Exercise 13.1: Study of Patterns and Functions Apply your understanding of the learning from this chapter. When finished, submit your answers. Watch as this first-grade teacher introduces the ideas of a symbolic pattern. Lynda Penry 1st Grade: Using Symbols http://mediaplayer.pearsoncmg.com/assets/MM02_135_... What type of patterns are the children making in this video?How does the teacher engage the children to identify the core of the pattern?Near the end of the clip how does the teacher reinforce the learning of repeating patterns? "Repeating patterns are everywhere!" What happens in this lesson that demonstrates this to be true Exercise 15.1: Observing and Responding to Student Thinking Click the link below to watch a fifth-grade student solve the problem, "Use the ruler to illustrate the sums and differences" then answer the questions that follow. Adding and Subtracting Mixed Numbers: Linear Model http://mediaplayer.pearsoncmg.com/assets/chapter_16_p_377_mw_gr5 What is the approach that this particular student used to solve these problems?What question(s) might you pose to help the student recognize her error in the first problem?What can you conclude about this student's understanding of and use of the unit fraction?What are the advantages and disadvantages of using an inch ruler as a visual to find the results of these problems? Exercise 16.1: Developing Decimal Number Sense Apply your understanding of the learning from this chapter. When finished, submit your answers. Watch as this student demonstrates his ability to compare decimal fractions. Click the link to watch the video and then answer the questions. Sean, Decimal Assessment http://mediaplayer.pearsoncmg.com/assets/_video.true/imap-0375_iPad When the student in the video refers to the decimal point as the number behind a little dot, what concept is missing in his description?Based on this student's response what does he understand about decimal fraction place value?What would the next instructional step be to guide this student's thinking about comparing decimal fractions? Exercise 17.1: Observing and Responding to Student Thinking Click the link below to watch a sixth-grade student solve the problem, "Janet and Jeanette were walking to school, each walking at the same rate. Jeanette started first. When Jeanette has walked 6 blocks, Janet has walked 2 blocks. How far will Janet be when Jeanette is at 12 blocks?" Then answer the questions that follow. Proportional and Nonproportional Situations http://mediaplayer.pearsoncmg.com/assets/chapter_18_p_433_ng_gr6 Which type of relationship is described in this problem or situation (additive relationship, multiplicative relationship or constant relationship)? How do you know?In looking only at the student's work, and without considering the video evidence, what reasoning approach or error might you suspect he made?After watching the video, what does this student's error reveal about his understanding?How might prompting the student to show this situation using an equation advance his thinking? Exercise 18.1: Perimeter Apply your understanding of the learning from this chapter. When finished, submit your answers. Watch as this third-grade teacher introduces finding the perimeter. Measuring Perimeter http://mediaplayer.pearsoncmg.com/assets/_video.true/MMET_011_306_iPad How does the teacher personalize this activity to guide children's understanding of perimeter?According to the text "understanding length is the gateway to understanding perimeter." How is that idea being employed in this lesson?Explain how this lesson supported the three components of understanding measurement: selecting and attribute, selecting a unit with that attribute, and comparing. Exercise 19.1: Developing Geometric Thinking This class activity engages students in looking for common properties. Click the link to watch the video and then answer the questions. Identifying Properties of Shapes http://mediaplayer.pearsoncmg.com/assets/_video.true/Identifying_Properties_of_Shapes_iPad Based on your reading, what is the focused geometry content goal for this lesson?How do the teacher's questions guide the students to focus on the properties?How is this investigation informing the teacher about what her students' know about geometric properties? Exercise 20.1: Data Analysis and Graphical Representations Apply your understanding of the learning from this chapter. When finished, submit your answers. Watch as the teacher leads upper elementary students into interpreting the results of the graph they have made of the circumference and diameter of a variety of circular lids (objects). The Ratio Pi Grades 5 and 6 http://mediaplayer.pearsoncmg.com/assets/_video.true/LessonStudyMathLens_TheRatioPiGrades5and6_GH05051900_iPad What type of graph have the students constructed?Why is the teacher asking the students to show the best-fit line?Although we only see a short section of the "interpreting the results" part of the lesson, what is the value of the discussion and sharing thoughts about best-fit linepattern? Exercise 21.1: Simulations Read the scenario and apply your understandings about using simulations to answer the questions. The fifth-grade teacher wanted to set up a simulation to have her students test what the probability would be of getting 7 out of 10 questions correct if you guessed on atrue-or-false test. What would the purpose be for using a simulation over an experimental probability task?The first step in using a simulation is to identify the key component and assumption of the problem. Identify and explain what they are for this scenario.The next step is selecting a random device for the key component. What would you recommend that they use for this activity?An important part of a simulation is determining and defining what constitutes "one trial." The authors recommend 10 times as one trial. Why is that appropriate for thissimulation? Exercise 22.1: Operations with Positive and Negative Numbers Apply your understanding of the learning from this chapter. When finished, submit your answers. Watch as this eighth-grade teacher "goes big" to guide her students' knowledge of working with larger integers. What's Your Sign: Integer Addition https://www.teachingchannel.org/video/adding-integers-lesson-idea What strategies is this teacher using to guide her students conceptual understanding of operations with integers?What concept does the color-coding help the students grasp?Why is the number line more effective in this lesson than using two color counters? The teacher refers to a "system in their head" that is going to last. What system has she provided to her students that will stick with them?

For this option you will be representing a map by a graph and finding the coloring of the graph that uses the fewest number of colors. Complete the following tasks:Part 1:Find the county map of New Hampshire, and create a graph that represents it. Counties should be represented as the vertices and the edges should be drawn between them when two counties share a border.Determine if your graph is 2-colorable, 3-colorable, or 4-colorable.Discuss how you found your answer to part (b) and what real-world applications there might be for your findings.Part 2:Draw a map of a fictional state consisting of four counties that is 3-colorable.Discuss your method for creating the map in part (a). Be sure to explain how you verified that your map is indeed 3-colorable.Additional Requirements:Paper must be written in third person.Your paper should be 3-4 pages in length (not counting the title page and references page) and cite and integrate at least one credible outside source. Include a title page, introduction, body, conclusion, and a reference page.The introduction should describe or summarize the topic or problem. It might discuss the importance of the topic or how it affects you or society as a whole, or it might discuss or describe the unique terminology associated with the topic.The body of your paper should answer the questions posed in the problem. Explain how you approached and answered the question or solved the problem, and, for each question, show all steps involved. Be sure this is in paragraph format, not numbered answers like a homework assignment.The conclusion should summarize your thoughts about what you have determined from the data and your analysis, often with a broader personal or societal perspective in mind. Nothing new should be introduced in the conclusion that was not previously discussed in the body paragraphs.Include any tables of data or calculations, calculated values, and/or graphs associated with this problem in the body of your assignment.