Raven counts the tiles on the garage floor. "Six by six. Thirty-six square tiles, and I did not count them one by one."
"Six squared," Rocket says. "And the block tower in the corner is three cubed. Twenty-seven blocks."
"What do you notice about where squares and cubes show up?" Raven asks.
"Flat things are squares," Rocket says. "Solid things are cubes. Doubling things are powers of two."
Nova hovers at the doorway, where the morning light comes in. "And the order of operations shows up everywhere," she says. "Any time two steps compete."
"So the whole week fits on one card," Raven says, writing fast. "Powers, then the order."
Rocket grins. "Next week I am hiding a number in an envelope. Nobody will guess it." Nova hums. "We will see."
Area: a square floor 6 tiles by 6 tiles holds 6² = 36 tiles. We measure area in square units for exactly this reason.
Volume: a cube of blocks 3 long, 3 wide and 3 tall holds 3³ = 27 blocks. Volume uses cubic units.
Doubling: a paper chain that doubles each round, or a rumor that each person tells two friends, grows as powers of 2.
Place value: 10² = 100 and 10³ = 1,000. Every place in a number is a power of ten.
Whenever an expression has two different operations, the order of operations settles which goes first.
"Three rows of 4 beans plus 2 extra" is 3 × 4 + 2 = 14, not 3 × 6. The multiplication happens before the addition.
"Add 2 to each of 3 rows of 4" needs parentheses: 3 × (4 + 2) = 18. Parentheses are how you say "this first".
| Week review | True or false? |
|---|---|
| 2³ = 6 | ? |
| The exponent counts how many factors of the base to multiply. | ? |
| 2 + 3 × 5 = 17 | ? |
| In the order of operations, adding comes before multiplying. | ? |
| 7² = 49 | ? |
A whole week of powers and order. Tomorrow is Puzzle Day: a folding race and a bean square challenge with your family.