Decomposing Number Challenges

The mental arithmetic game ‘Make 20’ begins with students sitting in a circle. The teacher picks a student to call out a random number between 0 and 20. Students 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 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.

Inspired by Make 20, I developed a similar game for the NSF-funded Dynamic Number project.

On page 1 of the game below (and here), 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 presents the same game, but now with target sums of 30. On page 3, students get to set their own target sums. When students play the game in pairs and create challenges for each other, you can bet that the target sums go way up!

An annotated list of all our elementary-themed blog posts is here.