Part V: Teaching Division with the Picture Grid Manipulatives
To understand division, is simply to understand the wording. Division means “sets”.
If we look at whole numbers and we ask, “What is 10 divided by 5?” We are simply asking how many sets of 5 can be found in 10? We know that the answer is 2. If we place this in a reality-based scenario, we have 10 pieces of candy and want to divide it among 5 students. The answer is 2 pieces of candy per student.
Now, Harry wants to apply this knowledge with his students. He uses the idea of a square pizza pie. At the pizzeria, they sell long quarter slices to the public. A half of a pie is left over and he asks the students, “How many sets of quarter pie pieces can be found in a half of a pie?”
First the students have to determine which grid represents a half, and that is easy. Next they pull out the clear quarter grid. One group slides it over the half and then count the pieces:
1/2 ÷ 1/4 = 2 sets
The students determine that there are two sets or two quarter pieces. Easy!
Students continued to play with the picture grids:
1/4 ÷ 1/10 = 3 sets
A student asked, “What happens when the answer does not come out evenly?” Great question. The students examined the problem: 1/2 divided by 1/5th.
1/2 ÷ 1/5 = 2 and a half sets
At this point, students are encouraged to create their own scenarios with the grids to practice. With repetition, they get the hang of it. Then, Henry asks them to write one of their scenarios along with the diagrams in their Pic-Jour Math journal. Not until Henry is convinced that the pictures/diagrams are strongly linked to the numbers, does Henry move them away from the manipulatives and just use numbers in his teaching practices.
There are more sophisticated ways of teaching division using the Picture Grids. Can you discover them? (To reply, please click on the comment link next to the title or scroll down.)
Andi Stix is an educational consultant & coach who specializes in differentiation, interactive learning, writing across the curriculum, classroom coaching and gifted education. For further information on her specialties or social media, please email her on the Contact page.
Schubert, B. (1987). Mathematics journals: Fourth grade. In Toby Fulwiler (Ed.), The Journal Book. (348-358). Portsmouth, NH Boynton/Cook Publishers.
Stix, Andi N. (1992) .The Development and field Testing of a Multi-Modal Method for Teaching Mathematical Concepts to Preservice Teachers by Utilizing Pictorial Journal Writing. Ph.D. diss. Columbia University Teachers College. Ann Arbor, MI: U.M.I. Dissertation Information Service, Pub. #92-18719.
Stix, Andi N. (1994). Pictorial journal writing in mathematics. Arithmetic Teacher, 42:1, 264-269.
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