Take Away

The following lesson introduces elementary students to subtraction. The objective is to create a link between students' experiences and mathematics. By the end of the lesson it is expected that students have a deep understanding of subtraction and how it relates to their world. This lesson was adapted from "Helping Students Understand Subtraction" by Anita Page, which appeared in the November 1994 Teaching Children Mathematics, Vol. 1, No. 3.

The following teaching plan proposes recording subtraction experiences in the form of a chart with headings: Start With; Take Away; Have Left.

This recording device, which precedes the introduction of the algorithm, can be used as long as necessary. The children explore subtraction through problem solving with manipulatives, such as counters, which help students make connections to numbers. Thus they begin to discover the symbolic nature of manipulatives and, by extension, of number. The plan develops the language for discussing and recording subtraction situations that will give meaning to the algorithm.

Activity: Subtraction as Take Away

Materials: Six snack items, such as pretzels or crackers, for each child

This activity introduces the concept of subtraction as taking away. Give each child six snack items and ask, "Is it possible to eat some now and still have some left for snack time later?" Most children will easily see that possibility. Next, ask the children to plan how many pieces to eat now and how many to save. Elicit from the children a workable method of planning or pretending to eat so that they can investigate their options. For example, children might put part of the snack under a napkin to represent the "eaten" portion.

As the children manipulate the snacks, they share their discoveries. "If I eat three now, I'll have three left for snack time." Once the possibilities have been explored, each child makes a decision, which the teacher records on a chart, as shown.

When all decisions have been recorded, raise questions that encourage the children to explore the relationships among the numbers on the chart. "How many pieces did you start with? How many did you eat? How many do you have left?" "Was anyone's 'eat' number greater than his or her 'start with' number? Why not?" "Was anyone's 'start with' and 'have left' numbers the same?"

Activity: Solving and Creating Story Problems

In this activity the students handle manipulatives to solve subtraction story problems. They will also create subtraction story problems. When introducing the subtraction mat, remind the children that the counters that are part of the story stay on the mat. A specific area, such as the top of the desk, should be designated for counters not in use.

Inform the children that today they will be told only part of a subtraction story. They will use their counters and mats to help complete the story. Introduce the language that will later be used in recording. "I will tell you how many items the story starts with and how many to take away. You have to find out how many are left." The problem-telling models should include a wide range of situations - alligators to aliens, dinosaurs to daffodils - so that the children begin to understand the broad applicability of the operation. Again, model a variety of language forms. "How many aliens are in the spaceship now?" "Some daffodils are still in the garden. How many?"

Allow individual children to dictate story problems for the rest of the class to solve. While the children work, observe and guide the handling of the manipulatives. Children commonly fail to separate those counters not in use from those in use. A designated area for counters not in use is helpful.

Activity: Continuing Explorations

The children subtract with counters and mats and record their findings. They continue to explore the relationship between the algorithm positions. Tell the children that they will use their counters and mats to discover many subtraction facts. Ask, "If your 'start with' number is 6 and your 'take away' number is 4, what will your 'have left' number be? After the children have found the answer and the teacher has recorded it on a class chart, the children are asked to record the information on the Take Away Activity Sheet.

Take Away Activity Sheet

After setting a new task, circulate and observe, giving help where needed. The tasks should vary in structure: "Your 'start with' number is 4. Pick a 'take away' number and find the 'have left' number." "Your 'start with' number is greater than 4. Your 'take away' number is less than 3. Find a 'have left' number." "Can you find a fact that has the same 'start with' and 'take away' numbers?" Again, the kinds of questions the teacher asks will determine the kind of thinking the children do. In posing more open-ended tasks, the teacher sets the stage for an investigation that requires conjecture, trial-and-error testing, and mathematical reasoning.

Activity: Introducing the Algorithm

Tell the class that they will learn a new way of recording subtraction facts. Present a subtraction story problem for the children to solve; record their solution in chart from. Write the numerical representation under the chart headings.

The teacher might say, "Now that we know the names of the numbers, we don't need the chart to talk about subtraction facts." Make clear that in the subtraction sentence, the numbers keep the names they had on the chart: "start with," "take away," and "have left." The meaning of the minus sign should be discussed, and the equals sign, familiar from addition, should be reviewed.

Allow the children to solve equations that are written on the chalkboard. Encourage the children to read the completed equations by using the language of the chart: Start with 6, take away 4, have 2 left.

Follow this demonstration with a guided-practice session in which children work with counters and mats to solve addition equations. While circulating and observing, note which children need to use the chart to reinforce further the meaning of the symbolic form.