Subtracting Fractions with Regrouping
Summary:
This activity is used to help develop the students understanding of subtracting fractions using regrouping. The students will work with shape cut outs to help them visualize subtracting fractions. The students will trade in “big shapes” for “smaller shapes” to show the method of regrouping.
Subject:
· Math: ___
· 8.1 (A) Compare and order rational numbers in various forms
· 8.2 (A) Use appropriate operations to solve problems
· 8.2 (B) Add, subtract, multiply, and divide rational numbers in problems
Grade Level:
· Target Grade: ___ 8
· Upper Bound: ___ 8
· Lower Bound: ___6
Time Required: ___ ~35 minutes
Activity Team/Group Size: ___ individual or groups of 2-3 (individual recommended)
Materials:
· Worksheet
· Worksheet with answers (for teachers only)
· Pattern blocks (recommended item) or cut-outs of these shapes
Reusable Activity Cost Per Group [in dollars]: ___
Cost of paper for the shapes and/or the cost of pattern blocks (recommended).
Expendable Activity Cost Per Group [in dollars]: ___
The cost of paper for the worksheets.
Learning Objectives:
· This activity should help reinforce the concept of regrouping when dealing with the subtraction of fractions with regrouping. Additionally, the students will get hands-on, tangible experience with shapes. This will work well for patterns and/or variable representation of numbers.
Lesson Introduction / Motivation:
To begin the lesson it may be necessary to discuss the whole reason why we even deal with fractions, decimals and percents begins with. Explain to the students that everyday life requires us to be aware of fractions. While you may be able to get by without being good at it, your life will be much easier if you are able to comprehend adding and subtracting fractions. Some examples where these mathematical abilities occur are cooking and money. An example of what must be done when adding fractions may be given. Ask the students what is ½ + ½? Then, ask what is ¾ + ½ and have them explain that a common denominator must be obtained in order to perform this operation. Then, give them an example of subtracting fractions and how a common denominator still must be obtained. Then move onto an example of subtraction where the numerator of the minuend is less than the numerator of the subtrahend after obtaining a common denominator. What do we do now?
Lesson Plan:
Distribute the worksheet to the students as necessary. Begin with the basic introduction as to the necessity of learning this concept and a description as to what the concept of regrouping is. Have the students use the pattern blocks and/or shapes which will help them work through the first two sections of the worksheet. Have the students come to the board to work out the problems and explain why they did the things they did. Go through the logical process of solving a subtraction problem of fractions with regrouping.
Lesson Closure:
The students should be able to perform the subtraction of fractions with regrouping well after this lesson/activity. The experience the students gain from this will fit in well with the structure which must be completed in order to solve a mathematical problem. Remind the students that in order to add/subtract fractions that before they can add or subtract they must find a common denominator. Reiterate throughout the lesson this so that it becomes engrained in their brain as they work through these problems.
Assessment:
During the 3rd section of the worksheet a ‘contest’ may be played out where each student is required to come to the board and work one of the problems. Additional problems may be added in place of the ones which are present in the third section of the worksheet so the students may obtain more challenging problems (ones where the common denominators are not already obtained). The student who has the most correct answers for the third section may get a prize.
Vocabulary / Definitions:
· Regrouping is the act of forming numbers into a new or restructured group or grouping.
Background and Concepts for Teachers:
· The teacher should understand the basic concepts behind regrouping and why it is necessary. Additionally, the teacher and students should be aware of the steps needed in order add/subtract fractions/decimals/percents.
Lesson Scaling:
The problems and shapes used may be made simpler or more complex if desired. In the event that the classes are advanced the shapes can be made more complex or the problems asked may be much more difficult. Additionally, the fractions used may be modified to have more sophisticated common denominators or easier addition/subtraction operations. For more advanced students, try to have them work out all problems using only shapes but then writing the answers in numerical form.
Troubleshooting Tips:
Some students may not understand the term regrouping. This is because it is often mistakenly termed ‘borrowing’. If the students do not understand why it is called regrouping, a scenario which can be used to help describe the concept is given as:
“All regrouping does is move one set of values and represents them as another equivalent set. An example where this applies is with money. We all know that 4 quarters equals 1 dollar. If we had 6 quarters we could represent this as two groups: group 1 is dollars; group 2 is quarters. With 6 quarters we would have 1 in the dollar category and 2 in the quarter category. If we wanted to regroup we could represent the money in one group of quarters. In this instance, the single group will be 6 quarters. There will still be the same amount of money, but the way we represent the money is different.”
Hopefully this example, or one similar, will be sufficient for the students to get a better grasp on the concept of regrouping.
Multimedia Support and Attachments:
· Worksheet
· Shapes
Keywords:
· Addition
· Subtraction
· Regrouping
· Fraction
Authors:
Graduate Fellow Name: ___ Jason Wardlaw
Teacher Mentor Name: ___ Sondra Junek
Undergraduate Fellow Name: ___Matthew Horne
Date Submitted: ___ 09/23/2009
Date Last Edited: ___ 09/23/2009
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