Learning Portfolio for Share It
This portfolio represents [insert name]'s learning in ESTAR Academy I Grades 3-4, Version 1.0.
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Table of Contents
1.0 Day 1: Introduction
2.0 Day 1: Algebra Readiness and Supports for All Learners
Algebra Readiness
Attributes of Algebra Readiness
Identify TEKS
Concept Mapping Questions
Concept Map
TxRCFP and the National Mathematics Advisory Panel Recommendations
Knowledge Representations
Implications for Supporting Diverse Learners
3.0 Day 1: Fluency with Operations
Big Ideas
Learner Profiles
Let’s Explore
Additive to Multiplicative
Additive and Multiplicative Questioning
4.0 Day 1: Representing Multiplication
Engage – Multiplication Match
Pulling It All Together
5.0 Day 2: Fluency with Word Problems
Common Underlying Structures
Explore - Solving Problems on the Four Corner Cards
Explain – Problem Type Folded Notes
Elaborate – Create a Problem
Pulling It All Together
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6.0 Day 2: Fluency with Facts
Instructional Strategies
7.0 Day 2: Fraction Concepts
TxRCFP and the National Mathematics Advisory Panel Recommendations
Big Ideas and Word Web
Engage – Describe the Number
Explore – Fraction Stories
Pulling It All Together
8.0 Day 2: Equivalent Fractions
Explain – Equivalent Fractions Notes
Pulling It All Together
IES Practice Guide – Recommendation 1
9.0 Day 3: Relating Fractions to Decimals and Differentiated Instruction
Explore – Fraction Patterns
Explain – Fractions to Decimals
Elaborate – Metric Circuit
Pulling It All Together
IES Practice Guide - Recommendation 2
Differentiated Instruction - Looking Ahead
10.0 Day 3: Algebra Readiness and RtI
Iceberg Activity
IES Practice Guide - RtI
Reflections - Graffiti Write
Reflections
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1.0 Day 1: Introduction
Organize your notes for this lesson in this area. Ask yourself: How can I best represent my learning in this
lesson?
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2.0 Day 1: Algebra Readiness and Supports for All Learners
Organize your notes for this lesson in this area. Ask yourself: How can I best represent my learning in this
lesson?
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Day 1: Algebra Readiness and Supports for All Learners - Algebra Readiness
Respond to the following questions:
• What is algebra and what is its purpose?
• So...do our students understand the purpose of algebra? (Think about the student video you
watched)
• What does instruction that develops algebraic thinking look like in the primary grades?
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Day 1: Algebra Readiness and Supports for All Learners - Attributes of Algebra Readiness
Respond to the following questions:
• When you think of algebra readiness, what mathematics comes to mind?
• How do these activities compare to what you envisioned?
• How does knowing how to add or subtract fractions on a number line support algebra readiness?
• How might the context of a ratio problem differ from the context of a fraction problem?
• What implications might this have for instruction?
• What role does the language of mathematics play in algebra readiness?
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Day 1: Algebra Readiness and Supports for All Learners - Identify TEKS
Respond to the following questions:
• What Grade 3 and Grade 4 student expectations support the ability to add or subtract fractions on
a number line?
• What Grade 3 and Grade 4 grade student expectations support the ability to describe the
relationships that exist within a set of objects or between sets of objects?
• What Grade 3 and Grade 4 student expectations support multiple mathematical representations of
the same problem?
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Day 1: Algebra Readiness and Supports for All Learners - Concept Mapping
Consider a student who is "ready" to begin an algebra course, then answer the following questions:
• When you think of a student who would be successful in algebra, what behavioral characteristics does that student display?
• In what kind of situations would a student demonstrate algebra readiness?
• On what kind of problems would an algebra-ready student be successful?
• What does algebra readiness build towards?
Complete the concept map on the next page.
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Day 1: Algebra Readiness and Supports for All Learners - Concept Mapping
Another word in the category:
Behaviors:
Category:
Behaviors:
Another word in the category:
Algebra Readiness
Example 1
Example 2
Behaviors:
Example 3
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Day 1: Algebra Readiness and Supports for All Learners - TxRCFP and the National Mathematics
Advisory Panel Recommendations
Respond to the following questions:
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What statement resonated with you? Why?
What new insight did you gain? What are the implications?
What surprised you about the recommendations? Why?
Examine the focal points categorized as "Fluency with Operations."
