# Are Your Mathematics Games C, P, or A?

### Serious Play #4

Imagine this…you walk into a noisy, bustling classroom where students are spread out in small groups at tables, on the floor, at the counter. They’re everywhere, really. They’re huddled around game boards and decks of cards, playing mathematics games that engage them in mathematical thinking, discourse, and strategy.

As you reflect on what you’ve witnessed, what did you notice? What math concepts were being reinforced? Were all the students playing the same games, or was there a variety? Did you see evidence of different levels of thinking?

After several years of using mathematics games in my own classroom, I noticed that that most of my games centered on arithmetic and math-fact practice, almost always at the abstract level (e.g., using the symbols of mathematics). It was at this time that I started looking for games that included representations other than numerals. Could I find games that incorporated concrete manipulatives? Were there games out there that incorporated pictures, diagrams, or other graphic representations? It turns out that there are plenty of options if you know what you’re looking for! These days, when selecting great mathematics games, I look for a balance in concepts, DOK (Depth of Knowledge), thinking strategies, and representations.

For today’s post, let’s look at representations that promote thinking at different levels. Below you will find three games, each addressing one of the C-P-A levels: concrete – pictorial – abstract. Notice that they all exhibit the characteristics described in last week’s blog post that make mathematics games fun.

### 1) Mathematics Games That Use Concrete Representations

Since students often manipulate objects when exploring a concept, games in this category typically include a game tboard or concrete materials.  Race to 100 provides a concrete way for students to focus on grouping (and ungrouping) tens as they build numbers to 100.

When playing this game, students work as partners rather than as competitors. As they repeatedly group ten ones into one ten, the “concreteness” of the game promotes visualization of place value.

### 2) Mathematics Games That Use Pictorial Representations

Ruler Races involves the use of a 12-inch ruler marked in fractional parts of inches. Students are encouraged to think of the ruler as a number line marked in fractional parts. They physically identify different points on the fractional number line as they explore flexible ways to think of fractions and fraction addition.

Although one may think of a ruler as a concrete object, it is not mathematically concrete. It really is a pictorial representation of the 1-inch units (or 1-cm, or whatever unit is being used) used to measure objects. Some teachers even use rulers as number lines, which is the case in this game.

### 3) Mathematics Games that Use Abstract Symbols

Salute has been a favorite in my classroom for years! Students practice inverse operations (addition/subtraction OR multiplication/division) during game play. Students alternate between finding sums/differences and related missing addends/factors.

This game uses the numbers (abstract representations) on the playing cards to generate new problems for each round, and the students use mental math strategies to determine the missing values.

So…think about the games you use in your classroom. Do they offer students the opportunity to engage in mathematics beyond math-fact practice? Do your mathematics games include various levels of representations? How might you incorporate more concrete and pictorial games into your repertoire? Please share your thoughts in the comments box, below.

Next Steps for Teachers: Set up the games in this blog post (and others) and provide them for students to play. Also, take inventory of the games you already have in your classroom – do they provide concrete and pictorial opportunities as well as abstract practice?

Next Steps for Leaders: Lead your teachers in a conversation about this post. Have them list the mathematics games available in their classrooms and categorize them by C-P-A. Then walk through the classrooms to see how students are responding to the math games that use different levels of representation.