Friday, July 10, 2015

Activities for Exploring Number Sets

1) Who Has a Number Bingo Board:

Who Has a Number Bingo Board and Vocabulary Review (below) available here.

2) Students work in groups to review and learn vocabulary associated with number sets. (I plan to do the vocabulary review first to help student activate prior knowledge before playing the Bingo game above.)

3) Number Sets Search found on End of Year Resources post from Resourceaholic which came from here.

4) Number Experts: a Bitesize Gem from Assign a number to each student. They become an expert in that number, creating a display and giving a presentation about its interesting properties.

5) Find the Factors: I think these puzzles are brilliant and plan to use these during the first week of school to help my students practice their multiplication facts.

  • Stand when the number is prime; sit if it is composite
  • Stand when the number is even; sit if it is odd
  • Stand when the number is a multiple of 3; sit if it is not a multiple of 3
  • Stand when the number is a factor of 24; sit if it is not a factor of 24
  • Stand when the number is a perfect square; sit  if it is not a perfect square

Try to "trick" the students by standing up or sitting down when they should be doing the opposite.

6) I Have Who Has Games

Tuesday, July 7, 2015

Deposit and Withdrawal Cards

When we study negative numbers, we have the opportunity to learn about real world applications of this mathematical concept. In general, sixth grade students are unfamiliar with banks and how bank accounts work. The Bank Account Game is a fun way for students to explore these ideas and familiarize themselves with the vocabulary used in basic personal finance. Before we play the game in class, I ask the students to make two deposit cards and two withdrawal cards that we can use for the game. Making the cards themselves is a valuable learning experience and makes the game more fun for the students to play.

Here are some examples of student made cards:

Monday, July 6, 2015

Open Questions and Parallel Tasks for Sixth Grade Math

This book is a wonderful resource for good math questions. It contains questions:

  • that are perplexing so that students are engaged and want to use mathematics to explore the topic
  • that have multiple entry points for students of varying abilities
  • that are rich enough so that the exploration can drive the entire lesson
  • that allow students to solve a problem in many different ways and then explain and prove their results.

As I read this book it really made me think about what makes a good math question and how I could adapt and improve anchor questions that I have used in order to make them more open ended and accessible to all students. I decided to go through the book and pull out all the questions that I could use in my sixth grade math classroom and organize them by the topics that we cover, in the order that we cover them, giving me ready access to some model questions that I can use or adapt throughout the school year. This was a very valuable process for me because by reviewing all the questions, especially those aligned with the sixth grade common core standards, I was able to more clearly understand what makes a good question and how to create these type of questions for other topics we cover.

As the TIMSS video study found, Japanese teachers use a structured problem solving format for most of their lessons where the teacher poses a complex thought-provoking problem, students struggle with the problem, various students present ideas or solutions to the class and then the teacher leads a class discussion using the various solution methods provided by the students and summarizing the class' conclusions (from The Teaching Gap by James Hiebert and James Stigler and CT Regional School District #10 Math Program FAQ Page). This lesson format has proven to be an extremely effective method of teaching mathematics and a model I have tried to use in my classroom. But finding rich problems that create the set up for a student centered lesson for each of the topics covered in our curriculum can be a challenge. Japanese educators are part of a teaching community that uses "lesson study" as a way for teachers to share and refine the problems and questions they pose at the beginning of a lesson that create the conditions in the classroom where students are engaged in deep mathematical thinking. This book is one resource that teachers in the US can use to find good thought provoking questions.

Here are a few of my favorite open questions and parallel tasks from the book:

1) Percent:  72 is _____% of ______

2) Percent:  Choose something you have been wanting to buy that costs more than $50. Imagine you have $30 saved. What discount does the store need to offer before you can afford it?

3) Algebraic Expressions: An expression involving the variable has the value 10 when k = 4. What could the expression be?

4) Algebraic Expressions: Order these values from least to greatest. Will your order be the same no matter what the value of n is? Explain.
  • Choice 1:   n/2     3n     n^2     3n + 1     10 - n
  • Choice 2:   4n     3n     10n      3n + 1     5n + 2     -n
5) Geometry: You start with a parallelogram. You increase its height by the same amount as you decrease its base length. How does the area change?