PEMDAS Blueprint Worksheet PEMDAS BLUEPRINT
Step-by-Step Order of Operations
NAME:
DATE:
THE BUILDING STEPS (PEMDAS) Read Left to Right!
P
Parentheses Do groups ( first )
M / D
Multiply & Divide Go left to right × or ÷
A / S
Add & Subtract Go left to right + or -
Guided Blueprint Practice (Work with your substitute teacher!)
Model A Multiplication First
3 +
4 × 2 1st
3 +
8
Answer:
11
Model B Parentheses First
( 10 - 4 ) 1st
× 3
× 3
Answer:
Problem C Division First
15 -
6 ÷ 2 1st
15 -
Answer:
Work through these guides with the substitute teacher first! Page 1 of 3
BLUEPRINT PRACTICE: STANDARD LEVEL
Level up your PEMDAS skills!
Partner Approved
Problem 1 × first
20 -
5 × 3
20 -
Answer:
Problem 2 ( ) first
( 4 + 8 )
÷ 3
÷ 3
Answer:
Problem 3 ÷ first
12 ÷ 4
Answer:
Problem 4 ( ) first
6 ×
( 2 + 3 )
6 ×
Answer:
Problem 5 - first (L to R)
18 - 8
Answer:
Problem 6 ÷ first
5 +
12 ÷ 3
5 +
Answer:
LEVEL 1 BLUEPRINT TOOLKIT (Self-Checking)
If your final answer for any of Problems 1 to 6 matches one of these toolkit numbers, cross it out!
4 5 9 10 14 30
Ready for a bigger challenge? Flip to the next page! Page 2 of 3
BLUEPRINT PRACTICE: CHALLENGE LEVEL
Tackle the trickiest blueprint setups!
High Difficulty
Problem 7 ( ) first
( 15 - 9 )
× 4
× 4
Answer:
Problem 8 ( ) first
32 ÷
( 2 × 4 )
32 ÷
Answer:
Problem 9 × first
7 × 6
- 15
- 15
Answer:
Problem 10 ÷ first
45 ÷ 9
Answer:
Problem 11 ÷ first (L to R)
24 ÷ 3
× 2
× 2
Answer:
Problem 12 ( ) first
50 -
( 12 + 18 )
50 -
Answer:
LEVEL 2 BLUEPRINT TOOLKIT (Self-Checking)
Cross out your final answers for Problems 7 to 12 below!
4 16 19 20 24 27
Congratulations! You finished the entire blueprint sequence! Page 3 of 3
PEMDAS Blueprint Answer Key SUBSTITUTE TEACHER KEY
PEMDAS Blueprint • Grayscale & Photocopy Ready
Teacher Guide • Page 1
Small-Group Instruction Tips
1. Scaffold with Arrows: Encourage students to physically follow the arrows down. Visual movement helps prevent them from processing operations out of order.
2. Left-to-Right Team Rules: Remind students that Addition/Subtraction and Multiplication/Division are equal speed partners—they just go left-to-right!
3. Write Intermediate Steps: Many students try to jump directly to the final answer. Insist that they write down the simplified expression in the middle box.
4. Use the Self-Checking Toolkit: If a student's final answer is not in the toolkit box at the bottom of the page, prompt them to look at their middle box step again.
WORKSHEET PAGE 1: Guided Class Models
Model A
3 + 4 × 2
Step: 3 + 8
Final: 11
Model B
(10 - 4) × 3
Step: 6 × 3
Final: 18
Model C
15 - 6 ÷ 2
Step: 15 - 3
Final: 12
WORKSHEET PAGE 2: Level 1 (Standard Practice Answers)
Problem 1 20 - 5 × 3
Step: 20 - 15
Ans: 5
Problem 2 (4 + 8) ÷ 3
Step: 12 ÷ 3
Ans: 4
Problem 3 12 ÷ 4 + 7
Step: 3 + 7
Ans: 10
Problem 4 6 × (2 + 3)
Step: 6 × 5
Ans: 30
Problem 5 18 - 8 + 4
Left to Right
Ans: 14
Problem 6 5 + 12 ÷ 3
Step: 5 + 4
Ans: 9
Turn page for Worksheet Page 3 (Advanced Challenge Level) Answers. Page 1 of 2
SUBSTITUTE TEACHER KEY
Advanced Level Answers & Common Errors
Teacher Guide • Page 2
WORKSHEET PAGE 3: Level 2 (Advanced Challenge Answers)
Problem 7 (15 - 9) × 4
Step: 6 × 4
Ans: 24
Problem 8 32 ÷ (2 × 4)
Step: 32 ÷ 8
Ans: 4
Problem 9 7 × 6 - 15
Step:
Vocabulary Vault Worksheet VOCABULARY VAULT
Crack the Algebra Code • Dossier 1
NAME:
DATE:
CONFIDENTIAL MISSION DEBRIEF
Algebra has its own secret code! To crack the vault, you must learn the names of the mathematical players. Study the **Vault Map** and **Negative Number Warnings** below, then complete the security matching test.
