Welcome to

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• Welcome to
• Developed at
• Clemson University
• College of Engineering and Science
• Published by
• Carolina Biological Supply Company, Inc.

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Session Goals

• Develop a deeper understanding and broader view
  of mathematical content knowledge
• Introduce materials and manipulatives used in the
  lessons
• Reflect on personal beliefs about the teaching
  and learning of mathematics

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What is Math Out of the Box?

• Research-based
• Standards-based
• Inquiry-based

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Essential Components

• Development of a community of learners
• Explicit connections that make mathematics
  meaningful
• A model for verbal and written communication
• Balanced assessment practices
• A variety of problem solving experiences
• A diversity of materials, manipulatives, and
  models

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24 Modules Covering All Mathematics Strands for
Grades K 5
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Number and Operations Standards

• Read through the process standards.
• Read through the content standards for Properties
  of Numbers, Numbers and Operations, and
  Probability.
• Make a list of questions and/or comments about
  the process and content standards for your grade
  level, the prior grade level, and the following
  grade level.
• Create a chart to represent your groups
  questions and comments.

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Goals of Numbers Strand

• For students
• Develop strategies for becoming mentally fluent
  with basic facts.
• Make connections between basic facts and
  properties of numbers.
• Connect invented strategies with historically
  efficient algorithms.
• Connect properties of whole numbers and
  fractional numbers.
• Connect probability and discrete mathematics to
  real-world experiences.
• For teachers
• Improve content knowledge of number concepts.
• Provide information to support standards.
• Provide math lessons based on best practices.

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Teachers Manual Scavenger Hunt

• Where are the objectives of the lesson?
• What is provided to help plan and organize the
  lesson?
• What other kinds of teacher support are provided?
• What are the four main phases of the lesson?

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Research-Based Practice

• Connected Practice provides connections to
  concepts, facts, and procedures to other
  curriculum areas and to everyday life. These
  interconnected experiences provide opportunities
  for students to make coherent and meaningful
  connections between mathematical ideas.

• Reflective Practice provides students with
  opportunities to solve a variety of problems so
  that they are encouraged to think about their own
  learning.
• Answers for the practice pages are found at the
  end of their respective lessons.

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The Learning Cycle
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Basic Facts and Properties of Numbers

• Developed at
• Clemson University
• College of Engineering and Science

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Math Out of the Box develops basic facts fluency
in the following ways

• Helps students transition from counting to
  fluency with basic facts.
• Uses known basic facts to derive solutions to
  unknown basic facts.
• Emphasizes strategies that connect to the
  relationships in the base-10 number system.
• Develops strategies for solving basic facts that
  can be used in the computation of larger numbers.

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Task Sheet Directions
Follow the directions to explore a basic facts
strategy with your group. Be prepared to explain
how your strategy does any of the following

• Helps students transition from counting to
  fluency with basic facts.
• Uses known basic facts to derive solutions to
  unknown basic facts.
• Emphasizes strategies that connect to the
  relationships in the base-10 number system.
• Develops strategies for solving basic facts that
  can be used in the computation of larger numbers.

Plan a way to share your knowledge about this
strategy with the other groups.
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Investigating Properties of Numbers Lessons

• Read through the Teacher Information and
  vocabulary.
• Discuss together the engage activity.
• Do Investigate together.
• Read through the remainder of the lesson.

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Place Value

• Developed at
• Clemson University
• College of Engineering and Science

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Math Reflection

• What patterns and relationships can be identified
  in the base-10 number system.

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Beginning Concepts in Place Value
12 is 1 set of ten and 2 ones
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Lesson 14 Analyzing Thousandths

• Read through the Teacher Information and
  Preparation.
• Discuss together the Engage activity.
• Do Investigate together.
• Read through the Reflect and Apply phases.
• Discuss
• In what ways does this lesson prepare students to
  develop and apply strategies for addition and
  subtraction of decimals?

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Exploring Estimation
Developed at Clemson University College of
Engineering and Science
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Analyzing Addition and Subtraction

• Developed at
• Clemson University
• College of Engineering and Science

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Addition Strategies Story Problem

• On Monday, the third grade sold 28 raffle
  tickets. On Tuesday, the students sold 37
  tickets. How many total tickets were sold in the
  two days?

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Subtraction Model Lessons

• Divide the Engage, Investigate, and Reflect
  phases into parts so that each member of your
  group has a role.
• Plan your part and be ready to teach it to the
  others in your group.
• Take turns teaching the parts of the lesson.

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Lesson Discussion

• What prior knowledge and experiences will
  students need to succeed with the lesson?
• Which of the content standards were addressed in
  this lesson?
• Which of the process standards were addressed in
  this lesson?
• What assessment opportunities are in this lesson?

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Analyzing Multiplication and Division

• Developed at
• Clemson University
• College of Engineering and Science

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Multiplication Story Problem

• Fifteen students each wore clothing with 8
  buttons. How many buttons did they wear
  altogether?

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8

15 8 40 80 120
1
5
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Long Division Story Problem
Three friends shared a collection of 462 baseball
cards. How many cards will each friend receive if
they divide the collection evenly?
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Fractions, Decimals, and Percents

• Developed at
• Clemson University
• College of Engineering and Science

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Fraction Representations
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Probability and Discrete Math
Developed at Clemson University College of
Engineering and Science
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Introducing the Jigsaw

• The activities are designed for adult learners.
• These are representative of research-based math
  materials.
• You are doing six investigations representative
  of Math Out of the Box.
• You will become an expert on your piece of the
  jigsaw.

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Reporting Out

• Be prepared to share
• what you did.
• what you discovered.
• what concepts and skills were
• being developed.
• what questions emerged for further
• investigation.

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Discrete Math

• Read the assigned lesson.
• Discuss
• What skills are developed in discrete math
  lessons?
• What connections to other areas of math can be
  observed?
• Be prepared to share your knowledge of the lesson
  and discrete math with your original group.

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Reflection Session

• Developed at
• Clemson University
• College of Engineering and Science

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Essential Components

• Development of a community of learners
• Explicit connections that make mathematics
  meaningful
• A model for verbal and written communication
• Balanced assessment practices
• A variety of problem solving experiences
• A diversity of materials, manipulatives, and
  models

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Focus on the Essential Components

• Give examples of how your essential component was
  used to develop mathematical ideas during the
  three days of training.
• How did your essential component impact you as a
  learner?

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Reflection

• What part of the Institute was most helpful to
  you as a teacher and/or leader?
• What part of the institute challenged your
  mathematical thinking? Explain.
• Is there anything you would like to see changed
  or added to make the institute more helpful?

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Revisiting Standards

• Examine your groups questions about the
  standards.
• Add to your chart using the Bright Idea Marker.
• Plan a way to share one question and answer from
  your chart.

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Session Goals

• Develop a deeper understanding and broader view
  of mathematical content knowledge
• Introduce materials and manipulatives used in the
  lessons
• Reflect on personal beliefs about the teaching
  and learning of mathematics

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Fulfilling the mathematical promise that exists
in every child www.mathoutofthebox.org