1. Understanding the Traditional Algorithm with Subtraction Unit of Study 5: Using Algorithms for 2-Digit Addition and Subtraction Global Concept Guide: 2 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!  Place Value mats are essential for deep understanding of how the traditional algorithm works.  A teacher’s vocabulary can either hinder or help students’ understanding this algorithm. Please see next slide for words and phrases to avoid.  Continue to have students determine reasonable differences prior to solving problems.  Students should be encouraged to check their work throughout this GCG using the inverse operation (addition) or another strategy.

3. Words and Phrases to Avoid! o Borrow o Carry o Knock on your neighbor’s door o Go get some sugar from you neighbor o Bigger bottom, better borrow! o 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

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: Teacher facilitates a discussion about an equation that would match the actions in the story.  Mr. Nike wants to run 45 miles. He ran 27 miles. How many miles does he have left to run?  45-27 = is a direct model of the actions in the story.  Mr. Nike wants to run 45 miles. He ran some. He has 18 miles left. How many miles did he run?  45- = 18 is the direct model of the actions in the word problems. Students may use 45-18 to solve. A Part-Part-Whole mat would be beneficial as students solve this problem and deepen their understanding of the structure of subtraction. This will lead them to discover that part (the “missing” number) combined with the second part (the difference, in this case “18”) makes the whole (45).

5. Choosing an equation to match a story problem: Use either the Equation Cards to match equations to story problems.Equation Cards  Equation cards should be copied for pairs of students. Students will cut all the equations out. After discussing the action in the story they will find the equation that matches the action and place it in the first column. 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. Or use the same problems but students just write the letter of the matching equation next to the story problem.problems  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. 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 subtraction?  The focus of Day 2 is for students to make connections between base-ten blocks and the traditional algorithm. EVERY MOVE STUDENTS MAKE WITH BASE-TEN BLOCKS SHOULD BE RECORDED IN THE ALGORITHM.  A common misconception is that many students will build both the minuend and subtrahend when using base-ten blocks. The strategy of using number cards to represent the number you are taking away (subtrahend) would be beneficial for students.  Please read TE p. 241 A for more information on how to connect models to the standard algorithm.  Problems you may use are attached here.here.  By the end of Day 2, students will be able to use base-ten blocks to connect to the traditional algorithm with subtraction.

7. Day 3  Essential question: How can I use pictures to connect to the traditional algorithm with subtraction?  Day 3 should be an extension from Day 2 but will be focused on drawing pictures of base-ten blocks and connecting them to the traditional algorithm. Provide opportunities for students to practice through problem solving scenarios and other lesson components.  When students regroup tens for ones make sure they understand the value doesn’t change by asking similar questions to the picture. This is helping develop flexibility with numbers.  Problems you may use are attached here.here.  By the end of Day 3, students will be able to connect their pictures to the traditional algorithm.

8. Day 4  Essential question: How do I record tens and ones when subtracting two digit numbers?  Students should still be using base-ten blocks and quick pics to connect the action of the story problem to the record of the numbers.  Students can also play the game, “Race to Zero “,on this day using the following modified directions:Race to Zero  Each player starts at 99. They roll two dice and create a two digit number.  The student subtracts the two digit number from 99.  Play repeats by subtracting the new number from the previous difference.  The first player to reach or pass zero wins.  Students should record their trades on each turn.  Problems you may use are attached herehere  By the end of Day 4, students will be able to record tens and ones when subtracting two digit numbers.

9. Day 5  Essential question: How can I record the steps with subtracting two digit numbers?  Problems you may use are attached here.here.  On Day 5, students are going to record and EXPLAIN the steps they used when subtracting two-digit numbers. Teachers should encourage students to use language such as regrouped, traded, exchanged. Monitor students to ensure that they are appropriately recording steps and explaining their thinking.  There are a variety of games linked in the GCG that students can use to apply their understanding of subtracting two digit numbers.  PERFORMANCE TASK- This is a good time to administer the Performance TaskPerformance Task  By the end of Day 5, students will be able to, explain how subtraction works, record the actions in a subtraction problem, and explain when and why it is necessary to regroup.

10. Enrich/Reteach/Intervention Reteach  If students are struggling, have them spend more time using base-ten blocks and recording their trades in the algorithm as done in Day 1.  Enrich p. E53- Teacher may want to select appropriate numbers for students to use. Enrich  Riddle card Riddle card  Enrich p. E51  Enrich p. E52