Have you ever given your students an experience with manipulatives and then found when you shifted over to a textbook that the students didn’t make the connection between the two experiences? As a curriculum developer and researcher, I am constantly looking for more ways for students to make connections from the concrete (manipulatives) to the representational (pictures) to the abstract (numbers). I think word problems can help us do this because they are from the real world, and students can visualize themselves in the given situation.Now, word problems can be challenging for students because they require the students to have an understanding of the context or setting, an ability to read, and an understanding of the math concepts involved. Today I want to share with you something I recently field tested that allows kids to work with word problems and focuses on developing a better understanding of division. The students were doing division, but I have also created the sentence frames for you to do it with multiplication.
1. Start by having students work with manipulatives (concrete) and solve division or multiplication problems. If you want to use the setting of astronauts you can cut them out from the black line master. Solve problems like the following: 2. You can use the table to choose different problems and a class. 3. After students are comfortable with solving problems using the manipulatives, you can give them the task to independently represent the problem with the pictures of the astronauts on a word problem page. Students can do multiple problems,choosing easy or difficult problems to solve from the table. You can also later put the solved problems into a class book about division.When students are doing word problems they are interacting with a variety of the Mathematical Practice Standards: MP.1 Make sense of problems and persevere in solving them.MP.2 Reason abstractly and quantitatively.MP.6 Attend to precision.MP.7 Look for and make use of structure.Building the concept of division through solving word problems is so beneficial because the word problems connect the real world with math, engage the students, and support mathematical communication.How have you helped students connect the real world and the mathematical world?