Blue 10
See attached
Use the attached Final Project to answer the questions on the Final Project Part 2
2 years ago 5
FinalProjectPart2.pdf
FinalProject.pdf
FinalProjectPart2.pdf
Teachers are culturally responsive when they develop their:
1. Socio-cultural consciousness:A teacher’s ownway of thinking, behaving, and being are influenced by race, ethnicity, social class, and language.
2. Attitude:A teacher’s affirming attitude toward students from culturally diverse backgrounds significantly impacts student learning, belief in themselves, and overall academic performance.
3. Commitment and skills:A teacher’s role as an agent of change confronts barriers/obstacles to those changes and develops skills for collaboration.
4. Constructivist views:A teacher’s contention that all students are capable of learning requires building scaffolding between what students already know through their own experiences and what they need to learn.
5. A teacher’s learning about a student’s past experiences, home and community culture, and world in and out of school helps build relationships by increasing the use of these experiences in the context of teaching and learning.
6. Culturally responsive teaching:A teacher’s use of strategies that support a constructivist view of knowledge, teaching, and learning assists students in constructing knowledge, building on their personal and cultural strengths, and examining the curriculum from multiple perspectives, thus creating an inclusive classroom environment.
Effective Teaching is Culturally Responsive when it:
1. Holds high expectations for all students andhelp all students learn, as measured by value added or other test-based growthmeasures or by alternativemeasures
2. Contributes to positive academic, attitudinal, and social outcomes for students, such as regular attendance, on-time promotion to the next grade, on-time graduation, self-efficacy, and cooperative behavior
3. Uses diverse resources to plan and structure engaging learning opportunities, monitor student progress formatively, adapt instruction as needed, and evaluate learning using multiple sources of evidence
4. Contributes to the development of classrooms and schools that value diversity and civic mindedness
5. Collaborateswith colleagues, administrators, parents, and education professionals to ensure student success, particularly the success of high-risk students or those with special needs
Part 2 of the final project is to submit your best lesson plan that you deem to be culturally responsive. Use the actual template required by your school. Create, edit, or tweak a lesson plan you
would teach in real life in your content area.
1. Submit your detailed, complete lesson plan for a segment of teaching (i.e. morning literacy, 90-minute HS biology lesson, 45-minutes art connections class, etc.)
2. Write a 500-1000 words maximum reflection connecting your learning journey to the lesson plan you submitted. Use resources, activities, and “a-ha” moments in the course to justify your decisions in the lesson plan.
3. Include a reference list of the resources from the course that you mention in your final reflection. No formal styling is needed, but a simple numbered list with available information is sufficient using the template below:
Example: Author. Date. Name of Source. Link.
CRP Final Project Rubric:
100%: Student shows meaningful reflection and synthesizes class materials into 4 or more relevant connections. Module learning is applied to the educator’s respective pedagogical practices (content area, grade-levels, school-specific challenges, stakeholders, needs, ideas, etc.) in rich detail. Verbal, oral, and/or presentational communication is professional, polished, and visually organized.
90%: Student provides a satisfactory reflection but does not synthesize class materials into more than 2-3 relevant connections. Module learning is applied to the educator’s current practices in sufficient detail. Verbal, oral, and/or presentational communication is strong but lacks consistent professional polish and visual organization.
80%: Student identifies 1-2 new connections and has reflected in manner related to the prompt. Details in reflection could be more robust & clear. Student has attempted to apply materials and concepts to their current pedagogical sphere as an educator but could strengthen professional delivery and organization for ease of understanding.
70%: Student makes a general connection and/or reflection is superficial. Application of materials and concepts is lacking and/or disconnected from their current role in the classroom. Communication and organization are unclear in multiple areas.
60%: Student fails to make a connection or reflect appropriately. There is little to no application of materials and concepts to their current role as an educator. Message and structure are unclear, disconnected, or extremely lacking substance/detail throughout the work sample.
0%: Assignment not turned in on time.
Suggestions by content areas: ● MATH
○ https://www.edweek.org/teaching-learning/opinion-twelve-ways-to-make-math-more-cu lturally-responsive/2020/12#:~:text=For%20example%2C%20students%20can%20rol e,to%20collaborate%20(Kagan%202010).
● SCIENCE ○ https://activatelearning.com/culturally-responsive-science-curriculum-the-key-to-unlock
ing-student-potential/#:~:text=Culturally%20responsive%20science%20curriculum%20 allows,engaged%20and%20motivated%20to%20learn.
