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.
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.
SMP5
Use appropriate tools strategically
Using Open Number Lines
Today’s Learning Target
By the end of the session, participants will:
Understand the importance of SMP 5 Use
appropriate tools strategically in Claim 2, and
demonstrate this knowledge by solving problems.
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.
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.
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.
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.
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.
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)
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.
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
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.
Math Pratice #3
350 ÷ 28 = ____
___ x 28 = 350
28 x _____ 350
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
Fosnot Measuring for the Art Show 2011
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.
Today’s Learning Target
By the end of the session, participants will:
Understand the importance of SMP 5 Use
appropriate tools strategically in Claim 2, and
demonstrate this knowledge by solving problems.