Transcript Diapositiva 1

Place
Value
Perfection
Lindsey Molenaar, Cedar Hill Mathematics Coach
Jennifer Tomayko, Cedar Hill 4th Grade Teacher
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!
Do you have a strong sense of
number?
Adult Number Sense Quiz
Adult Number Sense Game
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
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
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).
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
Place Value Progression…
• Big Idea Five: “Really big” numbers are
best understood in terms of familiar realworld 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.
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.
Vertical Alignment
Kindergarten 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.
First Grade AKS
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.
Vertical Alignment
Second 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.“
Third Grade
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 >, =, or <, and justify the
conclusions (e.g., by using a visual fraction model).
Vertical Alignment
Fourth Grade
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 >, =, and < 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 >, =, or <, 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 >, =, <, and justify the conclusions, e.g., by using a visual
model.
Fifth 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.
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.
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
Greg Tang’s 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!
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?
Open Number Line
• A new tool in EVERY grade level’s
manipulative kit!
• A visual way to display students
thinking
place value number line
• Let’s explore:
–Making a chronological number line
–Subtraction on the number line
–Multiplication on the number line
Place Value Gallery Time
• View the place value
activities.
• Take pictures or note ideas.
• Read cards or ask questions
about any stations.
• Be inspired!
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?
Questions or Comments?