Disclaimer Leadership for the Common Core in Mathematics (CCLM^2) Project

1. Disclaimer Leadership for the Common Core in Mathematics(CCLM^2) Project University of Wisconsin-Milwaukee, 2013–2014 This material was developed for the Leadership for the Common Core in Mathematics project through the University of Wisconsin-Milwaukee, Center for Mathematics and Science Education Research (CMSER). This material may be used by schools to support learning of teachers and staff provided appropriate attribution and acknowledgement of its source. You may not use this work for commercial purposes. This project was supported through a grant from the Wisconsin ESEA Title II Improving Teacher Quality Program.

2. The Importance of SMP 5 Use appropriate tools strategically Common Core Leadership in Mathematics (CCLM)Tuesday April 1, 2014 This material was developed for use by the project staff and participants in the Common Core Leadership in Mathematics (CCLM^2) project through the University of Wisconsin-Milwaukee. Use by school district personnel to support learning of its teachers and staff is permitted provided appropriate acknowledgement of its source. Use by others is prohibited except by prior written permission.

3. SMP5 Use appropriate tools strategically Using Open Number Lines

4. Today’s Learning TargetBy the end of the session, participants will: Understand the importance of SMP 5Use appropriate tools strategically in Claim 2, and demonstrate this knowledge by solving problems.

5. What is an Open Number Line? The empty number line is a visual representation for recording and sharing students’ thinking strategies during the process of mental computation.

6. Noticing Levels of Sophistication The strong links between the empty number line and young children’s intuitive mental strategies are evident in the way that children naturally tend to focus on counting strategies – counting all, counting on, or counting down. Students who are more proficient mental calculators use a combination of counting strategies (usually in chunks of 10) with strategies. Children take apart numbers in flexible ways to make them more convenient to calculate mentally. --Bobis, J. (2007). The empty number line: A useful tool or just another procedure? Teaching Children Mathematics, 13(8), 410-413.

7. Addition A sunflower is 47 cm tall. It grows another 25 cm. How tall is it? After you have solved this using the open number line create a written method to model the steps of your computation.

8. Subtraction - Missing Addend I need 72 dollars to buy a skateboard. I have 39 dollars already. How many more dollars do I need to save? Solve using the open number line. Represent your strategy using a written method.

9. Subtraction A piece of string is 42cm long. If you cut off 25 cm how much will be left? Solve using the open number line. Represent your strategy using a written method.

10. Prerequisite Skills Needed for Empty Number Line Turn and Talk: What are some skills and understandings children need to confidently select the open number line as a tool? • Strong grounding in structured number lines • Counting by tens, both on and off the decade. (1.NBT.5 & 1.NBT.6) • Jumping across tens (bridging tens). (1.OA.6, 1.NBT.4)

11. Building to Success with the Open Number Line • Use a concrete model first when possible • 100 Bead strings or connecting cube trains • Huinker (2002) p. 2 offers a progression of tasks to scaffold thinking. • Move from structured  semi structured  open number line; eventually recording only relevant numbers. • Engage in “Who am I?” or “Nearest Answer” type tasks to build comfort and confidence. • Model how to record a written method to show the steps of computation.

12. Multiplication There are four 2nd grade classrooms and each classroom has 19 students in it. How many students are in 2nd grade? Solve using the open number line. Represent your strategy using a written method. • We can do 4 jumps of 20 to 80 and then jump back 4 spaces to 76. 19 x 4 = 76. Try 6 x 21; 19 x 8.
 Can you use the idea of adjusting by one to calculate multiples of 29 and 31?


13. Division If a box holds 28 apples, how many boxes can be filled with 350 apples? Solve using the open number line. Represent your strategy using a written method.

14. Math Pratice #3 350 ÷ 28 = ____ ___ x 28 = 350 28 x _____ 350

15. Advantages of the Open Number Line • place value patterns become visible adding on groups of ten • distance is measured as a series of iterated units • units used in measuring can vary in size, but the results will be equivalent • numbers can be decomposed and the subunits or smaller amounts can be added in varying orders, yet still be equivalent (associative and commutative properties) • unitizing FosnotMeasuring for the Art Show 2011

16. Rethinking the Use of Tools Claim 2: Problem Solving The Item specifications for Claim 2 for either grade 3-5 or 6-8 ask for evidence centered around specific math practices. Target B: Select and use appropriate toots strategically. Think back on the work done during our CCLM classes. • What tools were explored? • How were they used? • How did using the tool help demonstrate student understanding of the content standards? Be prepared to share at least one example in detail.

17. Today’s Learning TargetBy the end of the session, participants will: Understand the importance of SMP 5Use appropriate tools strategically in Claim 2, and demonstrate this knowledge by solving problems.