● SOCIAL STUDIES ○ https://www.edweek.org/teaching-learning/opinion-18-ways-to-make-social-studies-cla
ss-more-culturally-responsive/2022/09 ● ENGLISH
○ https://www.edweek.org/teaching-learning/opinion-10-ways-to-foster-a-more-culturally- responsive-english-class/2022/10
● SPECIAL EDUCATION ○ https://www.medbridge.com/blog/2022/04/the-importance-of-cultural-competency-in-sp
ecial-education/ ● ARTS
○ https://artsintegration.com/2016/07/13/culturally-responsive-teaching-and-the-arts/ ● ENGLISH-LEARNERS
○ https://www.edutopia.org/article/foundations-culturally-and-linguistically-responsive-tea ching/
● WORLD LANGUAGES ○ https://www.actfl.org/uploads/files/general/World-ReadinessStandardsforLearningLang
uages.pdf ● Example Lesson Plan Audit Questions (pages 5-6)
○ https://pbismissouri.org/wp-content/uploads/2017/12/6A_HO2_-Culturally-Responsive- lessonplans1.pdf
FinalProject.pdf
Math Lesson Plans Week of 09/23/2024 Standards for Review: 3.PAR.3: Use part-whole strategies to solve real-life, mathematical problems involving multiplication and division with whole numbers within 100. 3.PAR.3.1: Describe, extend, and create numeric patterns related to multiplication. Make predictions related to the patterns. 3.PAR.3.2: Represent single digit multiplication and division facts using a variety of strategies. Explain the relationship between multiplication and division. 3.PAR.3.3 - Apply properties of operations (i.e., commutative property, associative property, distributive property) to multiply and divide within 100. 3.PAR.3.4 - Use the meaning of the equal sign to determine whether expressions involving addition, subtraction, and multiplication are equivalent.
Deconstructing Standards
What should students know? (nouns) What should students be able to do? (verbs)
Math Part-whole strategies, Real-life mathematical problems, Whole numbers within 100, Numeric patterns, Single-digit multiplication and division facts, Strategies, Relationship between multiplication and division, Properties of operations (commutative property, associative property, distributive property)
Use, Solve, Describe, Extend, Create Make predictions, Represent, Explain Apply, Determine
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: Identity Property of Multiplication, Zero Property of Multiplication, Array, Column/Row, Associative Property, Commutative Property, Distributive Property, Repeated Addition, Double, Equal Groups, Equation, Expression, Factor, Product, Multiple, Skip Count, Bar Graph, Bar Model, Pictograph, Scale, Tape Diagram
Possible/Anticipated Misconceptions (Clarify any misconceptions that may come up when teaching this unit/lesson) Deriving the 9’s Facts
Traditionally, multiplication tables are emphasized when students begin learning about multiplication. Students are sent home with flash cards without a true understanding of what multiplication is. This way of learning multiplication can be difficult for students to understand. Naturally, students make groups and groups of groups. The creation of groups is a way to find the total of something in the most efficient way. The following learning plan allows students to build on their natural ability to form groups and learn multiplication without memorizing facts in isolation, but as number facts that can be related to each other in a multitude of ways (van Galen & Fosnot, 2007).
Building Arrays on a Multiplication Chart
One common misconception is that students must answer their problems using multiplication number sentences. Students may continue to use repeated addition equations to represent their work. It is important for teachers to use this time to relate multiplication to the student’s prior knowledge of repeated addition by introducing the multiplication sign and explaining what the two factors mean. (Taken from: Van de Walle, Teaching Student-Centered Mathematics, Vol. II 3-5)
School Picnic
Properties of arithmetic provide the conceptual foundations for computational strategies and the underpinnings of algebraic thinking. It can be effective to introduce these properties at a basic fact level so that students can apply them easily and understand the concept behind them. Students are not to simply recognize and name the properties in their algebraic form (e.g., a x b = b x a). Properties should be identified correctly. Created names for properties (e.g., "flip flop") should not be used to describe the property. Students should use physical models and drawings to prove that the properties are true. Understanding these properties is critical for fluency with basic facts and multi-digit computation in later grades. (Source: Mathematics – HCPSS - https://hcpss.instructure.com/courses/97)
Instructional Strategies and Resources Identify teaching/ instructional strategies and resources to use with lessons. Instructional Strategies:
1. Modeling: Demonstrate the use of foundational 10’s facts to derive the 9’s facts through a think- aloud process. Show students how to subtract a group from the 10’s fact to find the 9’s fact.
