Name:
Date:
Score:
How to use this worksheet. Work one part at a time. There are two forms (A and B) so you can practice twice — use Form B to check your progress after you review Form A.
- For fill-in problems, write your answer on the line. For circle one problems, circle the single best choice.
- Every part has a Clarify hint. Try the problems first; read the hint only if you get stuck. It gives you a method, never the answer.
- Show your thinking. Do one step at a time — you do not have to solve the whole line at once.
Form A
PART 1
Exponents (Powers)
Solve the exponent.
1.2² (Two squared)
2.3² (Three squared)
3.1⁵ (One to the power of 5)
4.5² (Five squared)
5.True or False: 2³ means 2 + 2 + 2. (circle one) True | False
Clarify — A small raised number (the exponent) tells you how many times to multiply the base by itself, not how many times to add it. "Squared" means to the power of 2. Multiply the base by itself; do not add.
PART 2
The Parentheses Rule
Remember: do what is inside the parentheses ( ) FIRST.
6.(2 + 3) × 4
7.2 × (3 + 4)
8.10 − (2 + 3)
9.(10 − 2) + 3
10.2 × (5 − 1)
Clarify — Parentheses always go first. Simplify what is inside the ( ) to a single number, then carry out the operation left outside. Rewrite the line after each step so you don't lose your place.
PART 3
Putting It All Together
Use the full order of operations.
11.2² + 3
12.(3 + 1) × 2
13.5 + (2 × 3)
14.3² − 5
15.2 × (10 ÷ 2)
Clarify — Follow the order every time: (1) parentheses, (2) exponents, (3) multiply and divide, (4) add and subtract. Take one step per line and cross out what you have already handled.
PART 4
Translation
Turn words into math, and name the steps.
16.Write as math: "The sum of 2 and 3, times 4." (Hint: use parentheses)
17.Write as math: "Two times the difference of 5 and 1."
18.What is the first step in: 3 + (4 × 2)?
19.What is the first step in: 5 + 2²?
20.Solve: 2 × (3²)
Clarify — "Sum" means add, "difference" means subtract, "times" means multiply. Group the words that belong together inside parentheses before attaching the outside operation. For a "first step" question, just name the operation you would do first — you don't have to finish the whole problem.
Form B
PART 1
Exponents (Powers)
Solve the exponent.
1.3² (Three squared)
2.4² (Four squared)
3.1³ (One to the power of 3)
4.2³ (Two to the power of 3)
5.True or False: 4² means 4 × 4. (circle one) True | False
Clarify — A small raised number (the exponent) tells you how many times to multiply the base by itself, not how many times to add it. "Squared" means to the power of 2. Multiply the base by itself; do not add.
PART 2
The Parentheses Rule
Remember: do what is inside the parentheses ( ) FIRST.
6.(4 + 1) × 3
7.3 × (2 + 2)
8.10 − (5 + 1)
9.(8 − 2) + 4
10.3 × (4 − 2)
Clarify — Parentheses always go first. Simplify what is inside the ( ) to a single number, then carry out the operation left outside. Rewrite the line after each step so you don't lose your place.
PART 3
Putting It All Together
Use the full order of operations.
11.3² + 1
12.(2 + 2) × 5
13.4 + (3 × 2)
14.4² − 6
15.3 × (8 ÷ 2)
Clarify — Follow the order every time: (1) parentheses, (2) exponents, (3) multiply and divide, (4) add and subtract. Take one step per line and cross out what you have already handled.
PART 4
Translation
Turn words into math, and name the steps.
16.Write as math: "The sum of 5 and 1, times 2." (Hint: use parentheses)
17.Write as math: "Three times the difference of 6 and 2."
18.What is the first step in: 5 + (3 × 3)?
19.What is the first step in: 4 + 3²?
20.Solve: 2 × (2²)
Clarify — "Sum" means add, "difference" means subtract, "times" means multiply. Group the words that belong together inside parentheses before attaching the outside operation. For a "first step" question, just name the operation you would do first — you don't have to finish the whole problem.
FOR MENTOR USE — STUDY THIS TOGETHER
Mentor Guide
How to work through exponents and order of operations with your student
1. What this worksheet builds
It builds two foundations for algebra: reading exponents as repeated multiplication (not addition) and applying the order of operations — parentheses, then exponents, then multiply/divide, then add/subtract. Two forms (A and B) let the student practice, review, and then prove the skill stuck. The goal is a reliable, step-by-step habit, not speed.
2. Run it with gradual release: I do → we do → you do
- I do: Work one Part 1 problem aloud, saying each step so the student hears how you decide what comes first.
- We do: Do Part 2 together — you point to the parentheses, they tell you what to simplify first.
- You do: Let them attempt Part 3 alone, stepping in only when they reach for a Clarify hint. Save Form B for independent practice.
3. Using the Clarify hints
Let the student try each part first; read the Clarify box only if they stall. The hints coach method ("parentheses first," "multiply, don't add"), never the numeric answer. Over time, ask the student to say the hint back to you before reading it — that is the strategy becoming their own.
4. Common mistakes to watch for
- Exponent as addition: a student may read 2³ as 2 + 2 + 2. Have them write it out as 2 × 2 × 2 to feel the difference.
- Ignoring parentheses: working strictly left-to-right. Point back to the ( ) and ask, "What goes first?"
- Skipping steps: encourage rewriting the whole line after each step so nothing gets dropped.
5. Reviewing it together — without an answer key
- This sheet has no answer key on purpose. Have the student re-solve a problem a second way and see if they land on the same number — matching results is the check.
- For any disagreement, ask them to walk you through each step out loud; the wrong step usually reveals itself as they explain.
- Use Form B to confirm a skill after reviewing Form A. If they can talk through the order of operations unprompted, they've got it — no key required.