th
35

Where to Accelerate????
36

The Only Reasonable Answer for Learning: 9 th Grade!!!!
37

38

Preassessment
Instruction
Expert
Investigation
Instruction FAL
Instruction
Final
Assessment
1 day 5 - 10 days 2 days 1 day
39

A program to foster school-wide participation in math and problem solving
.
40

George Polya,
(1887 - 1985 )
Father of Problem Solving;
“
How to Solve It ” , 1945
Mathematics, you see, is not a spectator sport. To understand mathematics means to be able to do mathematics. And what does it mean doing mathematics? In the first place it means to be able to solve mathematical problems.
41

School Wide Use of POM ’ s
42

Problem of the Month
Party Time
Level A
Cindy had a party. She invited two guests. Her guests each invited four guests, and then those guests each invited three guests.
How many people were at Cindy’s party?
Explain how you determined your solution.
43

Problem of the Month
Party Time
Level C
Mia, Jake, Carol, Barbara, Ford and Jeff are all going to a costume party. Figure out which person is wearing what costume and when they arrived at the party.
·
T h e person that arrived fourth was wearing bathing suit.
·
B arbara was the last to arrive.
·
J a k e and Mia arrived and stayed together.
·
The first person was dressed as a French Maid.
·
S uperman arrived right before Barbara.
·
The Potato Heads were always together at the party.
·
F o r d was a Surfer Dude.
·
The French Maid was not Carol.
·
T h e Vampire arrived after Superman.
44

Second Grade - Working on Party Time Level C
45

School Wide Use of POM ’ s
46

Gallery Walk for Party Time
47

“ Mathematics is not a careful march down a well-cleared highway, but a journey into a strange wilderness, where the explorers often get lost.
”
Fermat ’ s Enigma , p.
71

Curriculum inspired by the CCSS
MAP ’ s Formative Assessment Lessons and Professional Development Modules
Assessment For Learning
Formative Assessment Lessons (2 days) for High School and Middle
School 49

Optimizing: Security Cameras
50

Security Cameras
A shop owner wants to prevent shoplifting.
He decides to install a security camera on the ceiling of his shop.
The camera can turn right round through 360 ° .
The shop owner places the camera at point P, in the corner of the shop.
The plan view shows where ten people are standing in the shop.
P-1
51

52

Plan View
P-2
53

Sharing Individual Solutions
1. Take turns to share your work.
2. Describe how you did the task and how you think it could be improved.
3. If explanations are unclear, ask questions until everyone in the group understands the individual solutions.
P-3
54

Security Cameras
1. Which people cannot be seen by the camera at P?
Explain your answer, showing clearly on the diagram how you know.
2. The shop owner says, “ 15% of the shop is hidden from the camera.
” Show clearly that he is correct.
3. The shop owner decides to move the camera so that it can see as much of the shop as possible.
a. Show on the plan view the best place for the camera, so that it can see as much of the shop as possible.
b. Explain how you know that this is the best place for the camera.
P-4
55

Sample Response to Discuss
1. What mistakes have the students made?
2. What assumptions have the students made?
3. In what ways could the students ’ work be improved?
4. To help you to understand the students ’ work, what questions could you ask them?
P-5
56

P-57
Sample Responses to Discuss:
Simon

P-58
Sample Responses to Discuss:
Ellie

P-59
Sample Responses to Discuss:
Rhianna

Classroom Challenges: Formative Assessment Lesson – Security Cameras
60

61

Number Talk: Word Problem
62

63

Other Types of Math Talks
64

Silicon Valley Mathematics Initiative www.svmimac.org
David Foster
Silicon Valley Mathematics Initiative www.svmimac.org
65

• SVMI ’ s Resources and Programs
Professional Development
Summer Institutes and Math
Workshops throughout the school year.
Problems of the Month
Performance Assessments
Math Talks
School-wide Problem Solving
Lesson Study Project
Promoting Classroom Discourse and Conceptual Understanding
Math Coaching
Math Network Meetings and
Workshops for Coaches and
Principals
66 School Team Mini - Grants

This site gets 17,000 hits each week.
Approximately 10,000 to download POMs.
67

68

Inside Mathematics Website http://www.insidemathematics.org
Mathematics Assessment Project
UC Berkeley & Shell Centre for Mathematical Education http://map.mathshell.org/materials/lessons.php
Silicon Valley
Mathematics Initiative http://www.svmimac.org
69