How does America say hello?

Oct 6, 2026 · Dustin Purdy | @MrPurdyMath | Original blog post

Overview

Nearly 1 in 4 people in the U.S. speak a language other than English at home. This data talk uses real 2024 Census data to bring that fact into the middle school math classroom. Students start with "What do you notice? What do you wonder?" and then use percents, ratios, and estimation to explore which languages Americans speak, how that changes from state to state, and what it means for fairness in their communities. The talk builds toward one closing question: Who is missing? Each slide plants a small seed for that question, so by the end students are ready to think about who the data leaves out and why that matters.

Grade level: 6–8

Time frame: 10 minutes 

(Short on time? Use Slides 1 and 2 and go straight to the closing question.)

Resources: Google Slides

CCLS alignment

• 6.RP.A.1 Use ratio language to describe a relationship between two quantities.

• 6.RP.A.3c Find a percent of a quantity as a rate per 100.

• 7.RP.A.3 Use proportional relationships to solve multistep ratio and percent problems.

• 7.EE.B.3 Assess the reasonableness of answers using mental computation and estimation.

• 6.SP.B.5 Summarize data in context, including how it was measured.

• 7.SP.A.1 Understand that a sample gives information about a population, and that inferences are valid only if the sample is representative.

• MP3 Construct viable arguments and critique the reasoning of others. MP4 Model with mathematics.

Math topics

• Percents as "out of 100"

• Part-to-whole relationships

• Ratios and proportional reasoning: scaling

• Multiplicative comparison: asking "about how many times bigger?" instead of "how much bigger?"

• Estimation and mental math: making reasonable estimates before calculating

• Reading data displays: interpreting a 10-by-10 grid and bar graphs

• Comparing data

• Samples and populations

Key vocabulary

• Percent

• Ratio

• Proportion

• Multiplicative comparison

• Data

• Survey

• Population

• Sample

• Representative sample

• Bias

Plan

On every slide, start with: "What do you notice? What do you wonder?" Give 30 seconds to think, 30 seconds to share with a partner, then take a few answers before asking the questions below. Record wonders on the board, since several will come back during the closing question.

Slide 1: If the US were 100 people (2 minutes)

• How many people out of 100 do not speak another language at home? How do you know without counting?

• If our class of 30 matched the country, about how many students would speak another language at home?

• Does 23 out of 100 seem higher, lower, or about right for our community? What makes you think so?

• This data counts people age 5 and older. Who isn't in these 100 squares?

Slide 2: Which languages?  (2 minutes)

• About how many times bigger is the Spanish bar than the Chinese bar?

• Why might one language be so much bigger than the others?

• What languages do you hear in your community that aren't shown on this graph?

• The last bar groups dozens of languages together. Whose languages are hidden inside "all other languages"?

Slide 3: It depends where you live  (2 minutes)

• California's percent is about how many times West Virginia's?

• Where do you think our state lands? Why?

• Could our town or county be very different from our state's number? What might cause that?

• What can a state average hide about smaller communities inside that state?

Slide 4: Speaking English "very well"  (2 minutes)

• Out of 100 people who speak another language at home, about how many speak English very well?

• What could make school, a doctor's visit, or voting easier for someone still learning English?

• People rated their own English on this survey. How might that affect the numbers?

Closing: Who is missing?  (2 minutes)

Ask: "Who is missing from this data?" Give students think time, then a partner share. Use the wonders on the board and the student responses from each slide to guide the discussion.

Ideas students may raise:

• Children under 5, who aren't counted

• People who speak languages grouped into "all other languages," including many Indigenous languages

• Smaller communities that state and national averages hide

• People who didn't respond to the survey, since the data comes from a sample, not a count of everyone

• Differences between how people rate their own English and how they actually use it

Optional Follow-up questions:

• Why does it matter if some groups are missing from data like this?

• Who in our community might be missing from this data? How could we find out more about them?

• If decisions about schools, hospitals, or voting materials are based on this data, who might be left out?

Assessment and extensions:

Formative assessment

• Exit ticket: "Write one thing this data tells us and one group it might be missing. Explain why that group matters."

• Math check: "If a school of 600 students matched the U.S. rate, about how many would speak another language at home? Show your reasoning." (About 138, since 600 × 0.23 = 138.)

Extensions

• Local data: Look up your county or school district in Census Table S1601 on data.census.gov and compare it with the national and state numbers.

• Sampling: Discuss how the American Community Survey picks households. Ask students how they would design a fair survey of their own school.

• Make a graph: Have students turn one slide's data into a different kind of graph and explain which one tells the story better.

• Take action: Students identify one place in their community, such as a school office, clinic, or library, and propose a way to make it more welcoming for people who speak other languages.

Source

U.S. Census Bureau, American Community Survey 2024 (language spoken at home, Table S1601 and detailed language tables), as compiled by USAFacts. "Very well" is how people rated themselves on the survey. These are survey estimates, not a count of every person.

What Can 126 Dots Tell Us About Peace?

Oct 10, 2026 · Dustin Purdy | @MrPurdyMath | Original blog post

Overview

Students see a grid of 126 dots, some filled and some empty, with no title or labels. Over three slow-reveal slides they count, find patterns and predict what the empty dots mean before learning that each dot is a year of the Nobel Peace Prize, and each empty dot is a year with no prize awarded. Students use fractions and percents to compare how often the prize went unawarded before and after 1973, then question what the data can and cannot tell us about peace.

Grade level: 6–8

Time frame: 40 minutes (Short on time? Skip the counting slide and the critical-thinking slide, and assign the closing question as homework, for a 25-minute version.)

