Explore · MATH-5B-C12-L02-OPEN
Four test scores average 11. Three are [7, 9, 12]. Find the fourth.
Great Inheritance Mathematics Term B · Original independent course
Average — Part 2
Watch for: Using the average as though it were the total.. Explain what the quantities mean before calculating.
Opening task
Prerequisite check
Before instruction · MATH-5B-C12-L02-PREREQ
Three scores total 27. What is their average?
Show worked answer (after attempting)
Answer: 9
Mean = total ÷ count = 27 ÷ 3 = 9.
Understand the idea
Find a missing value or unknown total from a stated average and count, explaining constraints. The essential earlier idea is: Chapter 12 L01 mean and algebraic reasoning from expressions.. The model below will always use the actual quantities from the worked problem. Check using the average as though it were the total when you explain your answer.
Three worked examples
Worked example 1 · MATH-5B-C12-L02-Q01
Four test scores average 10. Three are [7, 9, 12]. Find the fourth.
Solution: 12
Required total = 10 × 4 = 40. Known sum = 28. Missing = 40 − 28 = 12.
Worked example 2 · MATH-5B-C12-L02-Q02
Four readings average 11°. Three are [6, 11, 14]. Find the missing reading.
Solution: 13°
Required total = 11 × 4 = 44. Known sum = 31. Missing = 44 − 31 = 13.
Worked example 3 · MATH-5B-C12-L02-Q03
If four values have average 12, find a missing value when the others are [8, 12, 13]. Explain the total.
Solution: 15
Required total = 12 × 4 = 48. Known sum = 33. Missing = 48 − 33 = 15.
Check understanding
1 · MATH-5B-C12-L02-Q04
Four test scores average 11. Three are [7, 9, 12]. Find the fourth.
Show worked answer (after attempting)
Answer: 16
Required total = 11 × 4 = 44. Known sum = 28. Missing = 44 − 28 = 16.
2 · MATH-5B-C12-L02-Q05
Four readings average 12°. Three are [6, 11, 14]. Find the missing reading.
Show worked answer (after attempting)
Answer: 17°
Required total = 12 × 4 = 48. Known sum = 31. Missing = 48 − 31 = 17.
3 · MATH-5B-C12-L02-Q06
If four values have average 13, find a missing value when the others are [8, 12, 13]. Explain the total.
Show worked answer (after attempting)
Answer: 19
Required total = 13 × 4 = 52. Known sum = 33. Missing = 52 − 33 = 19.
Guided practice
1 · MATH-5B-C12-L02-Q07
Four test scores average 12. Three are [7, 9, 12]. Find the fourth.
Show worked answer (after attempting)
Answer: 20
Required total = 12 × 4 = 48. Known sum = 28. Missing = 48 − 28 = 20.
2 · MATH-5B-C12-L02-Q08
Four readings average 13°. Three are [6, 11, 14]. Find the missing reading.
Show worked answer (after attempting)
Answer: 21°
Required total = 13 × 4 = 52. Known sum = 31. Missing = 52 − 31 = 21.
3 · MATH-5B-C12-L02-Q09
If four values have average 14, find a missing value when the others are [8, 12, 13]. Explain the total.
Show worked answer (after attempting)
Answer: 23
Required total = 14 × 4 = 56. Known sum = 33. Missing = 56 − 33 = 23.
4 · MATH-5B-C12-L02-Q10
Four test scores average 13. Three are [7, 9, 12]. Find the fourth.
Show worked answer (after attempting)
Answer: 24
Required total = 13 × 4 = 52. Known sum = 28. Missing = 52 − 28 = 24.
Independent practice
1 · MATH-5B-C12-L02-Q11
Four readings average 14°. Three are [6, 11, 14]. Find the missing reading.
Show worked answer (after attempting)
Answer: 25°
Required total = 14 × 4 = 56. Known sum = 31. Missing = 56 − 31 = 25.
2 · MATH-5B-C12-L02-Q12
If four values have average 15, find a missing value when the others are [8, 12, 13]. Explain the total.
Show worked answer (after attempting)
Answer: 27
Required total = 15 × 4 = 60. Known sum = 33. Missing = 60 − 33 = 27.
3 · MATH-5B-C12-L02-Q13
Four test scores average 14. Three are [7, 9, 12]. Find the fourth.
Show worked answer (after attempting)
Answer: 28
Required total = 14 × 4 = 56. Known sum = 28. Missing = 56 − 28 = 28.
4 · MATH-5B-C12-L02-Q14
Four readings average 15°. Three are [6, 11, 14]. Find the missing reading.
Show worked answer (after attempting)
Answer: 29°
Required total = 15 × 4 = 60. Known sum = 31. Missing = 60 − 31 = 29.
5 · MATH-5B-C12-L02-Q15
If four values have average 16, find a missing value when the others are [8, 12, 13]. Explain the total.
Show worked answer (after attempting)
Answer: 31
Required total = 16 × 4 = 64. Known sum = 33. Missing = 64 − 33 = 31.
6 · MATH-5B-C12-L02-Q16
Four test scores average 15. Three are [7, 9, 12]. Find the fourth.
Show worked answer (after attempting)
Answer: 32
Required total = 15 × 4 = 60. Known sum = 28. Missing = 60 − 28 = 32.
7 · MATH-5B-C12-L02-Q17
Four readings average 16°. Three are [6, 11, 14]. Find the missing reading.
Show worked answer (after attempting)
Answer: 33°
Required total = 16 × 4 = 64. Known sum = 31. Missing = 64 − 31 = 33.
8 · MATH-5B-C12-L02-Q18
If four values have average 17, find a missing value when the others are [8, 12, 13]. Explain the total.
Show worked answer (after attempting)
Answer: 35
Required total = 17 × 4 = 68. Known sum = 33. Missing = 68 − 33 = 35.
Challenge and error analysis
1 · MATH-5B-C12-L02-ERR1
The assigned question is: “Four readings average 19°. Three are [6, 11, 14]. Find the missing reading.” A learner wrote: “19 × 4 = 76.1. I used this intermediate value to finish the assigned problem.” Identify a concrete invalid step or assumption. Work out the correct result and explain why it is valid.
Show worked answer (after attempting)
Answer: Correct result: 45°
The attempted reasoning or reported result does not satisfy the specified operation, units or geometric conditions. Correct mathematical result: 45°. Recompute from the given data: Required total = 19 × 4 = 76. Known sum = 31. Missing = 76 − 31 = 45.
2 · MATH-5B-C12-L02-ERR2
The assigned question is: “If four values have average 20, find a missing value when the others are [8, 12, 13]. Explain the total.” A learner wrote: “20 × 4 = 81. I used this intermediate value to finish the assigned problem.” Identify a concrete invalid step or assumption. Work out the correct result and explain why it is valid.
Show worked answer (after attempting)
Answer: Correct result: 47
The attempted reasoning or reported result does not satisfy the specified operation, units or geometric conditions. Correct mathematical result: 47. Recompute from the given data: Required total = 20 × 4 = 80. Known sum = 33. Missing = 80 − 33 = 47.
Exit check
Exit · MATH-5B-C12-L02-Q19
Four test scores average 16. Three are [7, 9, 12]. Find the fourth.
Show worked answer (after attempting)
Answer: 36
Required total = 16 × 4 = 64. Known sum = 28. Missing = 64 − 28 = 36.