Global Concept Guides: Direct Modeling, Place Value Strategies, Choosing a Strategy
Prior Learning: MAFS.1.OA.1.1, MAFS.1.OA.1.2
Progressions Document Link – page 6
Sample Show What You Know Task: Use the Go Math Ch. 4 & 5 Show What You Know or the Diagnostic Interview Task TE p.170 & 226
Mathematics Florida Standards for Mathematical Content:
Represent and solve problems involving addition and subtraction.
MAFS.2.OA.1.1Use 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 within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.
MAFS.2.NBT.2.6Add up to four two-digit numbers using strategies based on place value and properties of operations.
MAFS.2.NBT.2.9Explain 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:
Assessment: Modified Unit 4
Students will be using quick pictures, open number lines, and hundred charts to complete this assessment.
See common performance task link below. Students will need to have exposure in this unit with explaining how they used open number lines. Administer after the 2nd GCG.
Unpacking the Standards for this Unit:
The focus of this unit is modeling addition and subtraction with and without regrouping. Connections to standard algorithms are not the focus of this unit of study. “Second grade students add a string of two-digit numbers (up to four numbers) by applying place value strategies and properties of operations.” These strategies include: place value strategies, decomposing into tens, commutative property, associative property and think addition. “There are various strategies that second grade students understand and use when adding and subtracting within 100 (such as those listed in the standard). Students use multiple strategies for addition and subtraction in Grades K-3.” Because of this our focus is on developing fluency of addition and subtraction within 100 using these strategies. (For more information read p. 18-23)
Common Performance Task with Rubric for this Unit:
School Garden -Students will apply their understanding of place value strategies and open number lines to solve problems and explain which strategy is most efficient for them.
Click here for performance task and rubric.
Future learning:
By developing a sound understanding of the strategies listed above, students will be able to make connections to the standard algorithms in future units of study. “By the end of third grade students use a range of algorithms based on place value, properties of operations, and/or relationships between addition and subtraction to fluently add and subtract within 1000. Students are expected to fluently add and subtract multi-digit whole numbers using the standard algorithm by the end of grade 4.” For more info click here.
2nd / Unit 4: Global Concept 1 of 3:Unit of Study: Direct Modeling / Projected Time Allotment: 5 days
Sample Essential Questions:
Day 1: How can I use base-ten blocks to directly model the actions in a word problem?
Day 2: How do I draw a picture using a place value chart to model a problem?
Day 3: How can I explainthe actions in a word problem using a place value chart?
Day 4: How can using expanded form of a number help me add numbers?
Day 5: How can I solve multi-step word problems?
Related Unit 4 Assessment:Go Math Modified Ch. 4 and 5 # 1, 3, 4, 7, 10, 13, 14, 15
Instructional Resources
Manipulatives:
- Base-tenBlocks to directly model the value of the digits and the actions in the word problems.
- Unifix cubes or snap cubes for students that are struggling with base-ten concepts.
- Place value mat with ten frames to organize and structure problems with and without regrouping.
- Go Math Lesson 4.4 & 5.3 Essentials: Listen and DrawTE p. 185 and 237; p. 188 #11-13 and p. 240 – students should model or draw using base-ten blocks.
- Go Math Lesson 5.4 Essentials: Listen and Draw TE p. 240; Problem Solving p. 244- students should model or draw using base-ten blocks.
- Go Math Lesson 4.5 Essentials: Listen and Draw TE p. 189, Share and Show p. 190, Problem Solving p. 192- students should model or draw using base-ten blocks.
- Modeling Word Problems- Students can use these problems,base-ten blocks, and place value charts to solve on Day 1.
- Word Problems- Students can use these problems on Day 2.
- More Word Problems- Students can use these problems on Day 3.
- Expanded Form Word Problems- Students can use these problems on Day 4.
- Multi-Step Word Problems,More Multi-Step Word Problems Students can use these problems on Day 5.
- Who’s Got The Most? - ETA game for modeling addition/subtraction with regrouping.
- Race to Clear the Mat- ETA game for modeling subtraction with regrouping.
- Race for a Flat- ETA game for modeling addition with regrouping.
- Sum it Up – ETA game for modeling addition with grouping.
- iTools Base-Ten Blocks – virtual manipulative
- Grand Slam Baseball, Soccer is Fun -Online games that have students practice addition and subtraction
- Numberopolis: Carnival Stories (Level P: 2-Digit Addition) – online game
- Numberopolis: Carnival Stories (Level Q: 2-Digit Subtraction) – online game
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 do your base-ten blocks represent what’s happening in the problem?
- What does your collection of base-ten blocks represent in the problem? (e.g. Students may say 27 giraffes.)
- 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?
- When regrouping ask, “is 7 tens and 11 ones the same as 8 tens and 1 one?” Justify your thinking.
- How do you know when you need to regroup?
- Explain how you regroup when adding or subtracting?
Our students are better able to…
- Directly model the actions of addition and subtraction using base-ten blocks (SMP 2, 5).
- Explain when and why you would need to regroup in addition or subtraction (SMP 3).
- Record the steps of regrouping when adding or subtracting (SMP 7, 8).
- Provide opportunities for students to directly model the actions in a word problem using base-ten blocks.
- Help make connections with regrouping and representing numbers flexibly. (See power point) (SMP 3).
