1. Strategies to Add and Subtract Two-Digit Numbers Unit of Study: Two-digit Addition and Subtraction Global Concept Guide: 2 of 3

2. Content Development  Students have learned several strategies for adding and subtracting. Understanding how they work is key for students to develop fluency. Students should be able to choose a strategy and explain how it helped them solve the addition or subtraction problem.  It is important for students to be exposed to different strategies. They should be given the opportunity to compare different strategies.  Students should learn to choose the strategy that is most efficient in particular situations or the one that works best for them.  Hundreds charts have been used earlier this year for basic facts. Students can visually follow along and see how numbers change when they are adding or subtracting. They can also touch numbers as they count across rows or up and down columns.

3. Content Development  After students have used base ten blocks to model addition, they can transition to drawing a quick pic of their model. It is important for students to see the similarities between the base ten blocks and the quick pics to help them transition from the concrete stage to the pictorial stage.  It is important to incorporate problem solving, using different problem types, into this GCG.problem types  It is also important to give students the opportunity to take a given problem and write a story that matches the problem. This correlates to SMP 2 Reason Abstractly and Quantitatively.  Open number lines are an important tool for students to learn to use. More info can be found on Day 4 of this PowerPoint.

4. Day 1 Essential Question: What strategies can I use to add or subtract to 20?  Day 1 should be used as a review of different strategies learned to add and subtract through 20. Strategies that students have already learned are doubles +1/-1, make a ten, doubles, counting on, counting back, related facts/inverse operations, and think add to subtract.  Engage/Building Conceptual Knowledge: Basic Facts Problem SolvingBasic Facts Problem Solving  The teacher can project these problems individually on the Elmo or write on poster paper for all students have access to the problem.  With each problem, the teacher should read it to the students and provide ample time for students to solve using their strategy.  Teachers should be strategic and purposeful about what strategies are shared and help students see the differences and similarities among the strategies. A discussion about efficiency can also be had at this point. The teacher can ask, “What is another way I can solve this problem?”  Independent Practice: Go Math Lesson 8.1, Problem Solving p. 320 #44/45. Students apply addition and subtraction strategies to different problem types.  Closure: Go Math HOT p. 319 #43. Students are asked to determine the missing addend for an addition fact. By the end of Day 1, students should be able to apply the addition and subtraction strategies to numbers within 20.

5. Day 2 The number sentence is 32 + 20….. I can start at 32 and add ten twice.

6. Day 2 Continued… Essential Question: How I can use a hundreds chart to add or subtract?  Students should be exposed to using a hundreds chart to add or subtract. Laminated hundreds charts that students can write on with a dry-erase marker would be good to use for this.  A connection should be made to unit 7 when students used the hundreds chart to count by ones or tens from any given number to 120. Students should be encouraged to use their knowledge of the patterns of numbers to move up and down rows when adding or subtracting tens rather than counting the ten ones. If some students are still counting all the ones, they can share and then have their strategy compared to a student who is counting by tens. An efficiency conversation can also be held here.  Having students using a hundred chart to add/subtract tens or ones will lay the foundation when the students are asked to add/subtract both tens and ones.  It is critical that all students have access to a hundreds chart for this day since it is the essential learning for today.  Engage: Ask students, “How can you use a hundred chart to solve 24 +4?”. “How can you use a hundred chart to solve 31 + 40?”  Go Math Lesson 8.4, Model and Draw p. 330. This model and draw should serve as guidance on how to use the hundred chart to add tens or ones. Supply a hundred chart to each student so they can begin modeling the provided problems. Students should be using a hundreds chart to solve these problems- the teacher should not be modeling under the Elmo for students to watch. The purpose of this lesson is for students to practice using the hundred chart and explain how to use it. The teacher can probe students and select students to share their models.

7. Day 2 Continued… Essential Question: How I can use a hundreds chart to add or subtract?  Building Conceptual Knowledge: Problem Solving on a Hundred ChartProblem Solving on a Hundred Chart  The teacher can project these problems individually on the Elmo or write on poster paper for all students have access to the problem.  With each problem, the teacher should read it to the students and provide ample time for students to solve using the hundred chart.  Teachers should be strategic and purposeful about what strategies are shared and help students see the differences and similarities among the strategies. A discussion about efficiency can also be had at this point. The teacher can ask, “What is another way I can solve this problem?”  The teacher can use the Go Math Math Talk on p. 331 to facilitate a discussion about the efficiency when the problem is 2 + 84.  Independent Practice: Go Math Standards Practice Book p. P157 #s 1-6. Students practice using a hundred chart to add. The essential question is to add and subtract so additional problems will be needed for subtraction.  Closure: Write a number sentence to add 6 tens to 21. By the end of Day 2, students should be able to use a hundreds chart to add and subtract.

