# Base 10 and Powers of 10.

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Base 10 and Powers of 10

Explain what you see. Open the discussion to groups or partners. Allow a few students to share their thinking and explanations. Then proceed to the next slide.

Now, what do you think? Ten to the power of zero = 10º = 1 One Unit
Open the discussion to groups or partners. Allow a few students to share their thinking and explanations. Explain to the students that mathematicians established a long time ago that any number raised to the power of zero would equal 1. Let them know that it will make more sense as we proceed and look for patterns. Cube

Explain what you see. Open the discussion to groups or partners. Allow a few students to share their thinking and explanations. Then proceed to the next slide.

Now, what do you think? Ten to the power of one = 10¹ = 10
Open the discussion to groups or partners. Allow a few students to share their thinking and explanations. Ask the students if they are beginning to see a pattern. Long or Rod

Explain what you see. Open the discussion to groups or partners. Allow a few students to share their thinking and explanations. Then proceed to the next slide.

Now, what do you think? Ten to the power of two = 10² = 100 Why do we say (10²) ten squared? 10 x 10
Students should discover that the shape resembles a flat or square. This comes from sliding ten of the ten rods side by side. This helps make sense of saying ten squared. It is also correct to say ten to the second power. Square or Flat

Explain what you see. Open the discussion to groups or partners. Allow a few students to share their thinking and explanations. Then proceed to the next slide.

Now, what do you think? Ten to the power of three = 10³ = 1000 Why do we say (10³) ten cubed? 10 x 10 x10 Students should discover that the shape resembles a cube. This comes from stacking ten 100 blocks on top of each other. This helps make sense of saying ten cubed. It is also correct to say ten to the power of 3. Cube

What patterns do you discover when you make a comparison?
10º = 1 10² = 10 x 10 = 100 Students should be discovering the patterns. The power of zero is always 1. With the powers of 10 the number of zeros is equal to the exponent. 10 to the first power has one zero; 10 to the second power has two zeros; 10 to the third power has three zeros. On to the next slide. 10¹ = 10 10³ = 10 x =1000

What do you think will come next?
Are you able to predict? Explain your thinking Give the students time to write or draw out their thinking. Allow a few students to share. Move on to the next slide.

What do you think will come next?
10 x 10 x 10 x 10 = 10,000 = 10 to the 4th power 10 x 10 x 10 x 10 x 10 = 100,000 = 10 to the 5th power 10 x 10 x 10 x 10 x 10 x 10 = 1,000,000 = 10 to the 6th power 10 x 10 x 10 x 10 x 10 x 10 x 10 = 10,000,000 = 10 to the 7th power 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 = 100,000,000 = 10 to the 8th power 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 = 1,000,000,000 = 10 to the 9th power Could we continue from here? By now students should be able to see the pattern between the Base 10 and the Exponent (power). The students should also predict that in each section there will be a pattern of cube, rod, and a square/flat.

What do you notice about this pattern? How would you label each section? Write each number in exponential form. 100 10 1 100,000 10,000 1,000 100,000,000 10,000,000 1,000,000 100,000,000,000 10,000,000,000 1,000,000,000 Ask the students to take a few minutes to label each section and write the numbers in exponential form. Open the discussion to groups or partners. Allow a few students to share their thinking and explanations. Then proceed to the next slide.

How do your conclusions compare. How did you label each section
How do your conclusions compare? How did you label each section? Were your numbers written in exponential form correct? How do you know? Flat or Square ’s Long or Rod ’s Cube ’s ² ¹ º 100,000 10,000 1, ³ 100,000,000 10,000,000 1,000,000 100,000,000,000 10,000,000,000 1,000,000,000 Ask the students if their thinking was correct or where they might have to adjust their thinking. Open the discussion to groups or partners. Allow a few students to share their thinking and explanations.

Let’s clarify Base Ten and Exponents (Powers)
10³ Exponent By now the students should have an understanding of base 10 and exponents. Make sure to take time to explain each part and how it is written. The exponent is the driving power for the number of times a base will be multiplied by itself. Explain to the students that mathematicians came up with exponents as a way to simplify writing large numbers. Base The base (10) is the number which will be multiplied by itself the number of times that the exponent indicates. 10³ = 10 x 10 x 10 = 1000