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What do these focal points have in common?
What implications could this have for instruction?
Refine your concept map as needed.
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Day 1: Algebra Readiness and Supports for All Learners – Knowledge Representations
Choose one student expectation. Create a graphic that describes the three knowledge representations
(foundational, bridging, target) for the chosen student expectation. Use the following questions to guide
your work:
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What is the target knowledge for your grade level?
What foundational knowledge is necessary?
How could you bridge from foundational knowledge to target knowledge?
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Day 1: Algebra Readiness and Supports for All Learners – Implications for Supporting Diverse
Learners
Now that you have read the English Language Proficiency Standards and the Teaching Mathematics to
Gifted Students in a Mixed-Ability Classroom article, create a visual that summarizes the readings'
suggestions for supporting ELL and G/T students.
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3.0 Day 1: Fluency with Operations
Organize your notes for this lesson in this area. Ask yourself: How can I best represent my learning in this
lesson?
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Day 1: Fluency with Operations – Big Ideas
Record the "big ideas" that were embedded in each of the four tasks and the foundational knowledge
needed to complete each task. Group your observations according to any common characteristics.
• How could "facts with five" be used to determine the product of 7x6?
• How could the partial products be represented with an open area model?
• How could the strip diagram be partitioned to show the time it takes to jog 20 miles?
• How could the product be determined if 49 was represented as 40 and 9?
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Day 1: Fluency with Operations – Learner Profiles
Record your observations and respond to the following questions:
• What academic strengths does the student appear to have?
• What gaps in understanding does the student appear to have?
• Does the student work appear to support the data in the learner profile?
• What types of activities/lessons will these three students need to explore in order to develop
fluency with operations?
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Day 1: Fluency with Operations – Let’s Explore
Two flowers were measured with heights of 3 inches and 6 inches. Now they are
respectively 9 inches and 12 inches tall. Which flower grew more?
Find and defend two different answers to this problem.
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Which response represents additive thinking?
Which response represents multiplicative thinking?
How are additive thinking and multiplicative thinking different?
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Day 1: Fluency with Operations – Additive to Multiplicative
Complete Additive to Multiplicative Problem A and Problem B and Folded Notes activities.
What are some similarities and differences between the two problems?
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Day 1: Fluency with Operations – Additive and Multiplicative Questioning
Complete the Round Robin activity, then respond to the following questions:
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How are your strategies alike/different?
How are the models alike/different?
How do the models connect to the context of the problem?
Why is it important for students to be aware of multiple strategies?
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4.0 Day 1: Representing Multiplication
Organize your notes for this lesson in this area. Ask yourself: How can I best represent my learning in this
lesson?
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Day 1: Representing Multiplication – Engage – Multiplication Match
Respond to the following questions:
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What number sentence could be used to represent the picture on your card?
What is the product of the picture or expression on your card?
If the product is a result of multiplying two factors, what is the product of six times five?
How could you verify that your 4 cards represent the same product?
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Day 1: Representing Multiplication – Pulling It All Together
Add notes, record ideas, and/or additional strategies for this lesson. Respond to the following questions:
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What student supports were in the lesson?
Who would benefit from the supports?
What concepts may require pre-teaching?
How could the enrichment activity be used as a Tier 1 differentiation activity?
What supports were in place to address the ELPS (reading, writing, speaking, and listening)?
What additional strategies might be incorporated?
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5.0 Day 2: Fluency with Word Problems
Organize your notes for this lesson in this area. Ask yourself: How can I best represent my learning in this
lesson?
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Day 2: Fluency with Word Problems – Common Underlying Structures
Respond to the following questions:
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What student-friendly words could be used to describe each group?
Would you use the same solution strategy for all of the problems in one group?
Is it possible to solve each problem in the group with a strip diagram? Why or why not?
Choose one of the problem cards. Use a strip diagram to model the problem. Is there more than
one way to model the problem on a strip diagram?
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Day 2: Fluency with Word Problems – Explore - Solving Problems on the Four Corner Cards
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How many groups do you need to represent the number of pizzas? How many counters could you
put in each group to represent the number of slices on each pizza?
If you have 8 groups with 5 in each group, which numbers would you need to multiply to find the
solution?
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Day 2: Fluency with Word Problems – Explain – Problem Type Folded Notes
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How could you describe all of these similar problems?
What name could you give this group?
