Strand: NUMBER AND OPERATIONS IN BASE TEN (2.NBT)

Understand place value (Standards 2.NBT.1-4). They use place value understanding and properties of operations to add and subtract (Standards 2.NBT.5-9).
• Boxes and Cartons of Pencils
In this task students are given information about quantities of pencils packed in boxes and cartons and asked to solve problems such as "Jem has 1 carton and 4 boxes. How many pencils does Jem have all together?"
• Bundling and Unbundling
In this task students determine the number of hundreds, tens and ones that are necessary to write equations when some digits are provided. The student must, in some cases, decompose hundreds to tens and tens to ones.
• Choral Counting
This task was designed to support students in developing the concept of ten more and ten less, moving from concrete representation to understanding of the unit of ten within ten more and ten less. Students will also understand the value of ten(s) within any number as they mentally add or subtract 10 from a given number 100-900.
• Comparisons 1
This task requires students to compare numbers that are identified by word names and not just digits. The order of the numbers described in words are intentionally placed in a different order than their base-ten counterparts so that students need to think carefully about the value of the numbers.
• Comparisons 2
The comparisons here involve sums and differences - not primarily to provide an opportunity to calculate, but rather in order to stimulate studentsâ€™ thinking about the magnitudes of the base-ten units of which numbers are composed.
• Counting Stamps
This is an instructional task related to deepening place-value concepts. The important piece of knowledge upon which students need to draw is that 10 tens is 1 hundred. So each sheet contains 100 stamps.
• Digits 2-5-7
This task asks students to use all the digits 5, 7, and 2 to create different 3-digit numbers.
• Ford and Logan Add 45+36
This task was designed to give students opportunities to solve a problem and analyze other students solutions while working on adding two-digit numbers.
• Grade 2 Math Module 1: Sums and Differences to 100 (EngageNY)
Module 1 sets the foundation for students to master sums and differences to 20. Students subsequently apply these skills to fluently add one-digit to two-digit numbers at least through 100 using place value understanding, properties of operations, and the relationship between addition and subtraction.
• Grade 2 Math Module 3: Place Value, Counting, and Comparison of Numbers to 1,000 (EngageNY)
In this 25-day Grade 2 module, students expand their skill with and understanding of units by bundling ones, tens, and hundreds up to a thousand with straws. Unlike the length of 10 centimeters in Module 2, these bundles are discrete sets. One unit can be grabbed and counted just like a banana-1 hundred, 2 hundred, 3 hundred, etc. A number in Grade 1 generally consisted of two different units, tens and ones. Now, in Grade 2, a number generally consists of three units: hundreds, tens, and ones. The bundled units are organized by separating them largest to smallest, ordered from left to right. Over the course of the module, instruction moves from physical bundles that show the proportionality of the units to non-proportional place value disks and to numerals on the place value chart.
• Grade 2 Math Module 4: Addition and Subtraction Within 200 with Word Problems to 100 (EngageNY)
In Module 4, students develop place value strategies to fluently add and subtract within 100; they represent and solve one- and two-step word problems of varying types within 100; and they develop conceptual understanding of addition and subtraction of multi-digit numbers within 200. Using a concrete to pictorial to abstract approach, students use manipulatives and math drawings to develop an understanding of the composition and decomposition of units, and they relate these representations to the standard algorithm for addition and subtraction.
• Grade 2 Math Module 5: Addition and Subtraction Within 1,000 with Word Problems to 100 (Engage NY)
In Module 5, students build upon their mastery of renaming place value units and extend their work with conceptual understanding of the addition and subtraction algorithms to numbers within 1,000, always with the option of modeling with materials or drawings. Throughout the module, students continue to focus on strengthening and deepening conceptual understanding and fluency.
In order to assist educators with the implementation of the Common Core, the New York State Education Department provides curricular modules in Pre-K-Grade 12 English Language Arts and Mathematics that schools and districts can adopt or adapt for local purposes.
• Grade 2 Unit 1: Extending Base Ten Understanding (Georgia Standards)
In this unit, students will understand the value placed on the digits within a three-digit number, recognize that a hundred is created from ten groups of ten, use skip counting strategies to skip count by 5s, 10s, and 100s within 1,000 and represent numbers to 1,000 by using numbers, number names, and expanded form, compare two-digit number using >, =, <.
• Grade 2 Unit 2: Becoming Fluent with Addition and Subtraction (Georgia Standards)
In this unit students will cultivate an understanding of how addition and subtraction affect quantities and are related to each other, will reinforce the multiple meanings for addition (combine, join, and count on) and subtraction (take away, remove, count back, and compare), further develop their understanding of the relationships between addition and subtraction, recognize how the digits 0-9 are used in our place value system to create numbers and manipulate amounts and continue to develop their understanding solving problems with money.
• Grade 2 Unit 4: Applying Base Ten Understanding (Georgia Standards)
In this unit students will continue to develop their understanding of and facility with addition and subtraction, add up to 4 two-digit numbers, use a variety of models (base ten blocks- ones, tens, and hundreds only; diagrams; number lines; place value strategies; etc.) to add and subtract within one thousand and continue to develop their understanding of, and facility with, money.
• How Many Days Until Summer Vacation?
