the question to solve?
If all three frisbees land in the bins, how many different total scores can he make?
First, represent the frisbees with color code chips
Now, make a systematic list table chart that will show possible ways the frisbees can get into the bins
There are 10 different ways that that the frisbees can be thrown into 3 different bins when given a chance to throw 3 times at each time.
The table shows different ways the freebees can be put in the bin.
Problem 2:
Student Self-Talk Questions
- How can I organize my list so I don’t miss any possibilities?
- What information do I need to list?
- Did my systematic list help me find all the solutions?
- What am I trying to find all the possibilities for?
Problem 1.
What do we know?
- The object frisbee is to be thrown three times
- The bin contains three different sizes
- Each size represents a point
What is the question to solve?
If all three frisbees land in the bins, how many different total scores can he make?
Teacher Notes and Instructional Tips
Lesson Launch Ideas
I will ask for three students to volunteer and give each student picture representation of snack and ask the student to choose on drink each for the snack . I will ask the student what the total possible outcomes is.
Teacher Questions & Anticipated Student Responses
I will provide the student with the pictures of the snacks and the drinks . I will create a scenario so the students can understand: “Imagine a packing your lunch for school, you can only take one snack and one drink , how many ways can you pack your lunch?”. I will remind the to make a list and check if any possible outcomes are not forgotten or written twice.
Differentiation Suggestions
Support:
-
- Model the first possible combinations for the student.
- Put students in groups to discuss how an organized system helps.
- Provide students picture care of the snacks, juice and water.
- Provide students with manipulatives.
Extend:
-
- Add another, similar problem.
- Challenge students to find the greatest and least possible numbers.
- Ask students to find all numbers that are even or odd.
Formative Assessment Tools
I will ask my student to solve the question using a systematic list as an exit ticket. I will ensure my student does not repeat numbers and the list are organized.
Student Reflection Prompts
- How did using a systematic list help you solve today’s problem?
- What pattern did you notice while making your list?
- What was challenging about creating a systematic list, and how did you overcome it?
What prior knowledge do students need?
- Understanding that a combination or possibility is one possible outcome in a problem.
- Basic multiplication and division facts. ·
- Finding factor pairs of a number.
- Understanding place value when creating numbers from digits. ·
- Have the knowledge of how to organize tables.
What classroom challenges commonly arise?
- Students may overlook some combinations or solutions because they do not follow an organized pattern
- Students may accidentally count the same combination more than once.
- Some students may record possibilities randomly, making it hard to determine whether all solutions have been found.
Media Attributions
- Solving the Frisbin Problem, Step 1 © Tayo Olowoniyi is licensed under a CC BY-NC-SA (Attribution NonCommercial ShareAlike) license
- Solving the Frisbin Problem, Step 2 © Tayo Olowoniyi is licensed under a CC BY-NC-SA (Attribution NonCommercial ShareAlike) license
