TITLE:    Connections In Fractions (Flores, 2005)

CONTENT  AREAS/ Key Concepts (What areas of mathematics does this lesson cover?):  Equivalent Fractions, Division, and Equal sign usage  

GRADE  LEVEL:    4th

MATERIALS   NEEDED: Construction Paper (7 rectangles/brownies), Scissors, Glue Sticks, and Worksheet for pasting rectangles, Ruler

KEY   CONCEPTS/Goals:  How to divide seven brownies among 4 people.  Showing equivalent relationships between fractions, division of fractions, and 3 ways of writing division problems.

EALR'S and GLE'S (Make the connections clear and specific)

EALR 1: The student understands and applies the concepts and procedures of mathematics.

1.1.1 Understand the concept of decimals (money) and fractions.

Explain or show how a fraction can be decomposed into smaller fractions (e.g., ¾ = ¼ + ¼ + ¼).

1.1.2 Understand the relative values of fractions and decimals

Model and describe equivalent fractions (e.g., paper folding, geo-boards, parallel number lines). [CU]

Learning Goals/Objectives: (What do you expect students to learn and be able to do from this lesson?)   Students should be able to see relationships between equivalent fractions; express the division of whole numbers; make connections about different concepts related to fractions;

PROCEDURES:  (Label each step in the process:  Activating Prior Knowledge, Disequilibration, Elaboration, Crystallization)

• Introduction/Pre-assessment (Do some activity to see what your students know.)

Starting with an un-scored/cut sheet of brownies. Ask how to divide it where there isn’t an even number to share (either brownies or people)?

(If no one starts) Ask how to start. If we start with 1 sheet, then split it down the middle—what do we have? 2 1/2 sheets. If we split ½ again, we get 2 1/4 sheets

Notation: does anyone know how we would write fractions? [The top number (numerator) represents how many you have; the bottom number (denominator) represents how many parts the original 1 was divided into.]

Now how would we start dividing a piece of paper, which we’ll use instead of brownies today? (Ruler or just fold in half)

• Activity (Imagine that you were writing this for a substitute to teach. Be detailed and specific.)

• Give each student a set of 7 rectangles (brownies) of the same size.
• Each student collects scissors, glue sticks, rulers (?) and worksheet for pasting.
• Pose the Following Problem (brownie) to the Students:
• Each rectangle (7) represents 1 brownie. You need to evenly divide them among 4 people (for example, you, your parents, and your sister). It is important that each person gets the same amount. Your dad likes to sneak extra brownies, watch out for him!
• Arrange the brownies (whole and/or portions) on the worksheet with 4 areas. Glue the rectangles to the worksheet once you’ve solved it.
• Write the number sentence (using whole numbers and fractions) to represent your solution (for example if I were dividing 5 brownies between 2 people, I might write: 2+1/2 or 1+1+1/2)
• Students work on the problem on their own – students are allowed to share their thoughts with neighboring students
• After students solve the problem and have recorded their solutions on their paper, ask students to share their strategies and solutions with the rest of the class.
• As students describe their solution – model the process on the board (with larger versions of the brownie rectangles or if available use overhead projector) – label each square with corresponding fraction (i.e. ¼, ½, etc…)
• Help students see relationships between equivalent fractions. Ask students to share their number sentences. Ask students to decide if they represent the same amount.

• Closure

Have students write in their reflections notebook - what they learned, how they might use this information in the future, and how they have used it in the past.    

Accommodation Plan: Note how the following are accommodated in lesson (race/ethnicity, language, gender, class) Each must include reference to Trentacosta text (Trentacosta, 1997).

1. Race/Ethnicity:  We’ll share some history about fractions. According to Wikipedia, fractions go back to nearly 3000 BC near present-day Pakistan. Then the Egyptians, and later the Greeks. (I’ll have my computer)

2. Language:  If there are English language learners (ELL) we will arrange a plan to provide tutors that understand the lesson in order to translate for them.

3. Gender:  We will try to equally call on students of both genders; use examples that contribute to both genders; be sensitive to overly dominating boys and passive girls if that occurs.

4. Class:  Class issues have to do with code switching, time and place for homework, relevance.  I don’t know for sure what to do with this lesson

POST-ASSESSMENT   ( How does your post assessment evaluate progress toward learning goals and EALRs and GLEs)

As students work with their worksheets, walk around and note who’s having trouble. When using the on-the-board models, check on them. Perhaps ask them to help each other.

TEACHER REFLECTION (What went well, what you would do differently?)