Using Models to Represent Numbers & Operations

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  • 0:04 Math Models in Real Life
  • 0:41 Number Blocks as Models
  • 1:26 Number Lines as Models
  • 2:42 Integer Chips
  • 3:16 Using the Different Models
  • 4:01 Lesson Summary
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Lesson Transcript
Instructor: Sabrina Cook
In math, models or pictures can be used to represent numbers and operations like addition and subtraction. In this lesson, we'll look at three types of models used to solve problems in math.

Math Models in Real Life

Can you think of any occupations where people may draw pictures to help them understand situations or subjects? For example, a police officer might draw a diagram of a car accident to help him or her remember where the cars collided and where the damage to them occurred. An engineer may draw a picture of a new building site to see where streets and sidewalks are located. Or, a teacher may draw pictures of his/her classroom to see where to put desks, chairs, and bookshelves.

In everyday life, we use pictures to achieve goals and solve problems. In math, we call these pictures models.

Number Blocks as Models

In math, number blocks are commonly used as models, where a small square equals 1, a long rectangle equals 10, and a large square equals 100. As models, blocks can be used for addition, subtraction, multiplication, and division. You can represent a problem given by using the correct models.

For example, we can use blocks to illustrate the following addition problem: 123 + 123 = _____

Here, 123

Number block problem1

+ 123

Number block problem2

equals 246 or:

  • 2 hundreds
  • 4 tens
  • 6 ones

Number Lines as Models

Another type of model we often use is a number line. A number line is used to represent problems and show the direction that the numbers are moving. Number lines are very useful when working with word problems, negative numbers, and numbers that are close together.

To use a number line, first draw a line and label it with numbers related to the problem. Place a dot at the first number, or where the problem begins. To solve the problem: move right for addition and left for subtraction, depending on the second number in the problem.

Let's look at an example: The high temperature for today will be 25 degrees Fahrenheit. By midnight, the temperature will have decreased by seven degrees. What will the temperature be at midnight?

  • Step 1: Draw a line and label the numbers.
  • Step 2: Represent the first number (25) in the problem with a dot.
  • Step 3: Move seven times left because the temperature is decreasing, or going down.
  • Step 4: Identify your final answer, in this case 18: 25 - 7 = 18. At midnight, the temperature will be 18 degrees Fahrenheit.

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