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How Many Children Got off the Bus?

Assessing Students’ Knowledge of Subtraction

Introduction

This video shows Ana Vaisenstein working with a small group of fourth graders
on a subtraction word problem. Ana worked with this group of students, who were
struggling with math, throughout the year and knew that subtraction was espe-
cially difficult for them. In previous years, they had been taught to subtract using
the standard algorithm. They had neither mastered this procedure nor understood
what subtraction means. Ana’s goals were to help them:

• recognize and solve a subtraction situation (removal, comparison, differ-
  ence between numbers, distance between numbers)


• find an entry point (a model or representation or drawing that was useful
  for them to solve subtraction)


• build fluency with counting and number relationships (e.g., counting
  forward and backward by 10, knowing that subtraction is the inverse of
  addition—if 5 – 2 3, then 3  2 5)


• develop a stronger number sense (be able to break up numbers into parts
  that are easier to work with; e.g., 62 can become 50 12)

In the video, the students share their strategies for solving the following word
problem that Ana wrote: There were 62 children on the school bus this morning.
48 children got off at the Sumner School. How many children continued the trip
on the bus? She chose this problem because most of the children take the bus so
it was a familiar context.
This problem is one that should be easy for most fourth graders to solve. But
Ana knew that these students had not yet developed strategies for solving sub-
traction problems that they could use consistently and with understanding, so she
chose to have them work on developing strong, efficient strategies for solving sub-
traction problems with smaller numbers before moving on to apply these strate-
gies to problems with larger numbers. She also chose this problem because she felt
they were still most comfortable with two-digit numbers, but she wanted them to