Dividing Fractions #1

Lesson Goals

Students are able to:

divide whole numbers by fractions and vice versa
illustrate the conceptual knowledge behind the flip and multiply procedure using concrete materials, e.g. divide 3 by 1/2 using fraction strips, relational rods and linking cubes
divide whole numbers by fractions using word problems

Syllabus Outcomes

Multiply and divide fractions and decimals using efficient written strategies and digital technologies(ACMNA154)

multiply and divide fractions and mixed numerals using written methods
multiply and divide fractions and decimals using a calculator

Working Mathematically

explain, using a numerical example, why division by a fraction is equivalent to multiplication by its reciprocal (Communicating, Reasoning)

Prior Knowledge

Understanding of the following vocabulary: dividend, divisor, quotient, numerator, denominator, mixed number, improper fraction, and simplest form.

Convert between mixed numbers and improper fractions

Multiplication of fractions and mixed numerals and write fractions in it's simplest form

LESSON PLAN

Introduction

Concept Teaching ~ 15 minutes

Students will be exposed to the conceptual knowledge behind the flip and multiply method of division of fraction.

Using fractions strips, students will be dividing whole number by fractions using 2 simple examples - see in powerpoint.

Body

Fraction strips ~ 10 min

Pose the following questions related to division and have students solve questions in pairs using manipulatives - fraction strips.

6 divided by 3
6 divided by 1/3
6 divided by 2/3

Students to share their solutions using a whiteboard or overhead.

Discuss different representations (numerical, graphical, concrete materials) of student solutions.

Create a problem - Gallery Walk ~ 20 minutes

As a class – discuss and list the various real-life examples and applications of dividing whole numbers by fractions

In pairs - students are to create and solve a realistic problem (division of whole numbers by fractions or vice versa) and represent their solution in 2 ways (manipulatives, pictures, numbers, etc.)

Students do a gallery walk (walk around, observe various questions and solutions and leave comments on the sticky notes)

Students discuss their observations during the gallery walk (context of questions, representations used, any number solutions, etc.).

Disclaimer: This activity was retrieved from https://www.oame.on.ca/main/files/Gr7TIPS-2009/gr7Unit7.pdf (p.30)

Teacher responsibilities...

Concept Teaching

Teachers to use this powerpoint + speaker notes to guide their teaching of the concept.
Powerpoint includes addressing student misconceptions.
Instruct students to write down their answers on their worksheets - to stick into their books.Ensure there is plentiful number of fraction strips for students to use in their process of modelling the equations.

concept.pptx

Fraction strips

Encourage students to solve questions in a variety of ways and be prepared to explain their thinking / reasoning.
During activity, take not of the language students are using as they try to illustrate the question/answer using the materials.
During student sharing solution time, give opportunity for students to volunteer

Create a problem - Gallery Walk

Encourage student participation by asking one person or more from each table group to given an answer
Hand out 2/3 sticky notes
While students are creating a realistic problem, reinforce that it is to be a problem related to division of whole numbers by fractions or vice versa, e.g. Su has 4 cups of chocolate chips to make cookies. The recipe uses 1/3 cup of chips in each batch. How many batches of cookies can Winton make?
- Walk around and help out students who may be struggling to come up with a question.
- Write some prompts up on the board like pizza etc. to help students formulate their questions.
- During discussion, have several different students share their problems and solutions

Conclusion

Summative Assessment on Division of fractions ~ 15 minutes

1st page of Source: https://www.cpalms.org/uploads/resources/29168/SummativeAssessment.pdf

Students to hand it at the end of class.

Homework

Students to complete the worksheet and bring back next lesson for teacher to mark

Dividing whole number by a fraction.pdf

Source: https://www.oame.on.ca/main/files/Gr7TIPS-2009/gr7Unit7.pdf

Assessment(s)

Observation
Use of concrete materials
Verbal justification/reasoning
Group Work - communication
Peer review
Homework

Lesson Evaluation Questions

Was the concept teaching at the beginning of the lesson helpful for students to understand why the flip multiply method works?
Did students enjoy using the fraction strips? Should I have used other forms of manipulatives?
Should the Gallery Walk be more scaffolded?
Was the summative assessment too soon?

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