Place Value Perfection

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Place Value Perfection

• Lindsey Molenaar, Cedar Hill Mathematics Coach
• Jennifer Tomayko, Cedar Hill 4th Grade Teacher

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Math Name Game

• Use alliteration and math terms to create a new
  math name.
• Write your math name and your position for next
  year on your paper.
• Last, create a table tent and introduce yourself
  to your neighbors!

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Do you have a strong sense of number?

• Adult Number Sense Quiz

Adult Number Sense Game
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Place Value Progression

• Big Idea One - Sets of ten (and tens of tens) can
  be perceived as single entities or units. For
  example, three sets of tens and two singles is a
  base-ten method of describing 32 single objects.
  This is the major principle of base-ten
  numeration.
• National Library of Virtual Manipulatives

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Place Value Progression

• Big Idea Two - The positions of digits in numbers
  determine what they represent and which size
  group they count. This is the major organizing
  principle of place value numeration and is
  central for developing number sense.
• Greg Tang Place Value Game

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Place Value Progression

• Big Idea Three  There are patterns in the way
  that numbers are formed. For example, each decade
  has a symbolic pattern reflective of the 0-9
  sequence (e.g., 20, 21, 22 29).

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Place Value Progression

• Big Idea Four The groupings of ones, tens, and
  hundreds can be taken apart in different but
  equivalent ways. For example, beyond the typical
  way to decompose 256 of 2 hundreds, 5 tens, and 6
  ones, it can be represented as 1 hundred, 14
  tens, and 16 ones but also as 250 and 6.
  Decomposing and composing multi-digit
• numbers in flexible ways is a necessary
• foundation for computational estimation
  and
• exact computation.
• 3 other ways
  activity

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Place Value Progression

• Big Idea Five Really big numbers are best
  understood in terms of familiar real-world
  referents. It is difficult to conceptualize
  quantities as large as 1000 or more. However, the
  number of people who will fill the local sports
  arena is, for
• example, a meaningful referent for
• those who have experienced that
• crowd.

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Place Value Vertical Alignment

• Read the foundation of our place value standards.
• Determine how the standards build from
  Kindergarten through Sixth grade.
• Sort the standards by grade level from K-6.
• Discuss your findings.

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Vertical Alignment

• Kindergarten AKS

• First Grade AKS

Count to 100 by ones and tens.
Count forward by ones, beginning from a given number within the known sequence (instead of having to begin at 1).
Count up to 20 objects arranged in a line, rectangular array, or circle or up to 10 objects in a scattered configuration.
Compare two numbers between 1 and 10 presented as written numerals.
Compose and decompose numbers from 11 to 19 into ten ones and some further ones (e.g., by using objects or drawings), and record each composition or decomposition by a drawing or equation (e.g., 18 10 8) understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones.
Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral.
Model and explain that a two-digit number represents amounts of tens and ones.
Explain that 10 can be thought of as a bundle of ten ones called a "ten."
Model the numbers 11 to 19 showing they are composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones.
Using mental math strategies identify one more than, one less than, 10 more than, or 10 less than a given two-digit number explaining strategy used.
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Vertical Alignment

• Second Grade

• Third Grade

Determine whether a group of objects up to 20 has an odd or even number of members using various concrete representations (100s chart, ten grid frame, place value chart, number line, counters or other objects).
Explain that the three digits of a three-digit number represent amounts of hundreds, tens, and ones (e.g., 706 equals 7 hundreds, 0 tens, and 6 ones).
Read, write, and represent numbers to 1000 using a variety of models, diagrams and base ten numerals including standard and expanded form.
Explain that 100 can be thought of as a bundle of ten tens, called a "hundred.
Add and subtract fluently within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.
Multiply one-digit whole numbers by multiples of 10 in the range 10 ? 90 (e.g., 9 x 80, 5 x 60) using strategies based on place value and properties of operations.
Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operation (e.g., observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends).
Compare two fractions with the same numerator or the same denominator by reasoning about their size recognize that comparisons are valid only when the two fractions refer to the same whole and record the results of comparisons with the symbols gt, , or lt, and justify the conclusions (e.g., by using a visual fraction model).
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Vertical Alignment

• Fifth Grade

• Fourth Grade

Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left.
Explain patterns in the number of zeros of the product when multiplying a number by powers of 10 and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10 use whole-number exponents to denote powers of 10.
Use place value understanding to round decimals to any place.
Read, write, order, and compare place value of decimals to thousandths using base ten numerals, number names, and expanded form (e.g., 347.392 3 x 100 4 x 10 7 x 1 3 x (1/10) 9 x (1/100) 2 x (1/1000).
Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
Explain that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right (e.g., recognize that 700 70 10 by applying concepts of place value and division).
Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using gt, , and lt symbols to record the results of comparisons
Use place value understanding to round whole numbers to any place using tools such as a number line and/or charts.
Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols gt, , or lt, and justify the conclusions, e.g., by using a visual fraction model.
Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols gt, , lt, and justify the conclusions, e.g., by using a visual model.
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A Quick Place-Value Formative Assessment!

