How can I add and subtract Tens and Hundreds using regrouping? / Key Concepts / Cross Curricular Connections
- Strategies for Adding and Subtracting within 1,000
- Strategies for Composing Tens and Hundreds within 1,000*
- Strategies for Decomposing Tens and Hundreds within 1,000
- Students Explanations for Choice of Solution Methods**
Social Studies: Compare the various populations of the different types of communities, also compare the various services in each community, compute the number of miles traveled in a daily commute and compare the distance traveled in the different
communities. Determine the distance needed to travel to get to the different resources, such as, hospital, grocery store, and school.
Unit Vocabulary
Algorithm Compensation Compose DecomposeNew groups below
Simplifying strategy
Assessments
*Mid-Module Assessment: After Session B (2 days, included in Unit Instructional Days)
**End of Module Assessment: After Session D(2 days, included in Unit Instructional Days)
Mathematical Practices
MP.3 Construct viable arguments and critique the reasoning of others. Students use place value reasoning to explain how each step in their drawing relates to a step in the written method. They choose and explain various solution strategies such as number bonds, chip models, the vertical method, arrow notation, and tape diagrams. They critique the reasoning of others when they listen to their peers explain their strategies for solving problems, and they discuss the efficacy of those strategies.
MP.6 Attend to precision. Students attend to precision when they use place value language to explain their math drawings and calculations. They articulate the arithmetic properties they use to solve a variety of problems. For example, when adding 825 + 80, a student may show understanding of the associative property by saying, “I know that 20 + 80 equals 100, so I added 800 + 100 + 5, which equals 905.”
MP.7 Look for and make use of structure. Students look for and make use of the base ten structures when composing and decomposing. They extend their understanding from Module 4, viewing 10 tens as forming a new unit called a hundred, just as they understand that 10 ones forms 1 ten. They apply this understanding of base ten structure when adding and subtracting three-digit numbers, repeatedly bundling and unbundling groups of ten. They also make use of structure when they use simplifying strategies, such as compensation, to create a multiple of ten or a hundred.
MP.8 Look for and express regularity in repeated reasoning. As students repeatedly manipulate models and record the work abstractly, they recognize the cyclic pattern of the addition or subtraction of like units and the subsequent potential composition or decomposition of units through the place values. They see that the written form represents the same cycle they use with the manipulatives.
Grade 2 UNIT 5: Addition and Subtraction within 1,000 with Word Problems Suggested Range: 24 days
Unit Outcome (Focus)In Unit 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 unit, students continue to focus on strengthening and deepening conceptual understanding and fluency.
UNIT 5 SECTION A: Strategies for Adding and Subtracting within 1,000 Suggested Number of Days: 7
Essential QuestionHow can I add and subtract Tens and Hundreds using regrouping? / Key Objectives
- Relate 10 more, 10 less, 100 more, and 100 less to addition and subtraction of 10 and 100.
- Add and subtract multiples of 100 including counting on to subtract.
- Add multiples of 100 and some tens within 1,000.
- Subtract multiples of 100 and some tens within 1,000.
- Use the associative property to make a hundred in one addend.
- Use the associative property to subtract from three-digit numbers and verify solutions with addition.
- Share and critique solution strategies for varied addition and subtraction problems within 1,000.
Comments / Standard No. / Standard
Major Standard Supporting Standard Additional Standard / Priority
Begins at Grade 3
Section A focuses on place value strategies to add and subtract within 1,000 (2.NBT.7). Students relate 100 more and 100 less to addition and subtraction of 100 (2.NBT.8). They add and subtract multiples of 100, including counting on to subtract (e.g., for 650 – 300, they start at 300 and think, “300 more gets me to 600, and 50 more gets me to 650, so… 350”). Students also use simplifying strategies for addition and subtraction: they extend the make a ten strategy to make a hundred, mentally decomposing one addend to make a hundred with the other (e.g., 299 + 6 becomes 299 + 1 + 5, or 300 + 5, which equals 305) and use compensation to subtract from three-digit numbers (e.g., for 376 – 59, add 1 to each, 377 – 60 = 317). The topic ends with students sharing and critiquing solution strategies for addition and subtraction problems. Throughout the topic, students use place value language and properties of operations to explain why their strategies work (2.NBT.9). / 2.NBT.7
2.NBT.8
2.NBT.9 / Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds.
