Make 9

Task

Make 9 in as many ways as you can by adding two numbers between 0 and 9.

IM Commentary

Because of the limited reading skills of kindergarten students, this task should be introduced by the teacher, followed by the students carrying out the activity. Teachers should have counters on hand for students to use.

There are two other tasks that are very similar to this but which have contexts. As with several other tasks in the set, any number between 2 and 10 can be used in place of 9 to address K.OA.3.

Although not necessary to meet this standard, listing the possible pairs of numbers in a systematic way might help the student show that s/he has found all of the possible number pairs that make 9.

The Standards for Mathematical Practice focus on the nature of the learning experiences by attending to the thinking processes and habits of mind that students need to develop in order to attain a deep and flexible understanding of mathematics. Certain tasks lend themselves to the demonstration of specific practices by students. The practices that are observable during exploration of a task depend on how instruction unfolds in the classroom. While it is possible that tasks may be connected to several practices, only one practice connection will be discussed in depth. Possible secondary practice connections may be discussed but not in the same degree of detail.

This particular task helps illustrate Mathematical Practice Standard 7, Look for and make use of structure. Kindergartners are introduced to an exploration that builds the underpinnings of understanding the commutative property. MP. 7 emphasizes the importance of students recognizing relationships and making connections between different ideas. In this case, students observe that when they tried to find all the sums of 9 they could add the same 2 addends but in a different order.  This eventually leads to recognizing that the structure of the commutative property basically cuts their learning of addition facts in half.

Solution

Students may use objects or drawings to find the decompositions and then should record each decomposition by drawing pictures or writing equations. Students should include two or more of the following possible decompositions. Note that the “9” may appear on either side of the equal sign.

Possible equations:
0+9 = 9; 1+8 = 9; 2+7 = 9; 3+6 = 9; 4+5 = 9;
5+4 = 9; 6+3 = 9; 7+2 = 9; 8+1 = 9; 9+0 = 9