Exploring Applications of Arithmetic with Powers of 10

In lesson 12, students explore arithmetic applications with powers of 10, focusing on real-world scenarios involving meter sticks and the moon. The lesson includes warmup questions, an activity, and calculations to determine the number of meter sticks needed to match the moon's mass and whether they can reach the moon. Students also calculate how far the meter sticks would reach in light-years. The lesson emphasizes the use of exponent rules and powers of 10 to simplify calculations and encourages reflection on the problem-solving process.

What information is needed to determine how many meter sticks equal the mass of the moon?

• The length of the meter stick and the distance to the moon

• The mass of the moon and the mass of the meter stick

• The distance to the moon and the mass of the moon

• The length of the meter stick and the mass of the moon

What is the mass of an average classroom meter stick?

• 0.5 kilograms

• 0.1 kilograms

• 1 kilogram

• 0.2 kilograms

How far is the moon from Earth?

• 1.5 times 10 to the 11 meters

• 7 times 10 to the 22 meters

• 3.8 times 10 to the 8 meters

• 2.5 times 10 to the 6 meters

How do you express the mass of a meter stick using powers of 10?

• 2 times 10 to the negative 2nd power

• 2 times 10 to the 1st power

• 2 times 10 to the negative 1st power

• 2 times 10 to the 2nd power

What is the result of dividing the mass of the moon by the mass of a meter stick?

• 3.5 times 10 to the 22nd

• 3.5 times 10 to the 23rd

• 7 times 10 to the 22nd

• 7 times 10 to the 23rd

How many times farther will the meter sticks reach compared to the distance to the moon?

• 100 times farther

• 10 to the 8 times farther

• 10 to the 15 times farther

• 10 times farther

How many light-years away would the meter sticks reach?

• 3.5 times 10 to the 6 light years

• 3.5 times 10 to the 7 light years

• 4 times 10 to the 7 light years

• 4 times 10 to the 6 light years

What is the approximate length of one light-year in meters?

• 10 to the 8 meters

• 10 to the 23 meters

• 10 to the 16 meters

• 10 to the 7 meters

How do powers of 10 make calculations easier?

• They make numbers smaller

• They make numbers larger

• They make numbers easier to express and interpret

• They make numbers more complex

When are estimates acceptable in these types of problems?

• When the question is very specific

• When comparing or providing general information

• When exact answers are needed

• When the numbers are very small