Official Sensei Score
____ / 10
[ ] Pass (≥ 80%) [ ] Retest
Student: Date:
Multiply outside by all inside terms • 8/10 to earn belt
1. Expand: \(5(3x + 7)\)
Answer:
2. Expand: \(7(4y - 6)\)
Answer:
3. Expand: \(-4(3a + 8)\)
Answer:
4. Expand: \(-6(2m - 5)\)
Answer:
5. Expand: \(8(-x + 9)\)
Answer:
6. Expand: \(-(7p - 12)\)
Answer:
7. Expand: \(-3(-8k - 6)\)
Answer:
8. Expand: \(4(5w - 3v + 6)\)
Answer:
9. Expand: \(-5(4x - 2y - 7)\)
Answer:
10. Expand: \(6(-3a + 5b - 2)\)
Answer:
Official Karate Math Mastery Test • Level 3 (Green Belt) Advance to Blue Belt upon 80% score
🥋
Official Belt Test
Standard 7.EE.A.1 • Distributive Property with Rational Numbers
Official Sensei Score
____ / 10
[ ] Pass (≥ 80%) [ ] Retest
Student: Date:
Fractions and decimals • 8/10 required to earn belt
1. Expand: \(\frac{1}{2}(10x - 14)\)
Answer:
2. Expand: \(\frac{1}{3}(15y + 21)\)
Answer:
3. Expand: \(\frac{3}{4}(16a - 20)\)
Answer:
4. Expand: \(0.5(8m + 12)\)
Answer:
5. Expand: \(0.3(10p - 20)\)
Answer:
6. Expand: \(-\frac{1}{4}(24k - 16)\)
Answer:
7. Expand: \(2.5(4w - 8)\)
Answer:
8. Expand: \(-\frac{2}{5}(15x + 35)\)
Answer:
9. Simplify: \(0.4(15n + 10) - 0.5(8n - 4)\)
Answer:
10. Simplify: \(\frac{1}{4}(8x - 12) + \frac{1}{3}(9x + 6)\)
Answer:
Official Karate Math Mastery Test • Level 4 (Blue Belt) Advance to Red Belt upon 80% score
🥋
Official Belt Test
Standard 7.EE.A.1 • Subtracting Linear Expressions
Official Sensei Score
____ / 10
[ ] Pass (≥ 80%) [ ] Retest
Student: Date:
Distribute the negative sign carefully • 8/10 to earn belt
1. Simplify: \((6x + 9) - (4x + 2)\)
Answer:
2. Simplify: \((8y - 5) - (3y + 7)\)
Answer:
3. Simplify: \((5a + 4) - (11a - 6)\)
Answer:
4. Simplify: \((-6m - 4) - (2m - 10)\)
Answer:
5. Simplify: \((12p - 8) - (-5p + 3)\)
Answer:
6. Simplify: \((-9k + 6) - (-4k - 8)\)
Answer:
7. Simplify: \((7x - 9y + 5) - (3x + 4y - 8)\)
Answer:
8. Simplify: \((5a - 6) - (9a - 2) + (4a - 5)\)
Answer:
9. Simplify: \((10w + 7) - 3(2w - 5)\)
Answer:
10. Simplify: \(4(3x - 2) - (8x - 11)\)
Answer:
Official Karate Math Mastery Test • Level 5 (Red Belt) Advance to Black Belt upon 80% score
🥋
Grandmaster Test
Standard 7.EE.A.1 • Comprehensive Multi-Step Linear Expressions
Official Sensei Score
____ / 10
[ ] Black Belt Master [ ] Retrain
Student: Date:
The Ultimate Challenge • Score 8/10 to earn your Black Belt!
