This document outlines the agenda for a professional development session on algebraic readiness. The day-long session is divided into three parts. Session I focuses on setting the stage for algebraic readiness by exploring number sense, patterns, and the development of algebraic thinking from kindergarten through 5th grade standards. Session II examines the trajectory of algebra concepts through middle and high school standards. Session III provides lesson planning resources and interactive activities centered around algebraic thinking and the Standards for Mathematical Practice.
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Setting the Stage for Algebra Readiness
1. SESSION I - Setting the Stage for
Algebra Readiness
Jacqueline Burns
1 March 2017
Qatar
9.00am-3.30pm
2. Agenda
• 09:30 – 11:00 Session I – Setting the Stage for Algebra Readiness
• 11:00 – 11:15 Break
• 11:15 – 12:45 Session II – The Algebra Trajectory: Where are we going?
• 12:45 – 01:45 Lunch
• 01:45 – 03:00 Session III - Lesson Planning and Resources in the Algebra Strand
• 03.00 – 03.30 Closing, certificates, and prizes
3. Today’s Objectives
• Increase awareness of algebra readiness and what it looks like in the work and
thinking of a proficient math student
• Work through the math standards that align with algebraic thinking in
preparation for middle grades math concepts
• Explore a variety of resources to use to support teaching and learning of algebraic
thinking with 21st Century learners
5. Mental Math
• 1000 – 98 = ?
• 99 + 17 = ?
• 12.6 x 10 = ?
• How might a student with
proficient number sense solve
this problem?
• How might a student with
limited number sense solve this
problem?
6. "Looking for patterns trains the mind to search out and discover the
similarities that bind seemingly unrelated information together in a whole.
. . . A child who expects things to 'make sense' looks for the sense in things
and from this sense develops understanding. A child who does not see
patterns often does not expect things to make sense and sees all events as
discrete, separate, and unrelated.”
- Mary Baratta-Lorton
(cited on p.112 of About Teaching Mathematics
by Marilyn Burns)
11. How students prepare for algebra
Operations and Algebraic Thinking – OA (K-5)
• Concrete uses and meanings of the basic operations
• Mathematical meaning and formal properties of the basic operations
• Prepare for later work with expressions and equations in middle school
12. Concrete uses and meanings of the basic
operations
Understanding Arithmetic
• Understanding numbers
• Developing computational fluency
• Examining the behavior of the operations
19. Mathematical meaning and formal properties
of the basic operations
Interpreting the Equal sign
6 + 2 makes 8
6 + 2 = 8
…putting together or adding to…
*readiness for Expressions and Equations work in middle school*
22. True or False - How do you know?
7 = 3 + 4
8 = 5 + 13
6 – 1 = 7
27 = 7 + 10 + 10
10 – 3 = 11 - 4
23. 6 + = 5 + 9
Explanation #1
Since 5 + 9 is 14, I need to figure
out 6 plus what equals 14. It is 8,
so the box is 8.
Explanation #2
Six is one more than the 5 on the
other side. That means the box
should be one less than 9, so it
must be 8.
24. Encouraging Relational Thinking
37 + 54 = 38 + 53
48 + 63 – 62 = 49
650 + 450 = 700 + 400
126 – 37 = – 40
Relational thinking means attending to
relations and fundamental properties of
arithmetic operations.
25. True or False?
6 + 9 = 9 + 6
4 – 3 = 3 – 4
90 – 0 = 0 - 90
7 + 50 = 50 + 7
6 + = 10 + 6
10 + = + 10
Commutative property of addition
states that changing the order of
the addends does not change the
sum.
30. How students prepare for algebra
Operations and Algebraic Thinking – OA (K-5)
• Concrete uses and meanings of the basic operations (word problems)
• Mathematical meaning and formal properties of the basic operations
• Prepare for later work with expressions and equations in
middle school
31. Prepare for later work with expressions and
equations in middle school
S – T – R – E – T – C – H
x + 3
x + 3 = 11
x = _____
(x + 2) x (x + 4) = ______________
32. Reflection
Write one new or interesting thing you learned or did so far.
How will it impact your teaching?
33. SESSION III - Lesson Planning and
Resources in the Algebra Strand
Jacqueline Burns
1 March 2017
Qatar
9.00am-3.30pm
34. 1. Make sense of problems and
persevere in solving them.
2. Reason abstractly and
quantitatively.
3. Construct viable arguments and
critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of
structure.
8. Look for and express regularity in
repeated reasoning.
Learning through the
Standards for Mathematical Practice
Which of
these SMPs
did we
explicitly do
in today’s
activities?
36. 47 ____ 35 ____ 24 = 36
Fill in the gaps to make the answer 36.
You may use these signs: + -
37. Balancing Scales To Solve Equations
Predict the number of blocks you need to equal the weight of one bag and then
test your theory. This interactive exercise focuses on using critical thinking skills to
add and subtract items on the scales to achieve balance and visual problem solving.
https://gpb.pbslearningmedia.org/resource/mgbh.math.ee.balance/balancing-
scales-to-solve-equations/
38. Finding patterns to make predictions
https://gpb.pbslearningmedia.org/resource/mgbh.math.oa.steps/finding-patterns-to-make-predictions/
39. 3.OA Markers in Boxes
• Presley has 18 markers. Her teacher gives her three boxes and asks her to put an
equal number of markers in each box.
• Anthony has 18 markers. His teacher wants him to put 3 markers in each box until
he is out of markers.
• What is happening in these two situations? How are they similar? How are
they different?
• Figure out how many markers Presley should put in each box. Show your
work. Then figure out how many boxes Anthony should fill with markers.
Show your work.
https://www.illustrativemathematics.org/content-standards/tasks/1540
40. 3.OA Markers in Boxes
• Presley has 18 markers. Her
teacher gives her three boxes
and asks her to put an equal
number of markers in each box.
• Anthony has 18 markers. His
teacher wants him to put 3
markers in each box until he is
out of markers.
In the first problem we are trying
to figure out how many are in
each group, and in the second we
are trying to figure out how many
groups there are. So the first is a
"How many in each group?"
division problem and the second
is a "How many groups?" division
problem.
41. Interactive and Immediate Feedback
Plickers
Plickers is a powerfully simple tool that lets teachers collect real-time formative
assessment data without the need for student devices.
• Tailor instruction with instant feedback
• Use Plickers for quick checks for understanding to know whether your
students are understanding big concepts and mastering key skills.
43. Closing
• Processing, Next Steps, Reflections, Questions
"The essence of mathematics is not to make simple things
complicated, but to make complicated things simple."
– Stan Gudder, American mathematician
• Written reflection: Write one action you will take as a result
of today’s exploration of algebraic thinking.
