1. Understanding the Traditional Algorithm with Addition Unit of Study 5: Using Algorithms for 2-Digit Addition and Subtraction Global Concept Guide: 1 of 3

2. Content Development  When learning the traditional algorithm, slow and steady wins the race!  Students should NOT be rushed into learning the procedure. Instead, they should understand and make sense of HOW and WHY the procedure works!  The students being able to model the action is essential for deep understanding of how the traditional algorithm works.  A teacher’s vocabulary can either hinder or help students understand this algorithm. Phrases such as “borrow” and “carry the one” should NOT be used.  Students should be encouraged to check their work throughout this GCG with another strategy.  Continue to have students generate reasonable answers prior to solving.

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. Day 1  Essential question: How can I write a number sentence to match a word problem?  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. MAFS.2.OA.1.1  Sample engage problem: There were 15 math books in Ms. Lynn’s classroom. Twelve more were delivered. How many math books are now in Ms. Lynn’s classroom?  Teacher facilitates a discussion about an equation that would match the actions in the story.  15+12=  There were 15 math books. Some more were delivered. Now there are 27. How many math books were delivered?  15 + = 27 This is the direct model of the actions in the word problems. Students may use 27-15 to solve this problem.  Ms. Lynn had some math books. Twelve more were delivered. Now she has 27. How many did she have to start with?  + 12 = 27 This is also the direct model of the actions in the word problem. Students again may use 27-12 to solve.  By the end of Day 1, students will be able to write a number sentence that matches a word problem.

5. Day 1 continued  Use the Equation Cards to match equations to story problems.Equation Cards  Equation cards should be copied for pairs of students. Students should discuss the action in the story and find the corresponding equation card. It is important for students to understand the placement of numbers within an equation dictates the meaning. Students should justify with each other why the equation they selected matches the story problem.  Alternate activity- students write the letter of the equation next to the corresponding problem. Alternate activity-  Story problems may have multiple equations.  Teachers should facilitate discussion on which equations match which story. There should also be discussion on which equations directly model the story problem. There will be other equations that do not match directly but are useful for solving.  Jasmine earned some money on Saturday and $19 on Sunday. She now has $31. How much money did she earn on Saturday?  The direct model equation would be + 19 = 31.  A useful equation for solving would be 31-19=.  By the end of Day 1, students will be able to write a number sentence to match a word problem.

6. Day 2  Essential question: How can I use base ten blocks to connect to the traditional algorithm with addition?  Emily had 27 pieces of candy. Linda gave her 35 more. How many pieces of candy does Emily have now? ( This video could be shown to students.) You must be logged into your computer as a teacher to access the above link.  Because students have used this strategy in Unit 4, you may find that some students are ready to use the algorithm without the use of base ten blocks. Before they jump straight to the algorithm, they should understand the connection between the actions with the base ten blocks and the numbers written in the standard algorithm.  Teachers should use the terms standard and tradition algorithm interchangeably.  Attached is a bank of addition word problems that could be for days 2, 3, and 4.word problems  By the end of Day 2, students will be able to use base ten blocks to connect to the traditional algorithm with addition. ClickClick to watch a demonstration of addition with base-ten..

7. Try to mimic the teacher language as much as possible.

8. Day 3  Essential question: How can I use pictures to connect to the traditional algorithm with addition?  On this day, students should be drawing quick pics to connect to the traditional algorithm. If students still need to use base ten blocks that is acceptable. ( This video could be shown to students.) You must be logged into your computer as a teacher to access the above link.  Continue using word problems from Day 2.word problems  By the end of Day 3, students will be able to use pictures to connect to the traditional algorithm with addition. ClickClick to watch a demonstration of addition with quick pics.

9. Day 4  Essential question: How can I record my trades/regrouping in the traditional algorithm when adding?  Students will model using base ten blocks or quick pics and record their trades in the traditional algorithm.  Students should recognize that the value doesn’t change when regrouping.  Sample engage question:  There was a bake sale to raise money for the 2 nd grade field trip to Cracker County. Madison wanted a brownie for 36¢. She wanted a cookie for 48¢. How much will she spend at the bake sale? Questions you may ask to develop number flexibility and understanding of traditional/standard algorithm. ?Is 6 ones and 8 ones the same as 1 ten and 4 ones? How do you know? ?When is it necessary to regroup? ?Would you need to regroup in this problem? Why or why not? ?Madison thinks she owes 714¢. Is she correct? How do you know? ?Is 7 tens and 14 ones the same as 84. How do you know? ?What strategies could help you put 6 ones and 8 ones together? Additional word problems you may choose to use.word problems By the end of Day 4, students will be able to record their trades/regrouping in the traditional algorithm.

10. Day 5  Essential question: How do I add 3 and 4 addends with the traditional algorithm?  Students may need base ten blocks or quick pics to solve. They do not need to be fluent in the standard algorithm until 4 th grade. Students do need to understand the actions of addition as recorded in the standard algorithm. Students should use their fact strategies(make-a-ten, doubles, almost doubles, properties of addition, etc.) to solve with multiple addends.  Sample problems you may use are attached.problems  By the end of Day 5, students will be able to add 3 and 4 addends with the traditional algorithm.

11. Enrich/Reteach/Intervention Reteach  If students are struggling, go back to modeling with base ten blocks.  Use TE p. 173B as well as ideas from lessons 4.1 and 5.1. You must be logged into your computer as a teacher to access these links. Enrich  Enrich students through ideas used on TE p. 185B and 233B  Jana had 29 marbles. Some were red and some were blue. How many could have been red and how many could have been blue? Write at least 5 options.  Mr. Moneymaker earned $12 on Sunday, $14 on Monday, and $16 on Tuesday. If this pattern continues through Saturday, how much did he earn this week?  Enrich 4.11 TE p. 214-Students should prove their solution at least 2 ways. ClickClick to watch a demonstration of addition with base-ten. ClickClick to watch a demonstration of addition with quick pics.