Illustrative Mathematics 2.MD The Longest Walk

Illustrative Mathematics

2.MD The Longest Walk

Alignment 1: 2.MD.D.9

a. Pick two points on the outside borders of the United States map (excluding Hawaii and Alaska) so that the line between them stays within the borders. Draw the line. How far apart are the points? Measure the length of the line to find out. Do this 10 times and make a line-plot of your data.

b. Starting anywhere on the map of the United States and drawing in a straight line until hitting a border, what is the longest line you can draw? It might help to ask your classmates what lengths they found as well.

Commentary: The language in this task is above the reading level of many second grade students, so it is best for the teacher to explain the task to the students verbally. After students have drawn and measured their ten line segments, it might be more useful for the class to discuss part (b) as a whole group. It is a good idea to have the students use color to help them keep track of the connection between a line that they have drawn and the corresponding data point on the graph. If students draw 20 data points rather than 10, the lines will start to be hard to see so spare maps are recommended for students who need them. As this is a second grade standard, students are expected to round rather than use fractions, but some classroom discussion can include how some distances might be more than others even though they round to the same thing. The idea of the scale map is beyond this grade level but can be discussed in a holistic sense: how the longest line on the map will represent the longest line in the real United States. If a more concrete version of the activity is desired, it can be performed in an outdoor setting -- a playground, for instance -- on any irregular shape. Public domain US map, with different sizes: Doing the activity on a large wipeable mat will allow students to experiment. The size of the map and the type of units (centimeters or inches) should be chosen at the instructor's discretion to allow a reasonable difficulty level. (The example given in the answers uses the 1000px size from the link above.) Cliff Pickover has written about the problem: Submitted by Jason Dyer for Illustrative Mathematics Task Writing Contest Jan 17 - Jan 30, 2012 Solution: Solution

a. Sample of data collection:

b. The longest walk is from Washington to Florida. Note that getting the correct answer is not a trivial task, even for adults, so any

sufficiently long line should be acceptable and will allow for a good classroom discussion as students will likely have alternate answers.

2.MD The Longest Walk is licensed by Illustrative Mathematics under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License

Information Represented Graphically1

In the following lessons, students participate in activities in which they analyze information represented graphically. Students are asked to discuss, describe, read, and write about the graphs and the information they contain. The emphasis on using components of language is natural for students and helps them clarify the information depicted. The grade levels for the three activities are: Pre-K-2, 3-5, and 6-8. These lesson plans were adapted from the article "Ideas: Information Represented Graphically," by Calvin Irons and Rosemary Irons, that appeared in The Arithmetic Teacher, Oct. 1991, vol. 39, no. 2, pp 26-33.

Individual Lessons

Lesson 1 - What's the Weather? (K-2 focus) In this lesson, students analyze information represented by pictographs. Students are asked to discuss, describe, read, write, and make predictions about the graphs and the information they contain.

How will the data change with a larger classroom? More classrooms? A temperature differential in classrooms? Opportunities to represent data with various constraints to consider. Other options ? weather-related data collection over a longer period of time; students develop questions to ask about the data. Further ? construct temperature graph of data in previous extension.

Lesson 2 - Name Your Tune (Gr. 3- 4 focus to extend) Modify scale, if necessary, to meet student readiness.

The activities in this lesson focuses on studying information displayed in pictographs that report the sales of records, tapes, and compact discs for one week at a music store. The students are asked to discuss and then describe the information and to explain the numbers sold in each category. They are asked to defend their explanation.

OPTIONAL ASSESSMENT OPPORTUNITY: Students use pictographs and select one (CD, Tapes or Records) and create a bar graph for that period of time.

This lesson extends 2nd graders' experience to work with scaled pictographs. Other types of data can be collected at home, shared at school. Modifications, based on student readiness are included.

Lesson 3 - History of Populations This lesson recommended for 5th grade extension (circle graphs represent

content and concepts from middle school) and is not included here.

The activities at this level focus on studying a series of circle graphs that report the population of the United States and of selected states?"Massachusetts, New York, and Pennsylvania?"in fifty-year intervals from 1800 to 1950. The students are asked to discuss and describe the information and to explain why the percent of the total population changed for the three states. They are asked to write a justification for their explanation.

1 Downloaded from December 2012.

Curriculum, Instruction, & Assessment

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LESSON 1 (K-2 focus): What's the Weather? In this lesson, students analyze information represented

by pictographs. Students are asked to discuss, describe, read, write, and make predictions about the graphs and the information they contain.

Learning Objectives Students will: ? describe and explain information displayed in a pictograph ? make written predictions from the information

Instructional Plan Activities in this lesson focus on studying a graph that reports the number of students who wore sweaters to school each day for one week. The information is shown in a pictograph. The students are asked to discuss and describe the information and then predict what happened on the basis of the given information. They are encouraged to write an explanation to defend their predictions. Prior to distributing the activity sheet, ask students if they know what a pictograph is. You may wish to share examples of pictographs, such as those found in math textbooks or ones you have created. Ask students questions such as:

? How is data represented in a pictograph? ? What does each picture or symbol stand for? ? How are pictographs useful for looking at data?

Distribute the What's the Weather? activity sheet to each student. Individually, students should read the title of the graph and the words and numbers along the bottom and the side of the graph. As a class, students should describe the information in the body of the graph. Put students in groups of two or three. Within each group, read and discuss question 1. Ask the students to explain why:

? the number of sweaters on Monday was small, ? the number of sweaters increased on Tuesday, and ? the number of sweaters decreased on Wednesday. Allow enough time in the discussion for every student in the group to offer a suggestion. Repeat for questions 2 through 5. After they have completed these questions, the students can also ask their own questions about the graph and select other members of the class to answer their questions. Possible Solutions for the Activity Sheet Question 1. The temperature changed. Question 2. The weather was colder than the other days, as more students wore sweaters on Tuesday. Question 3. No, I do not think someone needed to wear a sweater on Saturday. After Tuesday, less and less students were wearing sweaters, as the temperature was getting warmer. Question 4. Friday. Question 5. 5 sweaters (7 - 2 = 5).

DIFFERENTIATION: 1. The classroom next door has 36 students. Represent your thinking with a pictograph. Explain why the data

could look like this. 2. There are ten classrooms at the school.

a) What might the data look like for the whole school? Represent your thinking with a pictograph and explain why you think the data could look like this.

b) Half of the classrooms report the indoor temperature of the classroom to be 68 degrees. The other half record an indoor temperature of 73 degrees. Will this change the data? Explain your thinking to support and justify your conclusions.

3. Every day for a week, collect some information that depends on the weather (the number of sweaters, sweat shirts, coats, etc., worn to school) similar to the data shown on the activity sheet. Construct a graph and discuss how to label the information. Have the students make up some questions about the graph and then ask another class to answer the questions.

4. Construct a temperature graph covering the same period of time as the graph in extension 3. Look at the information in the two graphs and discuss any relationships; for example, when the temperature was between 50 and 60 degrees, about half the class wore coats or sweaters.

5. Students who may need more scaffolding may need graphic support (blank lines to prompt titles, key, e.g.)

Curriculum, Instruction, & Assessment

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