Signed Decimal Showdown

Page 2 Points: 9 Pts

3

Multi-Factor Products & Exponents (2 Points)

7. \( (-1.5) \times 2.4 \times (-3.0) \) Two negatives = Positive

• Step 1: \( (-1.5) \times 2.4 = -3.6 \)

• Step 2: \( (-3.6) \times (-3.0) = +10.8 \)

Final Product: +10.8

8. Powers: \( (-0.5)^2 \) and \( (-0.5)^3 \) Even/Odd Power Rule

• \( (-0.5)^2 = (-0.5) \times (-0.5) = +0.25 \)

• \( (-0.5)^3 = 0.25 \times (-0.5) = -0.125 \)

\( (-0.5)^2 = +0.25 \) \( (-0.5)^3 = -0.125 \)

4

Real-World Rational Problems (3 Points - 1 Pt Each)

Require number sentence + correct signed units

9. Research Submersible Descent

Descent rate: \(-4.75\) m/min over \(6.4\) minutes.

Expression: \( (-4.75) \times 6.4 \)

\( 475 \times 64 = 30{,}400 \)
3 decimal places: \( 30.400 \)

Depth: −30.4 meters

(or 30.4 m below surface)

10. Robotics Club Subscription

Fee: \(-\$18.50\) per month over \(4.5\) months.

Expression: \( (-18.50) \times 4.5 \)

\( 185 \times 45 = 8{,}325 \)
2 decimal places: \( 83.25 \)

Balance: −$83.25

(a reduction of $83.25)

11. Indiana Cold Front Temperature Drop

Rate: \(-1.85^\circ\text{F}\) per hour for \(7.2\) hours.

Expression: \( (-1.85) \times 7.2 \)

\( 185 \times 72 = 13{,}320 \)
3 decimal places: \( 13.320 \)

Change: −13.32°F

(net drop of 13.32°F)

5

Error Analysis Solution (4 Points)

Marcus solved: \( (-3.4) \times (-2.15) = -73.1 \)

A) Marcus's Two Errors (2 Pts):

• Sign Error: Two negatives multiplied make a positive product. Marcus wrote a negative.
• Place Value Error: Total decimal places is 3 (1 in 3.4 + 2 in 2.15). Marcus placed only 1 decimal point instead of 3 (\(7.310\)).

B) Correct Calculation (2 Pts):

\( 215 \times 34 = 7{,}310 \)
Shift decimal 3 places left: \( 7.310 = 7.31 \)

Correct Product: +7.31

Signed Decimals Answer Key • Indiana 7.C.6 & 7.C.7 Page 2 of 2

Player 1 Target Round 1

\( (-0.8) \times (-7.5) \)

1. Call Sign (+1 pt): Positive (+)

2. Decimal Places (+1 pt): 2 places

3. Final Product (+2 pts): ?

Player 2 Target Round 1

\( 3.2 \times (-0.45) \)

1. Call Sign (+1 pt): Negative (−)

2. Decimal Places (+1 pt): 3 places

3. Final Product (+2 pts): ?

Game Rules: First to lock the sign shouts “SIGN!” (+1 pt). Multiply on whiteboard; reveal products simultaneously (+2 pts)!

Real-World Modeling • Indiana 7.C.6

Contextual Problem Solving

Oceanographic Exploration

An ocean research submersible descends at a constant rate of −4.5 meters each minute.

What is the submersible's change in depth after 6.2 minutes of continuous descent?

1. Algebraic Expression

\( (-4.5) \times 6.2 \)

2. Computation

• \( 45 \times 62 = 2{,}790 \)

• 1 place + 1 place = 2 decimal places

• \( 2{,}790 \rightarrow 27.90 = 27.9 \)

3. Contextual Answer with Units

−27.9 meters (27.9 meters below the surface)

Always verify that the sign makes sense: descending or losing money requires a negative answer!

Math Detective • Spot the Common Pitfall

Error Alert

Common Student Mistake Incorrect

\( (-0.4) \times (-0.2) \)

≠ 0.8   or   −0.08

Why does this happen? Students forget to insert a placeholder zero, or they mistakenly copy the negative sign into the answer!

The Correct Method Accurate

\( 4 \times 2 = 8 \) • Need 2 decimal places

+0.08

Leading Zero Rule: When the digits in your product are fewer than the required decimal places, insert zeros to the left of your product!

Remember: \( 2 \) decimal places means two digits behind the decimal point: 0.08!

Your Turn to Shine

Classroom Activities

Showdown Checklist

1. Sign

Determine (+) or (−) first before writing anything else.

2. Digits

Count every decimal digit across both factors accurately.

3. Units

Attach dollars, meters, or degrees for real-world scenarios.

Ready for the Decimal Duel Game Activity and practice worksheet!

Signed Decimal Showdown Indiana Academic Standards 7.C.6 & 7.C.7

Player 2 Turns (O) Verify each step

Turn 1: Factor A × Factor B [ ] +  [ ] −

Claim: ________ [   ] P1 Verified

Turn 2: Factor A × Factor B [ ] +  [ ] −

Claim: ________ [   ] P1 Verified

Turn 3: Factor A × Factor B [ ] +  [ ] −

Claim: ________ [   ] P1 Verified

Turn 4: Factor A × Factor B [ ] +  [ ] −

Claim: ________ [   ] P1 Verified

Turn 5: Factor A × Factor B [ ] +  [ ] −

Claim: ________ [   ] P1 Verified

Turn 6: Factor A × Factor B [ ] +  [ ] −

Claim: ________ [   ] P1 Verified

Sudden Death Grand Champion Tiebreaker Challenge

If grid ends in a draw

Both players race to solve this multi-factor expression: \( (-1.5) \times (-2.4) \times (-3.5) \). First to provide the correct signed decimal product wins!

Player 1 Tiebreaker Work:

Product:

Player 2 Tiebreaker Work:

Product:

Decimal Duel Activity • Indiana Standards 7.C.6 & 7.C.7 Page 2 of 2