2. Sample Wonders:
3. Distance from Zero Answers:
a. Distance of 3: 3 units
b. Distance of -3: 3 units
4. Similarity & Difference (3 & -3):
Similar: They are both the exact same distance (3 units) from zero.
Different: They are in opposite directions (one right, one left of 0).
5. Distance Duel (-4 vs 2):
-4 is farther from 0. Because -4 is 4 units away from zero, whereas 2 is only 2 units away. (4 > 2).
6. Twin Search:
Any matching positive/negative pairs, such as 5 and -5, or 2 and -2, etc.
Make a Prediction: What do mathematicians call these?
Acceptable: opposites, negative twins, mirror numbers, reverse numbers. Do not correct terminology yet, praise observations of "symmetry" or "opposites".
PAGE 4 ANSWER KEY: Readiness Check (Part 1) Diagnostic Fraction/Decimal Review (25 mins)
1. Simplify 12/18:
2 / 3
Divide numerator & denominator by GCF (6).
2. Equivalent of 3/5 with Denominator 20:
12 / 20
Multiply both by 4 (since 5 × 4 = 20).
3. Add: 2/3 + 1/4:
11 / 12
LCM of 3 and 4 is 12. Convert: 8/12 + 3/12 = 11/12.
4. Subtract: 5/6 - 1/3:
3 / 6 = 1 / 2
LCM is 6. Convert: 5/6 - 2/6 = 3/6. Simplifies to 1/2.
5. Mixed Numbers: 2 1/2 + 1 3/4:
4 1/4 (or 17/4)
Convert fractional parts: 2/4 + 3/4 = 5/4 = 1 1/4. Add whole numbers: 2 + 1 + 1 1/4 = 4 1/4.
6. Add decimals: 14.58 + 3.92:
18.50 (or 18.5)
7. Subtract decimals: 12.4 - 5.85:
6.55
Crucial step: line up decimal. 12.40 - 5.85 = 6.55.
7th Grade Math • Unit 1 Teacher Guide Page 2 of 4
Diagnostic & Reasoning
PAGE 5 ANSWER KEY: Readiness Check (Part 2) Diagnostic & Error Analysis (25 mins)
8. Compare: 0.45 > 0.405
0.45 can be written as 0.450. Since 450 thousandths is larger than 405 thousandths, 0.45 is larger.
9. Order: 1/10, 0.25, 1/2, 0.8
Decimal conversions: 0.1, 0.25, 0.5, 0.8. Order is clear once in decimal format.
10. Plot 1.75 on Number Line:
Point should be placed exactly halfway between 1.5 and 2.
11. Compare: 3/4 = 0.75
3/4 is equivalent to 75/100, which is exactly 0.75.
12. Distance: 1.2 to 2.5
Distance = 1.3
Subtract: 2.5 - 1.2 = 1.3 units.
13. Multiply: 24 × 1.5
36
14. Divide: 15.6 ÷ 3
5.2
15. Error Analysis (Leo's Work):
The Mistake: Leo added the numerators (1+1) and denominators (2+3) directly. This is a very common fraction misconception. You must find a common denominator before adding.
Correct Answer: 1/2 + 1/3 = 3/6 + 2/6 = 5/6.
PAGE 6 ANSWER KEY: Defend Your Answer Which One Doesn't Belong (10 mins)
Set 1: [4, 1/2, 8, 12] — Sample Defenses:
• 1/2: It is the only fraction (non-integer).
• 4: It is the only single-digit integer.
• 12: It is the only number that is not a power of 2 (or not a factor of 8).
Set 2: [3/4, 0.5, 5, 0] — Sample Defenses:
• 3/4: Only value written in fractional notation.
• 0.5: Only value written in decimal notation.
• 5: Only non-zero positive integer (not between 0 and 1).
• 0: Only number that represents "nothingness" (neither positive nor negative).
Set 3: [-3, 0, 3, 1.5] — Sample Defenses:
• -3: Only negative number.
• 0: Only number that has no positive or negative sign.
• 1.5: Only decimal / non-integer in the set.
7th Grade Math • Unit 1 Teacher Guide Page 3 of 4
Closing & Action Plan
PAGE 7 ANSWER KEY: What's the Relationship? Discovering Opposites (10 mins)
1. What is the SAME?
Answer: The numerals/digits are exactly the same (5, 2, 10, 1/2). Both have the same numerical size/absolute value.
2. What is DIFFERENT?
Answer: One has a negative sign (-) and the other is positive.
3. Location relative to 0 on a number line?
Answer: You walk the exact same distance (same number of steps), but in opposite directions (one to the right, one to the left).
4. What pattern do you notice?
Answer: Every positive number has a matching negative counterpart. They are balanced/mirrored around zero.
The Big Question:
Students are expected to describe the relationship as "mirrors", "opposites", "balanced", or "equal but opposite directions". This primes them beautifully for the concept of additive inverses tomorrow!
PAGE 8 ANSWER KEY: Before You Go… Exit Ticket (5 mins)
1. Classify -6: Integer, Rational Number.
2. Locate 1 3/4: Point plotted on the third quarter mark past 1 (between 1.5 and 2).
3. Distance Check: • 4 from 0: 4 units
• -4 from 0: 4 units
4. Relationship: They are opposites (equal distance from 0, in opposite directions).
📋 Action Plan: Using Today's Data for Tomorrow
• Rediness Check Analysis: Check Q3-Q5 for fraction fluency. If more than 50% of students struggle with common denominators, plan a 5-minute fraction warm-up for tomorrow.
• Opposites Setup: Use the student responses from Page 7 and Page 8 to kick off tomorrow's lesson. Write their "Big Question" descriptors on the board as anchor terms!
7th Grade Math • Unit 1 Teacher Guide Page 4 of 4
