Category Archives: Middle School Math

What makes a growth mindset math game? Hint: Avoid worksheets in disguise!

If you were to search for the term ‘math games’ on google, you would get instant access to many sites where you get the chance to practice skills in the guise of a ‘fun game’. For example, in the game Candy Stacker, you get to practice pretty much any skill in any grade and it stacks cake on top of an animal until it reaches a candy. As with many of these games, it is timed, and you ‘fail’ if you get on wrong. These types of games reinforce the fixed mindset that is so often observed in mathematics classrooms.

There are better ways of building fluency and understanding of number. Number talks and Formulator Tarsia are just two great examples. But, are there activities out there that both have that gaming element, and help build a deep understanding of number while promoting a growth mindset, that depth is more important than speed? Thankfully, yes, and here is a list of growth mindset games that I love my students to play, either in a dedicated lesson or in those moments where you have 10 minutes spare. None of these will have timers or ‘fail’ notices. (Note: There are many great card, board, and paper games out there, but I am going to focus on online interactive activities for this post). Click on the images to go to the game itself.

Factors and Multiples (nrich)

Screen Shot 2018-11-09 at 6.56.12 AM.png

This is probably my favorite of all, building sense of multiplication tables, but students also quickly come to realize that prime numbers are key in this game.

1 Player version: What is the longest chain you can make, clicking factors and multiples of the previous number (see the example in the picture). What is the longest chain that anyone can make? Are there numbers to be avoided at the beginning? Are there good numbers to start with at the beginning?

2 Player version: The winner is the person that can force the other player not to be able to build on the chain, cutting off all possible factors and multiples. Again, are there good numbers to start with? What are the key numbers to minimize the chances of losing the game?

Connect 4 Factors (Transum)

Screen Shot 2018-11-09 at 7.07.05 AM.png

Another fantastic game to build a sense of numbers, factors and multiples. No timer necessary!

One Player Game: Fill the game board with the counters from both boxes. Avoid lining up four numbers with a common factor (other than one).

Two Player Game: Each player has a box of counters to choose from. Take it in turns to drop a counter into the game board. The winner is the first to line up four numbers with a common factor (other than one).

Broken Calculator (author unknown)

Screen Shot 2018-11-09 at 7.12.06 AM.png

There are probably other versions out there but this one is the best I have found, even if is relatively basic. The idea is simple: Can you get the target amount using the keys on the calculator that are working. The levels get increasingly difficult, and it is a great way of building a sense of operations.

Double Take (Transum)

Screen Shot 2018-11-09 at 7.24.51 AM.png

Similar to the popular game on mobile devices, this game builds a sense of base-2 numbers and exponential growth. This one is a favorite with the students. Try to encourage your students to think of and discuss strategies to get further than you would by just trying different ways.

Got it! (nrich)

Screen Shot 2018-11-09 at 7.27.50 AM.png

A simple game with less than simple strategies. Once again, try to steer students to thinking strategically. Is there a better addition to start with? Is it better to go first or second? If you want a more challenging version of this game where you can’t choose the option that your opponent last chose, you could try transum’s 23 or bust.

Square it (nrich)

Screen Shot 2018-11-09 at 7.32.53 AM.png

Not a number game, but a great strategy game nonetheless. Students can play either another person or the computer. They must claim all 4 corners of one square to win. Can blue always win? Is there a way to force this every time? What is happening in the middle of the game? What does the end of the game look like?

I hope you enjoyed reading about these growth mindset math games. What are your favorites? Comment in the section below.

 

Ten Webites I Check Before Starting Every Unit

IMG_1907

There are many excellent resource sites out there with inspirational teachers making great resources. However, when it comes down to it, there are only a handful of websites I check on a very regular basis. To make it to this list, I am generally looking for tasks that:

  • Are ‘low floor/high ceiling‘ giving access and challenging everyone at their own level
  • Have multiple approaches, giving students room for creativity
  • Are challenging and hence interesting
  • Will give me permission to teach skills
  • Make skill practice, more interesting
  • Have a story for students to follow

There are many activities out there that fit these descriptions, but there is only so much time in the week. During breaks I have more time to explore but these are the sites that I can check quickly with high yield for your classroom (in no particular order):

1. Mathematics Assessment Project – A website produced from a partnership with the Shell Centre (University of Nottingham, UK) and the University of California at Berkley. Here you will find tasks that will help the common core standards come alive in your classroom. Full of rich activities that encourage discussion and investigation.

2. Standards Unit – This has been around for a while but is still one of the first publications I look at and is close to my picture of what mathematics education should like. A rich, dense set of activities that will give you great ways to work on various skills and topics.

