I think my first list was to Santa and I am sure the first thing on it was a pony. We all have opportunities in our daily lives to make lists; groceries, packing, daily to-dos. And making a list in math is a great way for students organize their thoughts as well. Some students might find it tedious and not want to put in the effort. Some might like the patterning of it all, I was a pattern person. But regardless of how they feel about it, making a list is a necessary problem solving skill.
Anytime there is a problem that has more than one solution or you are trying to solve a combination problem. Organizing the information in a list is a logical way to keep a student on track and ensure that all the possible solutions can be found.
Think about toppings on a pizza, if you have 3 different cheeses; mozzarella, Parmesan, ricotta, 3 different meats; pepperoni, sausage, Canadian bacon, and 4 different veggies; peppers, mushrooms, onions and olives and you can select one of each for your pizza. What are the different combinations you can have on the pizza?
If you just picking toppings without any strategy you might be making a much longer list than expected as it will be difficult to know if you repeat the same toppings, especially if they are in a different order. So, a student would have to figure out an order in which they know what
they have used and what they haven’t used.
A great strategy is to start with the 1st topping and then have go down the list;
Mozzarella, pepperoni, peppers
Mozzarella, pepperoni, mushrooms
Mozzarella, pepperoni, olives
Mozzarella, pepperoni, onions
Mozzarella, sausage, peppers
Mozzarella, sausage, mushrooms
Mozzarella, sausage, olives
Mozzarella, sausage, onions
A great example to get students motivated to make a list and be systematic about it, you can even do it with manipulative material that represent each topping.
A tree diagram is also a great way to visualize this.
MANGO Math has several lessons that requires students to make lists, like; Crack the Code in our 1st grade crate, What 2 Wear in our 3rd grade crate, and Horse Race in our 4th grade crate.
One great idea we will share is one that involves a paddle lock.
Buy a combination paddle lock and a box. Put something special in the box that you think your students would like. Then give them the numbers in the combination of the lock but not in the correct order. Example:
This locks actual combination is 14, 32, 9 so the students would get the numbers but not in the correct order. 4, 9, 1, 2, 3 – they are then to try and solve the combination.
This requires them making a detailed list which they can try the combination out on the lock to see if they work. If students are clever about it they will work together, or at least know from their friends which combinations didn’t work.
Hint: there can’t be a two-digit number that is greater than 39, as that is the highest number on the lock.