Updated: March 9, 2019
NOTE: Join us for our free webinar about teaching with graphs from The New York Times. Date: Wednesday, March 20 at 4 p.m. Eastern Time. Register here.
1. This graph shows the consumption of tobacco products by students, with e-cigarettes broken out separately, from 2011 to 2018. The graph originally appeared elsewhere on NYTimes.com.
After looking closely at the graph above (or at this full-size image), think about these three questions:
• What do you notice?• What do you wonder?What are you curious about that comes from what you notice in the graph?• What might be going on in this graph?Write a catchy headline that captures the graph’s main idea. If your headline makes a claim, tell us what you noticed that supports your claim.
The questions are intended to build on one another, so try to answer them in order. Start with “I notice,” then “I wonder,” and end with “The story this graph is telling is ….” and a catchy headline.
2. Next, join the conversation by clicking on the comment button and posting in the box that opens on the right. (Students 13 and older are invited to comment, although teachers of younger students are welcome to post what their students have to say or they can have their students use this same activity on Desmos.)
3. After you have posted, read what others have said, then respond to someone else by posting a comment. Use the “Reply” button or the @ symbol to address that student directly.
On Wednesday, March 6, our collaborator, the American Statistical Association, will facilitate this discussion from 9 a.m. to 2 p.m. Eastern Time to help students’ understanding go deeper. You might use their responses as models for your own.
4. On the afternoon of Thursday, March 7, we will reveal more information about the graph at the bottom of this post. Students, we encourage you to post an additional comment after reading the reveal. How does the original New York Times article and the moderators’ comments help you see the graph differently? Try to incorporate the statistical terms defined in the Stat Nuggets in your response.
• Read our introductory post, which includes information about using the “Notice and Wonder” teaching strategy.• Learn about how and why other teachers are using this feature, and use the 2018-19 “What’s Going On in This Graph?” calendar to plan ahead for the 25 Wednesday releases. • Go to the A.S.A. K-12 website, which includes This is Statistics, resources, professional development, student competitions, curriculum, courses and careers.
Updated: March 9, 2019
E-cigarettes were originally marketed as a method to help adults stop smoking. Vaping e-cigarettes (inhaling vaporized liquid or solid typically through a battery-operated electronic device) gives the smoker the stimulant of nicotine without the carcinogen tar. Before long, teenagers began vaping. More than 1 in 5 high school students and 1 in 20 middle school students reported to the Centers for Disease Control and Prevention (C.D.C.) that they vaped in the past 30 days. Major concerns about students vaping are that nicotine in e-cigarettes is more addictive to teens than to adults, the devices can be used for smoking marijuana, and those that vape are more likely to move on to smoking cigarettes with its deadly tar. The Food and Drug Administration announced in November that it plans to ban sales of most flavored e-cigarettes in retail stores.
This graph appeared in the New York Times article “F.D.A. Seeks Restrictions on Teens’ Access to Flavored E-Cigarettes and a Ban on Menthol Cigarettes.” What can be seen in the graph is that after years of tobacco consumption declining and then leveling off, we now see an increase in tobacco consumption and the increase is from e-cigarettes. To find answers to some of your medical questions on e-cigarettes, go to “Q & A: The ABCs of E-Cigarettes.”
Here are some of the student headlines that really capture the main ideas of this graph: “Smoking Tobacco... It’s Cool Again!” by Emma of McHenry, Illinois, “Tobacco Troubles” by Gage of California, “Tobacco Gets a New Disguise in E-Cigarettes!” by Adam of Chicago, and “Tobacco Products and E-Cigarettes Invade Schools” by Huggins’ 5th period class from Anacortes, Washington.
For the released graph, calculate the net difference between any tobacco products and e-cigarettes. This gives the percentage of students who smoke cigarettes and other tobacco products. Now, compare this to the percentage from this National Youth Risk Behavior Survey graph (PDF, page 11) which predates the New York Times graph. Combining what you notice from the two graphs, what do you conclude? What do you wonder?
■ This is the opening statement from the C.D.C. paper on Youth and Tobacco Use.
