Posted: April 25th, 2025

Purple Haze 4

See attached 

Help 4 Complete what is highlighted in yellow

 lesson plans and detailed annotations provided for assistance 

Answer the questions in yellow
Candidate Name:	Standard:  2 Instructional Planning: The teacher plans using state and local school district curricula and standards, effective strategies, resources, and data to  address the differentiated needs of all  students. Framework for Teaching Component(s) Domain 1: Planning and Preparation  1b. Demonstrating Knowledge of Students  1c. Setting Instructional Outcomes  1e: Designing coherent instruction
Description of the artifact: · 3 Day Lesson Plan (Math 3rd grade) · Detailed Annotations Document based on the above lesson plan Purpose (with “in order to” statement): The academic purpose of the students in this lesson plan is to develop a foundational understanding of and fluency with the properties of multiplication and division—specifically, the commutative, associative, and distributive properties. Through targeted activities, they learn not only to identify these properties but also to apply them to simplify problem-solving and find unknowns within multiplication and division equations. This understanding helps students build efficiency and flexibility in their mathematical reasoning, supporting their ability to: 1. Use properties to simplify calculations and solve unknowns, an essential skill as they progress in math. 2. Gain insight into the structure of math operations by recognizing patterns and relationships, fostering deeper comprehension beyond rote memorization. 3. Lay groundwork for algebraic thinking by equipping them to understand and manipulate equations and expressions. This academic purpose ensures that students are developing the skills needed for higher-level math, where properties are used for more complex problem-solving and equation balancing.
How does the artifact demonstrate proficiency in the TAPS standard and related Danielson competencies?	What did you learn? What insights have you gained about your professional practice?
What have you realized about what else you need to know and what skills you need to develop in relation to this standard and these competencies?	Identify one high-leverage action step that you can take that will have a positive impact on teaching and learning.

Standard 2 Annotation Explained

Here’s a breakdown of the planning process for the 3-day lesson plan aligned with standard

3.PAR.3.3. Each component was chosen based on best practices in math instruction for 3rd graders,
as well as data-driven decisions to meet varying student needs and support mastery of the properties
of multiplication and division. This explanation details the instructional choices, as well as the
qualitative and quantitative data considered.

This approach to planning, driven by both qualitative observations and quantitative
assessments, ensures that instructional decisions meet students’ needs at every level. Each
instructional choice aligns with the standard while providing tailored supports to address varying
levels of understanding, promoting conceptual mastery for all learners.

1. Understanding the Standard and Student Needs

 Standard Analysis: The primary focus of standard 3.PAR.3.3 is for students to apply
properties of multiplication and division (commutative, associative, distributive) within
100. This standard emphasizes not just rote calculation but conceptual understanding and
application of mathematical properties to solve problems.

 Pre-assessment Data: Before planning, a pre-assessment on multiplication and division
skills was conducted to gauge baseline understanding of these operations and properties.

o Quantitative Data: The data revealed that while most students could multiply and
divide within 100, many struggled to use properties effectively to simplify or solve
equations.

o Qualitative Data: Observations showed that students often relied on memorized facts
rather than understanding the properties that can make problem-solving easier, which
informed the decision to prioritize conceptual understanding and application.

2. Setting Learning Goals and Objectives
 Learning Goals: Based on the pre-assessment data, the objectives were set to ensure

students could:
o Recognize and define the commutative, associative, and distributive properties.
o Apply these properties to solve multiplication and division problems within 100.
o Use the properties strategically to simplify problem-solving and find unknowns.

 These objectives guided the sequence of activities, ensuring that by the end of the lesson
sequence, students could not only identify the properties but use them confidently in various
contexts.

3. Selection of Key Vocabulary and Instructional Strategies
 Vocabulary: The vocabulary (commutative, associative, distributive, equation, etc.) was

chosen to match the terminology in the standard.
o Instructional Decision: Introducing and reinforcing these terms early in the lesson

sequence allows for ongoing practice and familiarity, addressing potential
misconceptions around the properties.

o Data Support: Pre-assessment results showed limited familiarity with the terms
“associative” and “distributive,” indicating that students needed extra reinforcement.

 Instructional Strategies:

o CRA (Concrete-Representational-Abstract) Approach: This approach was selected
to scaffold learning from concrete manipulatives to abstract reasoning, supporting
students as they build confidence with each property.

 Data Support: Observational data showed that students grasp concepts better
when moving from hands-on exploration to more abstract problem-solving.

o Think-Pair-Share and Math Journals: These strategies support peer collaboration and
reflective learning. By discussing their ideas with peers and recording reflections,
students deepen their understanding.

