Investigations Math

“We are usually convinced more easily by reasons we have found ourselves than by those which have occurred to others.”

~ Blaise Pascal

4 v 2/9 =Please solve.

• Erica has 4 chocolate bars. If she gives 2/9 of a bar to each of her friends, how many friends can get some chocolate?

• How many 2/9s are in 4?

http://www.youtube.com/watch?v=vMY_-AQc-4s&feature=youtu.be

Framework for 21st Century Learning

• Learning and Innovation skills are what separate students who are prepared for increasingly complex life and work environments in today’s world and those who are not. The include:

–Creativity and Innovation

–Critical Thinking and Problem Solving

–Communication and Collaboration

• Students who do demanding work in school perform better than students who are given less demanding work (Chicago School Research Project)– Work that requires the construction of knowledge through disciplined

inquiry including the use of in-depth understanding

– Work that requires elaborate communication

– Work that has value beyond success at school

Balanced Mathematics Program

Conceptual Understanding

Students with Conceptual Understanding…

• know more than isolated facts and methods,

• know why a mathematical idea is important

and the kinds of contexts in which it is useful

• are able to learn new ideas by connecting

them to ideas they already know, and

• are able to remember or retain ideas• now more than isolated facts and methods,• know why a mathematical idea is important and the kinds of contexts in which it is useful• are able to learn new ideas by connecting them to ideas they already know, and • are able to remember or retain i

Conceptual Understanding

“Education is not just about learning ‘the answer’ but also about learning how to think, question, and continually learn.”- J. McTighe & G. Wiggins, “Opening Doors to Student Understanding”

Make a Fraction

• Make the smallest possible fraction

• Make the largest possible fraction

• Make the fraction closest to 2

• Make the fraction closest to 1

4 5 6 9

Decimal Computation

• 31 X 0.4865 = 1508150000

• 17 X 2.685 = 45186

• 2.5 X 0.9875 = 246875

The Observation Tool

Games in Investigations

• Games provide engaging opportunities for students to deepen their understanding of the number system and operations and to practice computation.

• Playing games encourages strategic mathematical thinking as students find an optimal way of “winning” the game.

Games in Investigations

• Games provide repeated practice without requiring the teacher to provide new problems.

• While students are playing the games, the teacher is free to observe students or to work with individuals or small groups.