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 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.

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 AKSCount 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 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 E 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 AlignmentFourth Grade Fifth 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.

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

• View the place value activities.

• Take pictures or note ideas.• Read cards or ask questions

about any stations.• Be inspired!

Place Value Gallery Time

• 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?

Reflection & Differentiation

Questions or Comments?