What do you want to remember about _____ problems?
What are the similarities between the problems? Differences?
What are the similarities between the solution processes? Differences?
How could you describe all of these similar problems? What name could you give this group?
What are some steps you used when looking at the word problems?
What is an example of a ______ problem?
How could you model the problem with a picture?
What do you want to remember about _____ problems?
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Day 2: Fluency with Word Problems – Elaborate – Create a Problem
Use the Create a Problem Card to create one word problem and record it below. Look at the Four Corners
Posters. How could the problem on the poster help you create each type of word problem?
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Day 2: Fluency with Word Problems – Pulling It All Together
Add notes, record ideas, and/or additional strategies for this lesson. Respond to the following questions:
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What student supports were in the lesson?
Who would benefit from the supports?
What concepts may require pre-teaching?
How could the enrichment activity be used as a Tier 1 differentiation activity?
What supports were in place to address the ELPS (reading, writing, speaking, and listening)?
What additional strategies might be incorporated?
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6.0 Day 2: Fluency with Facts
Organize your notes for this lesson in this area. Ask yourself: How can I best represent my learning in this
lesson?
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Day 2: Fluency with Facts – Instructional Strategies
Complete the instructional strategies table.
Instructional Strategies
Flash Cards
Benefits (Why?)
Drawbacks (Why?)
Practice Pages
Concrete Models
Numerical Fluency and
Relationships
Respond to the following:
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When might the use of each strategy help a student develop fluency with facts?
What might happen if a teacher used only one strategy to develop fluency of facts?
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7.0 Day 2: Fraction Concepts
Organize your notes for this lesson in this area. Ask yourself: How can I best represent my learning in this
lesson?
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Day 2: Fraction Concepts - TxRCFP and the National Mathematics Advisory Panel Recommendations
Respond to the following questions:
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Which focal points did you categorize as "Fluency with Fractions?"
What do those focal points have in common? What language is common to the focal points?
What implications could this have on instruction?
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Day 2: Fraction Concepts – Big Ideas and Word Web
Respond to the following question and create a word web to describe the attributes of a fraction.
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What are the "big ideas" embedded in each task and the foundational knowledge needed to
complete each task? Group your observations according to any common characteristics.
Use the following questions to build your word web:
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What is a fraction?
What does a fraction represent? What else could a fraction represent?
What are the different ways a fraction could be represented?
Fraction
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Day 2: Fraction Concepts – Engage – Describe the Number
Respond to the following questions:
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What is significant about having students describe numbers as "between?"
What do the pictorial models convey about the magnitude of the number?
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Day 2: Fraction Concepts – Explore – Fraction Stories
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What are some misconceptions about fractions that may be corrected by this activity?
How does context deepen students' understanding of concepts?
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Day 2: Fraction Concepts – Pulling It All Together
Add notes, record ideas, and/or additional strategies for this lesson. Respond to the following questions:
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What student supports were in the lesson?
Who would benefit from the supports?
What concepts may require pre-teaching?
How could the enrichment activity be used as a Tier 1 differentiation activity?
What supports were in place to address the ELPS (reading, writing, speaking, and listening)?
What additional strategies might be incorporated?
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8.0 Day 2: Equivalent Fractions
Organize your notes for this lesson in this area. Ask yourself: How can I best represent my learning in this
lesson?
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Day 2: Equivalent Fractions – Explain – Equivalent Fractions Notes
Respond to the following questions:
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How does your model represent _____?
How could you use numbers to represent your model?
Did removing or adding toothpicks to your adding machine tape change the size of the part that
was shaded?
Did removing or adding toothpicks to your adding machine tape change how you could name the
part shaded?
What conclusion can you draw about the fractions that named the shaded part of the adding
machine tape?
Describe the position of each fraction on the number line representation. What conclusion can you
draw about the position of equivalent fractions on a number line?
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Day 2: Equivalent Fractions – Pulling It All Together
Add notes, record ideas, and/or additional strategies for this lesson. Respond to the following questions:
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What student supports were in the lesson?
Who would benefit from the supports?
What concepts may require pre-teaching?
How could the enrichment activity be used as a Tier 1 differentiation activity?
What supports were in place to address the ELPS (reading, writing, speaking, and listening)?
What additional strategies might be incorporated?
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Day 2: Equivalent Fractions – IES Practice Guide – Recommendation 1
Respond to the following questions:
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What do you agree with most from Recommendation 1? Why?
