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 http://www.nytimes.com/interactive/2008/09/15/science/20080915_NUMBER_SENSE_GRAPHIC.html 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 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.

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 >, =, or <, and justify the conclusions (e.g., by using a visual fraction model).

Use place value understanding to round decimals to any place. 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 >, =, 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.

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? https://www.teachingchannel.org/videos/second-grade-math-lesson

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

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

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?

Making Tens in Action Let’s learn some ways to help students build the concept of a ten without base ten blocks! How would you use this in your classroom? https://www.youtube.com/watch?v=A7bEhBCebOY

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.

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.