Counting On and Counting Back Unit of Study: Addition and Subtraction Strategies PART 1 Global Concept Guide: 1 of 2

Content Development  This unit focuses solely on the strategies counting on/back and doubles. The next unit will focus on the strategies addition and subtraction with ten, think add to subtract, and adding three addends.  Counting on from a certain number is the same as adding to that number. Counting on from the greater addend (Commutative Property) is a helpful strategy that can foster mental math skills.  Students should have opportunities to model addition and subtraction strategies with a variety of manipulatives. For some lessons these manipulatives can be selected in advanced by the teacher, while in other lessons students should choose what will work for them.

Day 1 Essential Question: How can you count on to add?  Engage: Go Math Lesson 3.2, p. 104 Problem Solving #32- Students will use red and yellow counters to model the set of 8 and counting on 3. In the Math Talk in Action on p. 103, use guiding questions to probe students about the concept of counting on. Connect the counting on with red and yellow counters to the number line- for example, start the number line at 8 for the first set and count on 3 for a total of 11.  Ask students, “From which addend do you start counting? Why?” These questions are essential for students to realize to start with the greater addend to add more efficiently.  Ask students, “How are the counters and the number line related?”

Day 1 Continued… Essential Question: How can you count on to add?  Building Conceptual Knowledge: Continue using counters and number lines to explore counting on using problems on Go Math Lesson 3.2, Share and Show p Pose the problems to students without showing the Go Math book. This will allow students to communicate on their own about which addend to start with.  Encourage students to draw a model to match the counters or number line in a math journal.  Hot Question: Probe students about the most efficient way to count on. If you are adding 6 and 2, is it better to start with the 6 or 2? Why?  Journal Closure: Use pictures or words to explain how to add 3 and 9.  By the end of Day 1, students should be able to communicate which addend to add first and why. Students should be able to create or draw a model for a counting on scenario and explain what it represents.

109 Day 2 Essential Question: How can you count back to subtract?  Engage: Go Math Lesson 4.1, p. 156 Problem Solving #38- Students will use counters to model the set of 11 and counting back 2.  Allow students to select their strategy for solving the task- manipulative model, drawing a model of 11 and crossing out 2, number line, hundreds chart, etc…  Select and sequence strategies: use counters to model a set of 11 with taking away 2, drawing a model of 11 and crossing out 2, and number line with 11 with two backward jumps to 9.  Ask students, “How are the counters and model related?”, “How is the model and number line related?” Click twice to show how students can model counting back from train cars

Day 2 Continued… Essential Question: How can you count back to subtract?  Building Conceptual Knowledge: Utilize the Problem solving scenarios to highlight the counting back strategy. Allow students to choose their own strategy: manipulatives model, draw a model, number line or hundreds chart. Students should be able to explain how their model relates to the problem. For example, in the previous problem the 11 counters represented the train cars and then the 2 that were removed represented the cars on the track.Problem solving scenarios  Continue to emphasize the relationship between the strategies, similar to the engage task.  Journal Closure: Use pictures or words to explain how you can solve 7-3 by counting back.  By the end of Day 2, students should be able to create or draw a model to show counting back from a given number.

Enrich/Reteach/Intervention  Core/Enrich  Voyages: Tug of War GameTug of War Game  This game starts students at the number 11. Each student spins a spinner to add or subtract 1 or 2. This task could be used for a teacher small group with probing for the concept of counting on/back or as an independent task for students to practice counting on/back. Have students record the number sentence and model as they are completing the game.  Go Math Extend the Math Chapter 4 TE 155  Reteach  Go Math ELL Language Support Chapter 3 TE 101B  Intervention/Small Group  Strategic Interventions: Skill 8 – Counting On Strategic Interventions: Skill 8 – Counting On  Student pages Student pages  Strategic Interventions: Skill 9 – Counting Back Strategic Interventions: Skill 9 – Counting Back  Student pages Student pages

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