3. YouCubed – A relatively new site that has come out of Prof. Jo Boaler’s (Stanford) efforts to encourage the ‘growth mindset’ in the classroom. I am interested in anything that comes from the idea that anyone can be good at math.

4. Open Middle – I came across this site relatively recently and am sad that I didn’t find out about it sooner. it’s tag-line is: ‘Challenging Math Problems Worth Solving’ and tips the proverbial hat to the school of thought that says that you don’t need to have tenuous links to real world problems in order to get buy-in from students. It appeals to the problem solver in all of us.

5. Emergent Math – With its routes in Problem Based Learning (PBL), emergent math is useful not only for those who want to tear up the textbook and start again with an integrated curriculum, but also for people who just want great projects that they can slot into their established curriculum. Lots of links to sites not mentioned here so worth a look.

6. Mr. Barton Maths – Lots of great resources and activities that will make your classroom a more interesting place. Enough said.

7. Tarsia – Sometimes students just need to practice. There I just said it. But using Tarsia you can avoid ‘death by worksheet’ and get students to practice without really realizing it. It also great for discussion and you can tell very quickly if students have answered everything correctly or not. For more, see Why I Love Tarsia.

8. NRich – Great site for ‘low floor/high ceiling’ problems that will challenge anyone in your classroom. Students may like to explore this outside the classroom, too. Sortable by topic and I believe they are coming out with a common core curriculum map, quite soon.

9. Dan Meyer 3 Acts Spreadsheet – Act 1 –  You show a video or picture prompting discussion, prediction and estimation as well as the all important step of coming up with the variables that are to be investigated. Act 2 – Students get the information they need to solve the problem. Act 3 – Once students have solved the problem in various ways and presented you show them the solution. There is a lot more to it than this and to pull these lessons off well is a true art form. But the only way to get better at these is to try them. So try them! More info here.

10. Mathalicious – Math lessons based on the real world problems. $185 for 12 months subscription (I think currently they are also doing pay-what you can) but well worth it. Excellent for creating the need for the math you teach.

It takes me around 90 minutes to trawl through these websites at the beginning of a unit but is well worth it when it comes to lesson planning and I know half of the activities I am going to do already. As with any of these activities they will need to be (and should be) adapted for your classes and situation but they provide an excellent starting point from which to plan.

What websites are a must-check when you are planning a unit? Leave a comment, below.

Walk the Line – Adding and Subtracting with Negative Numbers

I wanted an activity that would give students a deep sense of adding and subtraction involving negative numbers. Both. At the same time. I figured the best way would be for them to actually walk through what happens to a number when it goes through these operations; so began ‘walk the line’.

photo 2

The idea is simple, have students walk through various sums increasing from adding two positive numbers, going through to subtracting two negative numbers, reviewing each time.

They will first need to stand in a line, then using sidewalk chalk, draw a zero on the floor and draw out a number line to the right and left of where they are in the positive and negative direction.

Here is the general dialogue that happens:

  • I am going to call out a sum and I would like to see how quickly you can get to the result. You start with the first number I call out and are permitted to move before I have finished calling out the sum.
  • 3 + 2 (call out slowly to give students time to move)
    • Review Questions
      • Now, what did you do when I first said 3? – Run to that number
      • What did you do when I said “add”? – Got ready to run away from zero
      • What did you do when I said 2? – Ran two spaces away from zero
  • Next:  5 – 8
      • Review Questions
        • Now, what did you do when I first said 5? – Ran to 5
        • What did you do when I said “subtract”? – Turned to face the zero (Why? etc)
        • What did you do when I said 8? – Ran 8 spaces and ended up at -3
  • What about  5 – ( -8)    (call out slowly)
    • Review: What was different when I said subtract -8 instead of 8? – Had to go the other way (Why? etc.)
  • At this point I bring student thinking together and explicitly clarify the rules:
    • Whatever number I say first is where you start
    • If I then say “add” you face this way (pointing in the positive direction) and if I say “subtract” you face the other way (pointing in the negative direction)
    • If my second number is positive you walk forward by that amount, if my second number is negative you walk backward by that amount (for example: 4 would be four steps forward, -4 would be 4 steps backward)
    • Let’s try this out
  • 3 – 8 (call out slowly to give students time to think and move)
  • -4 + 10
  • 2 + (-5)
  • -9 + 12
  • 2 – (-5)
  • -4 + (-7)
  • -6 – (-10)
  • etc
  • Then return to classroom and do the same sort of thing but students write (just) their answers on their mini whiteboards. We review each time going through the 3 step process.

This activity really worked and students were doing this all in their head by the end of 50 minutes which is what I was aiming for. There was no separation of addition and subtraction or positive and negative numbers. They were just different points on the number line and different ways to move.

How do you introduce adding/subtracting negative numbers?