Mentally add 10 or 100 to a given number 100–900, and mentally subtract 10 or 100 from a given number 100–900.
Explain why addition and subtraction strategies work, using place value and the properties of operations. (Explanations may be supported by drawings or objects.)
UNIT 5 SECTIONB: Strategies for Composing Tens and Hundreds within 1,000 Suggested Number of Days: 5
Essential QuestionHow can I add and subtract Tens and Hundreds using regrouping? / Key Objectives
- Relate manipulative representations to the addition algorithm.
- Use math drawings to represent additions with up to two compositions and relate drawings to the addition algorithm.
- Choose and explain solution strategies and record with a written addition method.
Comments / Standard No. / Standard
Major Standard Supporting Standard Additional Standard / Priority
Begins at Grade 3
In Section C, students continue to build on Module 4’s work, composing tens and hundreds within 1,000 (2.NBT.7). As each of these objectives begins, students relate manipulative representations to the algorithm, then transition to making math drawings in place of the manipulatives. As always, students use place value reasoning and properties of operations to explain their work. / 2.NBT.7
2.NBT.9 / Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds.
Explain why addition and subtraction strategies work, using place value and the properties of operations. (Explanations may be supported by drawings or objects.)
UNIT 5 SECTION C: Strategies for Decomposing Tens and Hundreds within 1,000 Suggested Number of Days: 6
Essential QuestionHow can I add and subtract Tens and Hundreds using regrouping? / Key Objectives
- Relate manipulative representations to the subtraction algorithm, and use addition to explain why the subtraction method works.
- Use math drawings to represent subtraction with up to two decompositions, relate drawings to the algorithm, and use addition to explain why the subtraction method works.
- Subtract from multiples of 100 and from numbers with zero in the tens place.
- Apply and explain alternate methods for subtracting from multiples of 100 and from numbers with zero in the tens place.
Comments / Standard No. / Standard
Major Standard Supporting Standard Additional Standard / Priority
Begins at Grade 3
In Section C, students continue to build on Module 4’s work, decomposing tens and hundreds within 1,000 (2.NBT.7). As each of these objectives begins, students relate manipulative representations to the algorithm, then transition to making math drawings in place of the manipulatives. As always, students use place value reasoning and properties of operations to explain their work. / 2.NBT.7
2.NBT.9 / Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds.
Explain why addition and subtraction strategies work, using place value and the properties of operations. (Explanations may be supported by drawings or objects.)
UNIT 5 SECTION D: Student Explanations for Choice of Solution Methods Suggested Number of Days: 2
Essential QuestionHow can I add and subtract Tens and Hundreds using regrouping? / Key Objectives
- Choose and explain solution strategies and record with a written addition or subtraction method.
Comments / Standard No. / Standard
Major Standard Supporting Standard Additional Standard / Priority
Begins at Grade 3
The unit culminates with Section D, wherein students synthesize their understanding of addition and subtraction strategies and choose which strategy is most efficient for given problems. They defend their choices using place value language and their understanding of the properties of operations (2.NBT.9). / 2.NBT.7
2.NBT.8
2.NBT.9 / Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds.
Mentally add 10 or 100 to a given number 100–900, and mentally subtract 10 or 100 from a given number 100–900.
Explain why addition and subtraction strategies work, using place value and the properties of operations. (Explanations may be supported by drawings or objects.)
Possible Activities
PLACE VALUE PUZZLES: (small group/whole class) The teacher writes dashes for an unknown number: ______and provides clues to help students solve the problem. Sample puzzles can be downloaded online (see right). Extend: Ask students to create puzzles for other students to solve.Ex: Clue 1: The digit in the hundreds place is the difference of 36 and 42. The digit in the ones place is the number of sides in an octagon, etc.
