This is the third lesson in a series of problem solving lessons. Click here for the first lesson. Click here for the second of three lessons. Students will use division skills to solve problem and make sense of remainders. For this lesson, students participate in a Gallery Walk activity.
I pair students and have them solve number 11 and 12 from the division problem solving sheet. As students work to solve these problems, I visit with pairs and ask questions or watch silently.Once students have solved the problems, they create 8.5 inch x 11 inch posters using crayons, markers, or colored pencils. Their poster shows their answer to the question and how they solved the problem. Then students hang up their poster for the Gallery Walk.
(I do not give my students very much time to solve and create their posters - about 20 minutes. Students understand that they need to work quickly and wisely in order to get their poster up for the Gallery Walk. If I had pairs of students finish very quickly with lots of time left over, I allow them to decorate their posters more. Occasionally I ask the partners to see if they can come up with another strategy to solve the problem to prove that their answers are correct.
Below is information about a Gallery Walk:
Gallery Walk is an interactive discussion technique that gets students out of their chairs and into a mode of focused and active engagement with other students’ mathematical ideas (Fosnot & Dolk, 2002). The purpose of the Gallery Walk is to have students and the teacher mathematically engage with a range of solutions through analysis and response. It is often carried out after students have generated solutions to a mathematics lesson problem. Solutions could be recorded on computers, pieces of paper on tables or posted chart paper. A Gallery Walk is often scheduled for about 10 to 20 minutes depending on the instructional purpose and depth of mathematical analysis expected. For students, Gallery Walk is a chance to read different solutions and provide oral and written feedback to improve the clarity and precision of a solution. On the other hand, for teachers, it is a chance to determine the range of mathematics evident in the different solutions and to hear students’ responses to their classmate’s mathematical thinking. Such assessment for learning data help the teacher to determine points of emphasis, elaboration and clarification for the ensuing whole class discussion (Fosnot & Dolk, 2002). Although there are different variations of a Gallery Walk, a common approach is outlined below:
(a) Small-group problem solving – Students, in small groups, develop one solution to the lesson problem on chart paper.
(b) Small-group discussion – Small groups take turns reading and analyzing one another’s solutions and recording comments, questions and/or suggestions for improvement, using stick-on notes (for later sorting) or writing directly on the chart paper. After three to five minutes, the groups rotate to the next solution. Rotation continues until all solutions are analyzed and responded to by all groups. As comments accumulate for each solution, the groups also review what previous groups have written and add only new comments, questions and/or suggestions for improvement.
(c) Teacher observation – As students are discussing their classmates’ solutions, the teacher circulates around the classroom, gauging student understanding and noting students’ use of mathematics vocabulary and symbolic notation as well as their mis-matched conceptions.
I run my Gallery Walk slightly different than the methods described above. Each partner hangs up their posters. Students tape Problem 11 on one wall, and problem 12 on another wall. At my signal, (all posters are hanging up) students walk slowly between the walls and look for similarities and differences among the posters. I ask students to look for posters that have the same answer that they came up with and to really analyze posters that have different answers than their own. When students come to a poster they think displays an incorrect answer, I ask them to figure out why the group came up with a different answer, and then to think about suggestions, comments, or questions they would tell that group.
Once students have had about 5 minutes to look at the posters, students form a standing circle in order to talk to the whole group about what they notice and what questions they have. This allows for great math talk and conversation. My students noticed that almost every poster had the same answer on it, except for 1. This was really important for me to hear their thoughts because the one poster that had a different answer was the only poster that displayed the CORRECT answer. The partners that made the correct poster were able to discuss and present their ideas to the entire group, which then helped many students to realize their mistakes. This is a great activity that incorporates Math Practice Standard 3. Students begin to develop skills to critique the reasoning of others and construct viable arguments about their strategies, methods, and answers.
This is one poster sample with an incorrect answer. Click here to hear my thoughts about this group's work.
This is a poster sample that shows the correct answer. click here to hear my thoughts about these student's work.
This is a poster for number 12 from the division sheet. This shows a correct answer. Click here to hear my thoughts about this pair's work.
This is also a sample poster for number 12 that shows an incorrect response. Click here to hear my thoughts about this groups work.