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Lesson 4: Write and Evaluate Numerical Expressions with Exponents6.AT.6c

Stuck? Start here. Read the steps, try the problem, then check your answer.

I can…

I can write numerical expressions from a real situation and evaluate them using the order of operations, including powers.

Write and Evaluate Numerical Expressions with Exponents — Turning a situation into a number sentence without an equal sign, then finding its value in the correct order.
Numerical expression — A math phrase built from numbers and operations, with no equal sign and no variable.
Evaluate — To find the single value an expression is worth by carrying out its operations in order.
Order of operations — The agreed order for evaluating: grouping symbols, then exponents, then multiply and divide left to right, then add and subtract left to right.
Power — A short way to write repeated multiplication of the same factor, such as 2³ for 2 × 2 × 2.
Base — In a power, the number being multiplied by itself. In 2³ the base is 2.
Exponent — In a power, the small raised number that says how many times the base is used as a factor.

Sofia buys 2 member tickets at $15, 4 non-member tickets at $20, and 8 student tickets at $2 each. I write one expression for each ticket type: 2 × 15, 4 × 20, and 8 × 2.
The whole order is the three costs added together: 2 × 15 + 4 × 20 + 8 × 2.
Now I evaluate. There are no grouping symbols and no powers yet, so multiplication comes first, left to right: 30 + 80 + 16.
Then I add: 30 + 80 + 16 = 126. The tickets cost $126.

Evaluate 2 × 15 + 8 × 2³.

Powers first: 2³ = 8. Then multiply left to right: 2 × 15 = 30 and 8 × 8 = 64. Then add: 30 + 64 = 94.

I know ___ because ___.

Goal: I can explain my steps using the words expression, evaluate, order of operations, base, and exponent.