2nd / Unit 4: Global Concept 2 of 3:Unit of Study:Strategies for Addition and Subtraction / Projected Time Allotment:5 days
Sample Essential Questions:
Day 1: How can making a ten help me add a string of numbers?
Day 2: How can we use an open number line todecompose numbers to solve problems?
Day 3: How can I strategically decompose ones to add and subtract numbers?
Day 4: How can I use an open number line to solve multi-step problems?
Day 5: How does using place value strategies make it easier to solve problems?
Related Unit 4 Assessment:Go Math Modified Ch. 4 and 5 # 2, 4,5, 7, 8, 9, 11, 16
Instructional Resources
Manipulatives:
- Base-ten Blocks to model addition problems using the properties to add.
- Place value mat with ten frames to organize and structure problems with and without regrouping.
- Open number line.
- Go Math Lesson 4.11 Essentials: Model and Draw TE p. 214 (Use to guide instruction.) Focus on making a ten and modeling the problem using an open number line and break apart strategy, Language Support TE p. 213B
- Go Math Lesson 4.12 - Essentials: Listen and Draw TE p. 217, Model and Draw TE p. 218 (Use to guide instruction). Focus on making a ten and modeling the problem using an open number line and break apart strategy, Problem Solving TE p. 220 #19.
- Make a Ten- Students can use these questions to apply the “make a ten” strategy on Day 1
- Open Number Line- Students can use these questions to solve problems using Open Number Lines on Day 2
- Addition/Subtraction Number Line problems
- Word Problems- Students can use these questions to decompose numbers on Day 3
- More Word Problems- Students can use these questions solve multi-step problems on Day 4
- Shell Game – Students can use this game on Day 5 to discuss efficient strategies
- Ghostblasters 2 - game that practices adding a sum that you set
- Ghostblasters 3 - practice adding 2-digit numbers
Sample HOT Questions: Use these to facilitate student discussions. (SMP 1, 3)
- What happens to my sum when I change the order of the addends?
- Explain why you grouped your addends the way you did.
- How does making 10 help me add quicker?
- Does changing the order in a subtraction problem, change the difference? Explain your thinking.
- How is the place value strategy (break-apart) similar in addition and subtraction? How is it different?
- How can skip counting by tens on a hundreds chart help me use an open number line to add or subtract?
- How is 33 + 48 like adding 23 + 58? How is it different?
- How can the place value strategy (break-apart strategy) help me add or subtract with regrouping?
- How can I use a number line to help me model how I combine and compare numbers?
Our students are better able to…
- Use place value strategy to solve 2-digit addition and subtraction problems (SMP 1).
- Relate a place value strategy to expanded forms of a number (SMP 1, 3).
- Use an open number line as a tool for applying the break-apart strategy to efficiently solve 2-digit addition and subtraction problems (SMP 5, 7).
- Strategically decompose numbers to add and subtract more efficiently (SMP 6).
- For more info on SMP’s click here.
- Allow students to persevere through problem solving (SMP 1).
- Provide opportunities for students to use open number lines and base-ten blocks to model strategies based on place value (SMP 5, 7).
- Help make connections between number patterns and place value in solving addition and subtraction
2nd / Unit 4: Global Concept 3 of 3for this Unit of Study: Choosing a Strategy / Projected Time Allotment:5 days
Sample Essential Questions:
Day 1: How can I apply strategies to real-world situations in two-digit addition/subtraction problems?
Day 2: How can I determine if my answer is reasonable in a multistep problem?
Day 3:How can I solve multistep word problems using efficient strategies?
Day 4: How can I explain my thinking in solving a multistep word problem?
Day 5: How can I apply efficient strategies in problem solving?
Related Unit 4 Assessment:Unit 4 Assessment: All
Instructional Resources
Manipulatives:
- Base-ten Blocks to model addition properties.
- Place value mat with ten frames to organize and structure problems with and without regrouping.
- Quick pictures to record their thinking instead of using base-ten blocks.
- Open number line
- Efficient Strategies Problems- Students can use these questions to select efficient strategies on Day 1.
- Reasonable Answers - Students can use these questions to determine reasonableness of answers on Day 2.
- Multi-Step Problems- Students can use these questions on Day 3.
- Explaining in Multistep Problems –Students can use these questions on Day 4.
- Multi-Step Sort- Students match scenarios to how they would solve the problem.
- Place Value Strategies- Variety of strategies to solve the same problem.
- Addition and Subtraction Word Problems- Students can apply their strategies in a game format.
- Addition with Multiple Addends- Students can apply their strategies in a game format.
Sample HOT Questions: Use these to facilitate student discussions. (SMP 1, 3)
- What strategy did you use to solve this problem? Why did you choose that strategy?
- How is your strategy for solving the problem the same as your neighbor? How is it different?
- How do you think you could record your work so that someone else could understand what you did?
- Solve the problem in a different way. How do your two strategies compare?
- How can decomposing a number help you subtract?
Our students arebetter able to…
- Apply critical thinking to their 2-digit addition/subtraction problem solving (SMP2, 3).
- Apply multiple strategies efficiently to solve
- Articulate their understandings of place value and properties of operations as they solve addition and subtraction problems (SMP 3, 7).
- Provide opportunities for students to use multiple strategies to solve 2-digit addition and subtraction problems (SMP 2, 7).
- Challenge students to use structure and patterns to help them solve real-world 2-digit addition/subtraction problems (SMP 7).