 Qualitative Support: Discussions in math journals provide a window into student
thinking, allowing for adjustments in instruction based on the clarity of student
responses.

4. Lesson Structure: Opening, Work Session, Closing
Each day’s structure was designed to ensure students had time for exploration, guided practice, and
reflection.

 Opening: The opening segments review prior knowledge and introduce daily objectives,
setting the context for each lesson.

o Rationale: The consistent review of terms and quick practice in the opening helps
activate students’ prior knowledge, providing a foundation for deeper learning during the
work session.

 Work Session: This segment involves interactive activities where students apply the
properties. Activities are sequenced to start with the commutative property (day 1), move to the
associative property (day 2), and conclude with the distributive property (day 3).

o Instructional Decision: The order was chosen to build gradually from simpler to more
complex concepts, reducing cognitive load.

o Data Support: Observational and formative assessment data collected throughout the
work sessions help inform real-time adjustments, such as providing additional examples
if students struggle with a property.

 Closing: Each day’s lesson ends with a review and reflection, allowing students to summarize
their understanding.

o Rationale: The daily reflection provides an opportunity for students to consolidate
learning and share insights, reinforcing the concepts through verbal explanation.

5. Check for Understanding and Intentional Questioning
 Check for Understanding: Formative checks, such as quick exit tickets or verbal questioning,

are embedded in each day’s work session and closing.
o Instructional Decision: These checks help identify misconceptions early and inform

real-time adjustments.
o Data Support: Analyzing responses allows for immediate feedback, and the data from

these checks can reveal which properties require additional practice.
 Intentional Questioning: Open-ended questions (e.g., “How does grouping the numbers help

make this problem easier?”) are used to prompt student thinking.
o Rationale: These questions guide students to verbalize their reasoning, helping to

assess conceptual understanding beyond procedural accuracy.
6. Differentiation

 Below Grade Level: Students who struggled with basic multiplication or division were given
additional concrete practice and simplified examples.

o Data Support: Based on formative assessments, these students needed more time
with manipulatives before transitioning to abstract reasoning, so they received additional
support with visual models and scaffolding.

 On Grade Level: On-grade students received a balanced approach with opportunities for
partner activities and practice problems that focused on applying each property.

o Instructional Decision: This approach ensures that they can independently apply each
property, with opportunities to discuss and justify their reasoning to peers.

o Data Support: Formative assessment data showed that this group benefited from
collaborative activities and moderate complexity in problem-solving.

 Above Grade Level: These students received extension activities, including multi-step
problems that required combining properties or applying them in complex scenarios.

o Rationale: Offering challenging tasks helps these students deepen their conceptual
understanding and provides opportunities for peer-teaching and independent
exploration.

o Data Support: Observational data showed these students could accurately apply the
properties and benefited from deeper, self-directed exploration.

7. Closing Reflection and Post-assessment

 Post-assessment: After the 3-day sequence, a post-assessment provides quantitative data to
evaluate student mastery of the properties and application within multiplication and division.

o Data Analysis: Comparing pre- and post-assessment results allows for an evaluation of
growth, identifying areas of strength and potential gaps.

 Reflection: Student reflections in math journals are used for qualitative insight, helping
teachers understand how students perceive and internalize the concepts, informing future
instructional planning.

Standard 2 Math Lesson Plans

Standards for Review:

3.PAR.3.3 – Apply properties of operations (i.e., commutative property, associative property, distributive property) to multiply and divide within 100.

Overview

This lesson plan introduces 3rd graders to the commutative, associative, and distributive properties in multiplication and division. Students will learn how these properties simplify calculations, explore real-life applications, and apply these properties to solve problems within 100.

Deconstructing Standards

What should students know? (nouns)

What should students be able to do? (verbs)

Math

· Properties of operations:
· Commutative property
· Associative property
· Distributive property
· Multiplication
· Division
· Equations
· Numbers within 100

·
Apply the properties of operations (commutative, associative, distributive)

·
Multiply numbers within 100

·
Divide numbers within 100

·
Solve problems using these properties to simplify calculations

·
Use properties to
find unknowns in multiplication and division equations

Learning Intentions (I am learning how to…) & Relevance (Why am I learning it?):

· Use part-whole strategies to solve real-life, mathematical problems involving multiplication and division with whole numbers within 100. 

· Solve real-life, mathematical problems involving length, liquid volume, mass and time.

