1. Direct Modeling Unit of Study 4: Modeling and Representing 2-digit Addition and Subtraction Global Concept Guide: 1 of 3

2. Content Development  This concept is focused on direct modeling with addition and subtraction scenarios. Direct modeling is when the student uses manipulatives and drawings along with counting to represent directly the meaning or actions of a story or problem. Most of this GCG will be done by students modeling with manipulatives and drawing pictures. The place value mats with ten frames are VITAL throughout this unit and should be used daily.place value mats  This concept combines lesson components from Chapters 4 & 5.  Continue to use problems solving strategies addressed in Unit 3- Basic Facts and Relationships. Prior to solving students should be asking themselves, “What might my answer sound like?” Students should think if the answer will be an increase or decrease and whether their answer is reasonable.  “MAFS.2.NBT.2.9 Explain why addition and subtraction strategies work, using place value and the properties of operations” This standard requires students to explain, therefore, make sure during this unit students are given the opportunity to explain their strategies both verbal and written.  For problem solving scenarios check out this excellent link.excellent link

3. Addition Properties According to the standard~ MAFS.2NBT.2.9- Explain why addition and subtraction strategies work, using place value and the properties of operations. Two properties of operations that students should be using are: Associative property- grouping addends together to make the addition more efficient ~ Strategies that support the associative property are doubles +/- 1. Commutative property- switching the order of the addends to make the math more efficient. A strategy that supports this is adding with the greater number first. If I have 2 + 8= I would use the commutative property and solve using 8+2 because it is more efficient to start with 8 and add 2. Students should be able to explain the properties but do not need to know the names of the properties.

4. Things to Avoid…  Avoid teaching “keywords” and having “keywords” posters hanging up. (For more information on this please attend the Problem Solving Training)  Avoid jumping to the algorithm too soon.  Avoid telling students when to add or subtract. Have students focus on the actions happening in the problem to help them determine what operation they will use.  Avoid relying on pictures of manipulatives from a worksheet or a textbook page. DO NOT replace the hands-on experiences students need to conceptually understand regrouping.  Avoid phrases and words such as “borrowing, carrying, getting sugar from your neighbor, knock on your neighbor’s door, etc.” Regrouping, trading and exchanging should be the only vocabulary words used to describe this action.

5. Day 1  Essential question: How can I use base ten blocks to directly model the actions in a word problem?  To engage students use a problem like:  Pac Man was playing his favorite video game. He earned 27 points in the morning and 44 points in the afternoon. How many points did he earn?  Students should be using base ten blocks and a place value mat to solve problems. Allow students time to solve. Some may try to solve using only unit cubes and some will use rods and units. Some students will leave the units and not regroup and some may regroup. Monitor strategies that students are using. Scaffold sharing from least efficient to most efficient strategies. Errors may include forgetting the ten they regrouped and thinking he earned 61 points or putting 2 digits in the ones place and saying he earned 611 points.place value mat Hot questions you may ask: Why did you use rods instead of unit cubes? Why did you regroup a rod for unit cubes? How could these students all solve a different way and get the same answer? Which is the most efficient strategy and why? Does the value of their number change when you regroup?  Continue giving students time to solve problems using base ten blocks. Modeling word problems. Modeling word problems.

6. Day 1 continued The next day Pac Man played the game again. He earned 21 points in the morning and 34 points in the afternoon. How many points did he earn?  Some students may regroup on this problem so this can help with the discussion of when to regroup. Ask hot questions throughout to develop students; understanding of regrouping and the values of digits in the tens and ones place. Mr. Pac Man scored 48 points and Mrs. Pac Man scored 26 points. How many more did Mr. Pac Man score than Mrs. Pac Man?  By the end of Day 1, students should be able to model addition and subtraction problems.

