Global Concept Guides: Model and Draw with 3-Digit Numbers; Regrouping Ones, Tens, and Hundreds with the Break-Apart Strategy; Regrouping Ones, Tens, and Hundreds with the Traditional Algorithm; Regrouping Across Zeros; Applying the Traditional Algorithm with 3-Digit Numbers
Prior Learning: MACC.1.NBT.3.4
Progressions Document Link
Sample Show What You Know Task:Use the Go Math Ch. 6 Show What You Know or the Diagnostic Interview Task TE p.278
Common Core State Standards for Mathematical Content :
Use place value understanding and properties of operations to add and subtract.
MACC.2.NBT.7Add 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 subtraction 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. / Comments:
Notes on Assessment:
Unit 7 Assessment: Go Math Ch. 6
See common performance task link below.
Unpacking the Standards for this Unit:
This unit adds on to the two previous units by adding and subtracting to 1,000. It is important to remember that students in second grade should have “ample experiences using concrete materials and pictorial representations to support their work. This standard also references composing and decomposing a ten. This work should include strategies such as making a 10, making a 100, breaking apart a 10, or creating an easier problem. The standard algorithm of carrying or borrowing is not an expectation in Second Grade. Students are not expected to add and subtract whole numbers using a standard algorithm until the end of Fourth Grade.” For more information click here. While the standard (traditional) algorithm could be used here, students’ experiences should extend beyond only working with the algorithm. Even though students have had three units of addition and subtraction it is important for students to have plenty of experiences using manipulatives (base-ten blocks, open number lines, pictorial representation, etc…)
Common Performance Task with Rubric for this Unit:
Crawford’s Candy Factory - Students will solve 3-digit addition and subtraction word problems using various strategies of their choosing and be able to show their answer.
Click here for performance task and rubric.
Future learning:
This will help the child develop mastery of the traditional algorithm by the end of Fourth Grade. By students decomposing numbers in efficient ways they are setting up the foundation for the distributive property for multiplication and division in future grades.
2nd / Global Concept 1 of 5 for this Unit of Study: Model and Draw with 3-Digit Numbers
This GCG focuses on connecting models and pictures with 3-digit addition and subtraction. / Projected Time Allotment:
4 days
Sample Essential Questions:
Day 1: How do you use models to add and subtract 3-digit numbers?
Day 2: How do I know what operation to use when adding and subtracting 3-digit numbers?
Day 3: How do I connect my models to drawings with 3-digit addition and subtraction?
Day 4: How do you draw pictures to add and subtract 3-digit numbers?
Related Unit 7Assessment: Go Math Ch. 6# 5, 10, 17, 21, 22
Instructional Resources
Manipulatives:
- Base Ten Blocksto directly model the value of the digits and the actions in the word problems.
- Place Value Mat with ten framesto organize and structure problems with and without regrouping.
- Go Math Lesson 6.1 Essentials: Model and Draw TE p. 282; Problem Solving p.284 #6-9
- Go Math Lesson 6.6 Essentials: Choose any parts from this lesson to guide your instruction.
- Problem Solving Scenarios– examples of word problems
- iTools Base- Hundred Blocks – virtual manipulative
Sample HOT Questions: Use these to facilitate student discussions. (SMP 1, 3)
- Based on the numbers in this problem, what do you estimate the sum/difference to be?
- How does your base ten blocks represent what’s happening in the problem?
- What does your collection of base ten blocks represent in the problem? (For example: students may say 127 marbles)
- What does the rod represent in this word problem?
- What happens if I add or take away a tens rod to one of the addends, how will your sum change?
- How would you use subtraction/addition to check your work? (use inverse operations)
- Teacher supplies the two 3-digit numbers, and the students create word problems that involve addition or subtraction.
- What patterns do you see when you are regrouping ones to tens and tens to hundreds? Explain your thinking.
- Why do you think we call our number system – “a base ten system”?
- What patterns do you notice when you are regrouping with addition compared to regrouping with subtraction?