Resources: Google Slides (Nobel Peace Prize slow-reveal data talk), chart paper or a whiteboard to record notices and wonders, calculators (optional)

CCLS alignment

• NY-6.RP.1: Understand the concept of a ratio and use ratio language to describe a relationship between two quantities (prize years to no-prize years).

• NY-6.RP.3c: Find a percent of a quantity as a rate per 100 (the percent of years with no prize).

• NY-7.RP.3: Use proportional relationships to solve multistep ratio and percent problems (comparing rates before and after 1973).

• NY-6.SP.1: Recognize a statistical question as one that anticipates variability in the data.

• NY-6.SP.5: Summarize numerical data sets in relation to their context, including the number of observations and how the attribute was measured.

• Mathematical Practices MP.3 (construct viable arguments) and MP.4 (model with mathematics).

Math topics

• Counting strategies and structure (rows of 10)

• Ratios and part-to-whole fractions

• Percents as a rate per 100

• Comparing rates across two time periods

• Reading and interpreting a data display

• Questioning what data measures and leaves out

Key vocabulary

• Data

• Data display

• Ratio

• Percent

• Rate

• Pattern

• Cluster

• Inclusive count (counting both endpoints, 1901 to 2026)

• Statistical question

Plan

1. Launch the routine (3 min, slides 1–2). Explain that a slow reveal shows data a little at a time. Set the norms: look quietly, share one notice and one wonder, and revise as new information appears. Post the stems "I notice…" and "I wonder…".

2. Reveal 1: notice and wonder (6 min, slide 3). Give one minute of silent think time, then take ideas from around the room. Record every idea without confirming or correcting it. Ask: "What could the filled and empty dots stand for?"

• Expected thinking: students notice the grid has rows of 10, the empty dots cluster near the top, and the bottom rows are all filled.

3. Reveal 1: count and look for structure (5 min, slide 4). Ask: "How many dots are there? How did you count?" Have two or three students share strategies.

• Look for: 12 full rows of 10, minus 1 at the start, plus 7 at the end = 126; or 13 rows of 10 = 130, minus 4 blanks = 126.

• Misconception: counting one dot at a time and losing track. Ask, "How could the rows help you?"

4. Reveal 2: each dot is a year (7 min, slide 5). Show the decade and digit labels and the ringed 2026 dot. Ask: "What year is the first dot? How many years does the grid show? Which decade has the most empty dots? When was the last empty dot?"

• Misconception: 2026 − 1901 = 125. Ask students to check with a smaller case, such as 2020 to 2026, to see why the count includes both ends (126).

• Expected answers: the 1940s have the most empty dots (5); the last empty dot is 1972; every year from 1973 on is filled.

5. Reveal 2: predict (4 min, slide 6). Ask: "What could the empty dots mean? What was happening in the world during the decades with the most gaps?" Turn and talk, then share a guess with one piece of evidence.

• Expected thinking: many students guess wars. Ask what evidence supports the guess (the 1910s and 1940s) and what does not (1972, the 1920s). Do not confirm yet.

6. Reveal 3: the answer (3 min, slide 7). Reveal the title: each filled dot is a year a Nobel Peace Prize was awarded, and each empty dot is a year with no prize. Share the totals (107 awarded, 19 not) and the 2026 laureate, Navi Pillay. Ask: "Which of your predictions held up?"

7. Do the math (6 min, slide 8). In pairs, students answer: "What fraction of years had no prize? About what percent? What percent of the 1940s had no prize? Compare the rate of empty years before 1973 with the rate since."

• Answers: 19/126 ≈ 15%; 1940s: 5 of 10 = 50%; 1901–1972: 19 of 72 ≈ 26%; 1973–2026: 0 of 54 = 0%.

8. Think about the data (3 min, slide 9). Ask: "Does an empty dot mean there was no peace? What does this chart actually measure? What does it leave out?"

• Key idea: the chart measures whether a committee awarded a prize, not whether the world was at peace. Some empty years match the World Wars; in others the committee chose not to award the prize.

9. Closing (3 min, slide 10). Pose the closing question and have students write their three numbers.

Closing: "If you could measure peace using only 3 numbers, what data would you want to know?" Students write their three numbers on the slide or a sticky note, then answer: "What is one thing your 3 numbers would miss?" Share two or three responses.

Assessment

Use this three-question exit ticket. During the talk, listen for students who use the rows of 10 to count, and for students who support a prediction with evidence from the grid.

1. From 1901 to 2026, how many years are there? Explain why the answer is not 125.

• Answer: 126. Both 1901 and 2026 are counted, so the count is 2026 − 1901 + 1.

2. The prize was not awarded in 19 of those years. About what percent of years had no Peace Prize?

• Answer: 19 ÷ 126 ≈ 0.15, or about 15%.

3. Name one thing this chart does not tell you about peace.

• Sample answers: whether wars were happening, who won, how many people shared a prize, or why the committee skipped a year.

Extensions

• Have students redraw the grid to show a different variable, such as individuals versus organizations, or the number of laureates who shared each prize.

• Ask students to find the longest run of empty years (5, from 1939 to 1943) and the longest run of filled years (54, from 1973 to 2026), then explain what each run might show.

• Have students research one of their three "peace numbers" and find a real data source for it.

• Build the same dot grid for another Nobel Prize category and compare the gaps.

Sources

• Nobel Prize facts, NobelPrize.org: the 19 years in which no Peace Prize was awarded.

• 2026 Nobel Peace Prize awarded to Navi Pillay, Al Jazeera, Oct 9, 2026.

• Navi Pillay, 2026, United Nations.