Unit of Curriculum Design

I. Introduction: 

Operation and algebraic thinking in grade three mathematics help learners in representation and solving problems that involve division and multiplications. It helps in the interpretation of whole numbers such as 6×5 being the total number of objects in 6 groups of 5 objects each. Furthermore, it helps in the use of multiplication and division within 100 in solving word problems in situations that involves equal groups, quantity of measurements, and arrays (Gwinnett County Public Schools, 2020) . I have chosen this topic because it is important in solving mathematical problems in real-world situations. Learners will find the unit much important in applying logical reasoning to make better decisions. This unit is organized in a way that makes the learning process easier for the learners. The unit will be introduced by mere representation and solving of problems that involves division and multiplication. Then learners will be guided to better understand multiplication properties and the relationship between division and multiplication. Thereafter, they will be taught ways of solving problems that make use of four operations in as well as identifying and explaining the arithmetic patterns. 

II . Curriculum Unit Map: 

Suggested Curriculum Map
Content Area: Mathematics
Unit: Operation and Algebraic thinking					Grade: Grade three
Elements		Day 1	Day 2	Day 3	Day 4	Day 5
Title		Represent and solve problems involving multiplication.	Understand multiplication properties and the relationship between multiplication and division.	Multiplication and division within 100	Solving problems that involve the four operations.	Identifying and explaining patterns in arithmetic
Time/ Length		45 minutes	45 minutes	45 minutes	45 minutes	45 minutes
Course Content: Knowledge and Skills	Standard(s)	Interpretation of whole numbers as the total number of objects in a group of each object.  Using multiplication and division within the range of zero to one hundred in solving word problems in situations that involves equal groups and quantities of measurements.  Determining the unknown whole numbers in the division an multiplication equations that involve 3 whole numbers.	Application of properties of operation as techniques of multiplication and division.  Understanding division as a problem of an unknown factor.	Fluent multiplication within 100	Using the four operations to solve two-word problems.	Identifying arithmetic patterns and using operation properties to explain them
	Knowledge	Interpreting products of whole numbers	Division is the inversion operation of multiplication	Memorize all products of two one-digit numbers.	Multi operations problem solving	Identifying the patterns besides and subtractions as well as multiplication and division patterns.
	Skills	Knowing the relationship between multiplication and addition.	When dividing, we separate into equal parts. When multiplying we join the separate groups.	Applying the relationship strategy	Using BODMAS	Using 100’s chart and multiplication chart.
	Objective(s)	Describing a context whereby a total number of objects can be expressed	Learners learn the connection between multiplication and division.	Fluently multiplying and dividing within 100.	Learners should be able to solve problems that involve the four operations	Identifying and using the four operations together.
Major Instructional Activities		Partitioning objects into shares that are equal and using the partitions to do multiplication.	Associative property of multiplication and distributive property of division	Relating the operations	Identify the four operands in a problem and how they are arranged.	Explaining using the properties of operation
Assessment(s)		Classroom discussion questions	short quizzes	Mind map assessment	Random assessment test	Formative assessment (Group project)

III. Curriculum Unit: 

1. Name of Unit: Operation and Algebraic thinking 

2. Grade level/band/content: This Curriculum unit is for grade three mathematics 

3. Model Used/Rational: 

When designing this curriculum unit, I am using a naturalistic model since it includes three important elements: platform, design, and deliberation. Platform is meant for the principles and briefs that are guiding me in the process of curriculum development. Platform principles and briefs lead the deliberation process which helps in decision making from the many alternatives available (Schreibman et al., 2015) . Ultimately, the deliberation process results in the design of the curriculum. 

4. How Stakeholders are Involved: 

Administrators - Administrators can easily be involved in the process by collaborating with institutions of higher education for both school administrators and teachers. 

Teachers – likewise, teachers can also be easily involved in the process by collaborating with institutions of higher education for teachers. 

Students – Students can be involved by involving institutions of higher learning, media outlets, and both governmental and non-governmental organizations. 

Parents – To involve parents in curriculum development is vital for the success of the process. That can be achieved by determining their needs, interest, and ideas that they may have concerning the curriculum. Their ideas can be collected through surveys and polls done to collect their views towards the development of the curriculum. 

