Instead today I want to take a peek at a few phrases lifted directly from the Standards for Mathematical Practice--and even if you do not teach in a Common Core state, I am hopeful that you will embrace these 8 essential "best practices" for math instruction. Take a peek at these two phrases for just a minute.
"Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt."
"Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, 'Does this make sense?'"
As you can see, at no point does this say "word problem"...consider the following problem. This is certainly not a "word problem" as we typically think about them...it's more a mathematical "situation" where students are asked to find a way to use what they know about numbers, addition, subtraction, and estimation to find a solution (or more than than one!). Let's cross check it with those two phrases from the standards.
Do you see what I mean? This problem is a perfect example of a problem that provides students with a ton of opportunity to apply what they know about math--without a word problem! (By the way...this is a part of my perseverance freebie in my store. Just CLICK HERE to grab it and try it with YOUR students!)
I want to show you another way I try to help my students understand that problem solving is far more than simply solving word problems. Because I start the year reviewing the addition algorithm, finding a way to kick that skill up a notch--in a way that will challenge even my "gifted-est" students was a goal of mine a few years back...I wanted something that would give TONS of math practice, have multiple solutions, be perfect to work on alone or collaboratively, have multiple levels, and need NO teacher assistance. Sounds easy, right?
It wasn't--but once I got going, I found something that I thought would work--and it was MAGIC! Not only did it accomplish all of the above, but it gave me a perfect opportunity to work with my students on having a growth mindset (need to know more? CLICK HERE!). Many of my top students come in not super used to struggling...and it really and truly is an essential skill to learn how to manage. Let me show you what this involves. First of all...the thought of writing this blog post made me realize that I hadn't changed this bulletin board in 3 years. So that had to happen first. From this...(wish you could see how faded it all is!)
To these fantastic plates (by they way, I've never seen a Star Wars movie. Ever. Any of them.)..
To a new color palette...
To THIS! I am SO much happier now...and feel I can continue with the blog post now!
Students use this board--which can be displayed in your room or just handed out as a printable--and the numbers on the board are used for a variety of different problem solving tasks, each of which is differentiated. The five main activities have a part 1 which is more computation based--and that's all some students try. It takes a fair amount of work to solve them...and I love having students use each other (and calculators at times) to check their work. The second part of each activity is far more open ended and asks students to create their OWN solution,based on what they did on the first part. It asks students to think about addition in a far more sophisticated way! They need to estimate...and guess and check..."trade" numbers to make things work ("Hmmm...436 was too high, so let me try the 367.") and really develop their number sense AND computation skills.
For students who manage to solve all of THESE challenges, there are more...all giving students a chance to refine their addition skills WHILE PROBLEM SOLVING...and continually thinking about their approaches to the problems. Trust me--there can be some pretty substantial frustration with some students! I love how we work as a class to talk about having grit and perseverance--and also how to support each other as we work through tricky learning situations.
If you want to try that freebie above, just click the image below.