Activities
Below is an outline of the lesson progression I plan for this curriculum unit. The unit should take approximately four weeks to complete. Following the lesson progression are examples of some activities to be used in classroom.
Lesson 1: Concept of the Unit Fraction
- Discussion of how students view fractions
- Units-Discussion of using the unit as a noun
- A Unit fraction as 1/d, d representing the number of pieces of the new unit that it takes to make the original unit
Lesson 2: Unit Fractions using Models
- Using the Linear Model: Emphasis should be placed on distance from the origin
- Using the Area Model
- Using the number line/ray to place 1/d
- Using area models to represent 1/d
Lesson 3: General Fractions
- Students will write various general fractions n/d as a sum of the unit fraction
- Students will show the general fraction n/d as a multiple of a unit fraction n x 1/d
- Using the linear model, students will show the location of a general fraction n/d as a multiple of the unit fraction 1/d
- Using the area model, students will show a general fraction n/d as a multiple of the unit of fraction 1/d
Lesson 4: Add and subtract general fractions with like denominator using both the linear and area model.
- Students will use their knowledge of the unit fraction in relation to the general fraction to add general fractions on a number line and an area model.
- Students will also do the same to subtract fractions on a number line and with the area model.
- Addition and subtraction should have the same unit (denominator) and relate to separate wholes.
Lesson 5: Comparing Fractions with like denominators
- Students will compare fractions with like denominators using the area model and the linear model
- Students will notice that if the denominators are the same, the numerator will be the deciding factor of which fraction is larger.
Lesson 6: Renaming fractions using the area model (equivalent fractions)
- Students will use the area model to create general fractions to be equal to another general fraction.
- They will understand that when a unit fraction 1/d is used to further divide the area model, it creates a new unit.
- Students will be able to create a common unit between two fractions with different denominators.
Lesson 7: Comparing Fractions with unlike denominators
- Students will use the area model to compare fractions with unlike denominators.
- Students then will be able to use the cross multiplication algorithm.
Activity Sample #1 Unit Fractions through Paper Folding.
Students will create their own fraction strips to create a visual of the "size" of each unit fraction. I recommend using different colors of construction paper equal in size to create the unit fractions. Focus will be in creating fraction strips for 1/2, 1/3, 1/4, 1/5, 1/6, 1/8, 1/10, and 1/12. The goal for this activity is for students to see that when the paper is folded, several parts are created to make one whole, thus creating the unit fraction. In addition students should be able to compare the different unit fractions and be able to reason that fractions with a larger denominator are actually less than fractions with a smaller number in the denominator. The fraction strips can also be used to show that a sum of a number of unit fractions can equal general fractions.
Activity Sample #2 - What is a fraction? See Appendix 1
Students will be asked to define/explain fractions in their math journal. They can write and/or draw a picture. They will then work in small groups or partners to chat about how they explain fractions. Then they will choose a presenter to present to the whole class their findings. I will record the findings on chart paper or on the board. This will give me an idea of my students' understanding of fractions.
I will then review with my class what we know about the noun adjective theme in relation to mathematics. The focus will be to remind students that units are important when working with numbers. In regards to fractions, it needs to be pointed out that it is just as important to pay attention to the unit. The Naming the Unit section further explains this concept. I will then read The Hershey's Milk Chocolate Bar Fractions Book and introduction to the Unit Fraction.
Students will be given a Hershey Bar and a sheet of Graham Crackers. These are already segmented therefore making it easier to partition. Pass out a paper plate, or napkin, and a Ziploc bag to each student. You can use actual Hershey's Bar and Graham Crackers or you can create copies and laminate to pass out. Students will also have a sheet to record information requested.
Activity Sample #3 Using the Area Model to write a Fraction-See Appendix 2
The goal of this activity is for students to become familiar with the area model. Students will be given a square piece of construction paper. It is important that the paper is not too small and not too big. They will then follow a set of instructions and questions given by the instructor to guide their understanding and writing of a fraction. They will be assigned partners for this activity. After this activity, students can be given graph paper to continue practice drawing and dividing the area model. It is important to stress the importance of EQUAL parts. Teachers can extend with students to do this with other fractions as well.
Extension: Addition can be used with the students' area models they created.
Activity Sample #4 Renaming Fractions with a Partner: I divide, You divide, We Rename See Appendix 3 This is an interactive partner activity to help with the practice of renaming fractions. You can have a print out or have white pieces of construction paper of various sizes of squares and rectangles.
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