5. Standards : 

The standards chosen in this unit include according to the "Common Core State Standards Initiative" (2020) includes : 

CCSS.MATH.CONTENT.3.OA.A.1 Interpretation of whole numbers as the total number of objects in a group of each object. 

CCSS.MATH.CONTENT.3.OA.A.2 Using multiplication and division within the range of zero to one hundred in solving word problems in situations that involves equal groups and quantities of measurements. 

CCSS.MATH.CONTENT.3.OA.A.4 Determining the unknown whole numbers in the division and multiplication equations that involve 3 whole numbers. 

These standards are important in the operation and algebraic thinking unit since they help in the representation solving of problems that are using multiplication and division. 

6. Objectives: 

To use contextual clues to differentiate division problems and real-world multiplication 

To translate problems in the real world into number sentences of multiplication and division as well as solving them by product or quotient computation. 

7. Rationale for Choices: 

I chose these objectives so that the learners can understand how mathematics is used to support effective communication. That is achieved when leaners to learn how to construct important arguments and criticize other’s reasoning. 

8. Explanation of Sequencing: 

This unit will require 45 minutes to accomplish each title within the unit. Each title will be taught daily during the morning hours.The reason for the time allocation is that learners need ample time to internalize what has been taught. Secondly, since the lesson requires deep thinking, the learners will be taught daily in the morning hours when the mind is still fresh. 

9. Pre-Assessment: 

Four corners inquiry technique will be used as a pre-testing. Learners will be given opportunity to come up with their opinions. They are told to consider the current topic and chose whether they may agree, strongly agree, disagree, or strongly disagree with the given statement. They are then allowed to move to the particular classroom corners identified by the choices. They then discuss with their fellows within those particular groups and present their opinion to the rest of the class. 

10. Post-assessment: 

The post assessment technique used for this unit is group discussion. It would provide a better opportunity in assessing what has been learned in the unit. Questions are written on the board and the students discuss the questions written on the board with the help of the teacher’s guidance. 

Lessons (Day 1 to Day 5) 

Day 1 

Title: 

Time Allocation and Rational: 45 minutes. Enough for better understanding 

Standard(s): 

Interpretation of whole numbers as the total number of objects in a group of each object. 

Using multiplication and division within the range of zero to one hundred in solving word problems in situations that involves equal groups and quantities of measurements. 

Determining the unknown whole numbers in the division and multiplication equations that involve 3 whole numbers. 

Objective(s): To describing a context whereby a total number of objects can be expressed 

Learning Activities: 

Using a set of multiplication in playing math baseball inside the classroom. Learners would take turns hoping on the card as they say the answers as the teacher see how far they can reach. 

Lesson Materials and Resources : Pieces of chalk, grade three learner’s mathematics text book, and teachers guide book, printable worksheets, and blackboard. 

Teaching strategies: Dividing the students into equal groups . Merging the students after the division. This will help them understand multiplication and division. 

Technology as a Learning Tool : Using sum dog to practice the core learning skills. Plickers for data collection is also important. 

Daily Assessment : Daily homework given to students. 

How the Needs of Individual Students are met : All students will be given equal opportunity in terms of answering questions and also asking the questions in class . 

Rigor/Relevance/Relationships : 

Rigor/Relevance/Relationships helps students to apply concepts knowledge and skills learned in class to solve real-world problems. 

Day 2 

Title: 

Time Allocation and Rational: 45 minutes is enough for students to understand. 

Standard(s): 

Application of properties of operation as techniques of multiplication and division. 

Understanding division as a problem of an unknown factor. 

Objective(s): Learners to learn the connection between multiplication and division. 

Learning Activities: 

Play multiplication square by using dice, game board, and two pens of different colors. The game will help them memorize multiplication and division. 

Lesson Materials and Resources : Pieces of chalk, grade three learner’s mathematics text book, and teachers guide book, printable worksheets, and blackboard, dice, game board different color pens. 

Teaching strategies: Dividing the students into equal groups . Merging the students after the division. This will help them understand multiplication and division. 

Technology as a Learning Tool : Using sum dog to practice the core learning skills. Plickers for data collection is also important. 

Daily Assessment : Daily homework given to students. 

How the Needs of Individual Students are met : All students will be given equal opportunity in terms of answering questions and also asking the questions in class . 

Rigor/Relevance/Relationships : 

Rigor/Relevance/Relationships helps students to apply concepts knowledge and skills learned in class to solve real-world problems. 