1. Simplify: \(4(3x - 4) + 3(2x + 9)\)
Answer:
2. Simplify: \(6(2a - 5) - 3(4a - 3)\)
Answer:
3. Simplify: \(-3(4m + 5) - 2(3m - 8)\)
Answer:
4. Simplify: \(\frac{1}{3}(9x - 15) + 4(3x + 2)\)
Answer:
5. Simplify: \(0.6(5y - 15) - (3y - 12)\)
Answer:
6. Simplify: \(5(2p - 3q + 2) - 3(4p + 2q - 5)\)
Answer:
7. Simplify: \(\frac{3}{4}(8k - 12) - \frac{1}{2}(6k + 10) + 4k\)
Answer:
8. Simplify: \(-(5x - 9) + 4(2x - 3) - 3(x + 4)\)
Answer:
9. Simplify: \(0.4(10w - 5) - 1.5(4w - 6) + 3w\)
Answer:
10. Simplify: \(18 - 3(2x - 5) - 4(x + 3)\)
Answer:
Official Karate Math Mastery Test • Level 6 (Black Belt) Final Rank: Expression Grandmaster
Step: \((12w - 15w) + (-5v + 8v)\)
Answer: \(-3w + 3v\)
Problem 8: \(-4x + 9 - 6x - 15 + 2x\)
Step: \((-4x - 6x + 2x) + (9 - 15)\)
Answer: \(-8x - 6\)
Problem 9: \(7n - 3 - 11n + 8 - 2n\)
Step: \((7n - 11n - 2n) + (-3 + 8)\)
Answer: \(-6n + 5\)
Problem 10: \(-9a + 4b - 6 - 3a - 7b + 11\)
Step: \((-9a - 3a) + (4b - 7b) + (-6 + 11)\)
Answer: \(-12a - 3b + 5\)
Teacher Guide • Karate Math Yellow Belt Page 2 of 6
Teacher Key
Karate Math Challenge • Full Solutions
Skill: Expanding Expressions Using Distributive Property Remind students that multiplying a negative by a negative results in a positive!
Problem 1: \(4(2x + 5)\)
Step: \(4 \cdot 2x + 4 \cdot 5\)
Answer: \(8x + 20\)
Problem 2: \(6(3y - 4)\)
Step: \(6 \cdot 3y - 6 \cdot 4\)
Answer: \(18y - 24\)
Problem 3: \(-3(4a + 7)\)
Step: \(-3 \cdot 4a + (-3) \cdot 7\)
Answer: \(-12a - 21\)
Problem 4: \(-5(2m - 6)\)
Step: \(-5 \cdot 2m - (-5) \cdot 6\)
Answer: \(-10m + 30\)
Problem 5: \(7(x - 8)\)
Step: \(7 \cdot x - 7 \cdot 8\)
Answer: \(7x - 56\)
Problem 6: \(-(5p + 9)\)
Step: \(-1 \cdot 5p + (-1) \cdot 9\)
Answer: \(-5p - 9\)
Problem 7: \(-2(-6k - 4)\)
Step: \(-2 \cdot (-6k) - (-2) \cdot 4\)
Answer: \(12k + 8\)
Problem 8: \(8(3w - 2v + 4)\)
Step: \(8 \cdot 3w - 8 \cdot 2v + 8 \cdot 4\)
Answer: \(24w - 16v + 32\)
Problem 9: \(-4(2x - 5y - 3)\)
Step: \(-4(2x) - (-4)(5y) - (-4)(3)\)
Answer: \(-8x + 20y + 12\)
Problem 10: \(9(-2a + 3b - 1)\)
Step: \(9(-2a) + 9(3b) - 9(1)\)
Answer: \(-18a + 27b - 9\)
Teacher Guide • Karate Math Green Belt Page 3 of 6
Teacher Key
Karate Math Challenge • Full Solutions
Skill: Distributive Property with Rational Numbers Support students in simplifying fractions by dividing denominators first!
Problem 1: \(\frac{1}{2}(6x + 10)\)
Step: \(\frac{6}{2}x + \frac{10}{2}\)
Answer: \(3x + 5\)
Problem 2: \(\frac{1}{4}(12y - 16)\)
Step: \(\frac{12}{4}y - \frac{16}{4}\)
Answer: \(3y - 4\)
Problem 3: \(\frac{2}{3}(9a + 15)\)
Step: \(2(3a) + 2(5)\)
Answer: \(6a + 10\)
Problem 4: \(0.4(5m - 10)\)
Step: \(0.4 \cdot 5m - 0.4 \cdot 10\)
Answer: \(2m - 4\)
Problem 5: \(0.25(8p + 20)\)
Step: \(\frac{1}{4}(8p + 20) = 2p + 5\)
Answer: \(2p + 5\)
Problem 6: \(-\frac{1}{5}(15k - 25)\)
Step: \(-\frac{15}{5}k - (-\frac{25}{5})\)
Answer: \(-3k + 5\)
Problem 7: \(1.5(4w - 6)\)
Step: \(1.5 \cdot 4w - 1.5 \cdot 6\)
Answer: \(6w - 9\)
Problem 8: \(-\frac{3}{4}(8x - 12)\)
Step: \(-3(2x) - (-3)(3)\)
Answer: \(-6x + 9\)
Problem 9: \(0.6(10n + 5) - 0.2(15n - 10)\)
Step: \((6n + 3) - (3n - 2) = 6n + 3 - 3n + 2\)
Answer: \(3n + 5\)
Problem 10: \(\frac{1}{3}(6x - 9) + \frac{1}{2}(4x + 8)\)
Step: \((2x - 3) + (2x + 4)\)
Answer: \(4x + 1\)
Teacher Guide • Karate Math Blue Belt Page 4 of 6
Teacher Key
Karate Math Challenge • Full Solutions
Skill: Subtracting Linear Expressions Ensure students distribute \(-1\) to ALL terms inside the second set of parentheses!