2. Scaffolding: Provide students with opportunities to practice with smaller numbers and gradually increase complexity as they become more comfortable with the concept.
3. Manipulatives: Use physical objects, such as blocks or tiles, to represent the 10’s and 9’s facts visually. This can help students understand the relationship between the two types of facts.
4. Collaborative Learning: Encourage students to work in pairs or small groups to discuss their strategies and problem-solving methods, providing opportunities for peer learning.
Resources: 1. Multiplication Charts: Provide students with blank multiplication charts to record their work as
they build scaled multiplication charts using arrays for each pair of factors. 2. Array Tiles: Use color-coded tiles to represent factors and products in multiplication situations.
Students can manipulate these tiles to understand how changing the order and grouping of factors does not change the product.
3. Math Games: Online games and activities that focus on multiplication facts, such as "Multiplication Bingo" or "Multiplication War," can be used to engage students and provide additional practice.
4. Multiplication Apps: There are numerous apps available for smartphones and tablets that help students practice multiplication facts and strategies, such as "Math Master" or "Math Fact Fluency."
Additional Strategies: 1. Mnemonic Devices: Teach students rhymes or songs to help them remember multiplication facts.
For example, "If you know your nines, you'll have a great time!"
2. Real-World Applications: Provide real-world scenarios, such as calculating the total number of students in a classroom or determining the cost of multiple items, to demonstrate the practical uses of multiplication.
Opening, Work Session, Closing Tasks given to students to meet the learning target.
Engage Explore Apply Reflect
Learning Plan Title Deriving the 9’s Facts
Begin with a brief review of the 10's multiplication facts, using a call-and- response technique to engage students and build confidence.
Ask students to share their strategies for memorizing or deriving 10’s facts.
Introduce the learning objective by writing two problems on the board: 10 x 5 and 9 x 5.
Engage students in a think-pair-share activity:
Think: Individually consider how to solve 9 x 5 using the 10’s fact.
Pair: Discuss ideas with a partner, focusing on the connection between the two problems.
Share: Ask volunteers to share their strategies and insights with the class.
Introduce the strategy of subtracting a group: 10 x 5 = 50, so 9 x 5 = (50 - 5) = 45.
Highlight the cultural relevance by discussing how different cultures use various strategies for multiplication and how this strategy might be useful in their own lives.
Provide additional examples, modeling the strategy step-by-step and emphasizing the connection between the 10’s and 9’s facts.
Involve students by asking them to contribute to the problem-solving process, both verbally and on the board.
Encourage students to make real-world connections and share personal experiences where they might use this strategy.
Distribute index cards with 10’s and 9’s multiplication problems to students.
Have students solve problems independently or in pairs, using the subtracting-a-group strategy.
Circulate the room, providing feedback and guidance as needed, and encouraging students to support one another.
Reflect on the lesson objective, asking students to share their understanding of the connection between 10’s and 9’s facts.
Discuss the importance of understanding multiple strategies for solving problems and the value of approaching problems from different perspectives.
Assign a worksheet for additional practice at home, or as part of a subsequent class, emphasizing the importance of practice in developing mastery.
Celebrate diverse ways of thinking and problem- solving by inviting students to share their unique strategies and experiences.
Encourage collaboration and peer support, creating a positive and inclusive learning environment.
Learning Plan Title
Show a completed scaled multiplication chart and ask
Review the concept of arrays and how they relate to multiplication.
Model creating an array for a specific pair of
Review the learning objective and discuss how arrays
Building Arrays on a Multiplicatio n Chart
students to discuss patterns they notice.
Ask students to share any prior knowledge or experience they have with arrays.
factors (e.g., 3 x 4) on grid paper, using colored pencils to outline the array and writing the corresponding multiplication fact.
Encourage students to create arrays for other factors, working collaboratively in small groups.
Facilitate a discussion about the patterns students notice as they build their arrays, emphasizing the cultural relevance and connections to real-world contexts.
Guide students in organizing their arrays to create a scaled multiplication chart on grid paper.
help visualize multiplication facts.
Invite students to share their observations and insights about patterns they noticed in their scaled multiplication charts.
