from a 1st grade teacher:
We are exploring strategies for solving subtraction problems where the starting amount is a teen number. On Friday we reviewed 3 previously learned strategies and another option. I believe some students had some difficulty with the last option. Here are the strategies we've discussed.
We are exploring strategies for solving subtraction problems where the starting amount is a teen number. On Friday we reviewed 3 previously learned strategies and another option. I believe some students had some difficulty with the last option. Here are the strategies we've discussed.
Make a picture.
Draw circles to show the starting amount.
Cross out.
Count what is left.
Draw circles to show the starting amount.
Cross out.
Count what is left.
This is a level 1 strategy in terms of complexity and would have been first used in kindergarten.
For the problem 14-8=?, draw 14 circles, cross out 8, count 6 left.
Count on to subtract.
Count up to the starting amount.
Use dots or your fingers.
Count up to the starting amount.
Use dots or your fingers.
This is a level 2 strategy that is introduced and mastered in first grade. An advantage to this strategy is that it can be done without paper.
For the problem 14-8=?, think 8 + ? = 14
Count on: 9, 10, 11, 12, 13, 14.
Six counts gets you to 14.
Count on: 9, 10, 11, 12, 13, 14.
Six counts gets you to 14.
Think addition and make a ten.
Put up/show the rest.
See the difference.
Use dots or your fingers.
Put up/show the rest.
See the difference.
Use dots or your fingers.
This is a level 3 strategy that is introduced and practiced in first grade. It is practiced and mastered in second grade. (I haven't spoken about the levels with the students or the grade level of mastery.)
For the problem 14-8=?, think about 14 = 10 + 4 and 8 + ?=10.
8 + 2 = 10 and 4 more are needed.
8 + 2 = 10 and 4 more are needed.
So 8+2+4=14 or 8+6=14 and 14-8=6.
This strategy, once grasped, is faster because the counting is eliminated (or minimized if one is still counting to make a 10).
This strategy, once grasped, is faster because the counting is eliminated (or minimized if one is still counting to make a 10).
Subtract across ten.
Take apart the starting amount in two steps.
The first step takes it down to ten.
The second step takes away the rest off of 10.
This level 3 strategy is introduced in first grade, and there is minimal practice. We did it with counters and drawings, but ideally the strategy would be used mentally. This strategy is the most complex because it involves taking apart both the starting amount and the amount being subtracted.
Take apart the starting amount in two steps.
The first step takes it down to ten.
The second step takes away the rest off of 10.
This level 3 strategy is introduced in first grade, and there is minimal practice. We did it with counters and drawings, but ideally the strategy would be used mentally. This strategy is the most complex because it involves taking apart both the starting amount and the amount being subtracted.
For the problem 14-8=?, first do 14-4 =10 (subtract to 10, an easy problem).
Then, think "I took away 4 of the 8, what is left still to take off the 8?" 4 is left.
Do 10-4=6 (subtract from 10, a second easier problem than the original subtraction problem).
Then, think "I took away 4 of the 8, what is left still to take off the 8?" 4 is left.
Do 10-4=6 (subtract from 10, a second easier problem than the original subtraction problem).
I.e.
14-8 = (14-4) - (8-4) = 10 - 4 = 6
All of these strategies are presented as options to students. They can choose to use any of the strategies. They are not tested on the strategies themselves. They are asked to solve problems and show their thinking. The current goal is accuracy and understanding. A larger, longer goal is flexibility and efficiency.
Of course, if someone already knows 14-8=6, then he or she should just write that! Each child can and should use the strategies that make sense to her.