- Describe how you modeled your problem.
Students arebetter able to…
- Directly model the actions within a word problem using base ten blocks. (SMP 1, 2, 4)
- Regroup 3-digit numbers within addition/subtraction problems. (SMP 1)
- Articulate when and why they need to regroup when seeing an addition/subtraction problem.
For more info on SMP’s click here. / Because as teachers we are…
- Provide opportunities for students to directly model the actions with a word problem using base ten blocks.
- Help make connections with regrouping and representing numbers flexibly. (See power point) (SMP 3)
- Emphasize precise use of vocabulary: ones, tens, hundreds, digits, values, regroup, regrouping, trading, addend, sum, subtrahend, minuend, difference, partitioning, represent, model (SMP 6)
2nd / Global Concept 2 of 5 for this Unit of Study: Regrouping Ones, Tens, and Hundreds with the Break-Apart Strategy
This GCG focuses on making connections with expanded form and open number lines to the break-apart algorithm with 3-digit numbers in addition and subtraction. / Projected Time Allotment:
3 days
Sample Essential Questions:
Day 1: How can I use expanded form to help me add with the break-apart algorithm?
Day 2: How can I use an open number line to help me add and subtract with the break-apart algorithm?
Day 3: How can I apply the break-apart algorithm with 3-digit addition and subtraction?
Related Unit 7Assessment: Go Math Ch. 6 # 6, 18
Instructional Resources
Manipulatives:
- Base Ten Blocks to directly model the value of the digits and the actions in the word problems.
- Place value mat with ten frames to organize and structure problems with and without regrouping.
- Secret code cards to model the place value strategy.
- Open number line (See PowerPoint from Unit 5 GCG2)
- Go Math Lesson 6.2 Essentials: Model and DrawTE p. 286; (Use to guide instruction.) Problem Solving p. 288
- Break apart 3-digit addendsmatching game
- iTools Base- Hundred Blocks – virtual manipulative
Sample HOT Questions: Use these to facilitate student discussions. (SMP 1, 3)
- Draw a quick pictures and write to explain how to break apart addends to find the sum of 324 + 231.
- How do you break apart addends to add hundreds, tens, and then ones?
- How do I use an open number line to subtract 3-digit numbers with the break apart strategy?
- How is the break-apart similar in addition and subtraction? How is it different?
- How does expanded form help me to add or subtract mentally or more efficiently?
- How is 233 + 548 like adding 133 + 648? How is it different?
- How can I use a number line to help me model how I combine and compare numbers?
Our students arebetter able to…
- Use break-apart algorithm to solve 3-digit addition and subtraction problems. (SMP 1)
- Relate the break-apart algorithm to expanded forms of a number. (SMP 1, 3)
- Use an open number as a tool for applying the break-apart strategy to efficiently solve 3-digit addition and subtraction problems. (SMP 5, 7)
- Strategically decompose numbers to solve addition and subtraction more efficiently.
For more info on SMP’s click here. / Because as teachers we…
- Provide opportunities for students to use open number lines and base ten blocks to model break-apart algorithm. (SMP 5, 7)
- Help make connections between number patterns and place value in solving addition and subtraction.(SMP 3, 7)
- Emphasize precise use of vocabulary: break-apart algorithm, ones, tens, hundreds, digits, values, regroup, regrouping, trading, addend, sum, subtrahend, minuend, difference, partitioning, represent, model, open number line. (SMP 6)
2nd / Global Concept 3 of 5 for thisUnit of Study: Regrouping Ones, Tens, and Hundreds with the Traditional Algorithm
This GCG focuses on making connections with models of 3-digit addition and subtraction to the traditional algorithm. / Projected Time Allotment:5 days
Sample Essential Questions:
Day 1: How do you connect pictures to algorithm when regrouping tens?
Day 2: How do you connect pictures to algorithm when regrouping hundreds?
Day 3: How do I record my steps in the traditional algorithm when adding 3-digit numbers?