If cigarette smoking continues at the current rate among youth in this country, it is estimated that 5.6 million of today’s Americans younger than 18 will die early from a smoking-related illness. That’s about 1 of every 13 Americans aged 17 years or younger who are alive today.
There are about 327 million Americans and approximately 22.6% of these individuals are younger than 18.
• Approximately how many individuals are younger than 18 in the United States?
• Based upon the graph, approximately how many of those individuals consume tobacco?
• Research online the average daily cost of consuming tobacco. How much money are these individuals paying annually to consume tobacco?
■ Want to learn more about tobacco consumption by students? Go to the C.D.C.’s report from the National Youth Tobacco Survey. There, you will find a table of tobacco consumption by use. Using statistics from the table, write a question about something that you wonder about that can be answered from statistics in this table. Then, make a graph that can be used to answer your question. Share your question, graph, and conclusion with your class and compare your findings.
■ The Learning Network has a Student Opinion lesson “Do You Vape?” based on the Times article “I can’t Stop’: Schools Struggle With Vaping Explosion.” Students are asked to read the article and write their opinion about one of the five listed questions.
Below in the Stat Nuggets, we define and explain mathematical terms that apply to this graph. Look into the archives to see past Stat Nuggets.
Thank you for participating in “What’s Going On in This Graph?”, which is intended to help you think more critically about graphs and the underlying data. Critical thinking is an essential element of statistics, the science of learning from data. Data visualizations, like these graphs, are an important part of statistics. They help us to understand and learn from data.
Keep noticing and wondering. We continue to welcome your responses.
Join us Wednesday, March 13 to notice and wonder about the sources of electricity generation in the United States. We look forward to your responses between 9 a.m. - 2 p.m. Eastern Time during the live online moderation.
Stat Nuggets for “F.D.A. Seeks Restrictions on Teens’ Access to Flavored E-Cigarettes and a Ban on Menthol Cigarettes”
SLOPE & RATE OF CHANGE
The slope of a line on a graph is a number that describes the direction and the rate of change (steepness) of the line. A positive slope denotes an increase in the y-values as the x-value increases. The greater the positive slope the greater is the rate of change (steepness). Conversely, a negative slope denotes a decrease in the y-values as the x-value increases. A slope equal to zero denotes no change in value and the line is horizontal because there is no change in the y-values as the x-values increase.
In the e-cigarettes graph, there are line segments with positive, negative and zero slopes. For example, for any tobacco products, from 2011 to 2015, there is a slope of approximately zero because there is minimal change in the percentage of students consuming tobacco products over this time period. From 2015 to 2017, there is a negative slope, meaning the percentage of students consuming tobacco products decreased over this time period. But, in 2017, once e-cigarettes became popular, we see a positive slope, indicating an increase in consumption.
The net difference is calculated by subtracting one value from the other.
In the e-cigarette graph, the net difference attributable to tobacco products other than e-cigarettes is calculated by subtracting the percentage consuming e-cigarettes from the percentage consuming any tobacco product. This net difference gives the percentage of students that consume tobacco products other than e-cigarettes, such as cigarettes and cigars. Note that for 2017 – 2018 the net difference is constant, meaning all of the growth of tobacco consumption is from e-cigarettes.
The graphs for “What’s Going On in This Graph?” are selected in partnership with Sharon Hessney. Ms. Hessney with Erica Chauvet, a professor at Waynesburg University in Pennsylvania, wrote the “reveal” and moderated student responses.
