Global Concept Guides:Understanding the Traditional Algorithm with Addition,Understanding the Traditional Algorithm with Subtraction, Applying the Traditional Algorithm
Prior Learning:MACC.1.OA.1, MACC.1.OA.2
Progressions Document Link
Sample Show What You Know Task: The Go Math Show What You Know was used for Unit 5. Use Unit 5 Modified Assessment and Unit 5 performance task and rubric to guide instruction.
Common Core State Standards for Mathematical Content:
Represent and solve problems involving addition and subtraction.
MAFS.2.OA.1.1–Use addition and subtraction within 100 to solve one and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g. by using drawings and equations with a symbol for the unknown number to represent the problem.
Use place value understanding and properties of operations to add and subtract.
MAFS.2.NBT.2.5–Fluently add and subtract with 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.
MAFS.2.NBT.2.6–Add up to four two-digit numbers using strategies based on place value and properties of operations.
MAFS.2.NBT.2.9–Explain why addition and subtraction strategies work, using place value and the properties of operations. / Comments:
This parent flyer and included video can be utilized by both you and parents to build content knowledge and understanding of the strategies highlighted in this unit.
Notes on Assessment:
Modified Unit 6 Assessment
See common performance task link below. Students will need to have exposure in this unit with explaining how they used open number lines.
Unpacking the Standards for this Unit:
This unit extends understanding of addition and subtraction from Unit 5 by connecting modeling with manipulatives to an algorithm. This unit focuses on the break-apart algorithm and the traditional algorithm. It is vital for students to not be pushed to the traditional algorithm too soon. Doing this will lead to procedural understanding rather than conceptual understanding. John Van de Walle states, “First, spend a significant time with invented strategies-months, not weeks. Do not feel that you must rush to the standard algorithms. Delay! The understanding students gain from working with invented strategies will make it much easier for you to teach the standard algorithms. If you think you are wasting precious time by holding back, think of how many years teachers teach the same standard algorithms over and over to students who are still unable to understand them and use them without making errors.”Another extension in this unit is introducing multi-step problems within 2-digit addition and subtraction. (For more information read pgs. 6-7)
Common Performance Task with Rubric for this Unit:
Apple Farm Field Trip – Students will apply their understanding of the break-apart algorithm and the traditional algorithm to solve problems with unknowns with all positions.
Click here for performance task and rubric.
Future learning:
By spending ample time with understanding these two algorithms, students will have a good foundation for applying these algorithms to 3-digit addition and subtraction. Students need to become comfortable with the break-apart model because this is the foundation for the distributive property in future grades.
2nd / Global Concept 1 of 3 for this Unit of Study: Understanding the Traditional Algorithm with Addition / Projected Time Allotment:5 days
Sample Essential Questions:
Day 1: How can I write a number sentence to match a word problem?
Day 2: How can I use base ten blocks to connect to the traditional algorithm with addition?
Day 3: How can I use quick pictures to connect to the traditional algorithm with addition?
Day 4: How can I record my trades/regrouping in the traditional algorithm when adding?
Day 5: How do I add 3 and 4 addends with the traditional algorithm?
Related Modified Unit 6 Assessment:# 6, 12
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.
- Go Math Lesson 4.6 Essentials: Model and Draw TE p. 194; H.O.T. p. 195 #13-15
- Go Math Lesson 4.11 Essentials: Enrich TE p.213B
- Equation Cards- Day 1
- Word Problems- These problems can be used over Days 2, 3 and 4 for students to practice using base ten blocks and pictures to connect to the traditional algorithm
- Multiple Addends- These problems can be used on Day 5 to practice adding with multiple addends.
- Stick em up, pg.2, pg. 3this resource can be used to help students practice the traditional algorithm.
- What’s the Story- Students can write stories based on various number sentences
- Activity 18 –2-digit addition gamefrom Grab and Go
- Race for a Flat– ETA game for addition with regrouping
- iTools Base-Ten Blocks – virtual manipulative
- Tutorial – Destination Math– sums less than 100
- Workout – Destination Math– sums less than 100
- Practice– Destination Math– practice sums less than 100
- Model and Record 2-Digit Addition – shows the connection between modeling and recording 2-digit addition
- Add 3 Numbers – tutorial/practice for 3 addends
Sample HOT Questions: Use these to facilitate student discussions. (SMP 1, 3)
- Which numbers did you add first in the problem? Explain why.
- 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?
- How can previous problems help you solve new problems with 3 and 4 addends?
- What is the value of the one when I regroup it into the tens column?
Our students arebetter able to…
- Articulate how and why the traditional algorithm works in addition with 2-digit numbers. (SMP 2)
- Record 2-digit numbers within addition problems with and without regrouping. (SMP 1)
- Articulate when and why they need to regroup when seeing an addition problem. (SMP 1, 3)
- Provide opportunities for students to directly model the actions of word problems using the traditional algorithm in addition. (SMP 1, 2, 4)
- Provide opportunities for students to work together to understand the traditional algorithm. (SMP 3)
- Emphasize precise use of vocabulary: ones, tens, digits, values, exchange, regroup, regrouping, trading, addend, sum, represent, and model. (SMP 6)
2nd / Global Concept 2 of 3 for this Unit of Study: Understanding the Traditional Algorithm with Subtraction / Projected Time Allotment: 5 days
Sample Essential Questions:
Day 1: How can I write a number sentence to match a word problem?
