Rational Steps Worksheet
Scaffolded Math
Rational Steps Practice
Adding & Subtracting Signed Numbers with Visual Models
Name:
Date:
1
Start Point: Find 1st number
2
Move: + Right → | − Left ←
3
Double Minus: −(−) flips to +
1 −4 + 7 =
Opposite Signs
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
A Step 1: Start
First number is:
B Step 2: Direction & Jump
Right (→) Left (←)
Jump units
C Step 3: Landing
Landed on:
2 2 − 6 =
Subtracting Larger Value
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
A Step 1: Start
First number is:
B Step 2: Direction & Jump
Right (→) Left (←)
Jump units
C Step 3: Landing
Landed on:
3 −1.5 + 4 =
Rational Decimal (0.5 steps)
-3 -2 -1 0 1 2 3 4 5
A Step 1: Start
First number is:
B Step 2: Direction & Jump
Right (→) Left (←)
Jump units
C Step 3: Landing
Landed on:
4 −2 − (−5) =
Rewrite: −2 +
-5 -4 -3 -2 -1 0 1 2 3 4 5
A Step 1: Start
First number is:
B Step 2: Direction & Jump
Right (→) Left (←)
Jump units
C Step 3: Landing
Landed on:
Self-Check: Plotted start dot Drew jump arrow Checked final sign (+ or −)
CCSS.7.NS.A.1
Rational Steps Key
Educator Key
Rational Steps Answer Key
Model Solutions & IEP Misconception Diagnostic Cues
Status
Master Key • 4/4 Pts
IEP Grading Criteria: Award 1 pt for correct model jump arrow, 1 pt for accurate landing solution. Total: 4 Problems
1 −4 + 7 =
3
Answer: 3
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 +7 Units Right →
Step 1: Start
−4
Step 2: Move
✓ Right • Jump 7
Step 3: Landing
3
Diagnostic Alert
Watch for 11 (ignoring − sign) or −11 (wrong direction).
2 2 − 6 =
−4
Answer: −4
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 ← Jump 6 Units Left (−)
Step 1: Start
2
Step 2: Move
✓ Left • Jump 6
Step 3: Landing
−4
Diagnostic Alert
Watch for positive 4 (flipping 6 − 2) or 8 (adding instead).
3 −1.5 + 4 =
2.5
Answer: 2.5
-3 -2 -1 0 1 2 3 4 5 +4 Whole Units Right (8 half-ticks) →
Step 1: Start
−1.5
Step 2: Move
✓ Right • Jump 4
Step 3: Landing
2.5
Diagnostic Alert
Watch for counting half-ticks as 1s (landing at 0.5 instead of 2.5).
4 −2 − (−5) =
3
Rewritten: −2 + 5 = 3
-5 -4 -3 -2 -1 0 1 2 3 4 5 +5 Units Right (Double Minus Flips to +) →
Step 1: Start
−2
Step 2: Move
✓ Right • Jump 5
Step 3: Landing
3
Diagnostic Alert
Watch for −7 (jumping left because of the first minus symbol).
IEP Prompting Tip: Have student point physical pencil eraser at the start number before jumping.
Standard: 7.NS.A.1