Encourage students to use their charts as a reference tool for future problem- solving and to consider different cultural perspectives in problem-solving strategies.
Assign a reflection activity where students write about their experiences creating the multiplication chart and how it connects to their own lives and cultures.
Learning Plan Title School Picnic
Write a multiplication problem on the board (e.g., 3 x 4) and ask students to solve it.
Discuss the result and introduce the idea that changing the order of factors does not change the product.
Model the commutative property of multiplication using manipulatives:
Arrange manipulatives in a 3 x 4 array, then rearrange them to create a 4 x 3 array.+ Emphasize that both arrays have the same number of objects, demonstrating the commutative property.
Guide students in practicing the commutative property with different factors, using manipulatives, drawings, or acting out scenarios.
Facilitate a discussion about the cultural relevance and real-world applications of the commutative property.
Have students work independently or in pairs to solve a set of multiplication problems, applying the commutative property and explaining their reasoning.
Review the learning objective and discuss the commutative property's significance in problem-solving.
Encourage students to share examples of how the commutative property applies to their own lives and cultural contexts.
Assign a reflection activity or worksheet for students to demonstrate their understanding of the commutative property and its cultural relevance.
Learning
Plan Title
Check for Understanding & Intentional Questioning
Type of formative assessment to check for understanding.
Monday
Tuesday DERIVING THE 9’s FACTS Page 4 & 5
Wednesday
Thursday BUILDING ARRAYS ON A MULTIPLICATION CHART Page 3 & 4
Friday
Differentiation
Identify how you are addressing students with varying levels of understanding (Below, On, & Above).
Monday Below Level: Provide additional
support through small group instruction or one-on-one guidance.
Offer visual aids, such as anchor charts or multiplication fact cards, to help students connect the 10's facts to the 9's facts.
Assign fewer practice problems initially, gradually increasing the number as students gain confidence.
On Level: Encourage students to
work collaboratively, sharing their problem- solving strategies and supporting one another's learning.
Challenge students to create their own word problems or real-world scenarios that demonstrate the connection between the 10's and 9's facts.
Provide opportunities for students to share their work and explain their reasoning during class discussions.
Above Level: Encourage students to
explore the connection between the 10's and 9's facts more deeply by analyzing patterns, making generalizations, and creating their own rules or shortcuts.
Challenge students to solve more complex problems, such as multi-step word problems, that require applying the 9's fact strategy.
Provide opportunities for students to act as peer tutors, helping classmates who may need additional support.
Tuesday
Wednesday Below Level: Provide students with
pre-drawn arrays or templates to help them focus on the concept of multiplication and the relationship between factors.
Offer manipulatives, such as tiles or blocks, for students to physically build arrays and visualize the concept more easily.
Allow students to work
On Level: Encourage students to
create their own arrays on grid paper, using colored pencils or markers to outline the arrays and write the corresponding multiplication facts.
Challenge students to analyze patterns in their multiplication charts, discussing their observations and findings with the class.
Above Level: Encourage students to
explore more complex multiplication problems, such as those involving larger numbers or decimals.
Challenge students to create and solve word problems that require the use of multiplication arrays or the commutative property.
Provide opportunities for students to act as peer
Thursday
in small groups or with a partner, promoting collaborative learning and support from peers.
Provide opportunities for students to share their strategies and problem-solving approaches with their classmates.
tutors, helping classmates who may need additional support in understanding the concepts.
Friday Below Level: Provide concrete
examples and manipulatives to help students visualize the concept.
Allow students to work in pairs or small groups, where they can support each other and discuss their understanding.
Offer additional practice opportunities with guidance and feedback.
On Level: Encourage students to
create their own examples and scenarios that demonstrate the commutative property of multiplication.
Provide opportunities for students to explain their thinking and problem-solving strategies to their peers.
Challenge students to apply the commutative property in multi-step problems or real-world scenarios.
Above Level: Encourage students to
explore the commutative property in more depth, examining its application in algebraic expressions or other mathematical contexts.
Challenge students to create proofs or justifications for the commutative property using their understanding of multiplication and other mathematical concepts.
Provide opportunities for students to act as peer tutors or mentors, supporting classmates who may need additional help.
ArtsNOW/STEAM Integration Students will demonstrate their understanding of the commutative, associative, and distributive properties of multiplication by creating visually engaging posters that incorporate mathematical examples and creative design elements.
