I saw this activity on a twitter page https://twitter.com/letsplaymath and thought it has some interesting potential for high school math students. The activity published by Math Forum asks participants to create expressions for whole numbers 1-100 using only the digits 2, 0, 1, and 5, in any order*, with the operations +, -, x, ÷, ^ (raised to a power), sqrt (square root), ! (factorial), and !! (double factorial). Grouping symbols may also be used, and multi-digit numbers such as 20, 210, .02 may be used this year. *The order 2, 0, 1, 5 is preferred.
For Algebra 1, Geometry, and Algebra 2 – it would be a great review for basic operations practice. There are so many ways to extend this activity. On example could be that every odd number has to use a negative integer in the expresseion. For upper level math, it would be interesting to see what they could do with the additional operations that they have used – like the log of a number etc.
Think about the conversations this could start if students were encouraged to share their responses and then asked if could they come up with different way for the same value. Just the thought of this makes me smile.
Students could also be asked if they could come up with a strategy of attack when thinking of different number sets…like even numbers or multiples of 10 etc..
How about asking students before they start – to predict the numbers will be the hardest to find a combination that will work and then reflect afterwards if they were correct. Wow think of the thinking! (I am really smiling now with that “evil” smile a math teacher has when they are thinking about making student think 🙂 )
The original directions and worksheets can be found at the link http://mathforum.org/yeargameWorksheets/2015/2015.worksheet.html . Happy New Year!
Use models in math? In high school level courses?? Isn’t that something only elementary teachers need to use??? High school students do not need models and there are not any models to use with high school topics anyway…this has been a reflection of my thoughts until recently. Boy have I made a lot of mistakes as a teacher – it is amazing that my students have been as successful as they have. During most of my teaching career I used models (Algebra Tiles mainly) as an afterthought in Algebra 1 because they had to be “shown” for the state standardized test. My students always complained about the algebra tiles and said that they were too “easy” and that they did need not them – they knew the math so why use the tiles. Duhhhh if I show them the tiles after I taught the standard algorithm they why would they use the tiles…which my students always felt were for “dummies”. I know that I encourage that thought now looking back on it.
Now my thinking has evolved…I have discovered models and how they give students an avenue to communicate and understand the concepts that we ask them to do. I have learned that our students (all students) need to experience most mathematical concepts through models first before they experience the standard algorithm. Students can make many more connections through the use of models and truly understand why the standard algorithm works. It is amazing that using models leads students to a true understanding.
I wanted to share this epiphany with everyone that I work with but how do I start???? Most teachers (high school anyway) that I know do not think that models are needed to help students conceptualize the math that they are teaching. I understand where they are coming from because like I said 2 years ago I was with them. So I decided to start with a group that I work with (or teach) bi monthly – instructional coaches. I started with the Junior High standards that addressed using models to teach and we discussed how important it was to make connections to how students learn specific topics so that students would see that what was being taught is not new – they have seen it before – it is just in a different format. So while I was working with the high school math instructional coaches, I used the practice sheet below for them to see how a linear equation can be solved in several different ways and using models can be used to differentiate so that teachers can reach all students… (you can download here…Modeling to solve equations practice)
This activity went over really well but now how do we get this knowledge to spread throughout the district? That is a question that the coaches and I will need to answer. What I was very pleased with was the fact that by showing the different forms shown while working this activity really showed how different learners might need different tools in order to make connections and gain a true understanding of the topic. Now I need to work on next steps and would love any input from others. I started with solving this set of linear equations but I have plans to continue this with other functions.