Grades 3-5 Information Math Night
September 30, 2014
How is Math in Focus different from
other programs?
• Focused curriculum
• More rigorous
• Less topics to devote more time to
• Deep understanding
• Goal is mastery
• Strong emphasis on problem solving
• Extensive use of visuals
• Aligned to the Common Core State Standards
Focus, Depth, and Mastery
Dr. Yeap Ban Har
Principal of Marshall Cavendish Institute, a global teacher
professional development institute.
https://www.youtube.com/watch?v=2Ss8xAXs_ns
Interlocking Concepts and Skills
Clear Visuals and Use of Models
Singapore’s Mathematics Framework
Emphasis on Problem Solving
Common Core State Standards:
Math Practices
Reasoning and Explaining
Habits of Mind of a
Productive
Mathematical
Thinker
MP1.
Make sense of
problems and
persevere in solving
them.
MP6.
Attend to Precision
MP2. Reason abstractly and quantitatively
MP3. Construct viable arguments and critique the reasoning
of others
Modeling Using Tools
MP4. Model with mathematics
MP5. Use appropriate tools strategically
Seeing structure and generalizing
MP7. Look for and make us of structure
MP8. Look for and express regularity in repeated reasoning
How will it look different…
• In school for students?
• At home for parents?
9
What to expect in the classroom…
Depth vs. Breadth (teaching to mastery through lesson structure)
Concrete – Pictorial – Abstract
Differentiation
10
Lesson Structure
Teach/Learn
Games
Hands-on
Let’s Explore
Practice Problems
Guided
Practice
Let’s Practice
Independent
Workbook
In class/homework
SCHOOL
POYTC
Math is thinking
Encourage perseverance
Synthesize learning
Non-routine problem solving
How might homework change?
What can you expect to see in work that
comes home?
 Use of visuals and language
 Standard algorithms
 High level questioning
Workbook
Place Value in Math in Focus:
More than just “digit location”
Place Value Activity:
Choose a concrete material:
•Base 10 blocks
•Place value chips
Place value mat
Place Value
Build 125 using the fewest materials possible.
_____ Hundreds _____ Tens _____ Ones
_____ Tens _____ Ones
_____ Hundreds _____ Ones
_____ Ones
Math as Thinking: 13 X 7 = 28
http://www.teachertube.com/viewVideo.php?video_id=46231
A farmer sells his crops to 3 restaurants.
He divides 525 heads of lettuce equally
among the 3 restaurants. How many
heads of lettuce does each restaurant
receive?
4th grade
Visual Models in Math in Focus:
Number Bonds
Number Bond:
• A tool used by students to represent and build
understanding and flexibility with numbers
•Builds number sense
PART
WHOLE
PART
Number Bonds Extend to Mental Math
8 + 6 =?
This strategy in Math In Focus is “you can add by making a 10.”
8 + 6
2
8 + 2 = 10
4
10 + 4 = 14
So, 8 + 6 = 14
Number Bonds Extend to Mental Math
Mentally Add
$ 5.35 + $ 2.40
$5.35
5
.35
+
$2.40
2
$5 + $2 = $7
.35 + .40 = .75
$7 + .75 = $7.75
.40
More Visual Models in Math in Focus:
Bar Models
What are bar models and why are they so
important?
 Provide a useful pictorial representation to illustrate a
problem, indicating known and unknown quantities
 Help students make sense of the relationship between
values given in real-world problems
 Modeling enables students to gain a deeper
understanding of the operations they may use to solve
problems.
 Allows students to engage in algebraic thinking long
before they experience formal Algebra.
 Modeling is called for in the CCSS.
Bar Models: 3 Major Types
Whole
Part
Part
Part-Whole
Comparison
Equal
Parts
Grade 2
Bar Models
• A drawing used to show the understanding of a problem.
Frank has 25 baseball and football cards altogether. He
has 11 baseball card. How many football cards does
he have?
25
11
?
There are a total of 36 students in the class.
There are three times as many girls as boys.
How many boys are in the class?
Three times as many girls
Girls:
9
9
9
36 children
altogether
Boys:
9
# of boys
4 units = 36
1 unit = 36 ÷ 4 = 9
There are 9 boys and 27 girls in the class.
Let’s take it up a notch…
Ricardo spends 8/9 hour reading the newspaper. He
spends 1/4 of the time reading the world news and
splits the remaining time equally between the sports
and the comics. How much time does he spend
reading the comics?
Ricardo spends 8/9 hour reading the newspaper. He spends
1/4 of the time reading the world news and splits the
remaining time equally between the sports and the comics.
How much time does he spend reading the comics?
1 hour
world news
sports
comics
Time reading newspaper
Ricardo reads the comics for 3/9, OR 1/3, of an
hour (20 minutes).
Future and Ongoing Support
Newsletters
Provides the
objectives
covered,
vocabulary that
can be
developed, and
an activity to
foster
understanding.
Getting Started with Think Central
Think Central
http://www-k6.thinkcentral.com/ePC/start.do
Math Background and Support Videos
(Think Central)
• Chapter Background
Videos with a
description of each
chapter’s content
• Parent Support
Videos with ‘at
home’ suggestions
• Singapore Math
Video Podcasts
www.hmhco.com
Singapore Math: Bar Models for the iPad
•Problem Solving Tools
•Visual Models
•Student Support
•Audio, Visual, and
Tactile interaction
How can I help my child?
• Talk to your son/daughter and ask him/her about what went on in class
• Did you use manipulatives in class today?
• Did you draw any pictures or visual models to help in
understanding?
•Ask your son/daughter to explain his/her thinking.
• Why? How do you know?
• Encourage work that comes home to be done independently.
• Help your child to develop perseverance in completing a task.
• Give your child problems to solve.
• What is 4 more than 7?
• Practice math facts in car rides or through using flash cards.
• Utilize Think Central at home for the Student Interactivities and the
Virtual Manipulatives.
Elementary Report Cards
We need to teach perseverance.
http://www.teachertube.com/viewVideo.php?video_id=176603
Thank you!
Twitter: @klemerich
E-mail: LemerichK@madisonpublicschools.org