Thoughts after Two Months of Using Illustrative Mathematics Alongside the Desmos Curriculum

It was time for a change. Our middle school needed a new curriculum that would meet the needs of our students and provide a rich and engaging environment to learn 6-8 Math. After spending months sifting through various curricula, with a little help from edReports, we were able to identify Illustrative Mathematics (IM) as the lead contender. It was not long before we discovered that the Desmos online platform followed the IM scope and sequence very closely and that they had the potential to be an amazing complement to each other. We are now two months into using both platforms and I can honestly say we are not looking back. So, I wanted to write a brief summary of what we are seeing after the first two months of using these curricula.

1) They are amazing together

The two platforms complement each other well, not only in sequence, but in the way that Desmos is designed with IM and OpenUp in mind. You can find complementary lessons for each topic and you can decide which lesson makes the most sense for your students and your own sequence. The material is engaging and the learning is rich.

2) There is a lot of material

Sometimes too much. In the case of IM, there is a lot to cover in a 50-minute lesson, and I often have to cut some of the material to ensure I spend enough time on the main ideas. I know they have to cover enough to meet state standards, but I regularly find that I need to skip certain lessons just to get through a unit in time to move on. Desmos is often closer to being able to get through all the activities in a useful and timely way.

3) They are truly discussion based, in the best way

In the last two months, I have had some of the best conversations I have ever had in my classroom. Students have been engaged and interested as IM and Desmos use prompts such as “which one doesn’t belong”, “what went wrong”, or “which student is correct?”. These are rich conversations that spark curiosity and help my students consider the mathematics from various angles. It is a more creative and interesting way to think about mathematical ideas and it has been amazing to see students engaging with ideas they have never considered. IM pledges that “selected activities are structured using Five Practices for Orchestrating Productive Mathematical Discussions (Smith & Stein, 2011)” and I believe it. Their prompts are excellent and I am already seeing deeper understanding as a result. As a side note, my students are huge fans of Desmos’s polygraph activity (the mathematical version of ‘Guess Who’) and this has seen some amazing results. They also enjoy the opportunity to create a challenge for a classmate (as long as they can solve their own problem first) and this has them engaged for significant periods of time.

4) The formative assessment you get through Desmos is unbeatable

I generally aim to know what every student is thinking at least 2-3 times during a lesson and Desmos makes this very easy to do. With its custom dashboard, it gives you the power to view all student activity and provide individual feedback to students. You can display student work on the screen and anonymize the screens to avoid embarrassment. You can compare answers with their screenshot function and instantly glance over the whole class’s level of understanding.

The Desmos dashboard makes it very easy to glance at students’ progress

5) IM is free and Desmos is very affordable!

At this point, I don’t understand why every school in the country is not jumping at the chance to use IM. It’s free and completely customizable. I have known some curricula to be prohibitively expensive and the idea that IM is completely free and a rich mathematics curriculum makes it a no-brainer to me (although you do have to pay the publishers if you want the extra workbooks etc). Desmos is also affordable compared to many textbooks and I would highly recommend this if your district has the resources.

In conclusion, barring an altogether different experience in future units, I would wholeheartedly recommend the IM/Desmos combination. With the richness of IM, coupled with the complementary manipulatives and discussions coming from Desmos, I have every hope that our students are going to fly. But, granted this is only two months in, and I could be completely wrong. I somehow doubt it.

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)

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)

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)

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)

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)

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)

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.

 

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’.

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?