Place Value Strategies Unit of Study 5: Modeling and Representing 2-Digit Addition and Subtraction Global Concept Guide: 2 of 3

Content Development Sample Anchor Chart This GCG provides many opportunities to make connections between previously learned content this school year. Students will develop a stronger understanding when the teacher helps connect the place value strategy (break-apart model). “Given the opportunity, children can and do invent increasingly efficient mental-arithmetic procedures when they see a connection between their existing count-by-tens knowledge and addition by ten. “ (Baroody & Standifer 1993,1992) This would be a perfect opportunity to create an anchor chart listing all the different strategies. Each time a new strategy is introduced, add it to the chart with an example. Base ten blocks are not the focus but should be available if students want to use. Encourage those students to draw quick pics. Sample Anchor Chart

Content Development continued There are many ways to make a ten. Number lines- Learn Zillion – Caution- Learn Zillion use the words larger, bigger, smaller instead of more precise vocabulary greater than, less than, increasing and decreasing in value so the video is not appropriate to show to students. Addition with an open number line LZ2580 Subtraction with an open number line LZ2856 Two step story problems with an open numberl ine LZ4261- Strategically decomposing numbers to help add and subtract. Spending time on different strategies will increase student accuracy as they are building on their own understanding in contrast to memorization of an algorithm.

Day 1 Essential question: How can making a ten help me add a string of numbers? Engage students with a question like: Mr. Finn had 3 bags of goldfish crackers. There were 17 crackers in the 1st bag, 15 in the 2nd bag, and 13 in the 3rd bag. How many goldfish crackers does Mr. Finn have? Have students solve using any strategy they would like. The goal for the day is for students to look for numbers that will make a 10 to solve more efficiently. Teachers should look for a student that makes a 10 to solve and highlight that strategy. Let a student share that first drew a quick pic and then used numbers. (Reminder: We are not teaching the traditional algorithm at this time.) If you can’t find a student who uses this strategy, show the strategy asking students what they think about it? I grouped my 7 ones and 3 ones together and made 10. I put my ten in the tens place. I then added my tens and ones. I know there are 45 fish in the 3 bags. I saw I had 7 ones and 3 ones and I knew that made 10ones so I grouped them together and made 1 ten. I counted my tens and my leftover ones. I got 45 fish in all 3 bags.

Day 1 continued Cora Vet had 4 boxes of cars. There were 6 in the 1st box, 3 in the 2nd box, 8 in the 3rd box, and 1 in the 4th box. How many cars does she have? This problem is designed to have students see that it may take 3 numbers to make 10. More questions to all students to solve to apply the make a ten strategy. - Make a ten. By the end of Day 1 students will be able to make a ten to add a string of numbers.

Day 2 Essential question: How can we use an open number line to decompose numbers to solve problems? The open number line will be useful because it will help students to decompose numbers. There are multiple ways to solve a problem using an open number line. Students will break apart one addend/subtrahend and use an open number line to solve the problem. The 2nd grade needs 91 grilled cheese sandwiches for the field trip. The lunchroom has made 36 grilled cheese sandwiches. How do many they still need to make? Examples show counting back and counting up on using an open number line. There are multiple ways to solve a problem. In each example 36 was subtracted from 91. Solutions counting back. Solutions counting up.

Day 2 continued At the end of the field trip 29 students were on 1 bus and 45 students were on another bus. How many students are on the two buses? Additional problems you can use to support using a number line to solve problems. By the end of Day 2 students will be able to use an open number line to strategically solve problems. Possible strategies students might use to find how many students are on the buses.

Day 3 Engage students with a problem such as: Essential question: How can I strategically decompose ones to add and subtract numbers? Today students will break apart the ones and may use a number line or number bonds to solve problems. The ultimate goal is that students are flexible with numbers so they should be encouraged to solve problems in more than one way. Engage students with a problem such as: Happy had 24 dog toys. She got 18 more for her birthday. How many toys does Happy have? Additional problems that can be used on this day. Problems are designed to be used to facilitate discussion about decomposition of numbers. By the end of Day 3 students will be able to strategically decompose ones to add and subtract numbers.

Day 4 Essential question: How do I use an open number line to solve multistep problems? Engage students with a problem like: Twenty-two students were in the cafeteria for lunch. A class of 18 came to the lunchroom. Seven left for lunch bunch. How many students are in the cafeteria? Additional problems that can be used on this day. By the end of Day 4 students will be able to solve multistep problems using an open number line.

Day 5 Essential question: How does using place value strategies make it easier to solve problems? Refer to anchor chart. Discuss each strategy and when each would be efficient to use. Give problems and have students select the strategy that would be the most efficient and explain why. Teacher facilitates discussion about solution strategies and their reasoning. As always, this is a good time to discuss what a reasonable answer might be. Have students explain in writing why their strategy works. Problems you could give: 28+12= (students may argue the make a ten strategy) 35+47= (students may decompose the 7 to 5 and 2 to make a ten) 59-11= (students may use expanded form) 35-19=(students may take away 5 to get to 30 and then take away 10 and 4) Give students strategies and they create a problem they might solve using the given strategy. Shell game – students can use to discuss efficient strategies. By the end of Day 5 students will be able to use place value strategies to solve problems more efficiently.

Enrich/Reteach/Intervention For students who are struggling, refer back to using base ten blocks to ensure they understand the concept. Some students just need more time in the concrete phase. Animated math models Make a ten Add 3 numbers Break apart numbers to add Enrich: Students can create their own word problems to solve using different strategies. Using the anchor chart, students create word problems that match the place value strategy for adding or subtracting.