Ernestine Saville-Brock MNPS Math Coordinator
Pam Pedigo & Sue CollierNumeracy Coaches
Elementary Balanced Math
Problem Solving
ComputationalFluency
ConceptualUnderstanding
• Standards based• Student centered
• Implementation of math components
• Research based• Best practices
• Workable schedule• Becomes routine
Support Balanced Math• Pacing
• Resources• Themes
http://guest.portaportal.com/
courseoutlines
Balanced Math Framework Elementary School
Day 15 min 40 minutes 5 minutes
1 Math Review Mental Math Concept LessonProblem solving, small groups intervention, centers, or manipulatives
Closure/math journals
2 Math Review Mental Math Concept LessonProblem solving, small groups intervention, centers, or manipulatives
Closure
3 Math Review Mental Math Concept LessonProblem solving, small groups intervention, centers, or manipulatives
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4 Math Review Mental Math Concept LessonProblem solving, small groups intervention, centers, or manipulatives
Closure
5 Assessment/Math Review Quiz Math activities, centers, games, small group, intervention
6 Math Review Mental Math Concept LessonProblem solving, small groups intervention, centers, or manipulatives
Closure
7 Math Review Mental Math Concept Lessonproblem solving, small groups intervention, centers, or manipulatives
Closure
8 Math Review Mental Math Concept LessonProblem solving, small groups intervention, centers, or manipulatives
Closure
9 Math Review Mental Math Concept LessonProblem solving, small groups intervention, centers, or manipulatives
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10 Assessment/Math Review Quiz Assessment
• Typically, this involves the teacher posting 4-6 varying math concepts for students to work.
• The teacher acts as a facilitator who encourages a variety of ways to solve problems and helps model efficient thinking when necessary.
• Students take turns sharing their individual strategies with the class.
• Concepts are consistently revisited throughout the year so that they are not taught in isolation and/or forgotten.
Spiral review of grade levelconcepts taught throughout the
year• Math morning work• Calendar activities• Estimation prompts
• Houghton Mifflin Transparencies• Thinklink practice probes
• Math warm-ups
Mountain Math http://www.mtmath.com/forum/mtmath.php?topic=mathKitsArithmetic Developed Daily http://www.growpub.com/cgi-bin/GRWstore.pl?user_action=detail&catalogno=AD3Week By Week Essentials
http://community.learnnc.org/dpi/math/archives/2005/06/grades_35_resou_1.php
Daily Math Review
Name_______________________________________________________________________
5 hundreds, 4 tens, 3 ones = _____
295 + 486
600 - 247
9 x 6 = ___
___ days = 2 weeks
___ min. = 1hr.
___ in. = 1 ft.
Place value Addition Subtraction Multiplication Measurement
“Math on Your Feet”
•Brief daily sessions •Opportunities to practice
mental computation •Opportunities to solve
problems in a variety of ways •Could occur during transition
times.
•One more/one less, before/after, a given number•Counting by twos, fives, tens•Doubles•Fact families•Measurement (time, money, calendar, feet, etc.)•Math Vocabulary/Math Word Wall•Addition &/ or Subtraction Facts•Estimation •Math Around the Room
Daily Mental Math Activities
• http://www.aea11.k12.ia.us/prodev/math/mentalmath/dailymm.html
• Students experience an inquiry-based method of understanding key concepts
• Use of concrete representation when introducing new concepts
• Embedded problem solving• Teachers implement strategies that help
students develop understanding• Utilize resources and methods beyond
the adopted textbook• Opportunities to work with small group
remediation, enrichment, etc.
Day 15 min 40 minutes 5 minutes
1 Math Review
Mental Math
Literature & Manipulative InquiryBig Book Base Ten, exploration, mats, vocabulary
Closuremath
journals
2 Math Review
Mental Math
Concept LessonBase ten number building, adding on, trading, writing numerically, eManipulatives
Closuremath
journals
3 Math Review
Mental Math
Problem Solving/Manipulative ActivitySuper Source lesson-Race For a Flat
Closuremath
journals
4 Math Review
Mental Math
Concept Lessontextbook
Closuremath
journals
5 AssessmentMath Review Quiz
Small Group InterventionActivities-centers/stations, games, problem solving
Balanced Math Framework Elementary School
• Content words• Current vocabulary• Interactive• Keep retired vocabulary
accessible (dictionary, index cards, center)
Day 15 min 40 minutes 5 minutes
1 Math Review
Mental Math
Literature & Manipulative InquiryBig Book Base Ten, exploration, mats, vocabulary
Closuremath
journals
2 Math Review
Mental Math
Concept LessonBase ten number building, adding on, trading, writing numerically, eManipulatives
Closuremath
journals
3 Math Review
Mental Math
Problem Solving/Manipulative ActivitySuper Source lesson-Race For a Flat
Closuremath
journals
4 Math Review
Mental Math
Concept Lessontextbook
Closuremath
journals
5 AssessmentMath Review Quiz
Small Group InterventionActivities-centers/stations, games, problem solving
Balanced Math Framework Elementary School
Goal: Get enough longs and units to trade for a flat worth 100
• One team rolls 2 number cubes. The players find the sum of the numbers they roll and take units to show that number.
• Then, put their units on the mat.• If team gets 10 or more, trade in for a
long. Take turns rolling, finding sums, putting units on the mats and trading for longs.
• As soon as a team has 100 or more, they trade for a flat and win that round!
