3rd Grade Fractions Unit v6o3a

3rd Grade Fractions Unit Jim Addison

Subject: Math – Introduction to Fractions Length of Unit: 8 Days Established Goal: Common Core Standards – 3rd Grade Math  CCSS.Math.Content.3.NF.A.1 Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.  CCSS.Math.Content.3.NF.A.2 Understand a fraction as a number on the number line; represent fractions on a number line diagram.  CCSS.Math.Content.3.NF.A.3 Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.

Essential Questions: 1. 2. 3. 4. 5.

What is a fraction? How can we write fractions? How can we represent a fraction on a number line? How can we simplify fractions or show equivalence? Why and how are fractions important in connecting math to everyday life?

These questions are essential for a foundation in the word of fractions for third graders. This is a new concept so the questions posed are crucial aspects of fractions. It is important to answer these questions well in order to progress with fractions in further grades.

Understandings: Students will understand that: o o o o o o o

Fractions represent a part of a whole. Fractions are written with a numerator and denominator. Fractions can be represented on a number line in a way much similar to an integer. Two fractions are equal if they are the same size. Fractions can be simplified by finding common factors between the numerator and denominator. Integers can be represented as a fraction. Fractions are used in money, cooking, measuring, percentages, and more!

The understandings listed above are important in developing knowledge of basic fractions. To work with addition, subtraction, multiplication, etc. with fractions, the above must be fully understood. These main ideas will be the focus of the unit and be examined thoroughly.

Knowledge: Students will know…     

A fraction is a part of a whole. Key vocabulary that is relevant to fractions. : Part/Whole, Denominator, Numerator, Improper Fraction, Simplest Form, Equivalent Fraction, Mixed Number, Factor, and Multiple. What fractions look like in reality using manipulatives. The process in simplifying a fraction. How to represent a fraction.

Students will expand their knowledge of fractions with the statements above. These key ideas are important to grasp to have a proficient understanding and the ability to form skills. Acquiring this knowledge will lay the foundation for their future in fractions which will be necessary for all grades ahead and beyond.

Skills: Students will be able to….     

Define key vocabulary, show examples, and relate concepts to actual numbers. Show fractions on paper and with manipulatives supplied. Simplify fractions using math learned previously. (GCF, LCM, Division, Multiplication, +/-) Use reasoning to show equivalent fractions. Develop a real life example in a situation where fractions are necessary.

These skill statements are used because they are linked with knowledge and understanding. Students will extract knowledge and understanding learned in the lesson to perform certain skills which are listed above. These skills are also defined in the Common Core State Standards.

Diagnostic Assessment: (Early Assessment)

Diagnostic Fraction Test - Day 1 Within this test, students will complete 24 multiple choice questions that pertain to basic fraction skills. It will test: o o

Introduction to fractions and mixed numbers Factors, Multiples, Primes

o o

Simplifying Estimation

The objective of this assessment is not for every student to ace the test, rather to get an understanding of previous knowledge students have had with fractions. This allows the teacher to get baseline idea that will be useful in measuring growth throughout the unit. Here is an example of how the assessment will look:

Alignment: This assessment contains all standards mentioned previously. Goals: The goal is to measure student understanding at its earliest stage before instruction. Essential Questions: 1. How much of the circle is shaded? 2. How can we represent ¾ on a number line? 3. How can we simplify 11/2? Cognitive Level: This is a ing/learned information activity in which falls under the Knowledge category of Bloom’s Taxonomy.

Formative Assessments: Overview: Students will be required to complete worksheets after each day’s lesson, participate in daily activities, and perform in a group setting.

Pizza Fractions – Day 2,3,4 Overview: Students will have the opportunity to play a fraction game while using pizza as a manipulative. Students will get into groups to play this game and are required to fill out a worksheet while participating. Materials will be ready and organized for students. Use: This is a helpful way to learn fractions at an early stage because it uses a real life application that many or all students can relate to. I will use the worksheet that is to be filled out during this lesson/game as a formative assessment. This will monitor the understanding for the day and give me insight on whether individuals need more practice. The worksheet will directly correlate to the game and focus on the introduction of fractions. The game itself will focus on teaching students that fractions are parts of a whole. Lesson Summary: Students will use construction paper to creat their pizza. Toppings will include peppers, pepperonis, cheese, and sausage. Once the dough has been created and the toppings have been cut out, students will draw an “order card” which have already been created. An example order may be: 1 Large pizza, ½ cheese, ½ cheese and pepperoni with ¼ sausage. Aligment: CCSS.Math.Content.3.NF.A.1 This lesson matches with this standard because it focuses on the idea that fractions are parts of a whole. Goals: Students will be engaged in this activity and be able to represent the order cards correctly. Students will also be required to draw their pizza correctly on their worksheet. The goal is to correctly draw the pizza with the correct toppings. Understandings:  

Fractions are a part of a whole in which can be represented as objects, such as parts of a pizza. The process of how fractions work in regards to size.

