Brandon Graham
Putting The Practices Into Action
March 20th
Focus on the Question
There are 420 students who ate lunch in the cafeteria. The
following are their lunch choices.
20
pizza
15
55
10
Nuggets
Hot Dogs
Salad
Thursday Question: Two thirds of the students who ordered the hot
dog took a ketchup packet, one seventh took a mustard packet and
the rest took one of each. How many ketchup packets, and how
many mustard packets were taken that day? Tell how you would get
the answer.
Focus on The Question
Discuss with a partner…
What is being asked, what data is
needed to solve the problem, and
what your strategy would be for
solving it.
Effective questioning should be open ended and require the
students to think like mathematicians.
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What is the question asking you to find?
What does this mean?
How do you know?
Can you say it another way?
What are the important facts/data?
What facts/ data is not needed?
Why/ why not?
What operation will you use? Why?
How do you know which operation to use?
Is there another way to solve this problem?
Could you have used a picture, diagram or manipulative to solve this? Explain how.
How do you know your answer is reasonable?
Have you thought of another way this could be done?
Do you think we have found the best solution? Justify this thinking.
Additional Open Ended Questions can be found on pg. 17 and 25 in Putting The
Practices Into Action
Standards for Mathematical Practices
The focus for this session will be #4 and #5.
Independently, review each practice.
Be prepared to share your thoughts with the
group.
CCSS – Standards for
Mathematical Practice - #4
SMP4: Model with mathematics.
• Mathematically proficient students can apply the mathematics they know to solve
problems arising in everyday life, society, and the workplace. In early grades, this
might be as simple as writing an addition equation to describe a situation. In
middle grades, a student might apply proportional reasoning to plan a school
event or analyze a problem in the community. By high school, a student might use
geometry to solve a design problem or use a function to describe how one
quantity of interest depends on another. Mathematically proficient students who
can apply what they know are comfortable making assumptions and
approximations to simplify a complicated situation, realizing that these may need
revision later. They are able to identify important quantities in a practical situation
and map their relationships using such tools as diagrams, two-way tables, graphs,
flowcharts and formulas. They can analyze those relationships mathematically to
draw conclusions. They routinely interpret their mathematical results in the
context of the situation and reflect on whether the results make sense, possibly
improving the model if it has not served its purpose.
Common Core State Standards for Mathematics – page 6
CCSS – Standards for
Mathematical Practice - #5
SMP #5- Use appropriate tools strategically.
• Mathematically proficient students consider the available tools when solving a
mathematical problem. These tools might include pencil and paper, concrete
models, a ruler, a protractor, a calculator, a spreadsheet, a computer algebra
system, a statistical package, or dynamic geometry software. Proficient students
are sufficiently familiar with tools appropriate for their grade or course to make
sound decisions about when each of these tools might be helpful, recognizing both
the insight to be gained and their limitations. For example, mathematically
proficient high school students analyze graphs of functions and solutions
generated using a graphing calculator. They detect possible errors by strategically
using estimation and other mathematical knowledge. When making mathematical
models, they know that technology can enable them to visualize the results of
varying assumptions, explore consequences, and compare predictions with data.
Mathematically proficient students at various grade levels are able to identify
relevant external mathematical resources, such as digital content located on a
website, and use them to pose or solve problems. They are able to use
technological tools to explore and deepen their understanding of concepts
Pictorial Representation of SMP #4
and #5
*Reread SMP #4 and #5
*Draw a picture, create a diagram or
graphic organizer to describe the
standard
*Include any school/network initiatives
that are currently being used in your
classroom
http://insidemathematics.org/index.p
hp/standard-4
Connections to ATLAS 2.0
Video
Consider the Following:
1. What were the models being used during this
lesson?
2. How did the teacher promote the student
behaviors described in SMP #4? SMP #5?
3. Is there anything you would have changed or
added to this part of the lesson that would
enhance the students’ behavior described in SMP
#4 and #5?
Our students are better able to…
Because as teachers we…
Make models to simplify a situation
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Identify models that are most efficient
for solving specific problems or
representing specific math ideas.
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Analyze models and draw conclusions
based on what they see.
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Model the use of diagrams and drawings to
represent problems.
Encourage students to create simple diagrams
to show problems.
Facilitate discussions in which students share
multiple ways to model mathematics.
Encourage students to revise diagrams as
needed.
Discuss specific models and their value. (e.g.,
Why does a 10x10 grid work well to represent a
decimal?)
Discuss times when a specific model might be
appropriate (e.g., Would a 10x10 grid also be
appropriate to model percents? Fractions?
Why?
Ask students to explain why they chose a
particular model.
Consistently ask for their insights after looking
at models.
Ask students to interpret models for their
classmates (i.e. describe or explain their model).
Have students write about what they learned
from their model.
Equivalent Fractions Activity
Magnified Inch
Materials: Sentence strips, and rulers
Multiplying and Dividing Fractions…
How do we develop these skills conceptually?
Gallery Walk
*Activities or Instructional Strategies to
incorporate in your classroom
*Open Ended Questions
*T Chart with Teacher Look Likes and
Sound Likes
*T Chart with Student Look Likes and
Sound Likes
*Report to a poster with your
group
*Use one colored marker to note
your groups ideas on SMP #4
(4, 3, 2, 1)
Collaborative Planning…