• Super Source Manipulative Kit Lessons
• Navigations Series (NCTM)• Marilyn Burns Math Lessons• Marilyn Burns Math and
Literature • Math Games
Mathwire– http://www.mathwire.com
Internet4Classrooms – http://internet4classrooms.com/
Learning Stages1st Students will use their prior knowledge to construct concrete representations of math
2nd Students must represent their understanding in a reflective &/or symbolic form
3rd One or both forms will be a visual reminder for the understanding of the higher-thinking abstract
Representation
AbstractConcrete
Learning Stages
Representation/Pictorial
Concrete Abstract
Day 15 min 40 minutes 5 minutes
1 Math Review
Mental Math
Literature & Manipulative InquiryBig Book Base Ten, exploration, mats, vocabulary
Closuremath
journals
2 Math Review
Mental Math
Concept LessonBase ten number building, adding on, trading, writing numerically, emanipulatives
Closuremath
journals
3 Math Review
Mental Math
Problem Solving/Manipulative ActivitySuper Source lesson-Race For a Flat
Closuremath
journals
4 Math Review
Mental Math
Concept Lessontextbook
Closuremath
journals
5 AssessmentMath Review Quiz
Small Group InterventionActivities-centers/stations, games, problem solving
Balanced Math Framework Elementary School
• Math Journals• Reflect individually and with
whole-group• Record representation of key
concepts• Opportunity to use math
vocabulary/word wall in context • Pose questions• Problem solving
JournalingDraw Have children draw a model of baseten blocks for any given number,such as 93.
Write (in complete sentences)How many more do you need to get to
100?What are all the possible combinations of numbers that could be rolled on the
numbercubes to get to 100?
• Problem solving tasks are…– using a strategy or strategies
to make sense of a problem.– Based on real-life experiences
whenever possible.– Investigative experiences that
encourage concept building and skill acquisition.
A problem is defined by…
Any task or activity for which a student has no prescribed or memorized rules or methods, nor is there a perception by the student that there is a specific “correct” solution method.
Hiebert, J., Carpenter, T. P., Fennema, E., Fuson, K., Human, P., Murray, H., Olivier, A., & Wearne, D. (1996). Problem solving as a basis for reform in curriculum and instruction: The case of mathematics. Educational Researcher, 25 (May), 12-21.
MinilessonsTasks that do not require the entire class period—the think-pair-share strategy is usefulWorkstations and gamesCan be setup around the room without the need to distribute and collect materials to allow students to work on different tasks and conceptsProblem-solving MenuA menu is a collection of activities for a student to do. A menu can provide class work activities for several days, a week, or a longer period of time. The tasks on the menu are not hierarchical and do not conceptually build upon each other.
What are some ways to incorporate more problem
solving?
Problem Solving Resources
NCTM Illuminations websitehttp://illuminations.nctm.org/
MNPS Math Wikispacehttp://mnpsmath.wikispaces.com
Sunshine Mathhttp://mnpsmath.wikispaces.com/Problem+Solving
MNPS Portaportalhttp://www.portaportal.com/mnpsmath
Computer Center– http://www.eduplace.com/elogin/– http://www.portaportal.com/
HM Math Center Resource Book Super Source Activities (from
previous lessons) Family Math Book Take It To Your Seat Folder
Games
Balanced Math Framework Elementary School
Day 15 min 40 minutes 5 minutes
1 Math Review Mental Math Concept LessonProblem solving, small groups intervention, centers, or manipulatives
Closure/math journals
2 Math Review Mental Math Concept LessonProblem solving, small groups intervention, centers, or manipulatives
Closure
3 Math Review Mental Math Concept LessonProblem solving, small groups intervention, centers, or manipulatives
Closure
4 Math Review Mental Math Concept LessonProblem solving, small groups intervention, centers, or manipulatives
Closure
5 Assessment/Math Review Quiz Math activities, centers, games, small group, intervention
6 Math Review Mental Math Concept LessonProblem solving, small groups intervention, centers, or manipulatives
Closure
7 Math Review Mental Math Concept Lessonproblem solving, small groups intervention, centers, or manipulatives
Closure
8 Math Review Mental Math Concept LessonProblem solving, small groups intervention, centers, or manipulatives
Closure
9 Math Review Mental Math Concept LessonProblem solving, small groups intervention, centers, or manipulatives
Closure
10 Assessment/Math Review Quiz Assessment
FORMATIVE—checking on learning as students progress
SUMMATIVE—checking on learning at the end of the learning experience
Assessment
“When the cook tastes the soup, that’s formative; when the guests taste the soup, that’s summative.”
(Stake, 2005)
Formative & Summative Assessment
Teacher ObservationMath Journals
Teacher Made TestsStudy Island, Compass, Accelerated
Math…Houghton Mifflin Chapter
and Unit TestsProjects
Thinklink Relay
MNPS 3rd Grade ELL teacher
Susanna Owensmodeling
Balanced Mathhttp://10.189.201.34/watch_video.php?v=244237dc39021b3
Think about the standards that wereincluded in all of the activities and
lessons In your teams, highlight the standards
which:• Were included in the activities and
lessons• ALSO, look for standards that were
“uncovered” today• Discuss and highlight other standards
that could be incorporated into specific grade levels.
• What is one significant thing you learned about Balanced Math?
• What is the first thing you think you will implement?
• What do you need next to support you as a Coach?
Elementary Balanced Math
Presented bySue Collier
Numeracy Coach Tulip Grove Elementary School
Pam PedigoNumeracy Coach/Math Specialist
Dodson Elementary School
Ernestine Saville-BrockMNPS Mathematics Coordinator K-12
Bibliography
• Five Easy Steps to a Balanced Math Program for Primary Grades (Paperback) (K-2) by Larry Ainsworth and Jan Christinson
• Five Easy Steps to a Balanced Math Program for Upper Elementary Teachers (Paperback) (Grades 3-5)
• by Larry Ainsworth and Jan Christinson