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

Content Development This GCG is a culmination of all of two digit addition and subtraction. Students should see the relationship between addition and subtraction. The bar model would be a good way to help students see the relationship between addition and subtraction. During this unit, fact strategies, problem solving strategies, strategies to regroup when adding and subtracting, as well as the traditional algorithm should be used. Students should be comfortable with solving problems in multiple ways. “When computational tasks are embedded in simple contexts, students seem to be more engaged than they are with bare computations. The choice of story problems influences the strategies students use to solve them.” (VandeWalle 2004 p. 205.) Remember, students do not need to be fluent in the traditional algorithm until 4th grade.

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.

Words and Phrases to Avoid! Borrow Carry Knock on your neighbor’s door Go get some sugar from you neighbor Bigger bottom, better borrow! You can’t take a bigger number from a smaller number Each of these words and phrases create misconceptions and hinder students from understanding the mathematics involved in the algorithm. Use the following words instead: Regroup Exchange Trade

Day 1 Essential question: How can I solve a variety of problems with the traditional algorithm? Pick Your Method Problems that can also be used. In order to help students see the relationship between addition and subtraction, you may want to use bar models or the number line. By the end of Day 1, students will be able to solve a variety of problems with the traditional algorithm.

Day 2 Essential question: How can I use the traditional algorithm with real-world multi-step problems? Teacher could use word problems in Lesson 5.11. Duncan’s Orders Shopping Spree- real-world problems involving buying items and making change based on a given amount of money. Additional word problems By the end of Day 2, students will be able to use the traditional algorithm with real-world multi-step problems.

Day 3 Essential question: How can I check my solution to see if it is correct? Students may check their subtraction by using the inverse operation of addition. They may check their addition using subtraction or by solving the problem a different way- quick pics, expanded form, etc. Bar models and number lines are great ways to show the relationship of these operations. Sample engage question: Leslie swam 24 laps at the pool on Monday and 27 laps on Tuesday. Her goal was to swim 50 laps. Di d she reach her goal? How do you know? Use the following questions to build understanding during the engage question. Explain how you know your answer is correct? Does your solution answer the question? Does your answer make reasonable sense based on the story? Explain how you got your answer? What is another way to solve this problem? Additional problems you may use. By the end of Day 3, students will be able to check their solution to see that it is correct.

Enrich/Reteach/Intervention Make a Plan More or Less Addition/Subtraction Sort- This could be helpful for students that are struggling with the actions of a story problem especially in multistep problems. Enrich Given a word problem, have students write another word problem that matches the inverse. Use some enriching questions like: Seymore Money earned the same amount of money as Mr. Bill mowing lawns. Seymore earned $32 on the first lawn and $19 on the 2nd lawn. Mr. Bill earned $24 mowing the 1st lawn. How much did he earn mowing the 2nd lawn? Donkey Kong played his video game 4 times. The 1st game he scored 17 more points than the 2nd time. The 2nd game he scored 5 less than the 3rd time. The 3rd game he scored 7 more than then 4th time. The 4th game he scored 14 points. How many points did he score combined? On Monday, Linda ate 8 Goldfish. On Tuesday, she ate 14 less than on Wednesday. On Wednesday she ate 6 less than on Thursday. On Thursday, she ate 12 more than on Friday. On Friday, she at 25 Goldfish. How many Goldfish did she eat all week?