🔒 ANATOMY OF AN ALGEBRA SENTENCE
Expression (The Whole Sentence)
Term 1
5
Coefficient Multiplies the variable
x
Variable Letter that can change
Term 2
9
Constant Plain number: stays same
SPY RADAR: THE NEGATIVE SIGN "STICKY" ALERT
A subtraction sign - is also a **negative sign**! It sticks to the number directly behind it like glue.
Example 1: 3x - 5
The sign - sticks to the 5 .-5 , not positive 5!
Example 2: -4y + 8
The sign - sticks to the 4 .-4 , not positive 4!
TEST 1: CONFIRM SECURITY ROLES
A. Variable
A
B. Constant
B
C. Coefficient
C
D. Term
D
A plain number standing completely alone (e.g. 9 or -5).
A single piece of an expression, separated by + or - signs.
A letter (like x or y) representing an unknown changing value.
A number multiplier sitting directly in front of a variable.
Review the "Negative Sticky Warning" with your teacher before starting! Page 1 of 2
VAULT DECRYPTOR PANEL
Dossier Practice • Solve to Decrypt
🔑 LEVEL 1 SECURITY
Break down the elements of each math expression. Write your answers clearly inside the designated vault slots. **Remember:** The negative sign sticks to the number directly behind it!
Decoder Code 01 3x + 8
Variable Letter:
Constant (Plain No.):
Coefficient (Multiplier):
How many Terms?
Decoder 02 Negative Alert!
7y - 5
Variable Letter:
Constant (With Sign!):
Coefficient (Multiplier):
How many Terms?
Decoder 03 Negative Alert!
-4a + 12
Vocabulary Vault Answer Key VOCABULARY VAULT KEY
Teacher Guide & Exit Ticket Key • Grayscale Ready
🔒 MASTER KEY
Instructional Strategies for Vocabulary
1. Visual Analogies: Link terms to visual roles: Variable is a "shape-shifter" (letter), Coefficient is a "bodyguard" (stands directly in front of the letter protectively).
2. Sticky Sign Rule: Emphasize that subtraction signs are also negative signs. They belong entirely to the number directly behind them.
3. The Hidden 1: Remind students that an isolated variable (like \(n\) in Decoder 04) has a **hidden \(1\)** coefficient standing in front of it.
4. Discussion Prompt: Ask, "Is the constant in \(2x - 9\) positive 9 or negative 9?" Emphasize the minus sign sticky rule.
Test 1: Matching Answers
A. Variable ➔ Def 3
B. Constant ➔ Def 1
C. Coefficient ➔ Def 4
D. Term ➔ Def 2
Exit Ticket Answers
Q1 (MC): Option C (-6)
Q2 (Matching): y ➔ Var | 3 ➔ Coeff | -5 ➔ Const
Q3 (Short): Constant value is -9
PAGE 2 KEY: Vault Decryptor Answers
Code 01: 3x + 8 Solved
Variable Letter: x
Constant: 8
Coefficient: 3
How many terms? 2
Code 02: 7y - 5 Negative Alert!
Variable Letter: y
Constant: -5
Coefficient: 7
How many terms? 2
Code 03: -4a + 12 Negative Alert!
Variable Letter: a
Constant: 12
Coefficient: -4
How many terms? 2
Code 04: n - 6 Hidden 1!
Variable Letter: n
Constant: -6
Coefficient: 1 (hidden)
How many terms? 2
💡 Common Misconceptions to Monitor:
Signs as Separate Operations: Students may think a minus sign is only subtraction and not part of the number. Redirection: "The operation symbol is also the sign of the next number!"
Vocabulary Vault Exit Ticket VOCABULARY VAULT EXIT TICKET
Dossier Clearance Check • Version A
NAME: DATE:
1. In the expression -6w + 10, what is the coefficient?
A w
B 10
C -6
D 6
2. Draw a line to match each part of the expression 3y - 5 to its correct role:
Letter "y" ●
Number "3" ●
Number "-5" ●
Coefficient (Multiplier)
Constant (Stays the Same)
Variable (Letter)
3. What is the constant in the expression 2x - 9?
CONSTANT VALUE =
(Remember the Negative Sticky Rule!)
