Developing Arithmetic Fluency Through “Drill and Thrill”

In a previous post, I described the game Chisla, an app that succeeds in making basic arithmetic both challenging and tense.  Given a numerical target, you have just 15 seconds to pick numbers from a list of possible addends that will sum to that value. A target of 10 is no big deal, but when the target escalates to 40 and beyond, you’ll find yourself breaking a sweat.

Playing Chisla reminded me of the mental arithmetic game ‘Make 20’ from the elementary curriculum ThinkMath. With everyone sitting in a circle, the teacher picks a student to call out a random number between 0 and 20. Students immediately raise their hands, and whoever is chosen by the teacher must say what number, when added to the first, makes 20. The game continues in this manner, with students picking random numbers between 0 and 20 and determining the missing addend to make 20. It’s impressive to watch a group of second graders play the game. You might expect there to be lots of pauses as students ponder their answers, but instead, you hear a steady stream of call and response: 3, 17; 5, 15; 6, 14; 10, 10; 1, 19 and so on. When students master sums of 20, the game progresses to sums of 30.

Both Chisla and Make 20 share a sense of age-appropriate urgency that ThinkMath‘s authors call “drill and thrill.” We all know what straight drill looks like, but the added piece of thrill comes from including elements that keeps the practice lively and engaging, and the students mentally alert. It’s tempting to say that speed is the thrill component of both Chisla and Make 20, but I think this undersells both games. Chisla takes traditional addition problems and flips them by providing the sum and requiring you to find the addends. Make 20 has a similar hook, but adds a social element by playing the game as a whole class and developing a steady rhythm to the responses.

Inspired by the “thrill” of ThinkMath, I developed a mental arithmetic game for the Dynamic Number project that pays hommage to Make 20.

On page 1 of the game below, students drag two numbers into each of the 10 circles so that the sum of the numbers in each circle is 20. Pressing Check Answer scores 10 points for each correct sum and 0 points for each incorrect one. Pressing New Puzzle generates a new randomly generated problem. Page 2 is the same, but now there is a time limit. To start the clock ticking, press New Puzzle. The default time limit is set at 60, but students can change this value in the lower-right corner of the sketch.

Pages 3 and 4 present untimed and timed games with sums of 30. On page 5 and 6, students get to set their own target sums and again decide whether to play untimed or timed games. When students play these games in pairs and create challenges for each other, you can bet that the target sum goes up and the time limit goes down!

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