Grade One - Sample Two

Five of the units in Bridges in Mathematics, Grade One feature problem solving with picture problems. These problem solving activities are thematic, and are based on the big mathematical ideas of each unit. Unit one problems revolve around bugs, unit two uses sea stars and crabs, unit three utilizes lobster legs, unit four focuses on penguins, and unit six on farm animals. In each unit, children solve five to seven premade picture problems posed by the teacher. After the sample problems are posed and solved, students create their own picture problems for the class to solve. The following four problems were constructed by a child of mid-range math ability.


Bug Picture Problem


Student-posed Bug Picture Problem

In the first problem she created, she starts off with a simple addition problem similar to the example problem presented to the class earlier, but she makes it with a larger number of bugs.


Sea Star Picture Problem


Student-posed Sea Star Picture Problem

The sea star problem she created is patterned after the easiest example problem, ignoring the thrust of the rest of the example problems where the number of arms and legs were the focus.

During the lobster unit in the middle of January, she produced a problem much like one of the example problems, now focusing on how many lobsters have what number of legs.


Lobster Picture Problem


Student-posed Lobster Picture Problem

Her Penguin problem from early March may look simple, but this type of problem can throw off many children who get confused about the concept of nests and babies, often ending up adding the two numbers together to provide a solution. She understood this perfectly.


Penguin Picture Problem


Student-posed Penguin Picture Problem

This child’s picture problems show the progression of increasing skills in creating and solving problems. The student’s ladybug picture demonstrates her understanding of addition. The familiarity and confidence with addition extends to the sea stars, although she did not demonstrate the concept transition to repeated addition or multiplication until January with the lobsters. By March she clearly demonstrates her understanding of multiples. In the follow-up whole group sessions she was able to solve most of the problems constructed by her classmates, and could show several ways of arriving at a solution. Her methods included pictures, counting patterns, tallying, and equations. By year’s end she was very capable of problem solving, having moved from solving simple problems to more complex ones for this age group.