Success Criteria (I am successful when I can…):

I Can:

· Model multiplication using equal groups, arrays, tape diagrams (bar models), and number lines. (3.PAR.3.2)

· Create and interpret equations to represent multiplication problems. (3.PAR.3.2)

· Solve practical, relevant problems using part-whole strategies, visual representations, and concrete models. (3.PAR.3.6)

· Solve multiplication problems using foundational facts, squares, derived facts, and relationships with known facts. (3.PAR.3.1-3)

· Explore graphical displays with varied scales. (3.MDR.5.1)

· Investigate multiplication properties through concrete models and drawings (commutative, associative, and distributive). (3.PAR.3.3)

Key Vocabulary:

Commutative Property, Associative Property, Distributive Property, Multiply, Divide, Equation

Possible/Anticipated Misconceptions
(Clarify any misconceptions that may come up when teaching this unit/lesson)

Misconceptions include the order of operations not mattering in all math, the associative property only applying to addition and multiplication, the associative property changing the order of numbers, the distributive property requiring memorizing steps, the distributive property only applying to addition, the distributive property only applying to division, the distributive property not applying to larger numbers, and the properties being only useful for smaller numbers or simple equations.
To address these misconceptions, it is essential to use hands-on examples and visual aids to clarify that the properties only apply to addition and multiplication, and to reinforce definitions with anchor charts. Additionally, it is important to explain that properties can simplify both multiplication and division problems, but look slightly different.
Lastly, it is crucial to use real-world examples to apply properties, such as using the commutative property or the distributive property in mental math. By addressing these misconceptions, students can better understand the importance of the properties in their daily math practice.

Instructional Strategies and Resources

Identify teaching/ instructional strategies and resources to use with lessons.

Instructional Strategies:

Instructional Strategies

The Concrete-Representational-Abstract (CRA) approach is a method for teaching properties in mathematics. It involves using manipulatives like counters, cubes, or tiles to visually demonstrate properties. Students are given problems to solve using properties, and they think independently and then pair up to discuss their methods. Anchor charts are created for each property, and real-world examples and word problems are used to make concepts concrete. Modeling and guided practice are used, with students guiding each other in solving problems. Math journals are used for reflective activities. Interactive group activities are set up, allowing students to practice applying properties in different contexts. Visual aids like large arrays and physical grids are used to show how numbers can be grouped or distributed. Problem decomposition is taught, and intentional questioning and reflection are used to encourage students to explain their thought processes, reinforcing their conceptual understanding of properties.

Resources

Whiteboards, markers, and erasers, Array mats and counters, Math manipulatives (e.g., tiles, cubes),Visual aids for each property, Worksheets with practice problems, Math notebooks, Anchor charts for properties of operations

Opening, Work Session, Closing

Tasks given to students to meet the learning target.

Day 1: Introducing the Commutative Property

Opening (10 mins)

· Begin with a quick review of multiplication. Ask, “If we know 3×43 \times 43×4, does it help us know what 4×34 \times 34×3 is?”

· Introduce the commutative property by showing how switching the order of factors doesn’t change the product.

Work Session (30 mins)

1.
Mini-Lesson

· Define the commutative property, demonstrating with counters and arrays. For example, show 3×43 \times 43×4 as an array with 3 rows of 4 counters, then rotate it to show 4×34 \times 34×3 with 4 rows of 3 counters.

· Emphasize that no matter the order, the total product remains the same.

2.
Guided Practice

· Give students pairs of multiplication facts to solve and check for the commutative property (e.g., 5×75 \times 75×7 and 7×57 \times 57×5).

· Ask students to use manipulatives or draw arrays to demonstrate the property visually.

3.
Independent Practice

· Provide a worksheet with multiplication pairs (e.g., 2×82 \times 82×8 and 8×28 \times 28×2, 6×96 \times 96×9 and 9×69 \times 69×6). Have students verify the commutative property and write a sentence explaining their observations.

Closing (10 mins)

· Review several problems as a class and ask students to share their thoughts on why the commutative property is helpful.

Check for Understanding & Intentional Questioning

·
Questions:

·
“Does changing the order of the numbers change the answer?”

· “Why might this property be helpful when solving multiplication problems?”

Differentiation

· Use visual aids and counters for students who need additional support.

· Challenge advanced students by giving them equations to verify with three factors, observing if they see patterns with the associative property.

Day 2: Exploring the Associative Property

Opening (10 mins)

· Begin with a quick review of the commutative property. Ask, “What if we have three numbers? How might we group them to make it easier to multiply?”
· Introduce the associative property, which shows that factors can be grouped differently to make calculations easier.

