Explore · MATH-5B-C13-L05-OPEN
Blue:red = 3:4 and total counters = 49. Find blue counters.
Great Inheritance Mathematics Term B · Original independent course
Word Problems
Watch for: Treating additive comparisons as ratio comparisons.. Explain what the quantities mean before calculating.
Opening task
Prerequisite check
Before instruction · MATH-5B-C13-L05-PREREQ
Divide 20 counters in a 2:3 ratio. What is the first share?
Show worked answer (after attempting)
Answer: 8
Five total parts; each part is 4, so first share is 2×4 =8.
Understand the idea
Model multistep ratio word problems with clearly identified quantities, constraints and reasonableness checks. The essential earlier idea is: Ch13 L01–L04 and multiplicative reasoning.. The model below will always use the actual quantities from the worked problem. Check treating additive comparisons as ratio comparisons when you explain your answer.
Three worked examples
Worked example 1 · MATH-5B-C13-L05-Q01
Blue:red = 3:4 and total counters = 42. Find blue counters.
Solution: 18
Total parts = 7; one part = 42 ÷ 7 = 6. First share = 3 × 6 = 18; second = 24; check sum = 42.
Worked example 2 · MATH-5B-C13-L05-Q02
A team divides 49 tokens in the ratio 2:5. How many go to the first group?
Solution: 14
Total parts = 7; one part = 49 ÷ 7 = 7. First share = 2 × 7 = 14; second = 35; check sum = 49.
Worked example 3 · MATH-5B-C13-L05-Q03
Find the first share when 55 items are split in the ratio 4:7; verify both shares sum correctly.
Solution: 20
Total parts = 11; one part = 55 ÷ 11 = 5. First share = 4 × 5 = 20; second = 35; check sum = 55.
Check understanding
1 · MATH-5B-C13-L05-Q04
Blue:red = 3:4 and total counters = 49. Find blue counters.
Show worked answer (after attempting)
Answer: 21
Total parts = 7; one part = 49 ÷ 7 = 7. First share = 3 × 7 = 21; second = 28; check sum = 49.
2 · MATH-5B-C13-L05-Q05
A team divides 56 tokens in the ratio 2:5. How many go to the first group?
Show worked answer (after attempting)
Answer: 16
Total parts = 7; one part = 56 ÷ 7 = 8. First share = 2 × 8 = 16; second = 40; check sum = 56.
3 · MATH-5B-C13-L05-Q06
Find the first share when 66 items are split in the ratio 4:7; verify both shares sum correctly.
Show worked answer (after attempting)
Answer: 24
Total parts = 11; one part = 66 ÷ 11 = 6. First share = 4 × 6 = 24; second = 42; check sum = 66.
Guided practice
1 · MATH-5B-C13-L05-Q07
Blue:red = 3:4 and total counters = 56. Find blue counters.
Show worked answer (after attempting)
Answer: 24
Total parts = 7; one part = 56 ÷ 7 = 8. First share = 3 × 8 = 24; second = 32; check sum = 56.
2 · MATH-5B-C13-L05-Q08
A team divides 63 tokens in the ratio 2:5. How many go to the first group?
Show worked answer (after attempting)
Answer: 18
Total parts = 7; one part = 63 ÷ 7 = 9. First share = 2 × 9 = 18; second = 45; check sum = 63.
3 · MATH-5B-C13-L05-Q09
Find the first share when 77 items are split in the ratio 4:7; verify both shares sum correctly.
Show worked answer (after attempting)
Answer: 28
Total parts = 11; one part = 77 ÷ 11 = 7. First share = 4 × 7 = 28; second = 49; check sum = 77.
4 · MATH-5B-C13-L05-Q10
Blue:red = 3:4 and total counters = 63. Find blue counters.
Show worked answer (after attempting)
Answer: 27
Total parts = 7; one part = 63 ÷ 7 = 9. First share = 3 × 9 = 27; second = 36; check sum = 63.
Independent practice
1 · MATH-5B-C13-L05-Q11
A team divides 70 tokens in the ratio 2:5. How many go to the first group?
Show worked answer (after attempting)
Answer: 20
Total parts = 7; one part = 70 ÷ 7 = 10. First share = 2 × 10 = 20; second = 50; check sum = 70.
2 · MATH-5B-C13-L05-Q12
Find the first share when 88 items are split in the ratio 4:7; verify both shares sum correctly.
Show worked answer (after attempting)
Answer: 32
Total parts = 11; one part = 88 ÷ 11 = 8. First share = 4 × 8 = 32; second = 56; check sum = 88.
3 · MATH-5B-C13-L05-Q13
Blue:red = 3:4 and total counters = 70. Find blue counters.
Show worked answer (after attempting)
Answer: 30
Total parts = 7; one part = 70 ÷ 7 = 10. First share = 3 × 10 = 30; second = 40; check sum = 70.
4 · MATH-5B-C13-L05-Q14
A team divides 77 tokens in the ratio 2:5. How many go to the first group?
Show worked answer (after attempting)
Answer: 22
Total parts = 7; one part = 77 ÷ 7 = 11. First share = 2 × 11 = 22; second = 55; check sum = 77.
5 · MATH-5B-C13-L05-Q15
Find the first share when 99 items are split in the ratio 4:7; verify both shares sum correctly.
Show worked answer (after attempting)
Answer: 36
Total parts = 11; one part = 99 ÷ 11 = 9. First share = 4 × 9 = 36; second = 63; check sum = 99.
6 · MATH-5B-C13-L05-Q16
Blue:red = 3:4 and total counters = 77. Find blue counters.
Show worked answer (after attempting)
Answer: 33
Total parts = 7; one part = 77 ÷ 7 = 11. First share = 3 × 11 = 33; second = 44; check sum = 77.
7 · MATH-5B-C13-L05-Q17
A team divides 84 tokens in the ratio 2:5. How many go to the first group?
Show worked answer (after attempting)
Answer: 24
Total parts = 7; one part = 84 ÷ 7 = 12. First share = 2 × 12 = 24; second = 60; check sum = 84.
8 · MATH-5B-C13-L05-Q18
Find the first share when 110 items are split in the ratio 4:7; verify both shares sum correctly.
Show worked answer (after attempting)
Answer: 40
Total parts = 11; one part = 110 ÷ 11 = 10. First share = 4 × 10 = 40; second = 70; check sum = 110.
Challenge and error analysis
1 · MATH-5B-C13-L05-ERR1
The assigned question is: “A team divides 105 tokens in the ratio 2:5. How many go to the first group?” A learner wrote: “105 ÷ 7 = 15.1. 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: 30
The attempted reasoning or reported result does not satisfy the specified operation, units or geometric conditions. Correct mathematical result: 30. Recompute from the given data: Total parts = 7; one part = 105 ÷ 7 = 15. First share = 2 × 15 = 30; second = 75; check sum = 105.
2 · MATH-5B-C13-L05-ERR2
The assigned question is: “Find the first share when 143 items are split in the ratio 4:7; verify both shares sum correctly.” A learner wrote: “143 ÷ 11 = 14. 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: 52
The attempted reasoning or reported result does not satisfy the specified operation, units or geometric conditions. Correct mathematical result: 52. Recompute from the given data: Total parts = 11; one part = 143 ÷ 11 = 13. First share = 4 × 13 = 52; second = 91; check sum = 143.
Exit check
Exit · MATH-5B-C13-L05-Q19
Blue:red = 3:4 and total counters = 84. Find blue counters.
Show worked answer (after attempting)
Answer: 36
Total parts = 7; one part = 84 ÷ 7 = 12. First share = 3 × 12 = 36; second = 48; check sum = 84.