Cut Here to Separate Tickets
VOCABULARY VAULT EXIT TICKET
Dossier Clearance Check • Version B
NAME: DATE:
1. In the expression -6w + 10, what is the coefficient?
A w
B 10
C -6
D 6
2. Draw a line to match each part of the expression 3y - 5 to its correct role:
Letter "y" ●
Number "3" ●
Number "-5" ●
Coefficient (Multiplier)
Constant (Stays the Same)
Variable (Letter)
3. What is the constant in the expression 2x - 9?
CONSTANT VALUE =
(Remember the Negative Sticky Rule!)
Integer Elevator Worksheet INTEGER ELEVATOR
Positive & Negative Floor Levels
NAME:
DATE:
Floor Dial
Penthouse
5
4
3
2
1
Lobby (0)
-1
-2
-3
-4
-5
Basement
ELEVATOR RIDE RULES
Positive floors are above the ground (Lobby = 0). Negative floors are below the ground in the sub-basement. Follow these instructions for every calculation:
1
Board the Elevator: Start on the floor level of the first number in the problem. Put your pencil there!
2
Addition + (Move UP): Count steps upwards on the dial.
3
Subtraction - (Move DOWN): Count steps downwards on the dial.
Adding a negative + ( - ): Adding debt pulls you down! Move DOWN instead of up.
GUIDED ELEVATOR TRIPS (Ride with your Substitute Teacher!)
Trip A Start Negative
-2 + 5 = ?
🚀 1st: Board at floor -2 ⬈ 2nd: Move UP 5 floors
Exit Floor:
Trip B Start Positive
3 - 7 = ?
🚀 1st: Board at floor 3 ⬊ 2nd: Move DOWN 7 floors
Exit Floor:
Trip C Add Negative
-1 + (-3) = ?
🚀 1st: Board at floor -1 ⬊ 2nd: Move DOWN 3 floors
Exit Floor:
Finish these guided elevator rides, then flip to the partner page! Page 1 of 2
PARTNER ELEVATOR SIMULATION
Simulate Rides & Log Exit Floors
🏢 SOLO OR PARTNER
5
2
0
-2
-5
Ride Log 01
-3 + 4 = ?
Exit Floor:
5
2
0
-2
-5
Ride Log 02
2 - 5 = ?
Exit Floor:
5
2
0
-2
-5
Ride Log 03
-1 - 4 = ?
Integer Elevator Answer Key INTEGER ELEVATOR KEY
Substitute Teacher Guide • Grayscale Ready
🏢 SYSTEM CONTROL
Substitute Pacing & Strategy Guide
1. Avoid the "Zero Start" Trap: The most common error is students starting at zero rather than the first number of the equation. Emphasize: "Get on the elevator at the first floor listed!"
2. Physical Pencil Hopping: Encourage students to physically place their pencil tip on the vertical number dial next to their problem and jump step-by-step to prevent counting errors.
3. Adding a Negative: Explain that adding a negative is like carrying a heavy weight—it drags the elevator down. Emphasize that \(+\ (-\text{number})\) translates directly to moving DOWN.
4. Check the Penthouse Bank: If a student's final floor level doesn't match a number in the Page 2 Penthouse Security Bank, have them re-locate their starting board floor.
WORKSHEET PAGE 1 KEY: Guided Class Elevator Rides
Trip A (-2 + 5)
Start at -2, move UP 5
Exit Floor: 3
Trip B (3 - 7)
Start at 3, move DOWN 7
Exit Floor: -4
Trip C (-1 + (-3))
Start at -1, move DOWN 3
Exit Floor: -4
WORKSHEET PAGE 2 KEY: Ride Log Solutions
Ride Log 01: -3 + 4
Start -3, UP 4 Floor: 1
Ride Log 02: 2 - 5
Start 2, DOWN 5 Floor: -3
Ride Log 03: -1 - 4
Start -1, DOWN 4 Floor: -5
Ride Log 04: 4 + (-2)
Start 4, DOWN 2 Floor: 2
Ride Log 05: -5 + 6
Start -5, UP 6 Floor: 1
Ride Log 06: 3 - 6
Start 3, DOWN 6 Floor: -3
Ride Log 07: -2 + (-3)
Start -2, DOWN 3 Floor: -5
Ride Log 08: 6 - 8
Start 6, DOWN 8 Floor: -2
💡 Lesson Discussion Questions (Substitute Closer):
"Why does subtracting a positive number make the elevator go down? (You are taking floors away!)"
"What is the difference between starting on floor level 3 and starting on floor level -3?"
Thank you for helping our students navigate positive & negative number scales today! Integer Elevator Key