看香港总彩开奖现场“【陈】【沐】【风】？！”【朱】【长】【生】【的】【瞳】【孔】【一】【缩】，【一】【眼】【便】【认】【出】【了】【眼】【前】【男】【子】【的】【身】【份】，【惊】【疑】【道】：“【呵】，【与】【虎】【为】【伴】【的】【你】，【终】【于】【自】【食】【恶】【果】【了】【吗】？” 【陈】【家】【被】【流】【放】【边】【疆】，【如】【果】【他】【们】【安】【安】【稳】【稳】，【不】【作】【妖】【的】【话】，【也】【能】【过】【上】【一】【些】【好】【日】【子】。【只】【可】【惜】，【陈】【沐】【风】【不】【识】【好】【歹】，【被】【内】【心】【的】【仇】【恨】【蒙】【蔽】【双】【眼】，【以】【至】【于】【让】【他】【找】【上】【欧】【阳】【家】。 【原】【以】【为】【可】【以】【借】【力】【东】【山】【再】【起】，
“【呼】……” 【缓】【缓】【吐】【出】【一】【口】【浊】【气】，【睁】【开】【眼】【睛】。 【唐】【星】【锋】【总】【算】【起】【了】【身】。 【眼】【下】【重】【伤】【之】【躯】，【外】【伤】【倒】【是】【其】【次】，【最】【糟】【糕】【的】【是】【全】【身】【经】【脉】【受】【损】，【花】【了】【两】【个】【时】【辰】，【也】【仅】【仅】【恢】【复】【了】【不】【足】【一】【成】。 【看】【来】，【短】【时】【间】【内】【不】【可】【能】【痊】【愈】，【灵】【气】【还】【是】【无】【法】【调】【动】，【也】【就】【无】【法】【控】【制】【石】【锁】【空】【间】，【放】【出】【老】【牛】，【不】【过】【再】【调】【养】【一】【两】【天】【应】【该】【就】【可】【以】【勉】【强】【做】【到】。
“【你】【怎】【么】【把】【自】【己】【弄】【死】【了】？”【君】【静】【璃】【落】【在】【了】【问】【馨】【儿】【旁】【边】。 【问】【馨】【儿】【白】【了】【她】【一】【眼】，“【还】【不】【是】【因】【为】【你】。” “【咋】【办】【呀】？”【君】【静】【璃】【鼻】【子】【有】【些】【酸】，【只】【是】【变】【魂】【体】【了】，【没】【事】【的】【一】【定】【没】【事】【的】。 “【我】【要】【走】【了】。”【问】【馨】【儿】【轻】【声】【说】。 “【去】【哪】？”【君】【静】【璃】【问】。 “【我】【也】【不】【知】【道】。”【问】【馨】【儿】【回】【答】。 “【别】【走】。”【君】【静】【璃】【说】。 “【好】
【帐】【篷】【打】【开】，【齐】【云】【从】【里】【面】【走】【了】【出】【来】。 【外】【面】，【天】【算】【师】【无】【一】、【过】【阴】【师】【阴】【无】【邪】、【血】【手】【屠】【夫】、【天】【煞】【老】【祖】、【魔】【笑】【天】【王】【纷】【纷】【回】【头】【看】【去】，【汇】【聚】【了】【过】【来】。 “【公】【子】！” “【走】，【去】【山】【脚】【下】，【范】【宗】【主】【那】【边】【已】【经】【回】【了】【消】【息】！” 【齐】【云】【开】【口】【道】。 “【教】【主】，【范】【宗】【主】【答】【应】【让】【我】【们】【进】【去】【了】？” 【三】【缺】【真】【人】【眼】【睛】【一】【亮】，【开】【口】【问】【道】。 “【不】
【这】【处】【池】【塘】【虽】【小】，【水】【中】【的】【鱼】【儿】【却】【都】【有】【半】【臂】【之】【长】，【小】【锦】【鲤】【随】【手】【洒】【下】【一】【把】【点】【心】【渣】【后】，【那】【些】【鱼】【儿】【便】【都】【围】【拢】【过】【来】，【争】【抢】【起】【那】【些】【点】【心】【来】。【等】【到】【那】【两】【块】【点】【心】【都】【掰】【碎】【撒】【完】【了】，【那】【些】【鱼】【儿】【也】【不】【散】【开】，【就】【在】【小】【锦】【鲤】【脚】【边】【那】【一】【小】【块】【地】【方】【游】【来】【游】【去】，【仿】【佛】【有】【灵】【智】【一】【般】【对】【她】【颇】【为】【亲】【近】。 