Writing Connection Assign a reflection activity where students write about their experiences creating the multiplication chart and how it connects to their own lives and cultures.
FinalProjectPart2.pdf
Teachers are culturally responsive when they develop their:
1. Socio-cultural consciousness:A teacher’s ownway of thinking, behaving, and being are influenced by race, ethnicity, social class, and language.
2. Attitude:A teacher’s affirming attitude toward students from culturally diverse backgrounds significantly impacts student learning, belief in themselves, and overall academic performance.
3. Commitment and skills:A teacher’s role as an agent of change confronts barriers/obstacles to those changes and develops skills for collaboration.
4. Constructivist views:A teacher’s contention that all students are capable of learning requires building scaffolding between what students already know through their own experiences and what they need to learn.
5. A teacher’s learning about a student’s past experiences, home and community culture, and world in and out of school helps build relationships by increasing the use of these experiences in the context of teaching and learning.
6. Culturally responsive teaching:A teacher’s use of strategies that support a constructivist view of knowledge, teaching, and learning assists students in constructing knowledge, building on their personal and cultural strengths, and examining the curriculum from multiple perspectives, thus creating an inclusive classroom environment.
Effective Teaching is Culturally Responsive when it:
1. Holds high expectations for all students andhelp all students learn, as measured by value added or other test-based growthmeasures or by alternativemeasures
2. Contributes to positive academic, attitudinal, and social outcomes for students, such as regular attendance, on-time promotion to the next grade, on-time graduation, self-efficacy, and cooperative behavior
3. Uses diverse resources to plan and structure engaging learning opportunities, monitor student progress formatively, adapt instruction as needed, and evaluate learning using multiple sources of evidence
4. Contributes to the development of classrooms and schools that value diversity and civic mindedness
5. Collaborateswith colleagues, administrators, parents, and education professionals to ensure student success, particularly the success of high-risk students or those with special needs
Part 2 of the final project is to submit your best lesson plan that you deem to be culturally responsive. Use the actual template required by your school. Create, edit, or tweak a lesson plan you
would teach in real life in your content area.
1. Submit your detailed, complete lesson plan for a segment of teaching (i.e. morning literacy, 90-minute HS biology lesson, 45-minutes art connections class, etc.)
2. Write a 500-1000 words maximum reflection connecting your learning journey to the lesson plan you submitted. Use resources, activities, and “a-ha” moments in the course to justify your decisions in the lesson plan.
3. Include a reference list of the resources from the course that you mention in your final reflection. No formal styling is needed, but a simple numbered list with available information is sufficient using the template below:
Example: Author. Date. Name of Source. Link.
CRP Final Project Rubric:
100%: Student shows meaningful reflection and synthesizes class materials into 4 or more relevant connections. Module learning is applied to the educator’s respective pedagogical practices (content area, grade-levels, school-specific challenges, stakeholders, needs, ideas, etc.) in rich detail. Verbal, oral, and/or presentational communication is professional, polished, and visually organized.
90%: Student provides a satisfactory reflection but does not synthesize class materials into more than 2-3 relevant connections. Module learning is applied to the educator’s current practices in sufficient detail. Verbal, oral, and/or presentational communication is strong but lacks consistent professional polish and visual organization.
80%: Student identifies 1-2 new connections and has reflected in manner related to the prompt. Details in reflection could be more robust & clear. Student has attempted to apply materials and concepts to their current pedagogical sphere as an educator but could strengthen professional delivery and organization for ease of understanding.
70%: Student makes a general connection and/or reflection is superficial. Application of materials and concepts is lacking and/or disconnected from their current role in the classroom. Communication and organization are unclear in multiple areas.
60%: Student fails to make a connection or reflect appropriately. There is little to no application of materials and concepts to their current role as an educator. Message and structure are unclear, disconnected, or extremely lacking substance/detail throughout the work sample.
0%: Assignment not turned in on time.
Suggestions by content areas: ● MATH
○ https://www.edweek.org/teaching-learning/opinion-twelve-ways-to-make-math-more-cu lturally-responsive/2020/12#:~:text=For%20example%2C%20students%20can%20rol e,to%20collaborate%20(Kagan%202010).
● SCIENCE ○ https://activatelearning.com/culturally-responsive-science-curriculum-the-key-to-unlock
ing-student-potential/#:~:text=Culturally%20responsive%20science%20curriculum%20 allows,engaged%20and%20motivated%20to%20learn.