Day 3 

Title: 

Time Allocation and Rationale: Provide the information on the time allocated for this lesson. Explain the rationale. 

Standard(s): Fluent multiplication within 100 

Objective(s ) : To fluently multiplying and dividing within 100. 

Learning Activities: 

Dividing the learners and merging them. 

Lesson Materials and Resources : Pieces of chalk, grade three learner’s mathematics text book, and teachers guide book, printable worksheets, and blackboard. 

Teaching strategies: Dividing the students into equal groups . Merging the students after the division. This will help them understand multiplication and division. 

Technology as a Learning Tool : Using sum dog to practice the core learning skills. Plickers for data collection is also important. 

Daily Assessment : Daily homework given to students. 

How the Needs of Individual Students are met : All students will be given equal opportunity in terms of answering questions and also asking the questions in class . 

Rigor/Relevance/Relationships : 

Rigor/Relevance/Relationships helps students to apply concepts knowledge and skills learned in class to solve real-world problems. 

Day 4 

Title: 

Time Allocation and Rational: 45 minutes for practical application. 

Standard(s): Using the four operations to solve two-word problems 

Objective(s): To be able to solve problems that involve the four operations 

Learning Activities: 

Sorting jelly beans into egg carton. This will help students know that there is a difference in the four operations. 

Lesson Materials and Resources : Pieces of chalk, grade three learner’s mathematics text book, and teachers guide book, printable worksheets, and blackboard. 

Teaching strategies: Students would use the jelly bags to do sorting of items of the same type together. And also learn how to divide large group of items into smaller equal groups. 

Technology as a Learning Tool : Using sum dog to practice the core learning skills. Plickers for data collection is also important. 

Daily Assessment : Daily homework given to students. 

How the Needs of Individual Students are met : All students will be given equal opportunity in terms of answering questions and also asking the questions in class . 

Rigor/Relevance/Relationships : 

Rigor/Relevance/Relationships helps students to apply concepts knowledge and skills learned in class to solve real-world problems. 

Day 5 

Title: 

Time Allocation and Rational: 45 minutes for contemplating. 

Standard(s):  Identifying arithmetic patterns and using operation properties to explain them 

Objective(s): To identify and use the four operations together. 

Learning Activities: 

Making use of anchor charts to support learning 

Lesson Materials and Resources : Pieces of chalk, grade three learner’s mathematics text book, and teachers guide book, printable worksheets, and blackboard. 

Teaching strategies: Differentiating the four operations from each other is the first step to learn them. Learners will learn their differences and master them before using the four operands in single problems. 

Technology as a Learning Tool : Using sum dog to practice the core learning skills. Plickers for data collection is also important. 

Daily Assessment : Daily homework given to students. 

How the Needs of Individual Students are met : All students will be given equal opportunity in terms of answering questions and also asking the questions in class . 

Rigor/Relevance/Relationships : 

Rigor/Relevance/Relationships helps students to apply concepts knowledge and skills learned in class to solve real-world problems. 

IV. Summary and reflection: 

From designing this unit, I have come to realize that learners in grade three needs to be well taken care of especially in the technical subject areas. For instance, if they are not taught well when how to use multiplication and division strategies, then they may find it difficult to cope with the higher-level mathematical problems. As a result, they lose interest in learning mathematics. Secondly, learners in grade three need to be given ample time so that they can have time to internalize what the teacher has taught them. Lastly, there is importance in involving teachers, students, and administration when designing a curriculum since their input is vital for the success of learning. From designing this unit, I will improve to be a better teacher by involving my learners in class as I teach technical subjects. All students need to be given equal priorities in class. 

References 

Common Core State Standards Initiative . Corestandards.org. (2020). Retrieved 8 October 2020, from http://www.corestandards.org/read-the-standards/. 

Gwinnett County Public Schools . (2020). Academic Knowledge and Skills 2020-21 Elementary School (1 st ed.). www.gcpsk12.org 

Schreibman, L., Dawson, G., Stahmer, A., Landa, R., Rogers, S., & McGee, G. et al. (2015). Naturalistic Developmental Behavioral Interventions: Empirically Validated Treatments for Autism Spectrum Disorder.  Journal of Autism and Developmental Disorders ,  45 (8), 2411-2428. https://doi.org/10.1007/s10803-015-2407-8