Work Session (30 mins)

1.
Mini-Lesson

· Define the associative property with a simple example: 2×(3×4)2 \times (3 \times 4)2×(3×4) and (2×3)×4(2 \times 3) \times 4(2×3)×4.
· Show both calculations step-by-step, highlighting that the product remains the same even when the factors are grouped differently.
2.
Guided Practice

· Divide students into small groups and give them a problem like 5×(2×6)5 \times (2 \times 6)5×(2×6). Ask each group to try it both ways, using either physical counters or drawings to show their calculations.
· Walk around to support students and ensure they understand how to group numbers in two different ways.
3.
Independent Practice

· Provide a worksheet with problems like (4×5)×2(4 \times 5) \times 2(4×5)×2 and 4×(5×2)4 \times (5 \times 2)4×(5×2). Ask students to solve each equation both ways to verify the associative property.

Closing (10 mins)

· Review examples as a class, asking, “How does the associative property help us when we have three numbers to multiply?”

Check for Understanding & Intentional Questioning

·
Questions:

·
“How can grouping numbers differently make multiplying easier?”

· “Does the associative property work with addition too? How do we know?”

Differentiation

· For students needing support, offer smaller numbers for calculations.
· Challenge advanced students with more complex three-factor equations within 100 and ask them to explain how they grouped the numbers.

Day 3: Applying the Distributive Property to Multiply and Divide

Opening (10 mins)

· Begin by reviewing the commutative and associative properties. Ask, “What if we have a larger multiplication problem, like 6×96 \times 96×9? Can we break it into smaller parts?”
· Introduce the distributive property by showing an example with arrays (e.g., breaking 6×96 \times 96×9 into 6×(5+4)6 \times (5 + 4)6×(5+4)).

Work Session (30 mins)

1.
Mini-Lesson

· Define the distributive property, showing how to decompose a multiplication problem. For example, demonstrate how to solve 6×96 \times 96×9 by breaking it down into 6×(5+4)=(6×5)+(6×4)6 \times (5 + 4) = (6 \times 5) + (6 \times 4)6×(5+4)=(6×5)+(6×4).
· Show how this strategy makes it easier to calculate large products.
2.
Guided Practice

· Work with students to solve problems using the distributive property. Have them break down problems into simpler steps, such as 8×78 \times 78×7 by using 8×(5+2)8 \times (5 + 2)8×(5+2).
· Let students use manipulatives or draw arrays to visualize the distributive property.
3.
Independent Practice

· Provide a worksheet with problems to solve using the distributive property (e.g., 7×87 \times 87×8 as 7×(5+3)7 \times (5 + 3)7×(5+3)). Ask students to decompose each problem and show their work.

Closing (10 mins)

· Discuss how the distributive property can make multiplication easier, especially when dealing with larger numbers.
· Ask a few students to explain how they broke down a problem to make it simpler.

Check for Understanding & Intentional Questioning

·
Questions:

· “How can breaking a multiplication problem into parts make it easier?”
· “Can you think of a time when you might use this property to solve a problem in real life?”

Differentiation

· Provide simpler numbers for students who need additional support.
· Challenge advanced students by having them apply the distributive property to word problems or combine it with the associative property.

Standard 2 Annotation Explained

Here’s a breakdown of the planning process for the 3-day lesson plan aligned with standard 3.PAR.3.3. Each component was chosen based on best practices in math instruction for 3rd graders, as well as data-driven decisions to meet varying student needs and support mastery of the properties of multiplication and division. This explanation details the instructional choices, as well as the qualitative and quantitative data considered.

This approach to planning, driven by both qualitative observations and quantitative assessments, ensures that instructional decisions meet students’ needs at every level. Each instructional choice aligns with the standard while providing tailored supports to address varying levels of understanding, promoting conceptual mastery for all learners.

1. Understanding the Standard and Student Needs

·
Standard Analysis: The primary focus of standard 3.PAR.3.3 is for students to
apply properties of multiplication and division (commutative, associative, distributive) within 100. This standard emphasizes not just rote calculation but
conceptual understanding and application of mathematical properties to solve problems.

·
Pre-assessment Data: Before planning, a
pre-assessment on multiplication and division skills was conducted to gauge baseline understanding of these operations and properties.

·
Quantitative Data: The data revealed that while most students could multiply and divide within 100, many struggled to use properties effectively to simplify or solve equations.

·
Qualitative Data: Observations showed that students often relied on memorized facts rather than understanding the properties that can make problem-solving easier, which informed the decision to prioritize conceptual understanding and application.