Problem 1: \((5x + 8) - (2x + 3)\)
Step: \(5x + 8 - 2x - 3\)
Answer: \(3x + 5\)
Problem 2: \((7y - 4) - (3y + 6)\)
Step: \(7y - 4 - 3y - 6\)
Answer: \(4y - 10\)
Problem 3: \((4a + 9) - (9a - 2)\)
Step: \(4a + 9 - 9a + 2\)
Answer: \(-5a + 11\)
Problem 4: \((-3m - 7) - (5m - 11)\)
Step: \(-3m - 7 - 5m + 11\)
Answer: \(-8m + 4\)
Problem 5: \((10p - 6) - (-4p + 8)\)
Step: \(10p - 6 + 4p - 8\)
Answer: \(14p - 14\)
Problem 6: \((-8k + 3) - (-2k - 9)\)
Step: \(-8k + 3 + 2k + 9\)
Answer: \(-6k + 12\)
Problem 7: \((6x - 12y + 4) - (2x + 5y - 7)\)
Step: \(6x - 12y + 4 - 2x - 5y + 7\)
Answer: \(4x - 17y + 11\)
Problem 8: \((3a - 8) - (7a - 5) + (2a - 4)\)
Step: \(3a - 8 - 7a + 5 + 2a - 4\)
Answer: \(-2a - 7\)
Problem 9: \((9w + 5) - 2(3w - 4)\)
Step: \(9w + 5 - 6w + 8\)
Answer: \(3w + 13\)
Problem 10: \(3(2x - 4) - (5x - 9)\)
Step: \(6x - 12 - 5x + 9\)
Answer: \(x - 3\)
Teacher Guide • Karate Math Red Belt Page 5 of 6
Teacher Key
Karate Math Challenge • Grandmaster Solutions
Mastery Skill: Multi-Step Linear Expressions (All Techniques) Stress systematic multi-step layout to avoid arithmetic errors!
Problem 1: \(3(4x - 5) + 2(6x + 7)\)
Step: \(12x - 15 + 12x + 14\)
Answer: \(24x - 1\)
Problem 2: \(5(2a - 3) - 4(3a - 1)\)
Step: \(10a - 15 - 12a + 4\)
Answer: \(-2a - 11\)
Problem 3: \(-2(5m + 4) - 3(2m - 7)\)
Step: \(-10m - 8 - 6m + 21\)
Answer: \(-16m + 13\)
Problem 4: \(\frac{1}{2}(8x - 14) + 3(2x + 5)\)
Step: \(4x - 7 + 6x + 15\)
Answer: \(10x + 8\)
Problem 5: \(0.8(5y - 10) - (2y - 15)\)
Step: \(4y - 8 - 2y + 15\)
Answer: \(2y + 7\)
Problem 6: \(4(3p - 2q + 1) - 2(5p + 3q - 4)\)
Step: \(12p - 8q + 4 - 10p - 6q + 8\)
Answer: \(2p - 14q + 12\)
Problem 7: \(\frac{2}{3}(6k - 9) - \frac{1}{4}(12k + 16) + 5k\)
Step: \((4k - 6) - (3k + 4) + 5k = 4k - 6 - 3k - 4 + 5k\)
Answer: \(6k - 10\)
Problem 8: \(-(4x - 7) + 3(2x - 5) - 2(x + 3)\)
Step: \(-4x + 7 + 6x - 15 - 2x - 6 = 0x - 14\)
Answer: \(-14\)
Problem 9: \(0.5(10w - 6) - 1.2(5w - 10) + 4w\)
Step: \(5w - 3 - 6w + 12 + 4w\)
Answer: \(3w + 9\)
Problem 10: \(14 - 2(3x - 4) - 5(x + 2)\)
Step: \(14 - 6x + 8 - 5x - 10\)
Answer: \(-11x + 12\)
Teacher Guide • Karate Math Black Belt Page 6 of 6
3. \(-4(3a + 8)\)\(-12a - 32\)
4. \(-6(2m - 5)\)\(-12m + 30\)
5. \(8(-x + 9)\)\(-8x + 72\)
6. \(-(7p - 12)\)\(-7p + 12\)
7. \(-3(-8k - 6)\)\(24k + 18\)
8. \(4(5w - 3v + 6)\)\(20w - 12v + 24\)
9. \(-5(4x - 2y - 7)\)\(-20x + 10y + 35\)
10. \(6(-3a + 5b - 2)\)\(-18a + 30b - 12\)
Sensei Diagnostic: In #6, an answer of \(-7p - 12\) reveals the student forgot to distribute the negative to the second term. Reinforce that \(-(a - b) = -a + b\).