The purpose of the task is to allow children an opportunity to subtract a three-digit number including a zero that requires regrouping.
• IXL Game: Mixed operations: Addition and Subtraction
This game helps second graders fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. This is just one of many online games that supports the Utah Math core. Note: The IXL site requires subscription for unlimited use.
• Jamir's Penny Jar
The purpose of this task is to help students articulate their addition strategies as in and would be most appropriately used once students have a solid understanding of coin values. It also provides a context where it makes sense to "skip count by 5s and 10s" for the combinations that involve more than one nickel or dime.
• Largest Number Game
In this task students are told "Dona had cards with the numbers 0 to 9 written on them. She flipped over three of them. Her teacher said: 'If those three numbers are the digits in another number, what is the largest three-digit number you can make?'" Students should be asked to think through possibilities and then draw on their ability to compare three digit numbers to complete the task.
• Looking at Numbers Every Which Way
This task gives students the opportunity to work with multiple representations of base-ten numbers. The standard asks students to read and write numbers to 1000 using base-ten numerals, number names, and expanded form. This task addresses all of these and extends it by asking students to represent the numbers with pictures and on the number line.
• Making 124
Not all students have seen base-ten blocks. This task should only be used with students who know what they are or have some on-hand to use themselves. Students are asked explain how they found all the possible ways to make 124 using base-ten blocks.
• Many Ways to do Addition 2
The purpose of this task is not to teach or model the addition strategies. Rather the purpose of this task is make explicit different ways students can solve problems so that they will be able to find the most efficient strategy in any given situation and increase their addition fluency.
• Number and Operations in Base Ten (2.NBT) - Second Grade Core Guide
The Utah State Board of Education (USBE) and educators around the state of Utah developed these guides for Second Grade Mathematics - Number and Operations in Base Ten (2.NBT)
• Number Line Comparisons
The purpose of this task is for students to use the number line to make comparisons between 3-digit numbers. The task is designed, in part, to help students understand how the number line works and that numbers on the right of the number line are greater than numbers on the left.
• One, Ten, and One Hundred More and Less
This task acts as a bridge between understanding place value and using strategies based on place value for addition and subtraction. Within the classroom context, this activity can be differentiated using numbers that are either simpler or more difficult to manipulate across tens and hundreds.
• Ordering 3-digit numbers
In this task each number has at most 3 digits so that students have the opportunity to think about how digit placement affects the size of the number. Each group also contains a two-digit number so that students have to do more than just compare the first digit, the second digit, etc.
• Party Favors
The point of this task is to emphasize the grouping structure of the base-ten number system, and in particular the crucial fact that 10 tens make 1 hundred.
• Peyton and Presley Discuss Addition
This purpose of this task is to support students in developing an understanding of a place value strategy for adding numbers.
• Regrouping
This task serves as a bridge between understanding place-value and using strategies based on place-value structure for addition. Place-value notation leaves a lot of information implicit. The way that the numbers are represented in this task makes this information explicit, which can help students transition to adding standard base-ten numerals.
• Saving Money 1
The purpose of this task is for students to relate addition and subtraction problems to money and to situations and goals related to saving money.
• Saving Money 2
The purpose of this task is for students to relate addition and subtraction problems to money and to situations and goals related to saving money. This problem shows the work advanced second graders might use for adding 2-digit numbers.
• Teaching Different Methods To Count Collections
This Teaching Channel video shows students recording and sharing strategies when skip counting. (8 minutes)
• Ten \$10s make \$100
This task uses one, ten, and one-hundred dollar bills to help students think about bundling by ten.
• Three Composing/Decomposing Problems
The purpose of this task is to help students understand composing and decomposing ones, tens, and hundreds. This task is meant to be used in an instructional setting and would only be appropriate to use if students actually have base-ten blocks on hand.
• Toll Bridge Puzzle
This task is intended to assess adding of four numbers as given in the standard while still being placed in a problem-solving context. As written this task is instructional; due to the random aspect regarding when the correct route is found, it is not appropriate for assessment.
• Using Pictures to Explain Number Comparisons
The purpose of this task is for students to compare three-digit numbers and explain the comparisons based on the meaning of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons.

http://www.uen.org - in partnership with Utah State Board of Education (USBE) and Utah System of Higher Education (USHE).  Send questions or comments to USBE Specialists - Trish  French or Molly  Basham and see the Mathematics - Elementary website. For general questions about Utah's Core Standards contact the Director - Jennifer  Throndsen.

These materials have been produced by and for the teachers of the State of Utah. Copies of these materials may be freely reproduced for teacher and classroom use. When distributing these materials, credit should be given to Utah State Board of Education. These materials may not be published, in whole or part, or in any other format, without the written permission of the Utah State Board of Education, 250 East 500 South, PO Box 144200, Salt Lake City, Utah 84114-4200.