● SOCIAL STUDIES ○ https://www.edweek.org/teaching-learning/opinion-18-ways-to-make-social-studies-cla
ss-more-culturally-responsive/2022/09 ● ENGLISH
○ https://www.edweek.org/teaching-learning/opinion-10-ways-to-foster-a-more-culturally- responsive-english-class/2022/10
● SPECIAL EDUCATION ○ https://www.medbridge.com/blog/2022/04/the-importance-of-cultural-competency-in-sp
ecial-education/ ● ARTS
○ https://artsintegration.com/2016/07/13/culturally-responsive-teaching-and-the-arts/ ● ENGLISH-LEARNERS
○ https://www.edutopia.org/article/foundations-culturally-and-linguistically-responsive-tea ching/
● WORLD LANGUAGES ○ https://www.actfl.org/uploads/files/general/World-ReadinessStandardsforLearningLang
uages.pdf ● Example Lesson Plan Audit Questions (pages 5-6)
○ https://pbismissouri.org/wp-content/uploads/2017/12/6A_HO2_-Culturally-Responsive- lessonplans1.pdf
FinalProject.pdf
Math Lesson Plans Week of 09/23/2024 Standards for Review: 3.PAR.3: Use part-whole strategies to solve real-life, mathematical problems involving multiplication and division with whole numbers within 100. 3.PAR.3.1: Describe, extend, and create numeric patterns related to multiplication. Make predictions related to the patterns. 3.PAR.3.2: Represent single digit multiplication and division facts using a variety of strategies. Explain the relationship between multiplication and division. 3.PAR.3.3 - Apply properties of operations (i.e., commutative property, associative property, distributive property) to multiply and divide within 100. 3.PAR.3.4 - Use the meaning of the equal sign to determine whether expressions involving addition, subtraction, and multiplication are equivalent.
Deconstructing Standards
What should students know? (nouns) What should students be able to do? (verbs)
Math Part-whole strategies, Real-life mathematical problems, Whole numbers within 100, Numeric patterns, Single-digit multiplication and division facts, Strategies, Relationship between multiplication and division, Properties of operations (commutative property, associative property, distributive property)
Use, Solve, Describe, Extend, Create Make predictions, Represent, Explain Apply, Determine
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: Identity Property of Multiplication, Zero Property of Multiplication, Array, Column/Row, Associative Property, Commutative Property, Distributive Property, Repeated Addition, Double, Equal Groups, Equation, Expression, Factor, Product, Multiple, Skip Count, Bar Graph, Bar Model, Pictograph, Scale, Tape Diagram
Possible/Anticipated Misconceptions (Clarify any misconceptions that may come up when teaching this unit/lesson) Deriving the 9’s Facts
Traditionally, multiplication tables are emphasized when students begin learning about multiplication. Students are sent home with flash cards without a true understanding of what multiplication is. This way of learning multiplication can be difficult for students to understand. Naturally, students make groups and groups of groups. The creation of groups is a way to find the total of something in the most efficient way. The following learning plan allows students to build on their natural ability to form groups and learn multiplication without memorizing facts in isolation, but as number facts that can be related to each other in a multitude of ways (van Galen & Fosnot, 2007).
Building Arrays on a Multiplication Chart
One common misconception is that students must answer their problems using multiplication number sentences. Students may continue to use repeated addition equations to represent their work. It is important for teachers to use this time to relate multiplication to the student’s prior knowledge of repeated addition by introducing the multiplication sign and explaining what the two factors mean. (Taken from: Van de Walle, Teaching Student-Centered Mathematics, Vol. II 3-5)
School Picnic
Properties of arithmetic provide the conceptual foundations for computational strategies and the underpinnings of algebraic thinking. It can be effective to introduce these properties at a basic fact level so that students can apply them easily and understand the concept behind them. Students are not to simply recognize and name the properties in their algebraic form (e.g., a x b = b x a). Properties should be identified correctly. Created names for properties (e.g., "flip flop") should not be used to describe the property. Students should use physical models and drawings to prove that the properties are true. Understanding these properties is critical for fluency with basic facts and multi-digit computation in later grades. (Source: Mathematics – HCPSS - https://hcpss.instructure.com/courses/97)
Instructional Strategies and Resources Identify teaching/ instructional strategies and resources to use with lessons. Instructional Strategies:
1. Modeling: Demonstrate the use of foundational 10’s facts to derive the 9’s facts through a think- aloud process. Show students how to subtract a group from the 10’s fact to find the 9’s fact.
