## Take Away

- Lesson

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.

**Introducing Subtraction**

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*

*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.

**Snack Chart**

Name | Start With | Ate | Have Left |

Jessica | 6 | 3 | 3 |

Jeffrey | |||

Alexandra |

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.

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.

**Subtraction Recording Chart**

Start With | Take Away | Have Left |

**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.

### Reference

Page, A. (1994). Helping Students Understand Subtraction. Teaching Children Mathematics. Vol. 1 , No. 3, 140-5.

- Six snack items, such as pretzels or crackers, for each student
- Ten counters for each student
- A subtraction mat: a 9 × 12 sheet of paper in the center of which is drawn a circle large enough to hold all the counters (one mat per student)
- Chart paper
- Take Away Activity Sheet

**Extensions**

As an extension of this lesson, present an equation for which the children make a concrete or semi-concrete model and construct a story problem.

**Questions for Students**

Move the students from experience to language, preparing them for the eventual use of the symbolic form.

- What was your 'start with' number? Your 'take away' number? Which was greater?
- Could your 'take away' number ever be greater than your 'start with' number? Why not? Could the two numbers ever be the same?
- Was your 'have left' number greater or smaller than your 'start with' number?
- Could your 'have left' and 'start with' numbers ever be the same?

### Learning Objectives

Students:

- Understand the effects of subtracting whole numbers.
- Use a variety of methods and tools to compute.
- Model situations involving subtraction.
- Identify the mathematical symbols connected with subtraction.

### NCTM Standards and Expectations

- Connect number words and numerals to the quantities they represent, using various physical models and representations.

- Count with understanding and recognize "how many" in sets of objects.

- Develop a sense of whole numbers and represent and use them in flexible ways, including relating, composing, and decomposing numbers.

- Understand the effects of adding and subtracting whole numbers.

- Understand various meanings of addition and subtraction of whole numbers and the relationship between the two operations.

- Develop and use strategies for whole-number computations, with a focus on addition and subtraction.

- Use a variety of methods and tools to compute, including objects, mental computation, estimation, paper and pencil, and calculators.

### Common Core State Standards – Mathematics

-Kindergarten, Algebraic Thinking

- CCSS.Math.Content.K.OA.A.1

Represent addition and subtraction with objects, fingers, mental images, drawings1, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations.

-Kindergarten, Algebraic Thinking

- CCSS.Math.Content.K.OA.A.2

Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem.

-Kindergarten, Algebraic Thinking

- CCSS.Math.Content.K.OA.A.5

Fluently add and subtract within 5.

Grade 1, Algebraic Thinking

- CCSS.Math.Content.1.OA.A.1

Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.

Grade 1, Algebraic Thinking

- CCSS.Math.Content.1.OA.B.4

Understand subtraction as an unknown-addend problem. For example, subtract 10 - 8 by finding the number that makes 10 when added to 8.

Grade 1, Algebraic Thinking

- CCSS.Math.Content.1.OA.C.5

Relate counting to addition and subtraction (e.g., by counting on 2 to add 2).

Grade 1, Algebraic Thinking

- CCSS.Math.Content.1.OA.C.6

Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 - 4 = 13 - 3 - 1 = 10 - 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 - 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13).

Grade 2, Algebraic Thinking

- CCSS.Math.Content.2.OA.A.1

Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.

Grade 2, Algebraic Thinking

- CCSS.Math.Content.2.OA.B.2

Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know from memory all sums of two one-digit numbers.

Grade 2, Number & Operations

- CCSS.Math.Content.2.NBT.B.7

Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds.

### Common Core State Standards – Practice

- CCSS.Math.Practice.MP4

Model with mathematics.

- CCSS.Math.Practice.MP5

Use appropriate tools strategically.

- CCSS.Math.Practice.MP6

Attend to precision.