Every Breath We Take

Author(s):

Verna Gilman and Nicole Woodruff

Grade Level:

3
Timeframe:
1-2 days
40 Minutes per day. One day for estimations and graphing, one day for researching and comparing with other animals. (This could be combined into one day if time is allowed.)

Indiana Curricular Standards


3.1.15 Record the possible outcomes for a simple probability experiment.Example: Have a partner toss a coin while you keep a tally of the outcomes. Exchange places with your partner and repeat the experiment. Explain your results to the class.

3.2.7 Use estimation to decide whether answers are reasonable in addition and subtraction problems.

3.6.5 Recognize the relative advantages of exact and approximate solutions to problems and give answers to a specified degree of accuracy.

3.6.8 Decide whether a solution is reasonable in the context of the original situation.


ISTE Standards

STANDARD 5 : DATA ANALYSIS, STATISTICS, AND PROBABILITYMathematics instructional programs should include attention to data analysis, statistics, and probability so that all students —
pose questions and collect, organize, and represent data to answer those questions;
interpret data using methods of exploratory data analysis;
develop and evaluate inferences, predictions, and arguments that are based on data;
understand and apply basic notions of chance and probability.
STANDARD 6 : PROBLEM SOLVINGMathematics instructional programs should focus on solving problems as part of understanding mathematics so that all students —
build new mathematical knowledge through their work with problems;
develop a disposition to formulate, represent, abstract, and generalize in situations within and outside mathematics;
apply a wide variety of strategies to solve problems and adapt the strategies to new situations;
monitor and reflect on their mathematical thinking in solving problems.

STANDARD 7 : REASONING AND PROOFMathematics instructional programs should focus on learning to reason and construct proofs as part of understanding mathematics so that all students —
recognize reasoning and proof as essential and powerful parts of mathematics;
make and investigate mathematical conjectures;
develop and evaluate mathematical arguments and proofs;
select and use various types of reasoning and methods of proof as appropriate.
STANDARD 8 : COMMUNICATIONMathematics instructional programs should use communication to foster understanding of mathematics so that all students —
organize and consolidate their mathematical thinking to communicate with others;
express mathematical ideas coherently and clearly to peers, teachers, and others;
extend their mathematical knowledge by considering the thinking and strategies of others;
use the language of mathematics as a precise means of mathematical expression.
STANDARD 9 : CONNECTIONSMathematics instructional programs should emphasize connections to foster understanding of mathematics so that all students —
recognize and use connections among different mathematical ideas;
understand how mathematical ideas build on one another to produce a coherent whole;
recognize, use, and learn about mathematics in contexts outside of mathematics.

Assessments
Formative/Summative

Curricular Knowledge or Skills: we will use a rubric to assess formally what the children understand and we will also do informal assessments by observations. We will use the rubric to assess their final graph and we will also ask the students to do a review of their information.

Technology Knowledge: We will use the graphs that they made and look at the information that they found. I think it is important to make the connections to the animal life too because this incorporates science into the curriculum as well. Open ended research on the respiration could help to further their knowledge and to show them that scientists use estimation all of the time too.

Prior Knowledge


Internet Resources: (please list URLs) http://www.factmonster.com/ce6/sci/A0860708.html


Software: Microsoft Excel, Internet Explorer



Technology

You can use excel spreadsheets, graphs, and charts to show what their findings were. This is a great way to show how technology can be incorporated. They can use the different technology applications to compare, contrast, and evaluate the information that they found. They could also use the internet to search respiration rated for many different animals and see the difference between us and other creatures. This also allows them to see that scientists estimate and it shows them how to use the scientific method to do this project. This is a great way to integrate the information that they have learned.

Procedure

Lesson Description
Begin the investigation by encouraging students to give an example of something that they do once a day such as eat breakfast, listen to school announcements, or play with a friend. Ask them to name something they do about ten times each day, which might include saying hello in the hall, changing the television channel, or writing their names on papers. Finally ask students to name something that they do at least one hundred times a day. A narrow range of responses often includes blinking and breathing. If not, take a deep breath and ask, "What about breathing?"

Ask students, "Do you take more than 100 breaths in a day? More than 100 or 1000 breaths in an hour?" After a brief discussion, distribute the Every Breath You Take activity sheet and ask each student to estimate the number of breaths a person takes each hour. Have each student write down an estimate.

Ask students to call out their estimates loudly and in unison. What did they notice about the collection of estimates? Being unable to hear many other estimates over the noise level should motivate them to choose a more organized approach to interpreting the data. Ask the students to state their estimates one by one so that the class can record them on an excel spreadsheet.
Then have the students think about why the estimates were different. Ask the students to work with a partner and discuss their answer and why they think they are right.

Each student should construct a graph of the data using the graph paper. Discuss an appropriate scale and label for the graph's vertical axis. Students will also need to determine whether to plot a scatter graph or a bar graph, depending on prior experience.

You may want to make a class graph instead of each person doing their own. You could graph the different estimates as a group or you can have the students actually count for one minute how many times they breathe. You can see how close the estimates were.

Explore the data in terms of, for example, an approximate mean, the median, and the outliers.
Discuss what makes a good estimate and why more than one estimate may be good. If you have a small group of students count how many breaths they take and show the class the differences, this could provoke conversations about the variations.

Encourage students to explore how they might use their estimates of the number of breaths taken in one hour to estimate the number taken in a day. Students who have been exposed to multiplication might suggest multiplying their estimates by 24, whereas other children might use a repeated-addition process on their calculators.

Discuss why this estimate might be considerably different from the actual number of breaths taken in a day.

You should give the options to work on these things as a group, with partners, or individually. You can also use the graphs as a form of assessment for the students. To show them how to check if their guess is reasonable, you can use something that relates to them. Ask them how many students are in your class. Then have them estimate how many there are school wide. To check you can say that there are roughly 30 children in your class, and there are 25 classrooms within the school. See what answer they get.

To differentiate this you can also have them use white erase boards instead of yelling out their guesses. They can still see that their estimates are different but if you have some students that aren't vocal or have issues, they won't feel left out.

Differentiated Instruction

ESL
You can differentiate for ESL students by showing more examples of what you are wanting. Most ESL students are able to understand graphs and they may also have the option of labeling their graphs in Spanish or their home language. The issue that I see, is that the students often understand more than we give them credit for so we need to expand it when needed for them as well.

Challenge/Extend

We can introduce multiplication to those students that need more of a challenge. We can ask them to predict how many breaths there will be in a day, week, month, and year. We could also ask them to find the percentages for the daily breaths that the class estimated. I am sure we could expand on their math knowledge by allowing them the freedom to make more predictions and taking the information to the next level.

Special Needs

For those with special needs, we need to also take into account where the students are. If they are having issues estimating how many breaths per minute, you may shorten the time and try for ten seconds. You also could ask them to count how many breaths they take within a minute instead of using estimation. We also could let them be in charge of recording the information and relaying it to us as we are putting it into the spreadsheet. I think that if they feel like they are helping me or feel like they have a chance to get the right answer, they can see that they can be part of the class.