Objectives/Strategies
My overarching objective for this unit is to thoroughly explore the process of subtraction through the study of word problems. Students will gain an understanding of the decimal number system and base-ten operations which will provide them with the tools to be able to compose and decompose tens in addition and subtraction problems. Thus, they will have an understanding of what is traditionally called borrowing and carrying, rather than just memorizing the procedures. As well, students will understand subtraction as an inverse process of addition. This unit assumes that, by fourth grade, students have a fairly solid background in addition, so although I include some problems in addition in the unit, it is mainly to strengthen the understanding of the relationship between addition and subtraction. I have emphasized subtraction because typically students have a much more difficult time with subtraction problems than with those of addition. By the end of the unit students will be able to identify and solve various subtraction situations, including take-away, difference, and comparison and part-whole relations, especially missing addend problems.
Because of understanding subtraction as a process of decomposing tens, when a digit in the minuend is smaller than the corresponding digit in the subtrahend, by the end of the unit students will be able to add and subtract across zeros with ease. The difficulty of the numbers will increase as students gain facility working with word problems and using base-ten strategies to solve them. Students will also learn techniques for subtracting mentally by breaking numbers into decimal units. Mental math increases brain agility and helps children understand addition and subtraction processes.
Another goal is for students to be able to identify what it is they are solving for in a word problem, particularly part-whole relations problems, and often comparison problems, where they are looking for a missing addend. Students will be able to identify whether they are solving for one of two parts, or for the whole. More about part-part-whole identification strategies follows in the Rationale section.
In addition to thoroughly knowing the process of subtraction and being able to identify various types of subtraction situations, students will gain skills in formulating mathematical conjectures, illustrating word problems, writing about their solution processes and revising their conjectures. They will improve their abilities to work interactively in small groups and will gain an understanding of group process.
I am writing this unit for fourth graders in a Dual Immersion (English/Spanish) class. As a bilingual teacher, I have frequently encountered difficulty in obtaining word problems in Spanish. Another goal therefore is to provide a body of word problems in both languages so that I have a pool of problems from which to draw and so that other bilingual teachers reading and perhaps adapting this unit for their students will also have access to them. You will find these word problems in an appendix at the end of the unit. Because I am a 50/50 Dual Immersion language teacher, which means I teach alternate days in English and in Spanish, the word problems are not translated, but simply switch back and forth from English to Spanish, so that I may choose problems in the language I need for any given day. Bilingual teachers may easily cull problems in either language and adapt the unit presentation to suit their individual teaching needs.
The beginning problems are at a third grade level in order to go back and re-establish a cognitive basis for understanding the subtraction process. A few of the problems attain a fifth grade arithmetic achievement level, and some will have two parts so that students of various achievement levels will be engaged. This strategy allows me to encompass the vast array of ability levels I always have in my class, as well as serves to revisit concepts previously learned and stimulate and motivate students to move forward in their understanding of mathematical concepts. Although the unit is written for a dual immersion Spanish/English class, it could be easily adapted for a monolingual English fourth grade class.
My underlying goal for this unit is to promote students' confidence in their own basic arithmetic understanding thereby instilling a confidence in their continuing mathematical abilities throughout their lives.
Comments: