Monthly Math Message
November 2015
Contact Region 2:
Book Giveaway!
Send us pictures of class work, a short article on a lesson you’ve
had success with or book study progress and we’ll send you a
book of your choice from out overflow:
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High Yield Routines for Grades K-8
How the Brain Learns
Implementing the Common Core State Standards through Mathematical Problem Solving
Mathematics Formative Assessment
Principles to Actions: Ensuring Mathematical Success for All
Strength in Numbers: Collaborative Learning in Secondary Mathematics
Styles and Strategies for Teaching Middle School Mathematics
Uncomplicating Fractions to Meet Common Core State Standards in Math K-7
Understanding RTI in Mathematics
Amy Page
Director
(208) 792-2093
[email protected]
Keesje Mills
Support Staff
(208) 792-2681
[email protected]
We’re still looking for our
next Mathematics Specialist
www.lcsc.edu/irmc
In This Issue
Ask Amy ………….…………. .2
Lesson Idea …………………. 2
In the Library ………………... 4
Professional Development … 5
App of the Month …………… 6
Classroom Conundrums …… 6
Ask Amy
Q: Number I have heard of “Number Talks” before, but want to learn more information about it. Is it
primarily for elementary student or can middle and high school teachers use it successfully?
A: Number Talks help provide a foundation with numerical and algebraic reasoning in ALL grade levels. They help to establish a culture where students are expected to make sense of mathematics in
their own ways, learn to defend their ideas mathematically, and learn to listen to and build on the
thinking of their peers. It takes a lot more productive mathematical strength to invent a strategy and
test it than it does to memorize a procedure. Middle school and high school students really benefit
from being able to explain and look at math in different ways, which is what Number Talks require
them to do.
There will be a Regional Mathematics Academy for all teachers in Regions 1 and 2 the second weekend in December. See page 5 “Upcoming Events” for more information.
Lesson Idea:
Number Talks for Middle School
By Amy Page
When students fail algebra, it is not because algebra is a really hard subject, it is because they do not have a
foundation of number sense. Through a simple number talk, students will learn that math problems can be
solved using different methods and pathways. Below I have shred a simple problem that can really be thought
about in complex ways.
Step 1
Write this basic problem on the board 16 x 35. (Yes, have middle and high school students solve this basic multiplication problem). Tell them they have to solve it in different ways then they have thought of before. Don’t just
let them line up the ones and tens and do the “carry” that they are used to. Make them think of different ways to
solve this. Student should quietly indicate they have an answer by holding a “thumbs up” to their chest. This
allows other students to solve in their own way without distraction. Have them hold up multiple fingers in addition to that thumb if they have thought of more than one way to solve it.
Step 2
Call on a student to fully explain the steps he/she followed to solve the problem. Record the steps precisely as
the student explains them to you. Ask clarifying questions as needed to ensure that you understand the flow of
the child’s thinking. Be explicit about the mathematics. “Why did you half 16?” “Does this strategy always
work? How do you know?” “What did you know about the number 35 that allowed you to do that?”
Call on a student to fully explain the steps he/she followed to solve the problem. Record the steps precisely as
the student explains them to you. Ask clarifying questions as needed to ensure that you understand the flow of
the child’s thinking. Be explicit about the mathematics. “Why did you half 16?” “Does this strategy always
work? How do you know?” “What did you know about the number 35 that allowed you to do that?”
Here is a video of some students solving the problem 16 x 35.
https://mathsolutions.wistia.com/medias/nq925vpf3y
Below are the written examples of how those students solved it.
Partial Products
16 x 35 =
10 x 30 = 300
6 x 5 = 30
30 x 6 = 180
5 x 10 = 50
300 + 180 + 30 + 50 =
480 + 80 = 560
Friendly Number
Doubling/Halving
Prime Factorization
16 x 35 =
16 x 35 =
16 x 35 =
20 x 35 = 700
8 x 70 = 560
8x2
x
7x5=
35 x 4 = 140
4x2x2x7x5=
700 – 140 = 560
2 x 2 x 2 x 2 x 7 x 5 = 560
(friendly number)
Step 3
As you may notice, Partial Products lends itself well to visualizing multiplication of polynomials. See the examples
below. Just starting with a simple multiplication problem can lend itself to easily move into an algebra lesson.
