The document explores various mathematical instructional strategies and emphasizes the importance of conceptual understanding in learning. It highlights how engaging methods such as games can deepen students' comprehension and promote critical thinking skills. Additionally, the text underscores the necessity for challenging work in educational settings to enhance student performance.

1. Investigations Math
“We are usually convinced more easily
by reasons we have found ourselves
than by those which have occurred to
others.”
~ Blaise Pascal

2. 4v
2/9 =
Please solve.

3. • 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?

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

5. 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

6. • 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

7. Balanced Mathematics Program
Conceptual Understanding

8. 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

9. “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”

10. Make a Fraction
4
•
•
•
•
5
6
Make the smallest possible fraction
Make the largest possible fraction
Make the fraction closest to 2
Make the fraction closest to 1
9

11. Decimal Computation
• 31 X 0.4865 = 1508150000
• 17 X 2.685 = 45186
• 2.5 X 0.9875 = 246875

12. The Observation Tool

17. 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.

18. 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.