7. Day 2  Essential question: How do I draw a picture using a place value chart to model a problem?  Students should continue to build a model with base ten blocks and then connect to a quick picture. Remember, this unit is NOT focused on algorithms. Teacher may want to remind students of efficient ways to make quick pics. It is VITAL during the next few days to make connections between representing numbers flexibly and regrouping. Students should be able to articulate every time they fill up a ten frame, they will need to regroup or trade for a ten.  Engage students by letting them solve with base ten blocks: Ima Hungry ate 18 peanuts and 22 walnuts. How many nuts did Ima eat?  After students have modeled the problem using base ten blocks and a place value mat, have them record their model using a quick pic in a place value chart. Select a student to share who recorded the action of regrouping.

8. Day 2 continued Mr. Celery Stalk had 34 leaves. Eighteen leaves fell off. How many are left?  Students should model first using base ten blocks and a place value mat. Then students will record their model using a quick pic and a place value chart.  Continue solving problems. Some students will continue to need base ten blocks to model first and then record their quick pics. Some students will be able to draw the quick pics without using the base ten blocks.solving problems.  By the end of Day 2, students should be able to draw a quick pic using a place value chart to model a problem.

9. Day 3  Essential question : How can I explain the actions in a word problem using a place value chart?  Use word problems like those provided. Today’s focus will be to continue drawing quick pics to solve problems, but students should explain their reasoning for regrouping rods and units, putting units together, and putting rods together. Students need to think flexibly about numbers.word problems  By the end of Day 3, students will be able to explain the actions in a word problem using a place value chart.

10. Day 4  Essential question: How can using expanded form of a number help me add numbers?  “The focus of this lesson is on applying place value concepts and using numbers flexibly to solve problems.” Go Math TE p. 181A  Students should be solving using expanded form. Students should be using the associative property, commutative properties and choosing efficient strategies to add numbers.  Sample question to engage students:  There were 36 students at Chuck E. Cheese on Thursday and 48 students on Friday. How many students went to Chuck E. Cheese?  Additional problems should be used. Additional problems  By the end of Day 4, students will be able to use expanded form of a number to add numbers. Two possible ways to show addition with expanded form. I know 36+48 is the same as 48+36. I started with the 48 because it is greater. I decomposed 36 into 30 + 6. I made 3 ten jumps on my number line and then added 6 ones.. I know that 84 students went to Chuck E. Cheese.

11. Day 5  Essential question: How can I solve multi-step word problems?  The focus of this lesson should be solving word problems and using place value strategies like expanded form, base ten blocks, and drawing quick pics. Students should also be using efficient fact strategies like make a ten, doubles, near doubles, properties of addition, and counting on using a greater addend. As always, students should be using problem solving strategies, such as, reading/rereading the questions, thinking about what the answer might be, considering what information is important, and checking if they have a reasonable answer.  K-W-P-R (or any variation) should be used to help students reason through the problem and organize information.  Word problems options – Option 1 and Option 2Option 1 Option 2

12. Day 5 continued  Ideas for implementation:  Gallery walk for students to solve problems.  Back to Back- Students are paired and given the same problem. They sit back to back. They solve independently using whatever strategy they choose. When both partners are finished they sit side by side and explain and compare their strategies.  Question stems for students to use:  I agree with you because….  I disagree with you because…  I heard you say…  Can you explain it to me a different way?  Why did you choose that strategy?  Could you have a chosen another strategy?  Which strategy do we think is most efficient?  Could we have done it a more efficient way?  How are our strategies similar or different?  Once students agree on a solution, they move on to the next problem.  By the end of Day 5, students will be able to solve multi-step word problems.

13. Enrich/Reteach/Intervention Reteach:  For students who struggle with the concept of regrouping, allow them to spend more time using base ten blocks and modeling addition and subtraction on the place value mat with ten frames. Continue to make connections to representing numbers flexibly throughout this unit and all of regrouping.  Race for a Flat and Race to Clear the Mat are good games to help students with composing tens and decomposing tens. Race for a Flat Race to Clear the Mat Enrich:  Enrich idea from TE p.185B  How is adding 42+38 like adding 52+28? How is it different?  You add two numbers that are almost 30 apart. The answer is almost 90. What might the numbers be?  Make up an addition question where there is a 2, a 3, and a 4 somewhere in the question or the answer.  Additional Questions to use Additional Questions to use