2. Scaffolding: Provide students with opportunities to practice with smaller numbers and gradually increase complexity as they become more comfortable with the concept.
3. Manipulatives: Use physical objects, such as blocks or tiles, to represent the 10’s and 9’s facts visually. This can help students understand the relationship between the two types of facts.
4. Collaborative Learning: Encourage students to work in pairs or small groups to discuss their strategies and problem-solving methods, providing opportunities for peer learning.
Resources: 1. Multiplication Charts: Provide students with blank multiplication charts to record their work as
they build scaled multiplication charts using arrays for each pair of factors. 2. Array Tiles: Use color-coded tiles to represent factors and products in multiplication situations.
Students can manipulate these tiles to understand how changing the order and grouping of factors does not change the product.
3. Math Games: Online games and activities that focus on multiplication facts, such as "Multiplication Bingo" or "Multiplication War," can be used to engage students and provide additional practice.
4. Multiplication Apps: There are numerous apps available for smartphones and tablets that help students practice multiplication facts and strategies, such as "Math Master" or "Math Fact Fluency."
Additional Strategies: 1. Mnemonic Devices: Teach students rhymes or songs to help them remember multiplication facts.
For example, "If you know your nines, you'll have a great time!"
2. Real-World Applications: Provide real-world scenarios, such as calculating the total number of students in a classroom or determining the cost of multiple items, to demonstrate the practical uses of multiplication.
Opening, Work Session, Closing Tasks given to students to meet the learning target.
Engage Explore Apply Reflect
Learning Plan Title Deriving the 9’s Facts
Begin with a brief review of the 10's multiplication facts, using a call-and- response technique to engage students and build confidence.
Ask students to share their strategies for memorizing or deriving 10’s facts.
Introduce the learning objective by writing two problems on the board: 10 x 5 and 9 x 5.
Engage students in a think-pair-share activity:
Think: Individually consider how to solve 9 x 5 using the 10’s fact.
Pair: Discuss ideas with a partner, focusing on the connection between the two problems.
Share: Ask volunteers to share their strategies and insights with the class.
Introduce the strategy of subtracting a group: 10 x 5 = 50, so 9 x 5 = (50 - 5) = 45.
Highlight the cultural relevance by discussing how different cultures use various strategies for multiplication and how this strategy might be useful in their own lives.
Provide additional examples, modeling the strategy step-by-step and emphasizing the connection between the 10’s and 9’s facts.
Involve students by asking them to contribute to the problem-solving process, both verbally and on the board.
Encourage students to make real-world connections and share personal experiences where they might use this strategy.
Distribute index cards with 10’s and 9’s multiplication problems to students.
Have students solve problems independently or in pairs, using the subtracting-a-group strategy.
Circulate the room, providing feedback and guidance as needed, and encouraging students to support one another.
Reflect on the lesson objective, asking students to share their understanding of the connection between 10’s and 9’s facts.
Discuss the importance of understanding multiple strategies for solving problems and the value of approaching problems from different perspectives.
Assign a worksheet for additional practice at home, or as part of a subsequent class, emphasizing the importance of practice in developing mastery.
Celebrate diverse ways of thinking and problem- solving by inviting students to share their unique strategies and experiences.
Encourage collaboration and peer support, creating a positive and inclusive learning environment.
Learning Plan Title
Show a completed scaled multiplication chart and ask
Review the concept of arrays and how they relate to multiplication.
Model creating an array for a specific pair of
Review the learning objective and discuss how arrays
Building Arrays on a Multiplicatio n Chart
students to discuss patterns they notice.
Ask students to share any prior knowledge or experience they have with arrays.
factors (e.g., 3 x 4) on grid paper, using colored pencils to outline the array and writing the corresponding multiplication fact.
Encourage students to create arrays for other factors, working collaboratively in small groups.
Facilitate a discussion about the patterns students notice as they build their arrays, emphasizing the cultural relevance and connections to real-world contexts.
Guide students in organizing their arrays to create a scaled multiplication chart on grid paper.
help visualize multiplication facts.
Invite students to share their observations and insights about patterns they noticed in their scaled multiplication charts.
Encourage students to use their charts as a reference tool for future problem- solving and to consider different cultural perspectives in problem-solving strategies.
