Math 485 Daily Math Workout

top

Mathematics for Elementary & Middle School Teachers
Math 485
Summer 2005

DAILY MATH WORKOUT

Because we won’t be meeting over the next two weeks, we wanted to make sure that we didn’t lose the great start we’ve made in our first two days. As a result, we’ve designed a daily mathematics workout program to help everyone “keep in shape” during our break.

Each weekday morning, from July 4 through July 16, we will post a mathematics problem or activity below. These activities have been selected to help you continue thinking about what it means to learn mathematics as a teacher. Some activities are problems designed to stretch your thinking or give you a chance to play around with some mathematical ideas; others are designed to engage you in the type of mathematical work you will do as a teacher, such as looking at student work or analyzing a textbook lesson.

You should complete the posted activity in your notebook each day. You are encouraged to collaborate and discuss the problems with your classmates. As you work, pay attention not only to the mathematics itself, but also to how you are thinking about and working on the mathematics—for example: What types of reasoning are you doing? What types of questions do you have? What activities are easier or harder for you? How do you get started? What do you do if you get stuck? How does what you are doing relate to your work as a teacher?

Click on a date to jump to that day's activities:

Sunday

Monday

Tuesday

Wednesday

Thursday

Friday

Saturday

July 9

July 10

July 16

DAILY ACTIVITIES:

Monday, July 4 – Happy 4th of July! How many different four-digit numbers can you make with the digits in today's date, 7/4/05? (e.g., 7405 and 5047). How do you know you've found them all?

Tuesday, July 5 – On our first day of class, we watched a video of fourth grade students working on the Grid Rectangle Problem. Through the course of their work on this problem, the students proposed a method for finding all of the factors of a given number. Today's daily math workout activity (click here to download) will give you practice interpreting and appraising students' methods for solving a problem.

Wednesday, July 6 – Write a definition for "rectangle" that is both mathematically precise and usable by fourth graders. Make sure your definition includes figures that are rectangles and excludes figures that are not rectangles. You might consider the definition we generated in class as a starting point.

Thursday, July 7 – Analyze examples of five common errors that students make when calculating with fractions and decimals (click here to download sheet with student errors). For each problem, describe what steps might have caused the error. Then calculate the correct answer to each problem --- can you explain why your method works?

Friday, July 8 – Test the definition of rectangle that you wrote on Wednesday against each of the figures on this sheet (click here to download). Does your definition include all of figures that are rectangles and exclude all of the figures that are not rectangles? In the case that your definition includes figures that are not rectangles, revise your definition to exclude these figures.
back to top
Monday, July 11 – Analyze a third grade quiz on even and odd numbers. First, answer the questions yourself (click here to download the quiz), and note any questions you have about any of the problems. If possible, discuss your answers with a classmate. Then reflect on the mathematics assessed in each of the questions. For example, why do you think question #8 is on a quiz about even and odd numbers?

Tuesday, July 12 – Review some students’ work on the even and odd number quiz (click here to download: sample 1, sample 2, sample 3). What does each student’s responses tell you about his or her mathematical understandings? What surprises you about their work?

Wednesday, July 13 – The purpose of this activity is to begin to think about the role of mathematics curriculum materials in the classroom. Please answer the following questions: 1) What do you think of when you hear the phrase “mathematics curriculum materials”? 2) What role do you think mathematics curriculum materials play in the classroom? 3) In what ways do you think teachers can use mathematics curriculum materials to help students learn mathematics?

Thursday, July 14 – Teachers need to be able to understand the mathematical goals of a lesson and determine how student tasks are tied to the mathematical purpose. Today’s workout activity gives you an opportunity to try sizing up the mathematics in a textbook lesson. Use the textbook pages available outside of Laurie's office to answer the following questions: What is this lesson about? What is the mathematics that students are supposed to be learning? Are the tasks for students well aligned with what the lesson is supposed to be about? Do the problems or tasks yourself to get a concrete idea of what will be involved, and to uncover possible surprises.

Friday, July 15 – Today’s activity is to get you thinking about mathematical proof in order to get us ready for the work we’ll be doing in our next class. Write about the following questions: What do you think it means to prove something is true in math? How do you prove something is true? For example, how could you prove that you found all of the four-digit numbers that can be made with 7, 4, 0, and 5? Or how could you prove one of your observations from the grid rectangle problem?