Day 2: How can I use base ten blocks to connect to the traditional algorithm with subtraction?
Day 3: How can I use pictures to connect to the traditional algorithm with subtraction?
Day 4: How do I record tens and ones when subtracting 2-digit numbers?
Day 5: How can I record the steps when subtracting 2-digit numbers?
Related Modified Unit 6 Assessment:# 6, 12
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.
- Go Math Lesson 5.5 Essentials:Choose any parts from this lesson to guide your instruction.
- Go Math Lesson 5.6 Essentials: Model and Draw TE p.250,H.O.T. p. 251 #16
- Go Math Lesson 5.7 Essentials: Listen and Draw p. 253; Explain p. 255 #21,Problem Solving p.256 #22-24
- Go Math Lesson 5.8 Essentials: Choose any parts from this lesson to guide your instruction.
- Go Math Lesson 5.10 Essentials: Listen and Draw p. 265- Choose any parts from this lesson to guide your instruction.
- Equation Cards- Day 1 students
- Subtraction Problems- Teachers can select questions to utilize on Days 2,3,4,5
- Spin and Subtract, More or Less
- Kaboom – subtraction game, Spinner Subtraction – subtraction game from Grab and Go
- Race to Clear the Mat–ETA game for subtraction with regrouping
- iTools Base-Ten Blocks – virtual manipulative
- Tutorial–Destination Math –difference within 100
- Workout – Destination Math –difference within 100
- Practice– Destination Math –difference within 100
- Model and Record 2-Digit Subtraction –shows the connection between modeling and recording 2-digit subtraction
- 2-Digit Subtraction – practice 2-digit subtraction, Practice 2-Digit Subtraction – more practice of 2-digit subtraction
Sample HOT Questions: Use these to facilitate student discussions. (SMP 1, 3)
- How is regrouping different in subtraction than addition? How is it the same?
- 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?
- When you regroup is the value of your new number the same as what you started with?
Our students arebetter able to…
- Articulate how and why the traditional algorithm works in subtraction with 2-digit numbers. (SMP 2)
- Record 2-digit numbers within subtraction problems with and without regrouping. (SMP 1)
- Articulate when and why they need to regroup when seeing a subtraction problem. (SMP 1, 3)
- Provide opportunities for students to directly model the actions with a word problem using the traditional algorithm in subtraction. (SMP 1, 2, 4)
- Help make connections with regrouping and representing numbers flexibly. (SMP 3)
- Emphasize precise use of vocabulary: ones, tens, digits, values, exchange, regroup, regrouping, trading, subtrahend, minuend, difference, partitioning, represent, and model. (SMP 6)
2nd / Global Concept 3 of 3 for this Unit of Study: Applying the Traditional Algorithm
This GCG focuses on applying the traditional algorithm through problem solving. Students will experience multi-step word problems and unknowns in all positions of the different problem structures. / Projected Time Allotment:
3 days
Sample Essential Questions:
Day 1: How can I solve a variety of problems with the traditional algorithm?
Day 2: How can I use the traditional algorithm with multi-step problems?
Day 3: How can I check my solution to see if it is correct?
Related Modified Unit 6 Assessment:# 7,8,10,15
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 4.10 Essentials: Choose any parts from this lesson to guide your instruction.
- Go Math Lesson 5.11 Essentials: Choose any parts from this lesson to guide your instruction.
- Multi-Step Problems – word problems that involve multi-steps that can be used on Day 1
- Pick your method- Students determine whether they need to add or subtract on Day 1
- Shopping Spree- Students solve multi-step real world problems on Day 2
- Duncan’s Orders- Students solve multi-step problems. This resource can be used on Day 2
- Mixed Problems- word problems that can be used on Day 2
- Word Problems- Word Problems can be used on Day 3
- Addition/Subtraction Sort
- iTools Base-Ten Blocks – subtract tens
- iTools Base-Ten Blocks – add tens
- Ghostblasters 2 –game that practices adding a preselected sum
- Ghostblasters 3 –practice adding 2-digit numbers
- Ghostblaster 3–practice subtracting 2-digit numbers
Sample HOT Questions: Use these to facilitate student discussions. (SMP 1, 3)
- How can estimation help me when I solve a problem?
- How do you decide what steps to do to solve a problem?
- Describe how you decided what steps were needed to solve problem.
- Explain how the regrouping was different in these two problems.
- Create a story problem using this number sentence: 25 + = = 42.
- Create a story problem using this number sentence: 24 = 68-23-21.
- Create a story problem with multi-steps that has a sum of 67.
- Create a story problem with multi-steps that has a difference of 15.
- I am thinking of a number. Double the number. Subtract 13. The answer is 37. What is the number? (Answer: 25)
Our students arebetter able to…
- Solve multi-step problems with 2-digit addition and subtraction. (SMP 1, 2)
- Regroup 2-digit numbers within addition/subtraction in multi-step problems and with unknown values in every position. (SMP 1)
- Articulate when and why they need to regroup when seeing an addition/subtraction problem. (SMP 1, 3)
- Provide opportunities for students to solve multi-step problems. (SMP 1, 2)
- Help make connections with regrouping and representing numbers flexibly. (SMP 3)
- Emphasize precise use of vocabulary: ones, tens, digits, values, exchanging, regroup, regrouping, trading, addend, sum, subtrahend, minuend, difference, partitioning, represent.(SMP 6)