CREATE A NUMBER ACTIVITY: Students have a piece of paper with ______written on it. The teacher calls out three digits, one at a time. The students place the digit on any open space on their paper. Once students have placed all three digits, students are asked to say their number aloud to their partner, and write their number in written and expanded form. Teacher then may ask some prompting questions, such as: Who has a number greater than 769? What is your number? Who has a number less than 599? Who has a number you will land on it that if you skip count by 5s? Who has a multiple of 10, etc.?Have the students write their answers in their math journal. Extend: Have them write a number story with their number as the sum, or difference, or addend, etc.
SKIP COUNTING ACTIVITY: Create a rhythm for skip counting. Have students write the numbers vertically as they count on by 5s to make the number pattern more apparent. Ask the students what kind of pattern they see. Do this same activity with 5s 10s and 100s. Worksheets can be found online (see right). Ex: Clap on 5, slap your knees for ten, clap for 15, etc.
“I HAVE, WHO HAS?” Students are given one card (or two if you have extra cards) from a deck of “I Have, Who Has?” cards. The teacher designates a student to begin the game. The student stands up and reads (loud and clear)…I have number 14, who has 8+5? The student who has number 13 stands up and says…I have 13,who has 6 + 3? The next student with 9 stands up, etc. The game continues until you get back to the first student. “I have, who has?” can created or found online (see Resources, below). To create the cards write a green number on the top “I Have” and a number sentence in red on the bottom “Who Has?” The deck needs to be created all at once as it is like a link and chain that has to have a beginning point and an end point. It is better to have too many cards as you can always give a few students two cards.
Extend: Track the time it takes to finish a round and have students try to beat their previous time.
SPIN, ROLL, COMPARE: (2 person game.) Reinforce place value and greater than and less than symbols: Each student receives a place value mat divided into ones, tens and hundreds, a blank template numbered 1–10 down the left side of the paper, a die (9 sided die is ideal), and a spinner. A spinner can be made with a paper clip and piece of cardboard. The spinner is divided into three areas: ones, tens, and hundreds. One student rolls the die and then spins the spinner. If the student rolls a 5 and the spinner points to tens, the student places 5 rods (place value blocks) in the tens column on the place value mat. If the spinner says ones, the students places 5 ones (place value cubes) on the ones portion of the mat. The students do this until they have rods in the ones, tens and hundreds place. Once the placemat is filled in across the number of place value cubes, each student has a number. The students each write their number on their paper. The students then compare the two numbers. Which is larger? Smaller? The students decide and write the appropriate symbol < or > to the right of their number and their partner’s number to the right of the comparison symbol. Extend: if students are ready, they can also include thousands in all aspects of this game.
More Comparing Games are available online (see Resources, below).
Ex: Student A has 514; Student B has 712. Student A’s paper will read 514 < 712 and student B’s paper will read 712 > 514.
Resources
Pre-made ‘I Have, Who Has?’ cards and math game boards can be found at rethinkmathematics.com. Click Math Games on the top right.
Additional Websites:
Math Class Games:
Common Core Specific Questions:
Multi-Step Word Problems:
Common Core Specific Questions:
Topic Specific Practice:
Topic Specific Practice:
Library of Virtual Manipulatives:
More Comparing Games can be found at math-play.com.
Premade worksheets can be found at: dadsworksheets.com
Comparison Lesson Ideas:
Apps:
Number Math – Free - Number Math App is for practicing basic elementary number facts. It includes: missing numbers, before/after, greater than/less than, skip counting, rounding, and more.
Pearl Diver HD and Lobster Diver HD – These apps, designed for grades 3-8, are great for understanding numbers, understanding fractions, reading a number line, and comparing and ordering fractions.
Arithmetic Invaders Express: Grade K-2 Math Facts – Defend the solar system by solving counting, addition, subtraction, and multiplication problems.
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