Methods/Materials
This lesson has four sections: initial presentation and story, class discussion, interactive computer activity and wrap-up discussion.Initial Concept Presentation and Story
Classroom activity
Before beginning the story, the teacher should ask students what, if anything, they know about division. The discussion will allow the teacher to ascertain any pre-existing knowledge or misconceptions that students have about division. This brief discussion should focus on what students know in a conceptual sense (not unique facts) and real world applications that they are aware of. The teacher will then read the students the Division Farm story.
UDL
The goal of the preliminary discussion and story is to get students thinking about division from a conceptual standpoint before they are presented with any numbers or symbols. The prototype story (available here) is presented in digital format, however the story is intended to be read to the students. If the digital book is made available to students, there would need to be reading supports embedded in the story, such as read-aloud, sound-it out, search functions and embedded comprehension supports. The focus of this project is not on universally designed texts, however, it is essential that this text be universally designed to support a wide range of learners, to ensure that all the students are able to access the content, as it sets the stage for the rest of the lesson.
Class Discussion
Classroom activity
After finishing the book, the teacher will present the same "sharing equally" concept that is presented in the story by acting out the sorting that's described in the story. With six apples or blocks and two baskets or buckets, the teacher should demonstrate sorting the apples into the baskets with a structured sorting technique. The teacher should place one apple in each basket, alternating between baskets, until there are no apples left. The teacher should then demonstrate counting the contents of one basket to determine the answer of the division problem. Once the teacher has demonstrated one problem, they can present the division sign, as well as the terms "divisor", "dividend" and "quotient" in terms of how a division problem is laid out graphically and numerically. The teacher should associate each of these terms with the different pieces of the problem, the dividend with the apples, the divisor with the baskets and the quotient with the number of apples that ended up in each basket. The teacher should demonstrate a few more problems using either the same or a similar format, with input from the class.
UDL
The goal in this section is to take each of the pieces of a division problem, which may be confusing, and associate them with real world models. Students with dyscalculia often have little or no strategies associated with solving mathematics problems, and often resort to memorizing large numbers of math facts in order to function in mathematical environments. While working with the numbers may still be a challenge for these students, providing alternate, concrete models with which to think about the mathematical operations may help students become comfortable with the concepts.
Interactive Computer Activity
Classroom activity
After the discussion period, students will work individually at computer workstations on an interactive activity that will reinforce concepts presented through the story and during the discussion. Students will be able to work at their own pace through multiple problems that will use the same conceptual model as the all of the previous instruction.
UDL
For a complete prototype of the computer activity, click here. While students could engage in a hands-on activity with physical objects much like their teacher was showing them, moving the activity to a digital environment makes it possible to scaffold the activity in ways that are not feasible otherwise. The digital activity will provide numerous scaffolds and support systems for students, such as setup, counting and sorting supports, and allow students to choose how much of each kind of support they want. Placing the activity in a digital environment also makes it possible to incorporate strategic supports, and reinforce different strategies that students can use while they are solving a division problem.
Wrap-up discussion
Classroom activity
After the students have completed the interactive activity, the teacher will lead another classroom discussion. This discussion will serve as the final assessment for the activity, for a complete discussion of the ongoing assessment throughout the activity please click here. During the wrap-up discussion, the teacher should focus on ways students can transfer the concepts presented over the course of the lesson in the context of apples and baskets to other real world scenarios. The teacher should prompt students to come up with additional situations where the concepts would apply (sharing cookies with a few friends, sharing pens with classmates, dividing blocks into bins, etc).
UDL
The wrap-up discussion should reinforce the "sharing equally" concept that was presented and give the teacher the opportunity to assess the students’ comfort level with division at a conceptual level. By maintaining an emphasis on the concept, this discussion will help students transfer the concept that they have been working on to other similar scenarios, and help students build a broader conceptual model of division in relation to the real world.