Grade 6 Mathematics · Unit 2: Understanding the World Around Us Through StatisticsStandard 6.DS.5

Lesson 2.22.2 Small Group · Group 1

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target With my small group, I can make and read a histogram to display data in intervals — one step at a time, with support.

Start hereWords for this lesson

Read each word before you begin. Say it out loud.

WordWhat it meansExample
HistogramSpanish: Histograma A bar graph that groups data into equal ranges. The bars touch. Bars that touch
FrequencySpanish: Frecuencia How many times a value shows up. Bar height shows the count
IntervalSpanish: Intervalo A range of numbers used to group data. 10-19 is one interval
DistributionSpanish: Distribución How the data is spread out. Tallest bar in the middle
VariabilitySpanish: Variabilidad How spread out the numbers are. Data in just 2 intervals = low variability. Data across 6 intervals = high variability
Frequency tableSpanish: Tabla de frecuencias A table that lists each interval and how many values fall in it. 10-19 . . . 3

How it worksWorked examplegrouping data into a frequency table

These numbers are not on your problems. The steps are. Follow them with your own numbers.

Seven plants grew these heights in cm: 61, 74, 88, 76, 63, 71, 79. Use ten-unit intervals.

  1. Choose equal intervals that cover the data with no gaps: 60-69, 70-79, 80-89.
  2. Tally each value into exactly one interval. 61 and 63 both land in 60-69.
  3. Count each interval. 60-69 holds two plants, 70-79 holds four, 80-89 holds one.
  4. Draw touching bars at those heights above the three interval labels.

Answer: The frequency table reads 60-69: 2, 70-79: 4, 80-89: 1, and the tallest bar is 70-79.

Now you trySame steps, your turn

The steps are the same as the worked example. The numbers are yours. Do the work.

Seven phone batteries held these charges: 34, 47, 31, 42, 38, 44, 49. Use ten-unit intervals.

  1. Write intervals that cover the data with no gaps: - and -
  2. Tally each value into exactly one interval, crossing it off as you go.
  3. Frequency of the lower interval: Frequency of the upper interval:
  4. Sketch two touching bars whose heights match those two counts.
Answer:frequency of each interval

Say it and write itSentence starters

Finish each sentence out loud with a partner. Then use them in your writing.

  • My intervals are wide and they do not .
  • The interval holds values.
  • The tallest bar is because .
  • The bars touch because the intervals .

Word bank histogramintervalfrequencytallyequaloverlapbarheightcounttouchdistributiondata

Watch outA common mistake

A common mistake in Display Data: Histograms is counting a boundary value in two intervals at once — for example, putting the value 10 in both the '0–9' bin and the '10–19' bin. Each data value belongs to exactly ONE interval. Before you submit, add up all your frequencies and check that the total matches the number of data values you started with.

Grade 6 Mathematics · Unit 2: Understanding the World Around Us Through StatisticsStandard 6.DS.5

Lesson 2.22.2 Small Group · Group 1

Group 1Supported practice

Mastery check☐ Exceeds☐ Meets target☐ Needs practice
Name Date Period

Learning target With my small group, I can make and read a histogram to display data in intervals — one step at a time, with support.

  1. 1Complete each step, then write the final answer.
    036912151821242730Scores
    Count the dots in each interval.

    Make a histogram of these 8 scores: 3, 9, 11, 14, 16, 18, 25, 28. Use intervals of 0–9, 10–19 and 20–29.

    1. 1How many values fall in 0–9?
    2. 2How many values fall in 10–19?
    3. 3How many values fall in 20–29?
    4. 4Which interval gets the tallest bar?
    Final answer:
  2. 2Complete each step, then write the final answer.
    012345620304050Jumps in one minuteNumber of students
    Now read the bars.

    A histogram shows how many jumps students made in one minute. 20–29 has 3 students, 30–39 has 6 students and 40–49 has 4 students.

    1. 1What does the height of the 30–39 bar tell you?
    2. 2How many students made 30 jumps or more?
    3. 3How many students are there in all?
    Final answer:
  3. 3Complete each step, then write the final answer.

    Data: 2, 5, 13, 16, 18, 21. Use intervals of 0–9, 10–19 and 20–29. What is the frequency of 10–19?

    Show your work

    Hint Frequency means how many values. Count the values from 10 to 19.

    Final answer:
  4. 4Complete each step, then write the final answer.

    Ten players scored these points per game: 4, 8, 12, 15, 17, 19, 22, 26, 31, 34. Use intervals of 0–9, 10–19, 20–29 and 30–39. How tall is the 10–19 bar?

    Show your work

    Hint The height of a bar is the number of values in its interval.

    Final answer:
  5. 5Complete each step, then write the final answer.
    0123450102030Plant height (cm)Number of plants

    A histogram shows plant heights in centimeters. 0–9 has 2 plants, 10–19 has 5 plants and 20–29 has 3 plants. How many plants are 10 centimeters or taller?

    Show your work

    Hint Find the bars that start at 10 or more. Add their heights.

    Final answer:
  6. 6Complete each step, then write the final answer.

    Kim makes a histogram of 4, 10, 15, 19, 20, 27. She says the 10–19 bar has a height of 4. She counted 10, 15, 19 and 20. What is the correct height?

    Show your work

    Hint Look at each value Kim counted. Is every one from 10 to 19?

    Final answer:

Explain your thinkingWhat does the height of a bar in a histogram tell you? Use the jump rope histogram to explain.

Sentence starter The height of the ___ bar is ___. · This means ___ students made ___ jumps.

How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help