Counting On & Back

Students should have many experiences with counting on and counting back to solve addition and subtraction problems. Students who learn to use "Touch Spots" on the numbers for counting on and back will have a dependable strategy to use if they become "stuck" while trying to solve a problem. Each number has spots to represent the value of the number. For the numbers 1 to 5, students touch each of the Touch Spots as he/she counts on or back to add or subtract. For the number 6, each spot is touched twice. In the enlarged version of 6 through 8, you can see that each red touch spot that needs to be touched twice is inside a black circle. The double circles represent the touching of each of the spots twice. For the number 7, one spot is touched once, and the three spots going down are touched twice. Each spot is touched twice for 8 and three times for 9.

Warning: Children should not become dependent on using Touch Spots as a means to compute facts. Touch Spots should be used as a strategy when a the child is "stuck." Tell your students that their goal is to learn the facts automatically and that the Touch Spots should be used only when necessary.  Children who become dependent on Touch Spots do not commit the facts to memory.

Make sure to teach the children to always start with the larger number when adding. If a child encounters the problem, 3+7, s/he should start with 7 and count on 3. The child says' "7.....8,9,10," as s/he touches the spots on the 3.

Touch Spots 6 through 9 are rarely used for addition because they are usually the larger number and other fact strategies are more efficient. For example, students should learn the doubles easily, ( 5+5, 6+6, 7+7, 8+8, 9+9) If the children know the doubles, you can teach them how to use what they know about doubles to learn the doubles plus 1 facts. (5+6, 6+7, 7+8, 9+9) If a child encounters the problem, 7+8, s/he might say, "7+7 is 14 so 7+8 must be 15 because this is a double + 1 more problem."

Download enlarged Touch Spots in PDF format to display on your bulletin board for student reference.

Worksheets for Counting on 1, 2, 3, and 4 in PDF file