Day 4: How do I record my steps in the traditional algorithm when subtracting 3-digit numbers?
Day 5: How do I explain why the traditional algorithm works?
Related Unit 7Assessment: Go Math Ch. 6 # 1, 2, 3, 4, 7, 8, 9, 11, 13, 14, 15, 16, 19, 20, 23
Instructional Resources
Manipulatives:
- Draw picturesto model the value of the digits and the actions in the word problems.
- Base Ten Blocks to directly model the value of the digits and the actions in the word problems.
- Place value mat with ten frames to organize and structure problems with and without regrouping.
- Go Math Lesson 6.3 Essentials: Listen and Draw p.289; Model and Draw TE p. 290, Problem Solving p. 292
- Go Math Lesson 6.4 Essentials: Listen and Draw p.293; Model and DrawTE p. 294; Problem Solving p. 296
- Go Math Lesson 6.5 Essentials: Listen and Draw p.297; Model and Draw TE p. 298; Language Support (TE p. 297B); H.O.T. p. 299
- Go Math Lesson 6.7 Essentials: Listen and Draw p.305; Model and Draw TE p. 306; Problem Solving p. 308
- Go Math Lesson 6.8 Essentials: Listen and Draw p.309; Model and Draw TE p. 310; Problem Solving p. 312
- Go Math Lesson 6.9 Essentials: Listen and Draw p. 313; Model and DrawTE p. 314H.O.T. p. 315 #16-18, Problem Solving p. 316
- Sum Fun –game topractice addition
- Snake Subtraction – game to practice subtraction
- iTools Base- Hundred Blocks – virtual manipulative
- Country Countdown, Block Busters, Level V – online practice
- Country Countdown, Block Busters, Level W – online practice
- Estimating and Finding Sums less than 1,000 – tutorial
- 3-Digit Addition: Regroup Tens – online practice
- Addition with Regrouping up to 3-Digits – online practice
- Estimating and Finding Differences within 1,000 – tutorial
- 3-Digit Subtraction: Regroup Tens – online practice
- 3-Digit Subtraction: Regroup Hundreds – online practice
Sample HOT Questions: Use these to facilitate student discussions. (SMP 1, 3)
- When do you regroup ones in addition? When do you regroup tens in addition?
- When do you regroup tens in subtraction? When do you regroup hundreds in subtraction?
- Explain why you did or did not regroup?
- How does the algorithm represent my actions with my base ten blocks?
- How can you record what you just did in the algorithm?
- How can you record what you are doing with base ten blocks and pictures?
- What is the value of the ten when I regroup it into the hundreds column?
- When you regroup is the value of your new number the same as what you started with?
Our students are better able to…
- Articulate how and why the traditional algorithm works in addition and subtraction with 3-digit numbers. (SMP 2)
- Record 3-digit numbers within addition/subtraction problems with and without regrouping. (SMP 1)
- Articulate when and why they need to regroup when seeing an addition/subtraction problem. (SMP 1, 3)
- Provide opportunities for students to directly model the actions with a word problem using the traditional algorithm in addition and subtraction. (SMP 1, 2, 4)
- Provide opportunities for students to work together to understand the traditional algorithm. (SMP 3)
- Help make connections with regrouping and representing numbers flexibly. (SMP 3)
- Emphasize precise use of vocabulary: ones, tens, hundreds, digits, values, exchange, regroup, regrouping, trading, addend, sum, represent, model, subtrahend, minuend, difference, partitioning, algorithm, record (SMP 6)
2nd / Global Concept 4 of 5 for this Unit of Study: Regrouping Across Zeros
This GCG focuses on recording subtraction using the standard algorithm when there are zeros in the minuend and using compensation to subtract across zeros. / Projected Time Allotment:
2 days
Sample Essential Questions:
Day 1: How do you regroup when there are zeros in the number you start with?
Day 2: How can I use compensation to help me subtract across zeros?