🥋 Level 4: Blue Belt Mastery Answers
Rational Coefficients (Fractions & Decimals)
1. \(\frac{1}{2}(10x - 14)\)\(5x - 7\)
2. \(\frac{1}{3}(15y + 21)\)\(5y + 7\)
3. \(\frac{3}{4}(16a - 20)\)\(12a - 15\)
4. \(0.5(8m + 12)\)\(4m + 6\)
5. \(0.3(10p - 20)\)\(3p - 6\)
6. \(-\frac{1}{4}(24k - 16)\)\(-6k + 4\)
7. \(2.5(4w - 8)\)\(10w - 20\)
8. \(-\frac{2}{5}(15x + 35)\)\(-6x - 14\)
9. \(0.4(15n + 10) - 0.5(8n - 4)\)\(2n + 6\)
10. \(\frac{1}{4}(8x - 12) + \frac{1}{3}(9x + 6)\)\(5x - 1\)
Sensei Diagnostic: In #9, note that \(0.4(10) = 4\) and \(-0.5(-4) = +2\), giving \(4 + 2 = 6\). Double signs with decimals are the most frequent student tripping point.
Advancement Rule: Blue belt holders have demonstrated mastery over fractions and decimal properties! Mastery Key • Part 2 of 3
Official Sensei Key
80% Mastery Threshold = 8/10 Correct
🥋 Level 5: Red Belt Mastery Answers
Subtracting Linear Expressions
1. \((6x + 9) - (4x + 2)\)\(2x + 7\)
2. \((8y - 5) - (3y + 7)\)\(5y - 12\)
3. \((5a + 4) - (11a - 6)\)\(-6a + 10\)
4. \((-6m - 4) - (2m - 10)\)\(-8m + 6\)
5. \((12p - 8) - (-5p + 3)\)\(17p - 11\)
6. \((-9k + 6) - (-4k - 8)\)\(-5k + 14\)
7. \((7x - 9y + 5) - (3x + 4y - 8)\)\(4x - 13y + 13\)
8. \((5a - 6) - (9a - 2) + (4a - 5)\)\(-9\)
9. \((10w + 7) - 3(2w - 5)\)\(4w + 22\)
10. \(4(3x - 2) - (8x - 11)\)\(4x + 3\)
🥋 Level 6: Black Belt Grandmaster Answers
All Multi-Step Skills Combined
1. \(4(3x - 4) + 3(2x + 9)\)\(18x + 11\)
2. \(6(2a - 5) - 3(4a - 3)\)\(-21\)
3. \(-3(4m + 5) - 2(3m - 8)\)\(-18m + 1\)
4. \(\frac{1}{3}(9x - 15) + 4(3x + 2)\)\(15x + 3\)
5. \(0.6(5y - 15) - (3y - 12)\)\(3\)
6. \(5(2p - 3q + 2) - 3(4p + 2q - 5)\)\(-2p - 21q + 25\)
7. \(\frac{3}{4}(8k - 12) - \frac{1}{2}(6k + 10) + 4k\)\(7k - 14\)
8. \(-(5x - 9) + 4(2x - 3) - 3(x + 4)\)\(-15\)
9. \(0.4(10w - 5) - 1.5(4w - 6) + 3w\)\(w + 7\)
10. \(18 - 3(2x - 5) - 4(x + 3)\)\(-10x + 21\)
Weekly Dojo Belt Promotion Ceremony Protocol (Classroom Implementation)
1. Weekly Belt Board Move: Every Friday, celebrate students scoring 8+/10 by moving their clothespin or name badge to the next belt color on the classroom wall tracker.
2. Re-Testing Dojo: Students scoring < 80% partner with a higher belt peer, complete targeted retraining, and attempt re-test without penalty.
3. Whole-Class Goal: As shown on Slide 5: when every student reaches Black Belt rank by year-end, award the official Master Dojo class celebration!
Official Mastery Key • Karate Math Dojo Page 3 of 3 (Complete Unit Key)
