Explore · MATH-5B-C13-L01-OPEN
There are 4 blue beads and 6 gold beads. Write blue:gold.
Great Inheritance Mathematics Term B · Original independent course
Finding the Ratio
Watch for: Treating 3:2 as interchangeable with 2:3.. Explain what the quantities mean before calculating.
Opening task
Prerequisite check
Before instruction · MATH-5B-C13-L01-PREREQ
There are 2 red and 3 blue counters. Write red:blue.
Show worked answer (after attempting)
Answer: 2:3
Put the named red count before the blue count.
Understand the idea
Compare two quantities multiplicatively in ordered form a:b and explain which quantity comes first. The essential earlier idea is: 5A fractions and multiplicative comparisons.. The model below will always use the actual quantities from the worked problem. Check treating 3:2 as interchangeable with 2:3 when you explain your answer.
Three worked examples
Worked example 1 · MATH-5B-C13-L01-Q01
There are 3 blue beads and 5 gold beads. Write blue:gold.
Solution: 3:5
Name the quantities in the stated order. For blue:gold write 3:5; for gold:blue write 5:3. Ratios are multiplicative comparisons.
Worked example 2 · MATH-5B-C13-L01-Q02
Compare 4 blue and 7 gold pencils by an ordered ratio.
Solution: 4:7
Name the quantities in the stated order. For blue:gold write 4:7; for gold:blue write 7:4. Ratios are multiplicative comparisons.
Worked example 3 · MATH-5B-C13-L01-Q03
Write the ratio gold:blue for 6 blue and 8 gold counters; explain the order.
Solution: 8:6
Name the quantities in the stated order. For blue:gold write 6:8; for gold:blue write 8:6. Ratios are multiplicative comparisons.
Check understanding
1 · MATH-5B-C13-L01-Q04
There are 4 blue beads and 6 gold beads. Write blue:gold.
Show worked answer (after attempting)
Answer: 4:6
Name the quantities in the stated order. For blue:gold write 4:6; for gold:blue write 6:4. Ratios are multiplicative comparisons.
2 · MATH-5B-C13-L01-Q05
Compare 5 blue and 8 gold pencils by an ordered ratio.
Show worked answer (after attempting)
Answer: 5:8
Name the quantities in the stated order. For blue:gold write 5:8; for gold:blue write 8:5. Ratios are multiplicative comparisons.
3 · MATH-5B-C13-L01-Q06
Write the ratio gold:blue for 7 blue and 9 gold counters; explain the order.
Show worked answer (after attempting)
Answer: 9:7
Name the quantities in the stated order. For blue:gold write 7:9; for gold:blue write 9:7. Ratios are multiplicative comparisons.
Guided practice
1 · MATH-5B-C13-L01-Q07
There are 5 blue beads and 7 gold beads. Write blue:gold.
Show worked answer (after attempting)
Answer: 5:7
Name the quantities in the stated order. For blue:gold write 5:7; for gold:blue write 7:5. Ratios are multiplicative comparisons.
2 · MATH-5B-C13-L01-Q08
Compare 6 blue and 9 gold pencils by an ordered ratio.
Show worked answer (after attempting)
Answer: 6:9
Name the quantities in the stated order. For blue:gold write 6:9; for gold:blue write 9:6. Ratios are multiplicative comparisons.
3 · MATH-5B-C13-L01-Q09
Write the ratio gold:blue for 8 blue and 10 gold counters; explain the order.
Show worked answer (after attempting)
Answer: 10:8
Name the quantities in the stated order. For blue:gold write 8:10; for gold:blue write 10:8. Ratios are multiplicative comparisons.
4 · MATH-5B-C13-L01-Q10
There are 6 blue beads and 8 gold beads. Write blue:gold.
Show worked answer (after attempting)
Answer: 6:8
Name the quantities in the stated order. For blue:gold write 6:8; for gold:blue write 8:6. Ratios are multiplicative comparisons.
