This is a great activity for younger students just learning about multiplication.

Distribute a set of bones to each student. Teachers may also allow students to share a set at a table or in a small group and/or project a set of bones to the class.

Explain to students they will be going on a scavenger hunt. Teachers will provide two values. Students should try to find both values on one rod.

Tell students you are thinking of a rod that contains the numbers 4 and 8; can they find it? Allow students time to examine the bones in their set to find one that contains both numbers. Allow students to share what they found. Some students may have collected the 2 bone, others may have collected the 4 bone, other possible bones are 1,3, 6, 7, 8, or 9. Allow students with unique bones to share.

Ask students what bones do not contain the digits 4 and 8 (only 5) and prompt them to consider why this is. (All the multiples of 5 end in a 0 or 5, so there are no other ones place values. As the rods only go up to 9, and 9×5=45, there is a 4 but there is not enough values to also have an 8 in the tens place.) Encourage students to determine how big their rod must be so that the 5 would have both a 4 and an 8. (The first 8 in the tens place would be 80. Look for different ways to determine what multiple of 5 this must be. For instance, a student may notice 80=8×10=8×2×5, and thus 16×5 must equal 80. A 5-rod would need to go up to 16 to include both a 4 and an 8.)

Circle back to your rod. Announce the rod you are thinking of contains the number 4 (displayed on a rod as 04) and the number 8 (08) (rather than simply the digits 4 and 8), can students find your rod? Students should now be able to throw out all rods except 1, 2, and 4. Model a systemic logical approach by asking students to explain, in order, the rods we know it cannot be. For instance, we can throw out all rods above 5, as 5×1 is more than 4 (as is 6×1, 7×1, etc.) so none of these rods could possibly contain the value 4. We are left with 1, 2, 3, and 4. We can also throw out 3 because we know skip counting by 3's skips over 4. Checking the final rods 1, 2, and 4 we see that each contain the values 4 and 8.

In Possible or Impossible, students will build on this exploration to determine the combinations that can or cannot be found. These activities are helping students build number sense while also developing more familiarity with the multiplication table/rods.