Adding 10 to any number
Given any number from 0 through 90, a child responds by saying the number 10 greater than that.
- Teacher: 43
- Student: 53
- Teacher: 7
- Student: 17
Children may need to count up ten from a number like 23, at first, to find out that ten more is 33, and count again to find out that 10 more is 43, and perhaps even once more to find 53, but children even in second grade typically then "lock in" to the pattern and happily chime in with 63, 73, and so on.
After 20, the English number names are designed to make it easy to add and subtract 10. (Some languages, like Hungarian, Thai, Japanese, Arabic, and Hebrew work that way from the start. Others, like English and Spanish, are irregular before 20.) The "last names" of the larger numbers like twenty-three, thirty-three, forty-three, and so on, are all the same, and the "first names" are the easy-to-learn counting by tens pattern. For this reason, children often find it easier to add 10 to larger numbers at first.
One lively method
- Invite a child to stand in front of the class and hold up some number of fingers (other than 10 or 0) that you might pick or you might ask the child to pick.
- Have the class chorus out how many fingers.
- Call up another child and ask that child to hold up all 10 fingers. You might put your hands on the two children's shoulders to indicate that both are to be counted and, again, have the class chime in with how many fingers they see.
- Repeat: Call up another child to hold up 10 more fingers. Indicate that you're including all three. How many fingers now?
- Repeat, adding another child (another 10 fingers) until you have all the children up.
- This works best if you keep the children moving up to the front quickly and do minimal talking that interrupts the sound pattern of 47, 57, 67, and so on. Beckoning children up without words also gets them to watch and listen more attentively; and beckon with an appeal to scurry up quickly so that the lesson literally keeps moving.
- One reason why this is best is that it keeps the lesson lively and fun, but another reason is because the children hear the pattern better when the numbers come quickly one after the other and there is no (or minimal) other talk interrupting that pattern.
Sometimes children "anticipate" the next number, and chorus out 73 when a child is first beckoned, so that they get mixed up and say 83 when the same child arrives. You can then zip back to the first child, say "start over," raise that child's hand and ask "how many?" (7) and then embrace the second child with the first (17), and the third child (27), and so on. For even better practice: when you zip back to the first child, ask that child to change his or her number! That way, the class that has just practiced 7, 17, 27, 37, ..., will now be practicing 3, 13, 23, 33, 43, ..., and might later "replay" and practice 6, 16, 26, 36, ..., all the way up to 206 or so.
The ability to add or subtract 10, starting at any number, is the foundation for many other mental arithmetic skills.
- If you can add 10 to any number, you can add 9 or 11 to any number mentally, by adding 10 and then adjusting. Most children also find this helps them add 8 or 12 to any number mentally. If you like to give names to strategies, you might call this "add ten and adjust."
- Children who have become comfortable adding 9 or 8 (or 11 or 12) using this strategy can then learn to subtract 9 or 8 the same way. Children enjoy "chains" of "add 8, now 8 more, now 8 more, 8 more..." just the way they added 10 many times over. Each time they think "10 more, oh, and then 2 less than that."
- This skill also helps children "sort out" place value by making a "counting-like" change in the tens' column rather than the ones' column (for example, ... 82, 92, 102, 112, 122, 132 ...).
- Comfort with knowing the effect of adding 10 makes it easy for children then to perform double-digit addition mentally, as long as there is no carry and as long as one of the numbers is a multiple of 10. So, children who become good at adding 10 to anything can generally quickly pick up skill at problems like 45 + 30, or 14 + 20.