Neft Teacher · Notes Packet

Unit 8 · Standard 6.SP.4

Display Data: Histograms

Lesson 8-6

Name:Date:Class:

Key Vocabulary Level 1 support

Picture first, then the word, then a plain-language meaning. Say each word out loud.

Illustration of Histogram: A bar graph that groups data into equal ranges. The bars touch.

Bars side by side: 0-9 pts (3 players), 10-19 pts (8 players), 20-29 pts (4 players)

Histogram

A bar graph that groups data into equal ranges. The bars touch.

Illustration of Frequency: How many times a value shows up.

If 5 players scored 10-19 points, the frequency for that interval is 5

Frequency

How many times a value shows up.

Illustration of Interval: A range of numbers used to group data.

0-9, 10-19, 20-29 are intervals of width 10 — each covers 10 values

Interval

A range of numbers used to group data.

Illustration of Distribution: How the data is spread out.

Most data in the middle with fewer at the ends = bell-shaped; most on one side with a tail = skewed

Distribution

How the data is spread out.

Illustration of Data distribution: How the data looks: where it sits and how spread out it is.

A histogram that is tallest in the middle and shorter on both sides is symmetric

Data distribution

How the data looks: where it sits and how spread out it is.

Illustration of Variability: How spread out the numbers are.

Data in just 2 intervals = low variability. Data across 6 intervals = high variability

Variability

How spread out the numbers are.

Key Ideas & Notes

Think About It

  • Where do most of the scoring averages seem to cluster?
  • Are there many players at the very low or very high end?
  • How could you group these numbers to see a pattern?

My Notes

Guided Examples

Example 1

A histogram shows these frequencies: 0–4: 3 players, 5–9: 8 players, 10–14: 12 players, 15–19: 5 players. How many players are represented in total?

Solution: Add all frequencies: 3 + 8 + 12 + 5 = 28 players.

Answer: A. 28

Example 2

In a histogram, what does the height of each bar represent?

Solution: Each bar's height shows the frequency — how many data values fall within that interval.

Answer: A. The frequency (count) of data in that interval

Example 3

How is a histogram different from a regular bar graph?

Solution: In a histogram, bars touch because each interval connects to the next (0–9, 10–19, etc.) — the data is continuous.

Answer: A. Histogram bars touch (no gaps) because the intervals are continuous ranges

Write About the Math The Writing Revolution

I can explain my histogram using the words histogram, frequency, interval, and distribution.

1. Kernel Sentence subject + verb

Model: Histogram is a bar graph that groups data into equal ranges. The bars touch.Histograma es una gráfica de barras que agrupa datos en rangos iguales. Las barras se tocan.

Write a kernel sentence about histogram. Use a subject and a verb.Escribe una oración base sobre histograma. Usa un sujeto y un verbo.

2. Sentence Expansion because · but · so

Kernel: Histogram matters in mathHistograma importa en matemáticas

Expand the kernel three ways. Add a reason, a contrast, and a result.

becauseporque

Histogram matters in math because ___.Histograma importa en matemáticas porque ___.

butpero

Histogram matters in math, but ___.Histograma importa en matemáticas, pero ___.

soentonces

Histogram matters in math, so ___.Histograma importa en matemáticas, entonces ___.

3. Sentence Types 4 ways to write a math idea

StatementAfirmación

Tell one true fact about histogram.Di un hecho verdadero sobre histogram.

Histogram ___.

QuestionPregunta

Ask a question about histogram.Haz una pregunta sobre histogram.

How does ___ ?¿Cómo ___ ?

ExclamationExclamación

Show excitement about histogram.Muestra entusiasmo sobre histogram.

Wow, ___ !¡Guau, ___ !

CommandMandato

Tell a partner what to do with histogram.Dile a un compañero qué hacer con histogram.

First, ___ .Primero, ___ .

4. Explain Your Reasoning use a sentence starter

A histogram groups data into ___.Un histograma agrupa los datos en ___.

The tallest bar shows ___.La barra más alta muestra ___.

This helps when ___.Esto ayuda cuando ___.

Try It

Solve on your own. Check the answer key when you are done.

1. A histogram has intervals: 0–4, 5–9, 10–14, 15–19. What is the width of each interval?

  1. 5
  2. 4
  3. 10
  4. 19
Show your work:

2. A histogram of test scores shows: 50–59: 2, 60–69: 5, 70–79: 10, 80–89: 8, 90–99: 3. Which interval has the most students?

  1. 70–79 with 10 students
  2. 80–89 with 8 students
  3. 60–69 with 5 students
  4. 90–99 with 3 students
Show your work:

Stretch Your Thinking Level 2 enrichment

Challenge task — explain your reasoning in full sentences.

A teacher collected test scores and made two different histograms — one with intervals of 5 (50–54, 55–59, etc.) and one with intervals of 20 (50–69, 70–89, 90–109). Both use the same data. How might the two histograms look different? Which interval size gives you more detail about the distribution? When might the larger interval be better?

Sentence starter: The histogram with intervals of 5 would have ___ bars and show ___. The histogram with intervals of 20 would have ___ bars and show ___. Smaller intervals are better when ___, and larger intervals are better when ___.

Show your work:

Reflect — Exit Ticket

A histogram of player heights shows: 60–63 in: 2, 64–67 in: 7, 68–71 in: 9, 72–75 in: 4. Which interval has the most players?

  1. 68–71 inches
  2. 64–67 inches
  3. 72–75 inches
  4. 60–63 inches
Your answer:

Answer Key & Teacher Guide

  1. Try It 1: A. 5 — Each interval covers 5 values (0,1,2,3,4 then 5,6,7,8,9 etc.), so the width is 5.
  2. Try It 2: A. 70–79 with 10 students — The 70–79 interval has the highest frequency of 10 students.
  3. Exit Ticket: A. 68–71 inches — The 68–71 inch interval has the highest frequency of 9 players.

Writing (TWR) — what to look for