2. Setting Learning Goals and Objectives

·
Learning Goals: Based on the pre-assessment data, the objectives were set to ensure students could:

·
Recognize and define the commutative, associative, and distributive properties.

·
Apply these properties to solve multiplication and division problems within 100.

·
Use the properties strategically to simplify problem-solving and find unknowns.

· These objectives guided the sequence of activities, ensuring that by the end of the lesson sequence, students could not only identify the properties but use them confidently in various contexts.

3. Selection of Key Vocabulary and Instructional Strategies

·
Vocabulary: The vocabulary (commutative, associative, distributive, equation, etc.) was chosen to match the terminology in the standard.

·
Instructional Decision: Introducing and reinforcing these terms early in the lesson sequence allows for ongoing practice and familiarity, addressing potential misconceptions around the properties.

·
Data Support: Pre-assessment results showed limited familiarity with the terms “associative” and “distributive,” indicating that students needed extra reinforcement.

·
Instructional Strategies:

·
CRA (Concrete-Representational-Abstract) Approach: This approach was selected to scaffold learning from concrete manipulatives to abstract reasoning, supporting students as they build confidence with each property.

·
Data Support: Observational data showed that students grasp concepts better when moving from hands-on exploration to more abstract problem-solving.

·
Think-Pair-Share and Math Journals: These strategies support peer collaboration and reflective learning. By discussing their ideas with peers and recording reflections, students deepen their understanding.

·
Qualitative Support: Discussions in math journals provide a window into student thinking, allowing for adjustments in instruction based on the clarity of student responses.

4. Lesson Structure: Opening, Work Session, Closing

Each day’s structure was designed to ensure students had time for exploration, guided practice, and reflection.

·
Opening: The opening segments review prior knowledge and introduce daily objectives, setting the context for each lesson.

·
Rationale: The consistent review of terms and quick practice in the opening helps activate students’ prior knowledge, providing a foundation for deeper learning during the work session.

·
Work Session: This segment involves interactive activities where students apply the properties. Activities are sequenced to start with the commutative property (day 1), move to the associative property (day 2), and conclude with the distributive property (day 3).

·
Instructional Decision: The order was chosen to build gradually from simpler to more complex concepts, reducing cognitive load.

·
Data Support: Observational and formative assessment data collected throughout the work sessions help inform real-time adjustments, such as providing additional examples if students struggle with a property.

·
Closing: Each day’s lesson ends with a review and reflection, allowing students to summarize their understanding.

·
Rationale: The daily reflection provides an opportunity for students to consolidate learning and share insights, reinforcing the concepts through verbal explanation.

5. Check for Understanding and Intentional Questioning

·
Check for Understanding: Formative checks, such as quick exit tickets or verbal questioning, are embedded in each day’s work session and closing.

·
Instructional Decision: These checks help identify misconceptions early and inform real-time adjustments.

·
Data Support: Analyzing responses allows for immediate feedback, and the data from these checks can reveal which properties require additional practice.

·
Intentional Questioning: Open-ended questions (e.g., “How does grouping the numbers help make this problem easier?”) are used to prompt student thinking.

·
Rationale: These questions guide students to verbalize their reasoning, helping to assess conceptual understanding beyond procedural accuracy.

6. Differentiation

·
Below Grade Level: Students who struggled with basic multiplication or division were given additional concrete practice and simplified examples.

·
Data Support: Based on formative assessments, these students needed more time with manipulatives before transitioning to abstract reasoning, so they received additional support with visual models and scaffolding.

·
On Grade Level: On-grade students received a balanced approach with opportunities for partner activities and practice problems that focused on applying each property.

·
Instructional Decision: This approach ensures that they can independently apply each property, with opportunities to discuss and justify their reasoning to peers.

·
Data Support: Formative assessment data showed that this group benefited from collaborative activities and moderate complexity in problem-solving.

·
Above Grade Level: These students received extension activities, including multi-step problems that required combining properties or applying them in complex scenarios.

·
Rationale: Offering challenging tasks helps these students deepen their conceptual understanding and provides opportunities for peer-teaching and independent exploration.

·
Data Support: Observational data showed these students could accurately apply the properties and benefited from deeper, self-directed exploration.

7. Closing Reflection and Post-assessment

·
Post-assessment: After the 3-day sequence, a post-assessment provides quantitative data to evaluate student mastery of the properties and application within multiplication and division.

·
Data Analysis: Comparing pre- and post-assessment results allows for an evaluation of growth, identifying areas of strength and potential gaps.

·
Reflection: Student reflections in math journals are used for qualitative insight, helping teachers understand how students perceive and internalize the concepts, informing future instructional planning.