A Math Story
I was recently asked to tutor an eight-year-old girl in math. Her problem was subtraction, especially when the number on the top was smaller than the one on the bottom and she had to borrow. Numbers with many zeroes sent her into a panic and she shut down completely, refusing to do any work.
When I teach, I automatically go into storyteller mode and it only made sense to find a way to help this girl subtract by using a story to help her remember the steps.
Step One: The first thing I needed to do was help her line up her columns, so we built houses.
I was recently asked to tutor an eight-year-old girl in math. Her problem was subtraction, especially when the number on the top was smaller than the one on the bottom and she had to borrow. Numbers with many zeroes sent her into a panic and she shut down completely, refusing to do any work.
When I teach, I automatically go into storyteller mode and it only made sense to find a way to help this girl subtract by using a story to help her remember the steps.
Step One: The first thing I needed to do was help her line up her columns, so we built houses.
Each column of numbers, ones, tens, hundreds, thousands, ten thousands and so on, became a house. Each house had a second floor and a bottom floor, represented by the numbers we were using. Each house also had an attic where our borrowed numbers went and a basement where our answers went. Depending on the place values the story might sound like this.
Step Two: “There were four houses. Mr. Two lived in the first house. Can we subtract 5 from 2? No. So, Mr. Two had to go next door to Miss Six's house and he said “Gimme ten!”
In this case Miss Six is large enough to give a ten to Mr. Two so she does. “And Miss Six got smaller. Mr. Two got larger.”
I taught my student to cross out the six and make it a five then place a one next to the 2 in the first house. While it would be better if she really understood the concept of ones, tens, hundreds place and so on, and that the one next to the two was really ten borrowed from the tens’ place, that was not my job at that time.
The student crossed out Miss Six and wrote a 5 in the attic.
Step Three: “Now do the subtraction. What number goes in the basement?” Write your answer in 5's basement (in the first house).
Step Two: “There were four houses. Mr. Two lived in the first house. Can we subtract 5 from 2? No. So, Mr. Two had to go next door to Miss Six's house and he said “Gimme ten!”
In this case Miss Six is large enough to give a ten to Mr. Two so she does. “And Miss Six got smaller. Mr. Two got larger.”
I taught my student to cross out the six and make it a five then place a one next to the 2 in the first house. While it would be better if she really understood the concept of ones, tens, hundreds place and so on, and that the one next to the two was really ten borrowed from the tens’ place, that was not my job at that time.
The student crossed out Miss Six and wrote a 5 in the attic.
Step Three: “Now do the subtraction. What number goes in the basement?” Write your answer in 5's basement (in the first house).
Step Four: “Now let's look at the second house. Can we subtract 6 from 5? No. So, Miss Five has to borrow from Mrs. Two in the third house. What does she say?” The student answered “Gimme ten!”
We worked on this for several sessions until she would sit down at the problem and start drawing houses and telling the story without my prompting and with very little reminder of the story. Each session that she became more confident made it easier to introduce more difficult problems until we finally did an all zeroes problem. When I felt it was needed, I introduced a game. I made my student the math detective and told her we now needed to make sure we checked the basement work by adding our numbers from the basement and the first floor to get the answers in the second floor or attic.
I created a game board about getting the bad guy to jail. Each time she remembered to build the houses without prompting, her playing piece (in this case a star) made it one block toward the jail. If she remembered to borrow and cross out the old number, her piece got closer still. Once her bad guy got to jail, we extended the game to court and then to a cell. When her bad guy got to the cell, she made Math Captain! Eventually she made Math Chief, but this only happened when she remembered to investigate the scene of the crime, in other words check her work by adding.
By the time my student was learning to check her work she had already internalized the story so that she did the work in her head and before too long, she stopped building the houses but just did the problem the way everyone else does. It was so exciting to see this process and watch her level of confidence grow. Getting my student to remember to check her work is something we just need to keep doing, especially when she discovers that her answer is wrong. She shuts down again. Practice will help this. When she does remember and her answer is right, it is so wonderful to see her face light up. I made a little sign to put in front of her SaC, Subtract and Check. Eventually checking should become part of her routine in all her work. We have now moved on to telling time.
We worked on this for several sessions until she would sit down at the problem and start drawing houses and telling the story without my prompting and with very little reminder of the story. Each session that she became more confident made it easier to introduce more difficult problems until we finally did an all zeroes problem. When I felt it was needed, I introduced a game. I made my student the math detective and told her we now needed to make sure we checked the basement work by adding our numbers from the basement and the first floor to get the answers in the second floor or attic.
I created a game board about getting the bad guy to jail. Each time she remembered to build the houses without prompting, her playing piece (in this case a star) made it one block toward the jail. If she remembered to borrow and cross out the old number, her piece got closer still. Once her bad guy got to jail, we extended the game to court and then to a cell. When her bad guy got to the cell, she made Math Captain! Eventually she made Math Chief, but this only happened when she remembered to investigate the scene of the crime, in other words check her work by adding.
By the time my student was learning to check her work she had already internalized the story so that she did the work in her head and before too long, she stopped building the houses but just did the problem the way everyone else does. It was so exciting to see this process and watch her level of confidence grow. Getting my student to remember to check her work is something we just need to keep doing, especially when she discovers that her answer is wrong. She shuts down again. Practice will help this. When she does remember and her answer is right, it is so wonderful to see her face light up. I made a little sign to put in front of her SaC, Subtract and Check. Eventually checking should become part of her routine in all her work. We have now moved on to telling time.
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