Assign a reflection activity where students write about their experiences creating the multiplication chart and how it connects to their own lives and cultures.
Learning Plan Title School Picnic
Write a multiplication problem on the board (e.g., 3 x 4) and ask students to solve it.
Discuss the result and introduce the idea that changing the order of factors does not change the product.
Model the commutative property of multiplication using manipulatives:
Arrange manipulatives in a 3 x 4 array, then rearrange them to create a 4 x 3 array.+ Emphasize that both arrays have the same number of objects, demonstrating the commutative property.
Guide students in practicing the commutative property with different factors, using manipulatives, drawings, or acting out scenarios.
Facilitate a discussion about the cultural relevance and real-world applications of the commutative property.
Have students work independently or in pairs to solve a set of multiplication problems, applying the commutative property and explaining their reasoning.
Review the learning objective and discuss the commutative property's significance in problem-solving.
Encourage students to share examples of how the commutative property applies to their own lives and cultural contexts.
Assign a reflection activity or worksheet for students to demonstrate their understanding of the commutative property and its cultural relevance.
Learning
Plan Title
Check for Understanding & Intentional Questioning
Type of formative assessment to check for understanding.
Monday
Tuesday DERIVING THE 9’s FACTS Page 4 & 5
Wednesday
Thursday BUILDING ARRAYS ON A MULTIPLICATION CHART Page 3 & 4
Friday
Differentiation
Identify how you are addressing students with varying levels of understanding (Below, On, & Above).
Monday Below Level: Provide additional
support through small group instruction or one-on-one guidance.
Offer visual aids, such as anchor charts or multiplication fact cards, to help students connect the 10's facts to the 9's facts.
Assign fewer practice problems initially, gradually increasing the number as students gain confidence.
On Level: Encourage students to
work collaboratively, sharing their problem- solving strategies and supporting one another's learning.
Challenge students to create their own word problems or real-world scenarios that demonstrate the connection between the 10's and 9's facts.
Provide opportunities for students to share their work and explain their reasoning during class discussions.
Above Level: Encourage students to
explore the connection between the 10's and 9's facts more deeply by analyzing patterns, making generalizations, and creating their own rules or shortcuts.
Challenge students to solve more complex problems, such as multi-step word problems, that require applying the 9's fact strategy.
Provide opportunities for students to act as peer tutors, helping classmates who may need additional support.
Tuesday
Wednesday Below Level: Provide students with
pre-drawn arrays or templates to help them focus on the concept of multiplication and the relationship between factors.
Offer manipulatives, such as tiles or blocks, for students to physically build arrays and visualize the concept more easily.
Allow students to work
On Level: Encourage students to
create their own arrays on grid paper, using colored pencils or markers to outline the arrays and write the corresponding multiplication facts.
Challenge students to analyze patterns in their multiplication charts, discussing their observations and findings with the class.
Above Level: Encourage students to
explore more complex multiplication problems, such as those involving larger numbers or decimals.
Challenge students to create and solve word problems that require the use of multiplication arrays or the commutative property.
Provide opportunities for students to act as peer
Thursday
in small groups or with a partner, promoting collaborative learning and support from peers.
Provide opportunities for students to share their strategies and problem-solving approaches with their classmates.
tutors, helping classmates who may need additional support in understanding the concepts.
Friday Below Level: Provide concrete
examples and manipulatives to help students visualize the concept.
Allow students to work in pairs or small groups, where they can support each other and discuss their understanding.
Offer additional practice opportunities with guidance and feedback.
On Level: Encourage students to
create their own examples and scenarios that demonstrate the commutative property of multiplication.
Provide opportunities for students to explain their thinking and problem-solving strategies to their peers.
Challenge students to apply the commutative property in multi-step problems or real-world scenarios.
Above Level: Encourage students to
explore the commutative property in more depth, examining its application in algebraic expressions or other mathematical contexts.
Challenge students to create proofs or justifications for the commutative property using their understanding of multiplication and other mathematical concepts.
Provide opportunities for students to act as peer tutors or mentors, supporting classmates who may need additional help.
ArtsNOW/STEAM Integration Students will demonstrate their understanding of the commutative, associative, and distributive properties of multiplication by creating visually engaging posters that incorporate mathematical examples and creative design elements.
Writing Connection Assign a reflection activity where students write about their experiences creating the multiplication chart and how it connects to their own lives and cultures.