What do you mean Compatible Numbers?

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What do you meanCompatible Numbers?

• DAY 2

Russell LarsonElementary Math Coordinator Pfluger
ville ISD Russell.larson_at_pflugervilleisd.net 512-5
94-0123
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Estimating withTrixUse the 100s chart to
pick your range.
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NORMS

• Collaborate with an open mind!
• Listen with intent to learn.
• Take care of your needs.
• Silence your cell phones.
• Suffering is optionalEnjoy yourself!
• What is learned hereLeaves here!

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GOALS

• Know the similarities and differences between
  rounding and compatible numbers
• Understand that the goal of the TEKS is that
  students can use multiple strategies to
  approximate quantities based on real world
  situations
• Understand that flexibility with numbers and
  numerical reasoning builds number sense that
  encourages various strategies for estimation.
• Understand how to build number sense at your
  grade level!

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AGENDA Day 2

• What is Number Sense?
• Decomposing Numbers
• and - Number Sense Strategies
• Multiplication Fluency
• Multiplication Fact Strategies
• Fluency Games

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At your table

• Discuss the relationship between
• Composing and Decomposing Numbers
• Number Sense
• Mathematical Fluency

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Some Sum!

• Find the sum of the following numbers
• 3996 4246

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Did you use the carrying algorithm?

• If you didnt, CONGRATULATIONS!

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Students Using Number Sense Might

• Remove 4 from 4,246 and make that 4,242. Combine
  the 4 with 3,996 to make the problem 4,000
  4,242.
• Other ways?

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What About

• 234 136
• 235 135
• 240 140 10
• 289 79
• 290 80 2
• 300 80 11 - 1

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The Algorithm Step by Step

• Write down the problem
• 3996
• 4246

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Childrens Struggles with Algorithms

• Remembering the steps
• Understanding the steps
• Children lose sight of place value since the
  numbers are treated as digits and not quantities.
• The steps seem nonsensical to children.
• Children simply begin to repeat procedures.
• Because it is nonsensical, meaning is lost.
• Children become satisfied with nonsensical
  answers. (dont question wrong answers)

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Sometimes algorithms use less paper.
Advantages of Algorithms
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248

• How many different ways can you make 248?
• List 3 numbers that are compatible with 248?

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• 12 12 18 6 8 X 3
• 6 x 4 2 x 2 x 2 x 3 20 4 2 x 12
• 9 x 3 3 36 12 2 (10 2)
• 48 2(10) 4(1) 48x½
• 2

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46 38

• Take a look at this math problem in a different
  way.
• How can decomposing help you make this problem
  easier.

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- Number Sense Strategies

• Gr. 1 Doubles and Near Doubles /- (p.133
  144)
• Gr. 2 Splitting and Swapping (p. 134 138)
• Gr. 3 Making Jumps of 10 backwards (p.136
  144)
• Gr. 4 Adding On vs. Removing (p. 140)
• Gr. 5 Moving to the next Friendly 10 (p. 137
  147)
• Gr. 6 Constant Difference (p. 148)
• Gr. 7 Canceling out common amounts (p. 150)

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The Digits Game
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BREAK Time

• Be back in 15 minutes

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What is the 1 mathematical complaint from MS
teachers who inherit your students?

• Multiplication Facts

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Brain Research Remembering Math Facts

• Human brain organizes information by patterns and
  associations.
• Associative memory causes problems when learning
  multiplication facts.

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Why Decompose?
Working Memory
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Brain Research Remembering Math Facts

• Say these math facts aloud
• 6 x 9 54
• 7 x 8 56
• 8 x 8 64

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Brain Research Remembering Math Facts

• 6 x 9
• 45? 54? 56? 58?

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Memorization Test

• Carl Dennis lives on Allen Brian Ave.
• Carl Gary lives on Brian Allen Ave.
• Gary Edwards lives on Carl Edward Ave.

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Test Time!

• Write your answers on scratch paper.

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Memorization Test

• Carl Dennis lives on Allen Brian Ave.
• 3 x 4 12
• Carl Gary lives on Brian Allen Ave.
• 3 x 7 21
• Gary Edwards lives on Carl Edward Ave.
• 7 x 5 35

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• How did you do?
• How did this test make you feel?
• Would you want the teacher to take a grade on
  your work?

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Math Facts???

• Do students have to know their math facts?
• What does knowing your math facts mean?

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Do the multiplication tables help or hinder?

• How do they hinder?
• If childrens introduction to arithmetic rests
  primarily on the rote memorization of addition
  and multiplication tables and other facts, then
  their intuitive understandings of number
  relationships are undermined and overwhelmed.
• Children then shift from intuitive processing to
  performing automatic operations without caring
  about their meaning.

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Do the multiplication tables help or hinder?

• How do they help?
• If instruction in beginning arithmetic takes
  advantage of number sense, subitizing, and
  counting strategies by making connections to new
  mathematical operations, then the tables become
  tools leading to a deeper understanding of
  mathematics, rather than an end unto themselves.

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Memorization vs. Automaticity

• Read pgs. 98-99 (YM_at_W)
• Teachers who use timed tests believe that the
  tests help children learn basic facts. Children
  who perform well under time pressure display
  their skills. Children who have difficulty with
  skills, or who work more slowly, run the risk of
  reinforcing wrong learning under pressure. In
  addition, children can become fearful and
  negative toward their math learning.
• (Burns, 2000, p. 157)

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Strategies for Multiplication Facts

• Doubles
• Fives Facts
• Zeros and Ones
• Nifty Nines

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SoWhat Else Can We Do?

• If you didnt know the answer to 6 x 8
• how could you figure it out by using something
  that you do know?
• Decompose multiplication facts daily!

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Helping Fact Strategies

• Double and Double Again 4 x 8
• 4 must be one of the factors
• Double and One More 3 x 7
• Facts w/ a factor of 3
• Half then Double 8 x 6
• One factor must be even
• Add one more set 6 x 7
• Known fact is one away

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Lets Practice

• 6 x 9
• 7 x 7
• 8 x 3
• 9 x 8
• 7 x 8

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Fact Remediation for the Upper Grades

• Recognize that more drill will not work!
• Inventory the known and unknown facts for each
  student in need.
• Diagnose strengths and weaknesses.
• Provide HOPE!
• Build in Success

Teaching for Mastery of Multiplication
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Lunch Time !
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Activity Rotation

• Product Game
• Broken Calculator
• Math Detective
• Contig

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BREAK Time

• Be back in 15 minutes

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Group Reflection

• Poster Rotation (thought or example)
• Compatible Numbers
• Rounding
• Number Sense
• Addition Subtraction Fluency
• Multiplication Fluency

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Tips for Estimation

• Help students learn strategies by having them use
  a specified approach. Later activities should
  permit students to choose whatever techniques
  they wish.
• Periodically discuss how different students made
  their estimates. This will help students
  understand that there is no single right way to
  estimate and also remind them of different
  approaches that are useful.
• Accept a range of estimates. Think in relative
  terms about what is a good estimate.
• Teaching Student Centered Mathematics Grades
  3-5
• 
  John A. Van de Walle

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Intention Statements

• I intend to.
• I will
• No matter what