Knowledge: 

Different sized fractions: Students will be able to know what certain fractions look like as far as size, and will be able to compare them with other fractions.

Skills:  

Create their own fractions and orders of pizza within the activity. Use correct math vocabulary and terminology in its proper form.

Essential Questions: 1. What is a fraction? 2. How can we represent ___(example fraction: ¼)___as a pizza? Cognitive Level: This activity is apart of both Application and Knowledge categories of Bloom’s Taxonomy.

Visual Fractions – Day 5,6,7 Overview: Students will practice working on fractions in relationship to a numberline. Students will be engaged by using computer generated programs to help teach this concept. Because we will be working in the computer lab, each student will need a computer to complete this activity. Assessment will be based on participation, a short quiz, and on a poster with an appropriate rubric. Use: This is a way for students to see fractions visually and interact with activities online. This lesson and assessment fullfills standard CCSS.Math.Content.3.NF.A.2, which states that students should have an understanding of fractions on a number line. Lesson Summary: We will begin the lesson by review number lines using integers. Students should have a proficient background with this idea which will be used to scaffold. Next I will introduce fractions on the number line and tie them in with the Pizza Fraction lesson that was previously given. We will then make our way to the computer lab to use the interactive number line activities and work on: 1. Identifying fractions on a number line 2. Create fractions on a number line 2. Show equivalent fractions on a number line (ex: 3/4= 6/8) Next we will discuss the activity the students completed and take a short quiz. The quiz will monitor the success of the day’s lesson and allow the teacher to see growth or struggle. Our last activity will be done in groups in which students will present fractions on tag board. Their project must fulfill the requirements on the rubric. (Day 5) Alignment: As previously stated, this aligns with standard CCSS.Math.Content.3.NF.A.2. Goals:   

Students will be able understand and work with fractions on a number line. Students will be able to place fractions on a number line individually. Students will be able to visually represent fractions on a number line and fulfill requirements as stated on the rubric.

Understandings: 

Why particular fractions belong where they do on a number line.

Knowledge: 

Where particular fractions belong on a number line.

Skill: 

To be able to place fractions appropriately on a number line.

Cognitive Level: This lesson and assessment is a part of the categories Analysis, Application, and Comprehension as stated in Bloom’s Taxonomy.

Summative Assessment: Fraction Exam: (Day 8) Overview: At the end of the introduction to fractions unit, students will each be given an exam to assess their understanding. The test will include the following: o o o o o

Basic vocabulary words discussed in lessons Writing fractions Showing fractions (shading in parts of a whole) Representing fractions (on a number line) Real life application questions (pizza)

Use: I will use this summative assessment for this unit because it wraps up all the key details, vocabulary, and concepts that are crucial for the next unit (simplifying, addition/subtraction of fractions). It allows me to monitor growth by comparing the outcome of this assessment to the diagnostic assessment taken in the beginning of the unit. This exam will give me insight on whether students have fully grasped key concepts or not. This assessment will be graded on content. Alignment: This exam will include all standards introduced in the unit. Goals: The goals for this exam will be to correctly identify, write, show, represent, and apply key ideas that are listed above in which I have listed the content of the exam. Understandings: o o o o o o

Fractions represent a part of a whole. Fractions are written with a numerator and denominator. Fractions can be represented on a number line in a way much similar to an integer. Two fractions are equal if they are the same size. Fractions can be simplified by finding common factors between the numerator and denominator. Integers can be represented as a fraction.

Knowledge:    

A fraction is a part of a whole. Key vocabulary that is relevant to fractions. : Part/Whole, Denominator, Numerator, Improper Fraction, Simplest Form, Equivalent Fraction, Mixed Number, Factor, and Multiple. What fractions look like in reality using manipulatives. How to represent a fraction.

Skills:    

Define key vocabulary, show examples, and relate concepts to actual numbers. Show fractions on paper and with manipulatives supplied. Use reasoning to show equivalent fractions. Develop a real life example in a situation where fractions are necessary.

Cognitive Level: This assessment best aligns with Application and Comprehension from Bloom’s Taxonomy.

Quality Control: My formative assessments will be valid and reliable through the math curriculum within the school that appropriately aligns with the Common Core State Standards. The rubric for the poster presentation will be given to students ahead of time to assure they are aware of their expectations. I will create an example poster to give students an idea of what is expected. The summative assessment will examine each benchmark. Tests, worksheets, quizzes, and posters will be graded fairly.