Chapters 11 and 12

1. The wrist measurement activity we did in class works with chapter 11 because the data is student-based. Chapter 11 is all about helping the students learn to use data; students learn everything better when it is based on themselves. Allowing students to come up with the different questions they have about their wrists gets students involved in the process and the data will be different and specific to each student, which personalizes the activity. Whereas we used a tally chart to document the different wrist circumferences, the activity could use whichever form of graph the class is learning or needs help with. If this activity was done in a first grade classroom, it would be a fantastic activity to teach how to tally and then how to transfer the data in a tally chart to a bar graph. In class we also focused on finding the most appropriate average. This corresponds better with the standards for higher elementary; in fact, the measures of central tendency are not even mentioned until fifth grade. However, the book says it is appropriate to discuss the "middle" of a set of data even if the MoCT are too advanced.

2. I am in a first grade classroom. We have learned a lot about different types of charts and graphs. One of the first days of school, we made a pictograph of months and birthdays on the back wall. The months start with January at the top of the wall and end with December at the bottom of the wall. We spent about an hour working on this graph one day. Each child received an index card on which they were instructed to write their name and birthday and to draw a cake. Then we started with January birthdays and taped each card onto the wall. This was fantastic according to chapter 11 because it was a student-centered form of data. Other than this activity, the students practice tally charts almost daily during math. Several weeks ago they learned how to transfer data from their tally chart to a bar graph. When I taught my lesson I focused on this concept. I gave each student a bag of M&M's; they sorted their candy by colors, made a tally chart of how many candies they had per color, then colored a bar graph to represent this data.

3. In Kindergarten, the standards focus on beginning to organize and interpret data. Sorting and tallying activities discussed in chapter 11 would relate to this. Even if the teacher did not discuss the proper way to tally (crossing number 5) it would be a start to learning to organize data, as the standard states.

Grade 1 says students should be able to collect, organize, and interpret data as well as make hypotheses about it. The book does not really discuss hypothesizing, but all of these pieces of grade 1 could be covered in a leaf activity. Before going outside the students could hypothesize about which color leaf they will find the most of as a class. Students can collect leaves, sort them by colors, make a tally chart, and then make a pictograph or a bar graph to help them determine if their hypotheses were correct.

Grade 2 includes everything from standard one and adds that students should be able to describe the trends of data. The book also does not focus specifically on data trends. A good activity to cover data trends is to have students graph their individual test scores for each subject and compare them from week to week and subject to subject.

Grade 3 adds that students should be able to understand the benefits of multiple representations of data, as well as basic concepts of probability. This is the first time the content in chapter 12 has even been mentioned. Chapter 12 is about basic probability and how to use tree charts, predictions, the range of impossible to certain, and various games to practice probability. In third grade, students should also know that different graphs and charts can make the same set of data appear different. Chapter 11 goes over the benefits and differences of multiple types of graphs.

Chapter 3 Reflection

Key Ideas:

• Addition and subtraction are connected by means of "part" and "whole." Addition is used to name the whole when the parts are known, and subtraction is used to name one part when the whole and the other part are known.
• Students need to learn these more broad definitions rather than "put together" or "take away."
• When teaching addition and subtraction, teach lesson using context/stories. Don't focus as much on the symbols involved.
• Multiplication and division are connected and relate back to addition and subtraction.
• For all math, as long as the students know the numbers in a problem (and their answer is a known number) they can answer the problems. Problems should not be "dumbed down."
• Models can be used to visualize math problems.
• There are properties in addition, subtraction, multiplication, and division that should be taught to help students remember how to do each operation.

How do these ideas inform your understanding of teaching numbers and operations?

Before reading, I had heard that we should teach addition and subtraction together and multiplication and division together, but I didn't fully understand why. This chapter explained how the operations are more similar than they are different and that teaching them together can actually help students learn more efficiently and effectively. The explanations and examples of different models you can use for teaching the operations were helpful and I will definitely use models in my class because I know children learn in different ways and some might need this visual example. Others might need an auditory or written example of the properties, so those will also be included in my classroom teaching.