8. Day 3 Essential Question: How can I use models to add or subtract?  On this day, students should be exposed to using base ten blocks and drawing a quick picture of them.  It is important to allow students to use base ten blocks to physically represent the problems today. As students seem ready they can be exposed to drawing a quick pic of the concrete model. It will be really important for the teacher to help students see the similarities between the concrete model and the pictures. At this point students should be encouraged to do both.  Engage: Go Math Lesson 8.5, Listen and Draw p. 333. Students are presented a word problem where they add 5 to a set of 14. Students are expected to use base ten blocks to model the set of 14 and add ones for the 5 more cars. The teacher can use the guiding question on p. 333 (TE Manual). Additional questions may include, “What does the 14 represent?”, “What does the the 5 represent?”, “How did you use base ten blocks to show the 14 cars?”, “Why did you use one ten and four ones to show 14?”, “What does the 19 represent?”

9. Day 3 Continued… Essential Question: How can I use models to add or subtract?  Building Conceptual Knowledge/Independent Practice: Base 10 Model Problem Solving ScenariosBase 10 Model Problem Solving Scenarios  Students should be using base ten blocks and tens/ones place value chart to model the problems. The Go Math book has students drawing a quick pic for each addend and circling the tens to count. The teacher can direct students to use the tens/ones place value chart so the tens and ones will be grouped together. The use of the tens/ones chart will be used in the Go Math Lesson 8.7. Tens/Ones Place Value ChartTens/Ones Place Value Chart  This resource has 8 problem solving scenarios for both the building conceptual knowledge and independent practice.  Closure: Go Math Problem Solving p. 336 #17 By the end of Day 3, students should be able to create a base ten model or quick pic for the addition or subtraction problem.

10. Day 4 Essential Question: How can I use a number line to add or subtract?  This day should be used to expose students to using an open number line to add or subtract. There is not a Go Math Lesson that is devoted to this concept, but any word problem can be used to teach this strategy. Any of the equations from a Go Math lesson can be changed into a story problem.  During this day it is important to include the open number line that was used in GCG 1. The concept that was introduced in the first GCG and can be used to add tens and ones as well. It is important for the teacher to help students see the connection between the open number line and simply counting by tens or ones. Also, teachers should facilitate a discussion about why an open number line may be more efficient to use than a closed number line. Students also need to be exposed to the idea that a number line does not need to start at one. Click here for more information on using number lines.here

11. Day 4 Continued… Essential Question: How can I use a number line to add or subtract?  Engage: Review the open number line with tens, such as 47 + 10. Ask students, “How does the number line help us solve this problem?” Pose the problem, 32 + 8, to students and encourage students to solve using a number line. Repeat the process with additional problems for students to practice using an open number line.  Building Conceptual Knowledge/Independent Practice: Open Number Line Problem Solving ScenariosOpen Number Line Problem Solving Scenarios  This resource has problem solving scenarios for both building conceptual knowledge and independent practice as well as additional practice for students.  For building conceptual knowledge, the teacher should follow the same process as the previous days. However, the strategy can changed from hundreds chart and base ten models to an open number line.  Closure: How can you use an open number line to solve, 44 + 7? By the end of Day 4, students should be able to use an open number line to add and subtract.

12. Day 5 Essential Question: What different strategies can you use to add or subtract?  This day should be used to encourage students to solve problems in more than one way. Students should be reviewing the strategies: hundreds charts, base ten models, quick pics, and open number lines. Scenarios can be posed to students and students have to identify the appropriate strategy and justify the reasoning. Different Strategies Problem Solving ScenariosDifferent Strategies Problem Solving Scenarios  Core:  Grade 1 Voyages: To 100: Use the section with hundreds chart to review numbers to 50 p. 169 and the sums/differences problems p. 170. With the sums and differences, the students could use the hundreds chart, base ten models, quick pics, or open number lines to solve. Students can also solve the problem using a second strategy.To 100  Enrich:  Grade 1 Voyages: To 100: Enrich students can complete the tasks listed in the core section, but they could also complete the sample Riddles p. 114 (top). Students could also create number riddles based on the clue categories.To 100  Reteach/Intervention:  Go Math ELL Language Support p. 333B: Students will use the vocabulary, tens and ones, to explain their base ten model. The task is described on p. 333B but additional problems will be needed.  Go Math Tier 1 p. 333B: Students will use a tens/ones place value chart to model an addition problem. The teacher will probe the students about the place value and action in the problem.  Go Math Reteach p. R64: Students will practice addition on a hundreds chart. The teacher can create additional scenarios for the hundreds chart. The performance task should be given in the last 15-20 minutes of the math block.

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