Related Unit 7Assessment: Go Math Ch. 6# 12, 24
Instructional Resources
Manipulatives:
- Base Ten Blocks to directly model the value of the digits and the actions in the word problems.
- Place value mat with ten frame to organize and structure problems with and without regrouping.
- Go Math Lesson 6.10Essentials: Choose any parts from this lesson to guide your instruction.
- Digging Deeper Into Math – blog about using compensation for subtraction
- Compensation Example – an example on how to use compensation when subtracting across zeros
- iTools Base- Hundred Blocks – virtual manipulative
Sample HOT Questions: Use these to facilitate student discussions. (SMP 1, 3)
- How do you regroup when there are zeros in the number you start with when subtracting?
- Describe how you will subtract to find the difference.
- How can you use addition to check subtraction? What would you do if you did not get the same whole?
- How does using the compensation strategy help me solve 3-digit subtraction problems?
- Does the compensation strategy help solve subtraction problems more efficiently? Why or why not?
- What suggestion(s) do you have for a student having difficulty subtracting across zeros?
- Give an example when you would the compensation strategy.
- Do you think you could apply the compensation strategy with larger or smaller numbers? Explain your thinking.
Our students arebetter able to…
- Articulate how and why compensation strategy works in subtraction with 3-digit numbers.
- Record 3-digit numbers within subtraction problems with regrouping across zeros. (SMP 1)
- Articulate when and why they need to regroup when seeing a subtraction problem. (SMP 1, 3)
- Provide opportunities for students to use the compensation strategy with subtraction. (SMP 7)
- Provide opportunities for students to work together to understand how to regroup when subtracting across zeros. (SMP 3)
- Emphasize precise use of vocabulary: ones, tens, digits, values, exchanging, regroup, regrouping, trading, addend, sum, subtrahend, minuend, difference, partitioning, represent. (SMP 6)
2nd / Global Concept 5 of 5 for this Unit of Study: Applying the Traditional Algorithm with 3-Digit Numbers
This GCG focuses on making connections with the traditional algorithm and real world problems. / Projected Time Allotment:
3 days
Sample Essential Questions:
Day 1: How can I use a variety of strategies to solve real world problems?
Day 2: How can I use inverse operations to help me check my work when adding and subtracting 3-digit numbers?
Day 3: How can I use another strategy other than inverse operations to help me check my work when adding and subtracting 3-digit numbers?
Related Unit 7Assessment: Go Math Ch. 6 # 10, 21, 22
Instructional Resources
Manipulatives:
- Base Ten Blocksto directly model the value of the digits and the actions in the word problems.
- Place value mat with ten frames to organize and structure problems with and without regrouping.
- Go Math Lesson 6.6 Essentials: Choose any parts from this lesson to guide instruction and model word problems.
- 3-Digit Addition/Subtraction Problems – problems to guide instruction
- iTools Base- Hundred Blocks – virtual manipulative
Sample HOT Questions: Use these to facilitate student discussions. (SMP 1, 3)
- Describe another way that you could solve the problem.
- How is your strategy for solving the problem the same as your neighbor? How is it different?
- How would your strategy change using an open number line?
- How does using inverse operations help me check my work in 3-digit addition and subtraction?
- What other strategy could help solve this problem?
- Create a story problem using addition and subtraction with 3-digit number.
- How can estimation help solving a problem?
Our students arebetter able to…
- Solve 3-digit addition and subtraction problems with a variety of strategies.
- Decontextualize word problems with 3-digit numbers. (SMP 2)
- Articulate when and why they need to regroup when solving word problems.
For more info on SMP’s click here. / Because as teachers we…
- Provide opportunities for students to directly model the actions of a word problem using the traditional algorithm in addition and subtraction. (SMP 1, 2, 4)
- Provide opportunities for students to work together to understand the traditional algorithm. (SMP 3)
- Emphasize precise use of vocabulary: inverse operations, estimate, ones, tens, digits, values, exchanging, regroup, regrouping, trading, addend, sum, subtrahend, minuend, difference, partitioning, represent.(SMP 6)