Jo Boaler asks college students to solve the same type of multiplication problem. Notice all the different ways those students solve the problem. How would you represent their thinking if you were
their teacher? What specific questions would you ask?
https://www.youtube.com/watch?v=yXNG6GKFhQM
In the Library
Number Talks
While the book may be used as an independent resource, it is
also structured to provide a framework for collaborative learning groups or to provide professional development opportunities through grade-level teams, individual schools, or districts.
The accompanying DVD provides a visual platform for teachers to reflect on their current practices and target essential
understandings from their readings.
MPJ’s Ultimate Math Lessons
MPJ's Ultimate Math Lessons is a resource for teachers of
Algebra, Pre-Algebra, and Geometry in grades 6–12. It contains 80 innovative lessons and 27 thought-provoking articles
taken directly from theMath Projects Journal, a periodical
that, for more than six years, has helped teachers around the
world improve student performance in mathematics.
Manipulative
Math literature books
We have recently added over 50 math literature books!
Please see our website for a complete list; here’s a sampling:
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Can You Count to a Googol? by Robert Wells
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The Grapes of Math by Greg Tang
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Great Estimations by Bruce Goldstone
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Measuring Penny by Loreen Leedy
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The Warlord’s Puzzle by Virginia Pilegard
Professional Development
Academy on Mathematics & Science Education
December 11-12, 2015, Coeur d’Alene ID
Keynote speaker, Dr. Brad Findell, will discuss the importance and methods for noticing students’ thinking and making decisions accordingly. Additionally, in grade band breakout sessions (K-2; 3-5; 6-8; 9-12) teachers and administrators will have the opportunity to engage in
discourse about number talks and how to ask questions that will elicit students’ understanding. There will be an administrator-specific afternoon breakout. One credit is available.
Idaho Middle Level Association Annual Conference
February 12-13, 2016, Nampa ID
The theme this year is “The Power to Change” with keynote speaker Derrick Boles, known
for his expertise in leadership and learning training models. The conference has been radically streamlined this year to allow members to keep some of their weekend. Participate in
peer collaboration opportunities, attend keynote and small group sessions and regional
meetings and more.
NCTM Annual Meeting & Expo
April 13-16, 2016, San Francisco, CA
Join more than 9,000 of your mathematics education peers at the premier math education
event of the year. Registration and travel information will be available in August.
Teaching Mathematical Thinking classes
at Lewis-Clark State College
We have dates set, but registration will not be open until December.
TMT K-2nd will be spread over 5 Saturdays:
January 30, February 27, March 12, April 23 & May 14.
TMT 3rd-5th will be the week of:
Monday– Friday, June 13-17, 2016
App of the Month:
Mental Math
The game features two parts. The first part “COUNT TO 100” consist
of problems within 100. It is helpful for kids who just learn how to add
and subtract. The second part “COUNT TO 1000” consists of problems within 1000. Addition and subtraction of the two-digit and threedigit numbers will be very helpful for older children and adults.
Classroom Conundrums
Elementary School
There are 4 classrooms in a school and 75 kids total. If one room has 2
more girls than boys; one has 3 more boys than girls; one has 3 less girls
than boys; and one has 1 more boy than girls, how many girls are in the
school?
Conundrum Answers:
September 2015
Elementary School:
Annie goes to school A
Ben goes to school B
Carol goes to school C
Middle School:
Middle School
A central 60 degree sector is removed from a circle of radius 5cm. The
straight edges of the remainder of the circle are taped together to make a
right circular cone. How high is the cone?
High School
The consecutive angles of a quadrilateral inscribed in a circle have
measures 2a, 4b—8, 2a, and 3b + 20.
What is the measure of the smallest angle?
It should take 10.52 minutes
for them to eat one pizza
High School:
The angle bisector goes through
the circles’ centers and forms
congruent 30-60-90 triangles
with the point of tangency.
The hypotenuse is twice the radius-leg of each. Solve for the radius of the second circle, then repeat for the larger.
∴ the ratio of the radii of the
smallest & largest circles is 1:9
~~Email us for the full proof~~