Explore · MATH-5B-C14-L01-OPEN
4 markers cost $16. What is the cost per marker?
Great Inheritance Mathematics Term B · Original independent course
Finding the Rate
Watch for: Dropping the denominator unit or treating rate as ratio of same units.. Explain what the quantities mean before calculating.
Opening task
Prerequisite check
Before instruction · MATH-5B-C14-L01-PREREQ
Three identical pens cost $12. What is the cost per pen?
Show worked answer (after attempting)
Answer: $4/pen
12 dollars ÷ 3 pens = 4 dollars per pen.
Understand the idea
Define rate as a relationship between unlike units and compute a meaningful per-one-unit value. The essential earlier idea is: Chapter 13 ordered ratios and 5A division of quantities into equal groups.. The model below will always use the actual quantities from the worked problem. Check dropping the denominator unit or treating rate as ratio of same units when you explain your answer.
Three worked examples
Worked example 1 · MATH-5B-C14-L01-Q01
4 markers cost $12. What is the cost per marker?
Solution: $3/item
Divide dollars by item count: $12 ÷ 4 = $3 per item. Unit order matters.
Worked example 2 · MATH-5B-C14-L01-Q02
A shop charges $25 for 5 identical notebooks. Find dollars per notebook.
Solution: $5/item
Divide dollars by item count: $25 ÷ 5 = $5 per item. Unit order matters.
Worked example 3 · MATH-5B-C14-L01-Q03
Find and label the unit rate: $40 for 8 identical items.
Solution: $5/item
Divide dollars by item count: $40 ÷ 8 = $5 per item. Unit order matters.
Check understanding
1 · MATH-5B-C14-L01-Q04
4 markers cost $16. What is the cost per marker?
Show worked answer (after attempting)
Answer: $4/item
Divide dollars by item count: $16 ÷ 4 = $4 per item. Unit order matters.
2 · MATH-5B-C14-L01-Q05
A shop charges $30 for 5 identical notebooks. Find dollars per notebook.
Show worked answer (after attempting)
Answer: $6/item
Divide dollars by item count: $30 ÷ 5 = $6 per item. Unit order matters.
3 · MATH-5B-C14-L01-Q06
Find and label the unit rate: $48 for 8 identical items.
Show worked answer (after attempting)
Answer: $6/item
Divide dollars by item count: $48 ÷ 8 = $6 per item. Unit order matters.
Guided practice
1 · MATH-5B-C14-L01-Q07
4 markers cost $20. What is the cost per marker?
Show worked answer (after attempting)
Answer: $5/item
Divide dollars by item count: $20 ÷ 4 = $5 per item. Unit order matters.
2 · MATH-5B-C14-L01-Q08
A shop charges $35 for 5 identical notebooks. Find dollars per notebook.
Show worked answer (after attempting)
Answer: $7/item
Divide dollars by item count: $35 ÷ 5 = $7 per item. Unit order matters.
3 · MATH-5B-C14-L01-Q09
Find and label the unit rate: $56 for 8 identical items.
Show worked answer (after attempting)
Answer: $7/item
Divide dollars by item count: $56 ÷ 8 = $7 per item. Unit order matters.
4 · MATH-5B-C14-L01-Q10
4 markers cost $24. What is the cost per marker?
Show worked answer (after attempting)
Answer: $6/item
Divide dollars by item count: $24 ÷ 4 = $6 per item. Unit order matters.
Independent practice
1 · MATH-5B-C14-L01-Q11
A shop charges $40 for 5 identical notebooks. Find dollars per notebook.
Show worked answer (after attempting)
Answer: $8/item
Divide dollars by item count: $40 ÷ 5 = $8 per item. Unit order matters.
2 · MATH-5B-C14-L01-Q12
Find and label the unit rate: $64 for 8 identical items.
Show worked answer (after attempting)
Answer: $8/item
Divide dollars by item count: $64 ÷ 8 = $8 per item. Unit order matters.
3 · MATH-5B-C14-L01-Q13
4 markers cost $28. What is the cost per marker?
Show worked answer (after attempting)
Answer: $7/item
Divide dollars by item count: $28 ÷ 4 = $7 per item. Unit order matters.
4 · MATH-5B-C14-L01-Q14
A shop charges $45 for 5 identical notebooks. Find dollars per notebook.
Show worked answer (after attempting)
Answer: $9/item
Divide dollars by item count: $45 ÷ 5 = $9 per item. Unit order matters.
5 · MATH-5B-C14-L01-Q15
Find and label the unit rate: $72 for 8 identical items.
Show worked answer (after attempting)
Answer: $9/item
Divide dollars by item count: $72 ÷ 8 = $9 per item. Unit order matters.
6 · MATH-5B-C14-L01-Q16
4 markers cost $32. What is the cost per marker?
Show worked answer (after attempting)
Answer: $8/item
Divide dollars by item count: $32 ÷ 4 = $8 per item. Unit order matters.
7 · MATH-5B-C14-L01-Q17
A shop charges $50 for 5 identical notebooks. Find dollars per notebook.
Show worked answer (after attempting)
Answer: $10/item
Divide dollars by item count: $50 ÷ 5 = $10 per item. Unit order matters.
8 · MATH-5B-C14-L01-Q18
Find and label the unit rate: $80 for 8 identical items.
Show worked answer (after attempting)
Answer: $10/item
Divide dollars by item count: $80 ÷ 8 = $10 per item. Unit order matters.
Challenge and error analysis
1 · MATH-5B-C14-L01-ERR1
The assigned question is: “A shop charges $65 for 5 identical notebooks. Find dollars per notebook.” A learner wrote: “I reversed the dollars/item unit ratio for the total beginning with 65, and wrote $13.1/item.” 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: $13/item
The attempted reasoning or reported result does not satisfy the specified operation, units or geometric conditions. Correct mathematical result: $13/item. Recompute from the given data: Divide dollars by item count: $65 ÷ 5 = $13 per item. Unit order matters.
2 · MATH-5B-C14-L01-ERR2
The assigned question is: “Find and label the unit rate: $104 for 8 identical items.” A learner wrote: “I reversed the dollars/item unit ratio for the total beginning with 104, and wrote $14/item.” 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: $13/item
The attempted reasoning or reported result does not satisfy the specified operation, units or geometric conditions. Correct mathematical result: $13/item. Recompute from the given data: Divide dollars by item count: $104 ÷ 8 = $13 per item. Unit order matters.
Exit check
Exit · MATH-5B-C14-L01-Q19
4 markers cost $36. What is the cost per marker?
Show worked answer (after attempting)
Answer: $9/item
Divide dollars by item count: $36 ÷ 4 = $9 per item. Unit order matters.