Mission Impossible – Connecting Arithmetic to Algebra: Making Sense of Large Numbers

Contributor: Marlene Vogel. Lesson ID: 10230

Imagine drifting helplessly in space while Mission Control tries to find you! But you don't know enough about big numbers to tell them where you are! Learn place values and don't drift through math!


Whole Numbers and Operations

learning style
Auditory, Visual
personality style
Beaver, Golden Retriever
Grade Level
Intermediate (3-5), Middle School (6-8)
Lesson Type
Quick Query

Lesson Plan - Get It!


You are the commander of a space ship that has become disabled in orbit. Mission Control is trying to locate you with a satellite. They are calling off numbers that represent what they think is your distance from Earth. You need to tell them if their guess is too high, too low, or correct. Are you familiar with the place values millions, billions, and trillions? You'd better be!

Take a moment to reflect on the opening to this lesson.

  • Would it be easier for Mission Control to guess your location if the numbers were between 1 and 100 or 1 and 1,000? What is the rationale behind your answer?

Read this downloadable article, Telescope as Time Machine (SpacePlace.nasa.gov). Notice the references made to numbers in the millions, billions, and trillions! This packet includes activities to complete to further your knowledge about outer space.

On the journey to learning algebra, you need to refer to skills you have already learned and build upon them.

For example, when working with large numbers, it is necessary to know and use place value. You first learned place value in your 3rd- or 4th-grade math lessons. Now, you are going to build upon that skill with larger numbers and their place value.

You should be familiar with two of the five categories in place value: ones and thousands. Please refer to Figure 1-1 below:

figure 1.1

(Figure 1-1)

By looking at Figure 1-1, you can see the number 9 is in the tens column, which means it represents 90 as the larger number.

  • What number is in the ten thousands column?
  • What number is in the ones column?

As stated earlier in the lesson, you are now going to add to your knowledge of place value.

You may be familiar with the millions category.

  • But did you know we can write numbers in the billions and trillions?

Below is the place value chart with the millions, billions, and trillions categories added to it. Please refer to Figure 1-2 (A larger version of the Place Value Chart is available in Downloadable Resources in the right-hand sidebar.).

figure 1.2

(Figure 1-2)

Try to identify some of the numbers in the newer parts of the place value chart.

  • What category does the number 0 represent?
  • What number is in the trillions category?
  • What number is in the hundred trillions category?

At this point, you are probably asking yourself, “Why do I need to know this information?”

This is a good question because it shows you are trying to make sense — or think critically — about the lesson you are involved in and the skills you are learning.

Knowing place value helps you know and understand the names for numbers. Just like you learned the number 1 is the same as writing one when you were in kindergarten and first grade, it is just as important to learn the millions, billions, and trillions categories. Knowing the names for numbers:

  • helps you recognize a number when it is written in word format instead of numerical format.
  • helps you relate different numbers to each other (which number is greater, how to work out an answer).

Now, you are going to learn to write numbers in word form and in number-word form. It will be necessary to use the place value skills you are learning now in order to be successful in other math situations, such as rounding numbers.

It is important for you to understand some terms before you start working on any problems. Refer to Figure 1-2 while reading the following information:

  • Standard form is the number written in its numerical form. In Figure 1-2, the number 1 is in the ten billions category. Writing that in standard form looks like 10,000,000,000.
  • Word form is when you write the number in words only. Using the same example, 10,000,000,000 looks like "ten billion" when written in word form.
  • Numerical-word form is a combination of standard form and word form. In this form, you write the number itself in numerical form and the category it falls in on a place value chart in word form. Again, we will use 10,000,000,000. When writing this number in numerical-word form, it looks like "10 billion."

Practice writing numbers in all three forms, using the Place Value Chart and Mission Control Exercise 1 documents (Downloadable Resources).

When you have finished exploring space, continue on to the Got It? section for some more educational (but fun!) activities!

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