Powers and Exponents

Lesson Goal

By the end of this lesson your student should be able to read 5³ as 5 used as a factor three times, write it out as 5 x 5 x 5, write a repeated product the other way as a power, and work out the value.

The lesson also adds a step to the order of operations from U1-L7: powers come right after grouping symbols and before multiplication.

Start With Something Square

If you have any square tiles, sticky notes or crackers, lay out a 3 by 3 square before reading. Ask how many there are and how the student got the number.

Then stack a cube if you can. The words squared and cubed stop being strange the moment the student has made each shape with his hands.

Where Students Get Stuck

🚨 The biggest trap is multiplying the base by the exponent. 3⁴ is not 3 x 4 = 12, it is 3 x 3 x 3 x 3 = 81. Have the student write the product out every time until the mistake stops.

The second trap is in the order of operations. In 2 + 3², the power goes first, so the answer is 11. Adding first and then squaring gives 25, which is wrong.

It also helps to say the exponent is a count, not a number being multiplied. It counts how many times the base appears.

Teaching Suggestion

Point at the small raised number and ask 'how many times?' Point at the big number and ask 'how many times what?' Those two questions carry the whole lesson.

For 10 to a power, have the student count the zeros. 10⁵ has five zeros, and that pattern is the reason the book opened on 100,000.

Key Vocabulary

Factors

Numbers that are multiplied together.

Base

The factor that is being multiplied over and over.

Exponent

The small raised number that counts how many times the base is used as a factor.

Power

A number written with an exponent, like 5² or 10⁵.

Squared

Raised to the second power, like the number of tiles in a square.

Cubed

Raised to the third power, like the number of blocks in a cube.