• Digital Correspondence Task(Ross 1986,2002)
• 1)Take out 36 blocks. Ask the student to count
  the blocks, and then have the student write the
  number that tells how many there are.
• 2) Circle the 6 in 36 and ask, Does this part of
  your 36 have anything to do with how many blocks
  there are?
• 3) Circle the 3 and repeat the question.
• Do not give clues. Based on their response, they
  
• can be identified at five levels of place value
  understanding.

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Levels of Place Value Understanding

• Level 1 Single numeral
• Student views the number 36 as one numeral
• Level 2 Position names
• Student identifies the tens and one position
  but makes not
• connection between the individual digits and
  the blocks
• Level 3 Face Value
• Student matches 6 block with 6 and three
  blocks with 3
• Level 4 Transition to Place Value
• The 6 is matched with six blocks and the 3
  with the remaining
• 30, but not as three groups of 10
• Level 5 Full Understanding

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Greg Tangs Funny Numbers

• -Step 1 Add the columns vertically. Leave the
  double digit number in the "ones" column.
• -Step 2 Add the number in the "tens" column to
  the tens number (1) from the "ones"
  column. HINT It will always be a 1 that you
  add.
• -Step 3 Bring the remaining "ones" number down.
  This is your final answer.
• This is a different way to look at addition,
  instead of "carry the one." With enough practice,
  the students will be able to do this in their
  heads without having to write out the funny
  number.
• You can add and subtract larger numbers too!

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Place Value in Action

• This second grade teacher models two games
• Trash Can 101 and Out
• How would you use an activity like this in your
  room?
• What (if any) modifications would you make?

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Using New Manipulatives

• Coins and Money!
• Use pennies, dimes, and dollars to help build the
  understanding of making groups and exchanges

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Using New Manipulatives

• Connecting Cubes, Snap Cubes, Unifix Cubes, or
  Color Tiles
• Composing groups, building the tens, composing
  and organizing materials
• Counting and grouping efficiently and correctly

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Open Number Line

• A new tool in EVERY grade levels manipulative
  kit!
• A visual way to display students thinking
• place value number line
• Lets explore
• Making a chronological number line
• Subtraction on the number line
• Multiplication on the number line

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Place Value Gallery Time

• View the place value activities.
• Take pictures or note ideas.
• Read cards or ask questions about any stations.
• Be inspired!

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Reflection Differentiation

• Reflect on your learning today
• How will you develop place value with your
  students next year?
• What activities will you use in your classroom?
• How or what would you modify in these activities?
  
• What concerns you mathematically about your
  students?
• What are you confident and excited about teaching
  your students in math?

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Questions or Comments?
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Making Tens in Action

• Lets learn some ways to help students build the
  concept of a ten without base ten blocks!
• How would you use this in your classroom?

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Place Value Background

• The value of a digit depending on its position in
  the number, such as ones, tens, hundreds, and
  thousands places. Any number can be broken down
  by its place value. For example, 32 can been
  broken down into 32 ones or 3 groups of ten and 2
  ones.
• Remind children that a number is made up of
  digits or numerals. For example, the number 3 has
  one digit, while the number 987 has three digits.
• Children should know that when writing a
  four-digit number, they should place a comma
  after the thousands place. They should notice
  that commas are placed after every three digits
  from the right.
• Reading numbers with zeros or ones in the middle
  can be challenging because they must remember to
  hold the place of the digit without saying its
  exact name. 
• Expose children to a large variety of numbers and
  use a variety manipulatives to explore and
  represent them.
• Use number lines, connecting cubes, base-ten
  blocks, place value charts, and hundred charts to
  help children visualize numbers in different
  ways.

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Place Value Background

• Place value is integral to truly understanding
  the process behind multi-digit addition and
  subtraction.
• Just because a student can identify the digit in
  the tens place, doesn't mean they understand what
  that digit means.  Students need lots of concrete
  opportunities to group objects into groups of
  tens and count them.
• They need to compose and decompose numbers in
  different ways.