Dividing Fractions With a Twist
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This learning activity provided by:
Author:
Samantha Wallace
System: Limestone County School: Cedar Hill Elementary School
General Activity Information
Activity ID:
2440
Title: Dividing Fractions With a Twist
Digital Tool/Resource: Red Licorice Problem
Web Address – URL:
Overview: Students will use red licorice candy to try to solve a real-world dividing fractions problem. This is an introductory activity to build a conceptual understanding of dividing a whole number by a fraction.
This activity results from the ALEX Resource Development Summit.
Associated Standards and Objectives
Content Standard(s):
Mathematics 15. Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.
a. Solve real-world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions and illustrate using visual fraction models, drawings, and equations to represent the problem.
b. Create a story context for a unit fraction divided by a whole number, and use a visual fraction model to show the quotient.
c. Create a story context for a whole number divided by a unit fraction, and use a visual fraction model to show the quotient.
Unpacked Content
Evidence Of Student Attainment:
Students:
Solve real-world problems involving division of a unit fraction by a non-zero whole number, or division of a whole number by a unit fraction.
Justify solutions using visual models, drawings, and equations to represent the problem context.
Explain quotients using the relationship between multiplication and division.
Create a story context for a unit fraction divided by a whole number and use models to illustrate the quotient.
Create a story context for a whole number divided by a unit fraction and use models to illustrate the quotient. Teacher Vocabulary:
Unit fraction
Whole number
Division
Dividend
Divisor
Quotient
Equation
Multiplication
Factor
Fraction models Knowledge:
Students know:
Contextual situations involving division with whole numbers and unit fractions. Strategies for representing a division problem with a visual model. Skills:
Students are able to:
Use previous understandings of operations to
Divide unit fractions by a whole number and whole numbers by unit fractions.
Use visual models to illustrate quotients.
Create story contexts for division.
Use the relationship between multiplication and division to explain quotients. Understanding:
Students understand that:
A variety of contextual situations are represented with division of a whole number by a fraction or a fraction by a whole number.
Quotients resulting from division of a whole number by a fraction or a fraction by a whole number can be illustrated and justified with a visual model.
The relationship between multiplication and division can be used to justify quotients resulting from division of a whole number by a fraction or a fraction by a whole number. Diverse Learning Needs:
Essential Skills:
Learning Objectives: M.5.15.1: Define quotient.
M.5.15.2: Multiply a fraction by a whole number.
M.5.15.3: Recognize key terms to solve word problems. M.5.15.4: Recall basic multiplication and division facts.
M.5.15.5: Express whole numbers as fractions.
M.5.15.6: Recognize fractions that are equivalent to whole numbers.
M.5.15.7: Recall basic multiplication and division facts.
M.5.15.8: Solve word problems involving multiplication of a fraction by a whole number.
M.5.15.9: Recognize key terms to solve word problems.
M.5.15.10: Recall basic multiplication and division facts.
Prior Knowledge Skills:
Find products of a fraction times a whole number and products of a fraction times a fraction.
Use area models, linear models or set models to represent products.
Create a story context to represent equations (a/b) × q and (a/b) × (c/d) to interpret products.
Find area of rectangles with fractional side lengths and represent products as rectangular areas.
Find the area of a rectangle by tiling the area of a rectangle with unit squares.
Alabama Alternate Achievement Standards
AAS Standard:
Learning Objectives: Students will be able to solve real-world problems involving the division of whole numbers by unit fractions by using visual fraction models.
Strategies, Preparations and Variations
Phase: Before/Engage
Activity:
Display the problem on the board for the students to see.
Have a student read it aloud and then tell the students they are going to try and solve it.
Give each student three red licorice pieces -- they don't have to be the full length, but they need to be big enough to divide into fourths.
Tell the students to try to solve the problem using the candy pieces. (Remind them not to eat the candy yet!) They can work in groups, partners, or individually.
Watch for conceptual understanding as they work -- students should be dividing each candy piece into fourths and then counting the total number of pieces (12).
If students are struggling, ask questions to help guide their thinking: How much of each licorice piece are we supposed to eat each day? How many of those pieces do we have in one piece of licorice? How many do we have in all three licorice pieces?
After students have had time to work, gather student attention and ask for someone to share his/her thinking. Encourage students to discuss their problem-solving strategies, not just the answer they found.
At the end of the activity, have the students help build the equation on the board for the problem. (3 divided by 1/4 = 12)
Assessment Strategies: Use informal assessment strategies during this activity. Observe to see if students are building a conceptual understanding of dividing by a unit fraction. At the end of the activity, ask students to show "fist to five" to describe how confident they would be at solving another problem just like this one. Showing a fist means they have zero confidence, one finger means a little confidence, all the way to five fingers and full confidence.
Advanced Preparation: Requirements for this activity:
a projector/display board to show the problem to the class
three red licorice candy pieces for each student
An alternative option is to print the problem and give a paper copy to each student -- they can cut out the paper version of the licorice from the problem and use those as a model instead of actual candy.
Variation Tips (optional): This activity can be done with other manipulatives (string, chocolate bars, pretzel sticks, straws, etc.)
Notes or Recommendations (optional): This activity can be used as an introduction to a lesson on dividing whole numbers by a fraction.
Keywords and Search Tags
Keywords and Search Tags:
divide, division, unit fractions, visual models