Did you disagree with anything in Recommendation 1? Why or why not?
What is a new idea or strategy that you found in Recommendation 1?
What is one way that you could apply a strategy found in Recommendation 1?
What is one question that you would like to ask the authors of this guide?
Have you ever taught students who lacked the fraction understandings described by
Recommendation 1? Why do you think the gap in understanding existed?
Refine your Fraction word web from Day 2: Foundations for Fractions – Big Ideas and Word Web as
needed.
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9.0 Day 3: Relating Fractions to Decimals and Differentiated Instruction
Organize your notes for this lesson in this area. Ask yourself: How can I best represent my learning in this
lesson?
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Day 3: Relating Fractions to Decimals and Differentiated Instruction – Explore – Fraction Patterns
Respond to the following questions:
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How could you fold the strips to divide it into the number of equal parts indicated by the
denominator of the given fraction?
How could you use the folds and the marks given on the decimal strip to find equivalent fractions?
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Day 3: Relating Fractions to Decimals and Differentiated Instruction – Explain – Fractions to
Decimals
Respond to the following questions:
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What patterns, similarities, and/or differences do you notice in the decimal representations of the
fractions?
How might a number line represent equivalent fractions and decimals?
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Day 3: Relating Fractions to Decimals and Differentiated Instruction – Elaborate – Metric Circuit
Respond to the following questions:
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Why is a meter stick an appropriate model for decimals?
Could you use the meter stick to solve problems that are not in a measurement context? Explain.
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Day 3: Relating Fractions to Decimals and Differentiated Instruction – Pulling It All Together
Add notes, record ideas, and/or additional strategies for this lesson. Respond to the following questions:
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What student supports were in the lesson?
Who would benefit from the supports?
What concepts may require pre-teaching?
How could the enrichment activity be used as a Tier 1 differentiation activity?
What supports were in place to address the ELPS (reading, writing, speaking, and listening)?
What additional strategies might be incorporated?
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Day 3: Relating Fractions to Decimals and Differentiated Instruction – IES Practice Guide –
Recommendation 2
Respond to the following questions:
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How did the activities explored support the implementation of Recommendation 2?
Create a visual that represents the big ideas of Recommendation 2.
Revisit your fraction word web and refine as needed.
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Day 3: Relating Fractions to Decimals and Differentiated Instruction – Differentiated Instruction –
Looking Ahead
Respond to the following questions:
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What student expectations are embedded in this activity?
What foundational knowledge must be in place for a student to be successful with this activity?
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10.0 Day 3: Algebra Readiness and RtI
Organize your notes for this lesson in this area. Ask yourself: How can I best represent my learning in this
lesson?
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Day 3: Algebra Readiness and RtI – Icebergs and Readiness Standards
Create an iceberg that represents the foundational, bridging, and target knowledge and skills needed for a
student to demonstrate understanding of Grades 3 and 4 readiness standards.
• Grade 3: 3.2C or 3.4B/3.4C
• Grade 4: 4.2D or 4.4D/4.4E
Use the following questions to guide your work:
• With what understandings about ______ do your students come into Grade 3 or Grade 4?
• What instructional activities and representations do you use to move students toward mastery of
the student expectation?
• How do you know when a student has mastered this student expectation? What evidence of
understanding does the student demonstrate?
• Does target always mean abstract? Does bridging always mean pictorial? Does foundational
always mean concrete?
• What other foundational, bridging, and target knowledge and skills are needed to build towards
mastery of this student expectation?
Target:
Bridging:
Foundational:
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Day 3: Algebra Readiness and RtI – IES Practice Guide - Response to Intervention (RtI)
Respond to the following questions:
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How did the activities and lessons lay a foundation for these recommendations for intervention?
What impact should these recommendations have on classroom instruction?
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Day 3: Algebra Readiness and RtI – Reflections – Graffiti Write
Think about what you have learned in this course and record any ideas, reflections, or take-aways from
the academy that support any of the four big ideas explored in the activities and lessons.
• Fluency with Operations
• Fluency with Word Problems
• Fluency with Facts
• Fraction Concepts
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Reflections
Answer these questions based on what you have learned from the course.
What do I need to change?
Your thoughts here…
What squares with my thinking?
Your thoughts here…
What’s still rolling around in my mind?
Your thoughts here…
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