【耿】【煜】【看】【着】【小】【锦】【鲤】【喂】【鱼】【时】，【一】【双】【翦】【水】【眼】【眸】【亮】【晶】【晶】【的】【小】【模】【样】，【心】看香港总彩开奖现场~~ “【放】【心】，【我】【一】【定】【拼】【尽】【全】【力】，【不】【负】【使】【命】。” 【王】【珍】【一】【脸】【严】【肃】，【郑】【重】【点】【点】【头】。 【知】【道】【这】【使】【命】【光】【明】【而】【艰】【巨】。 【叶】【楚】【在】【一】【旁】，【并】【未】【吭】【声】，【紧】【接】【着】，【他】【目】【光】【朝】【古】【武】【一】【方】【看】【去】。 【瞬】【间】【将】【古】【武】【一】【方】【代】【表】，【全】【部】【锁】【定】。 【抛】【开】【叶】【霜】，【以】【及】【没】【用】【的】【目】【标】【之】【外】，【有】【四】【人】【引】【起】【叶】【楚】【注】【意】。 【【幻】【想】【人】】：【黎】【白】。 【【年】
11【月】10【日】【消】【息】，【据】phonearena【报】【道】，【三】【星】Galaxy S11【系】【列】【产】【品】【将】【推】【出】3【种】【不】【同】【的】【尺】【寸】，【将】【分】【别】【为】6.4【英】【寸】、6.7【英】【寸】【和】6.9【英】【寸】，【其】【中】6.4【英】【寸】【与】6.7【英】【寸】【的】【产】【品】【将】【分】【别】【推】【出】4G【与】5G【版】，【而】6.9【英】【寸】【则】【仅】【推】【出】【一】【款】5G【版】。【按】【照】【三】【星】【之】【前】【的】【惯】【例】，Galaxy S【系】【列】【新】【一】【代】【产】【品】【一】【般】【会】【在】【每】【年】【的】2【月】【份】【左】【右】【推】【出】，【由】【此】【看】【来】，【三】【星】【有】【可】【能】【会】【在】2020【年】2【月】【的】【新】【品】【发】【布】【会】【中】【推】【出】5【款】【旗】【舰】【产】【品】。
“【这】【位】【老】【夫】【人】，【年】【纪】【大】【了】【就】【不】【要】【做】【幅】【度】【这】【么】【大】【的】【动】【作】，【很】【容】【易】【得】【内】【伤】【的】。” 【在】【一】【棵】【大】【树】【下】，【梁】【大】【夫】【简】【单】【的】【查】【看】【了】【刚】【刚】【那】【位】【老】【妇】【人】【的】【伤】【势】。 【由】【于】【老】【妇】【人】【年】【纪】【较】【大】，【加】【上】【刺】【客】【出】【身】，【身】【体】【本】【来】【就】【多】【毛】【病】，【刚】【刚】【一】【摔】【直】【接】【就】【在】【奈】【何】【桥】【前】【走】【了】【一】【圈】。 【老】【妇】【人】【感】【叹】【道】：“【哎】~【想】【当】【年】【对】【付】【你】【们】【这】【样】【的】【小】【屁】【孩】【啊】，【就】【一】【翻】
【五】【千】【异】【族】【骑】【兵】【两】【人】【带】【马】，【全】【部】【化】【成】【战】【场】【上】【的】【尸】【体】。 【即】【便】【是】【还】【有】【些】【出】【气】【的】，【也】【被】【守】【在】【营】【寨】【的】【三】【千】【士】【卒】【给】【补】【刀】【了】。 【至】【于】【俘】【虏】 【不】【好】【意】【思】，【要】【收】【的】【俘】【虏】【也】【是】【有】【些】【价】【值】【的】，【这】【些】【人】【的】【唯】【一】【的】【价】【值】，【就】【是】【他】【们】【的】【首】【级】。 【不】【过】【这】【些】【骑】【兵】【不】【是】【个】【人】【独】【杀】【的】【战】【绩】，【因】【此】【不】【能】【作】【为】【个】【人】【的】【战】【绩】。 【但】【这】【对】【众】【人】【来】【说】，