A focused Grade 6 learning session for Dot Plots and Histograms using visual models, worked examples, strategy guidance, and a short mastery check.
Student goal: I can solve problems involving dot plots and histograms.
Dot Plots and Histograms means reading, creating, and explaining displays so data can answer real questions.
Question: The dot plot shows the number of books read by students last month. How many students read exactly \(3\) books?
Why it works: Count the dots above the number \(3\): there are \(4\) dots, so \(4\) students read exactly \(3\) books.
Answer: \(4\)
Question: The dot plot below shows the number of hours sixth graders spent doing homework in one week. What is the mode (most common value) of the data?
Answer: \(6\) hours
Question: A histogram shows the test scores for a class of 30 students, grouped into ranges. The bars show: \(0\)--\(10\) has height \(2\), \(11\)--\(20\) has height \(5\), \(21\)--\(30\) has height \(8\), and \(31\)--\(40\) has height \(15\). How many students scored between \(21\) and \(30\)?
Answer: \(8\) students
Question: The histogram below shows the height (in inches) of tomato plants after \(4\) weeks. How many plants are between \(18\) and \(24\) inches tall?
Why it works: The bar for the \(18\)--\(24\) inch range has a height of \(14\), representing the number of plants in that height range.
Answer: \(14\) plants
Dot Plots and Histograms becomes easier when students connect the question to a model, use clear steps, and explain why the answer fits.
Read the scale before reading the answer.
Use scratch paper. The explanation matters more than simply seeing whether the choice is correct.
The dot plot shows the number of books read by students last month. How many students read exactly \(3\) books?
Answer C: \(4\)
Count the dots above the number \(3\): there are \(4\) dots, so \(4\) students read exactly \(3\) books.
A dot plot displays the ages of people visiting an ice cream shop. The dot plot shows \(5\) people aged \(9\) years old, \(8\) people aged \(12\) years old, and \(3\) people aged \(15\) years old. How many total people are represented in the dot plot?
Answer A: \(16\)
Add the number of people at each age: \(5 + 8 + 3 = 16\) total people.
The dot plot below shows the number of hours sixth graders spent doing homework in one week. What is the mode (most common value) of the data?
Answer A: \(6\) hours
Count the dots stacked above each value. The tallest stack is at \(6\) hours with \(5\) dots, which is more than at any other value, so \(6\) hours is the mode.
A histogram shows the test scores for a class of 30 students, grouped into ranges. The bars show: \(0\)--\(10\) has height \(2\), \(11\)--\(20\) has height \(5\), \(21\)--\(30\) has height \(8\), and \(31\)--\(40\) has height \(15\). How many students scored between \(21\) and \(30\)?
Answer B: \(8\) students
The bar for the \(21\)--\(30\) range has a height of \(8\), which represents the frequency (number of students) in that range.
A dot plot shows the number of pencils in each student's pencil case. Which statement is true about the data?
Answer B: Most students have \(6\) pencils
The value \(6\) has the most dots (\(5\)), making it the mode. The other statements are false: only \(2\) have \(4\) pencils, and there are \(2\) with \(7\) pencils.
The histogram below shows the height (in inches) of tomato plants after \(4\) weeks. How many plants are between \(18\) and \(24\) inches tall?
Answer D: \(14\) plants
The bar for the \(18\)--\(24\) inch range has a height of \(14\), representing the number of plants in that height range.
A dot plot shows the number of goals scored by different soccer teams during a season. If the dot plot shows \(3\) teams scored \(5\) goals, \(2\) teams scored \(6\) goals, \(4\) teams scored \(7\) goals, and \(1\) team scored \(8\) goals, what is the total number of goals scored by all teams combined?
Answer A: \(63\) goals
Calculate: \((3 \times 5) + (2 \times 6) + (4 \times 7) + (1 \times 8) = 15 + 12 + 28 + 8 = 63\) goals.
Which histogram correctly represents a data set where the frequency is highest for the \(20\)--\(30\) range and lowest for the \(50\)--\(60\) range?
Answer A: This histogram is correct
The histogram shows the \(20\)--\(30\) range with frequency \(22\) (highest) and the \(50\)--\(60\) range with frequency \(4\) (lowest), matching the requirement.
A dot plot displays the test scores: \(70, 75, 75, 80, 80, 80, 85, 90\). What is the median score?
Answer B: \(80\)
Order the data: \(70, 75, 75, 80, 80, 80, 85, 90\). There are \(8\) values, so the median is the average of the \(4\)th and \(5\)th values. Both are \(80\), so the median is \(\frac{80+80}{2}=80\).
The histogram shows the number of hours per week teenagers spend on social media. How many teenagers spend between \(5\) and \(15\) hours per week?
Answer B: \(34\) teenagers
Add the frequencies for the \(5\)--\(10\) and \(10\)--\(15\) ranges: \(16 + 18 = 34\) teenagers.
A dot plot shows the number of siblings each student has. The distribution is: \(0\) siblings: \(2\) students; \(1\) sibling: \(5\) students; \(2\) siblings: \(6\) students; \(3\) siblings: \(4\) students; \(4\) siblings: \(3\) students. Which best describes the shape of this distribution?
Answer C: Skewed left
The data peaks around \(2\) siblings and has a longer tail extending to the left (toward \(0\) siblings). This is a left-skewed distribution.
