Shift of Application
Module 3
Math Training
Sunnyside School District
Good Afternoon
Discuss the following with a partner:
Which procedural skill and fluency strategies
have you tried (mental math, spiral review,
fluency time)? What challenges have you
faced?
Subitizing
Number Combinations
Addition/Subtraction Strategies
Addition and Subtraction Math Strategies Posters
CCSS Math Shifts
1. Focus
2. Coherence
3. Rigor
Procedural Skill and Fluency
Conceptual Understanding
Math Practice Standards
1. Make sense of problems and persevere is solving
2.
3.
4.
5.
6.
7.
8.
them.
Reason abstractly and quantitatively.
Construct viable arguments and critique the
reasoning of others.
Model with mathematics.
Use appropriate tools strategically.
Attend to precision.
Look for and make use of structure.
Look for and express regularity in repeated
reasoning.
Math Practice 1 and 4
Read MP 1 and 4, then answer:
1. What does modeling mean in the
common core?
2. How can you assess these math
practice standards?
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Modeling and
Application
The
culmination
of it all!
Application (Problem Solving)
2 Levels with a full range of problems in between:
1. Word Problems
• Daily
• Related to standard you are teaching
• One and two step problems
2. Performance Tasks
• Multiple standards
• Complex problems (more than two steps)
• 45-60 minutes to solve
• Every two weeks
Daily Word Problem Example
Maria left her school supplies at school. She left 2
markers and 4 crayons on her desk. How many
school supplies did Maria leave at school?
2. Armando went to the beach. As he walked near the
shore, Armando found 11 seashells. A wave came
and washed 7 seashells away. How many seashells
are left near the shore?
3. There were 3 cats in the tree. More cats climbed up
and now there are 5 cats total. How many cats
climbed up the tree?
4. Angela has 12 markers and Jose has 16 markers.
How many more markers does Jose have than
Angela?
1.
Word Problem Types
The common core provides examples of all of the
types of basic word problems that should be done at
each grade level. Look at the problem types chart to
see the primary continuum.
1. Which of these types do you see most often in
your resources?
2. How can you help students become proficient at
all of these types?
Daily Word Problem Example
Maria left her school supplies at school. She left 2
markers and 4 crayons on her desk. How many
school supplies did Maria leave at school?
2. Armando went to the beach. As he walked near the
shore, Armando found 11 seashells. A wave came
and washed 7 seashells away. How many seashells
are left near the shore?
3. There were 3 cats in the tree. More cats climbed up
and now there are 5 cats total. How many cats
climbed up the tree?
4. Angela has 12 markers and Jose has 16 markers.
How many more markers does Jose have than
Angela?
1.
Daily Word Problems
Provide a structure for students.
 What is the problem asking us to do?
 What do we know?
 Show your steps:
 What is your solution and how do you know
it’s correct?
Remove the structure for basic word problems
throughout the year.
Graphic Organizer
Find the “Word Problem Graphic Organizer” in
Learn and edit it to meet your needs. Possible
edits to include:
1. Make a half page for simpler word
problems.
2. Change language for younger students.
3. Emphasize one part over another.
K-1 Examples
K-1 Examples
Problem Solving Strategies
Problem Solving Strategies
Problem Solving Strategies
Addition/Subtraction Strategies
Addition and Subtraction Math Strategies Posters
Suggestions
1. Read the problem for understanding 2-3 times
2.
3.
4.
5.
before beginning to solve (as a whole class).
Give students some independent work time (2-3
minutes) before partner or whole class solving.
When first starting word problems, emphasize
the process more than the correct answer.
Do not provide the steps to solve the word
problem. Students need to come up with them.
Expect independent solving of simple word
problems after about a month.
Chose Word Problems
Use your resources or go online to
chose/create 4-10 word problems that
you will use with students in the next
week. These should be 1-2 steps and
related to what you are teaching.
Share with other tables of your grade
level.
Examples in the Units
OKinder Unit 4 or 6
OFirst Grade Unit 7
Closure
1. How will you incorporate problem
solving into your math time?
2. How will you scaffold throughout the
year to help students master word
problems?
Example Scaffold
August
 2 word problems every day with form
September
 Performance task modeled by teacher (2 times)
 Continue daily problems, but remove form.
October
 Performance task once per week (partners/triads)
 Continue daily problems.
And so on………………..
Standards Study
When reading a standard, think about:
1. What are the procedures/skills students need
to learn during instruction?
2. What are the conceptual understandings that
students need to have during instruction (what
do they need to explain)?
3. What are the details in the standard that will
guide how far I go with it? Example: Only use
denominators 2, 3, 4, 6, and 8 (3rd grade).
Definitions
Procedures : A list of the skills that
students will master while learning this
standard. It’s what they will do with the
math.
Concepts: A list of what students will
understand while learning this standard.
It’s what they will explain about the math.
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Standards Study
1OA1:1.OA.1. Use addition and subtraction within 20 to solve
word problems involving situations of adding to, taking from,
putting together, taking apart, and comparing, with
unknowns in all positions, e.g., by using objects, drawings,
and equations with a symbol for the unknown number to
represent the problem. (See Table 1.)
Procedures: Add, subtract objects within 20. Identify
unknown numbers and position through objects and/or
drawings.
Concept: Explain Result Unknown, Total Unknown, Both
Addends Unknown
Change Unknown, Addend Unknown, Difference Unknown.
Start Unknown. Compare Bigger/Smaller Unknown.
Details: Word Problems. Add and Subtract within 20.
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Standards Study
K: K.CC.6-7
st
1 Grade: 1.OA.5-8
ADE Flip Books
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