Explore · MATH-5B-C12-L03-OPEN
Build a line plot for [3, 4, 4, 5, 6, 6]. How many observations are at 4?
Singapore Math 5B · Original independent course
Line Plots
Watch for: Counting tick positions rather than X marks.. Explain what the quantities mean before calculating.
Opening task
Prerequisite check
Before instruction · MATH-5B-C12-L03-PREREQ
In the data 2, 2, 3, 4, how often does 2 occur?
Show worked answer (after attempting)
Answer: 2 times
Count both occurrences of 2.
Understand the idea
Construct and interpret line plots from numerical data with stated scale, including repeated observations. The essential earlier idea is: Earlier frequency graph reading and fractions.. The model below will always use the actual quantities from the worked problem. Check counting tick positions rather than x marks when you explain your answer.
Three worked examples
Worked example 1 · MATH-5B-C12-L03-Q01
Build a line plot for [2, 3, 3, 4, 5, 5]. How many observations are at 3?
Solution: 2 observations at 3
Count every entry once. 3 occurs 2 times among 6 observations. One cross represents one observation.
Worked example 2 · MATH-5B-C12-L03-Q02
Students record [1, 2, 2, 2, 4, 5] books. State the most frequent observation and its count.
Solution: 3 observations at 2
Count every entry once. 2 occurs 3 times among 6 observations. One cross represents one observation.
Worked example 3 · MATH-5B-C12-L03-Q03
Plot each value in [3, 3, 4, 4, 4, 6] with one × per data item. What is the frequency at 4?
Solution: 3 observations at 4
Count every entry once. 4 occurs 3 times among 6 observations. One cross represents one observation.
Check understanding
1 · MATH-5B-C12-L03-Q04
Build a line plot for [3, 4, 4, 5, 6, 6]. How many observations are at 4?
Show worked answer (after attempting)
Answer: 2 observations at 4
Count every entry once. 4 occurs 2 times among 6 observations. One cross represents one observation.
2 · MATH-5B-C12-L03-Q05
Students record [2, 3, 3, 3, 5, 6] books. State the most frequent observation and its count.
Show worked answer (after attempting)
Answer: 3 observations at 3
Count every entry once. 3 occurs 3 times among 6 observations. One cross represents one observation.
3 · MATH-5B-C12-L03-Q06
Plot each value in [4, 4, 5, 5, 5, 7] with one × per data item. What is the frequency at 5?
Show worked answer (after attempting)
Answer: 3 observations at 5
Count every entry once. 5 occurs 3 times among 6 observations. One cross represents one observation.
Guided practice
1 · MATH-5B-C12-L03-Q07
Build a line plot for [4, 5, 5, 6, 7, 7]. How many observations are at 5?
Show worked answer (after attempting)
Answer: 2 observations at 5
Count every entry once. 5 occurs 2 times among 6 observations. One cross represents one observation.
2 · MATH-5B-C12-L03-Q08
Students record [3, 4, 4, 4, 6, 7] books. State the most frequent observation and its count.
Show worked answer (after attempting)
Answer: 3 observations at 4
Count every entry once. 4 occurs 3 times among 6 observations. One cross represents one observation.
3 · MATH-5B-C12-L03-Q09
Plot each value in [5, 5, 6, 6, 6, 8] with one × per data item. What is the frequency at 6?
Show worked answer (after attempting)
Answer: 3 observations at 6
Count every entry once. 6 occurs 3 times among 6 observations. One cross represents one observation.
4 · MATH-5B-C12-L03-Q10
Build a line plot for [5, 6, 6, 7, 8, 8]. How many observations are at 6?
Show worked answer (after attempting)
Answer: 2 observations at 6
Count every entry once. 6 occurs 2 times among 6 observations. One cross represents one observation.
Independent practice
1 · MATH-5B-C12-L03-Q11
Students record [4, 5, 5, 5, 7, 8] books. State the most frequent observation and its count.
Show worked answer (after attempting)
Answer: 3 observations at 5
Count every entry once. 5 occurs 3 times among 6 observations. One cross represents one observation.
2 · MATH-5B-C12-L03-Q12
Plot each value in [6, 6, 7, 7, 7, 9] with one × per data item. What is the frequency at 7?
Show worked answer (after attempting)
Answer: 3 observations at 7
Count every entry once. 7 occurs 3 times among 6 observations. One cross represents one observation.
3 · MATH-5B-C12-L03-Q13
Build a line plot for [6, 7, 7, 8, 9, 9]. How many observations are at 7?
Show worked answer (after attempting)
Answer: 2 observations at 7
Count every entry once. 7 occurs 2 times among 6 observations. One cross represents one observation.
4 · MATH-5B-C12-L03-Q14
Students record [5, 6, 6, 6, 8, 9] books. State the most frequent observation and its count.
Show worked answer (after attempting)
Answer: 3 observations at 6
Count every entry once. 6 occurs 3 times among 6 observations. One cross represents one observation.
5 · MATH-5B-C12-L03-Q15
Plot each value in [7, 7, 8, 8, 8, 10] with one × per data item. What is the frequency at 8?
Show worked answer (after attempting)
Answer: 3 observations at 8
Count every entry once. 8 occurs 3 times among 6 observations. One cross represents one observation.
6 · MATH-5B-C12-L03-Q16
Build a line plot for [7, 8, 8, 9, 10, 10]. How many observations are at 8?
Show worked answer (after attempting)
Answer: 2 observations at 8
Count every entry once. 8 occurs 2 times among 6 observations. One cross represents one observation.
7 · MATH-5B-C12-L03-Q17
Students record [6, 7, 7, 7, 9, 10] books. State the most frequent observation and its count.
Show worked answer (after attempting)
Answer: 3 observations at 7
Count every entry once. 7 occurs 3 times among 6 observations. One cross represents one observation.
8 · MATH-5B-C12-L03-Q18
Plot each value in [8, 8, 9, 9, 9, 11] with one × per data item. What is the frequency at 9?
Show worked answer (after attempting)
Answer: 3 observations at 9
Count every entry once. 9 occurs 3 times among 6 observations. One cross represents one observation.
Challenge and error analysis
1 · MATH-5B-C12-L03-ERR1
The assigned question is: “Students record [9, 10, 10, 10, 12, 13] books. State the most frequent observation and its count.” A learner wrote: “I plotted the sample starting with 9 using one less mark than the actual number of observations; I stated 3.1 observations at 10.” 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: 3 observations at 10
The attempted reasoning or reported result does not satisfy the specified operation, units or geometric conditions. Correct mathematical result: 3 observations at 10. Recompute from the given data: Count every entry once. 10 occurs 3 times among 6 observations. One cross represents one observation.
2 · MATH-5B-C12-L03-ERR2
The assigned question is: “Plot each value in [11, 11, 12, 12, 12, 14] with one × per data item. What is the frequency at 12?” A learner wrote: “I plotted the sample starting with 11 using one less mark than the actual number of observations; I stated 4 observations at 12.” 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: 3 observations at 12
The attempted reasoning or reported result does not satisfy the specified operation, units or geometric conditions. Correct mathematical result: 3 observations at 12. Recompute from the given data: Count every entry once. 12 occurs 3 times among 6 observations. One cross represents one observation.
Exit check
Exit · MATH-5B-C12-L03-Q19
Build a line plot for [8, 9, 9, 10, 11, 11]. How many observations are at 9?
Show worked answer (after attempting)
Answer: 2 observations at 9
Count every entry once. 9 occurs 2 times among 6 observations. One cross represents one observation.