A Fair Share of Fractions
Students will be able to illustrate sums of fair shares using a paper folded model.
- Hand out a plain sheet of paper (cut in a perfect square) to your students.
- Propose this challenge, "Who can fold this page into the least amount of equal parts where each part has less than four sides?"
- After allowing for some thinking and folding time, call on a few students to share their solutions with the whole class.
- Announce that today’s lesson, begins with the models where students folded their squares diagonally once to form two identical triangles!
Explicit Instruction/Teacher modeling(10 minutes)
- Tell your students the lesson objective has four parts:
- Fold a paper into equal parts.
- Label each part as a fraction
- Shade in some fraction of the whole.
- List the shaded amount.
- Display the teacher prepped poster of Lesson’s Four Steps.
- Demonstrate the process with a square that has been folded in half diagonally once. Write the fraction ½ in each triangular portion, shade in one half, and write “one-half is shaded” on the backside of the square.
- Refer to the square model and explain of the ½ that was labeled and shaded, ‘1’ part (the Numerator) describes what was in isolation, and ‘2’ (the Denominator) describes how many parts all together.
- Explain to your class, "The Fraction, like ½, is how we identify parts of a whole that we look at in isolation, compared to all parts as a whole."
Guided practise(10 minutes)
- Hand out new sheets of paper (8.5” x 11”) to your students and lead them through folding it into eight equal parts. The result should be a rectangle with ⅛ sized partitions.
- Have your class unfold the paper, label each equal part ⅛. Then, turn and tell a neighbour what the ‘1’ in the numerator, and the ‘8’ in the denominator stand for.
- Allow for the whole class to exchange in sharing, and answer any clarifying questions.
- Your class should then shade in 5 of the 8 equal partitions. Ask your students to turn and tell a neighbour the Sum, or the total, shaded parts, and write the sum on the back side. The answer should be ⅛ + ⅛ + ⅛ + ⅛ + ⅛ = ⅝.
- Let students share out their sums, confirming that it is ⅝, stated, ‘five-eighths’.
- Hand out paper strips to your class and lead them through to fold it into 16 equal parts. (The strip, horizontally will be folded once in half horizontally and three times in half, vertically.)
Independent working time(15 minutes)
- Restate the lesson objective and refer to the poster of four steps.
- Announce to your class they are to follow the lesson steps (refer to the poster), shade in an amount of their choice, and write the equation and sum on the back. Answer any clarifying questions and release students to work.
Enrichment: Students can write up to three equivalent fractions for shaded and unshaded portions of their models.
- Support: Students can make models fractions less than 18, like fourths or sixths.
- Google Classroom is a great resource in the Google Apps for Education suite, for posting such assignments. It’s also a handy repository for student work!
- Present a strip of paper folded in sixths with two partitions shaded.
- Display three optional answers and ask for the correct answer along with a four-step explanation of how to arrive at their choice.
Review and closing(5 minutes)
- Discuss the following question, "How could a fraction be greater than zero, but less than one?"
- Note relevant new student understandings on a poster for future reference.