Independent practice
1 · MATH-5B-C13-L01-Q11
Compare 7 blue and 10 gold pencils by an ordered ratio.
Show worked answer (after attempting)
Answer: 7:10
Name the quantities in the stated order. For blue:gold write 7:10; for gold:blue write 10:7. Ratios are multiplicative comparisons.
2 · MATH-5B-C13-L01-Q12
Write the ratio gold:blue for 9 blue and 11 gold counters; explain the order.
Show worked answer (after attempting)
Answer: 11:9
Name the quantities in the stated order. For blue:gold write 9:11; for gold:blue write 11:9. Ratios are multiplicative comparisons.
3 · MATH-5B-C13-L01-Q13
There are 7 blue beads and 9 gold beads. Write blue:gold.
Show worked answer (after attempting)
Answer: 7:9
Name the quantities in the stated order. For blue:gold write 7:9; for gold:blue write 9:7. Ratios are multiplicative comparisons.
4 · MATH-5B-C13-L01-Q14
Compare 8 blue and 11 gold pencils by an ordered ratio.
Show worked answer (after attempting)
Answer: 8:11
Name the quantities in the stated order. For blue:gold write 8:11; for gold:blue write 11:8. Ratios are multiplicative comparisons.
5 · MATH-5B-C13-L01-Q15
Write the ratio gold:blue for 10 blue and 12 gold counters; explain the order.
Show worked answer (after attempting)
Answer: 12:10
Name the quantities in the stated order. For blue:gold write 10:12; for gold:blue write 12:10. Ratios are multiplicative comparisons.
6 · MATH-5B-C13-L01-Q16
There are 8 blue beads and 10 gold beads. Write blue:gold.
Show worked answer (after attempting)
Answer: 8:10
Name the quantities in the stated order. For blue:gold write 8:10; for gold:blue write 10:8. Ratios are multiplicative comparisons.
7 · MATH-5B-C13-L01-Q17
Compare 9 blue and 12 gold pencils by an ordered ratio.
Show worked answer (after attempting)
Answer: 9:12
Name the quantities in the stated order. For blue:gold write 9:12; for gold:blue write 12:9. Ratios are multiplicative comparisons.
8 · MATH-5B-C13-L01-Q18
Write the ratio gold:blue for 11 blue and 13 gold counters; explain the order.
Show worked answer (after attempting)
Answer: 13:11
Name the quantities in the stated order. For blue:gold write 11:13; for gold:blue write 13:11. Ratios are multiplicative comparisons.
Challenge and error analysis
1 · MATH-5B-C13-L01-ERR1
The assigned question is: “Compare 12 blue and 15 gold pencils by an ordered ratio.” A learner wrote: “I put the categories in reverse order for the recorded amounts beginning with 12, and wrote 12.1:15.” 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: 12:15
The attempted reasoning or reported result does not satisfy the specified operation, units or geometric conditions. Correct mathematical result: 12:15. Recompute from the given data: Name the quantities in the stated order. For blue:gold write 12:15; for gold:blue write 15:12. Ratios are multiplicative comparisons.
2 · MATH-5B-C13-L01-ERR2
The assigned question is: “Write the ratio gold:blue for 14 blue and 16 gold counters; explain the order.” A learner wrote: “I put the categories in reverse order for the recorded amounts beginning with 14, and wrote 17:14.” 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: 16:14
The attempted reasoning or reported result does not satisfy the specified operation, units or geometric conditions. Correct mathematical result: 16:14. Recompute from the given data: Name the quantities in the stated order. For blue:gold write 14:16; for gold:blue write 16:14. Ratios are multiplicative comparisons.
Exit check
Exit · MATH-5B-C13-L01-Q19
There are 9 blue beads and 11 gold beads. Write blue:gold.
Show worked answer (after attempting)
Answer: 9:11
Name the quantities in the stated order. For blue:gold write 9:11; for gold:blue write 11:9. Ratios are multiplicative comparisons.