I’m always looking for ways to help students make connections between different mathematical concepts. For this activity, I’ve connected number combinations with graphing.

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Start with a Shake and Spill game. I absolutely love Shake and Spill for decomposing numbers. All you need is a mat with a simple graphic in the middle. You can see in the picture above that I used a pencil. I like to put the mat inside the workstation box to contain the “spillage”.

To play, students put the target number of counters into a cup, shake the cup, spill the counters onto the mat, and count the number of counters on the graphic and off the graphic. By repeating those four steps over and over, they see all the different combinations that make up a number. For example, if their target number is 5, they might first roll a 1 on and 4 off, then 3 on and 2 off, or even 5 on and 0 off. One way to use the Shake and Spill activity is to have students record all of their rolls. So in the previous example, the student might record this in their math journal:

1 + 4 = 5 OR 1 and 4 make 5

3 + 2 = 5 OR 3 and 2 make 5

5 + 0 = 5 OR 5 and 0 make 5

The power of this activity is the ability to differentiate by changing the target number. Decomposing activities should be differentiated so that each student is working on his or her “own number.” In other words, it does no good for a student to be working on combinations for 8 if they have not yet mastered combinations for 5. One way to determine a student’s number is through a version of the “hiding assessment.” Show the student a train of 5 cubes. Break off some cubes and put them behind your back, show the student the remaining cubes, and ask how many are behind your back.  

Continue doing this for all combinations of 5. If the student is successful with 5, move to 6. When the student can no longer fluently name all the combinations for a number, that becomes their number to work on.  he hiding assessment is quick and easy to do, and you’ll want to do it for each student every couple of weeks to make sure they are working on the right number. Carry cubes with you, and you can assess kiddos while you’re waiting in line at the restroom or cafeteria! So I think you can see that each student in your class could be working on this same activity, but students would be working on different numbers.

Finally, with this Shake and Spill activity, I’ve included a graphing component. As students Shake and Spill, they color squares on their graphing sheets to show the combinations they rolled. Sheets are included for graphing combinations from 5 to 10. Be sure to plan time to discuss the graphs! After a while, students could even write their own questions from the graphs. Click here to grab this activity.