Fractions:Partitioning Sets

Breaking Some Eggs

 

Suggested Books
 

 

Essential Questions for students (objectives):  How can fractions be created from sets of objects?  How many ways can equivalent fractions be represented?  Compare/contrast the difference between dividing a single object into parts and dividing a set of objects into parts.
Supplies:   The Underachievers by Holly Young, Manipulatives to represent eggs (2 sided chips), Part 2 pictures, part 3 pictures, first handout, second handout, first check handout, second check handout
 
Common Core Standards:  3.NF.1, 3.NF.3, Mathematical Practice #2 & #3
Time needed: 2.5 hours 
Instructional Format:  Student centers, student group discussion
Vocabulary for a Word Wall:  Equivalent fraction
Prior Knowledge/ Possible Warm-up Activities:  Students should have worked on fractions with a number line and partitioning shapes.  Read Underachievers up to page 21.

 
Step by Step Lesson Description:

1)  Read The Underachievers from page 21 – 29, showing the pictures.

2)  In order for the students to practice understanding breaking sets of objects into fractions, there are multiple practice rounds.  This lesson is designed to take students through the learning model of concrete examples first, then pictorial models, and then abstract work.

3)  First round of centers:  Give each student a copy of the first handout.  Break students into 4 groups.  Each group gets a model of eggs  - see pictures.   Students are asked to write 2 different fractions for their model.  If the students struggle with writing a reduced equivalent fraction, provide a structure hint to help them (I used egg cartons cut into a smaller group size).  Students are asked to write an explanation (or draw a picture) of how they found both representations.  Once groups are finished have them leave their written pages with their eggs.  Have the students “carousel” walk to all the other egg centers and mark on the bottom of the paper whether they agree with the work of the original group or if they feel that a mistake was made.  Discuss the final results as a class.  Click here to see pictures of the egg centers and the supports that I made.  If you don’t want to use actual eggs, I would recommend two-sided chips, using one side for the broken egg.

4) Give each child the first check in formative assessment.  [It is important to have physical objects each child can move around to help them solve the problem.  The first check in handout has pictures of eggs that can be cut out and put in envelopes for students to use as manipulatives.]  Show the answer and how it is calculated.  Ask students to judge their knowledge on the bottom of the first check in sheet.  If they feel very confident with their answer or just made a simple mistake, the students can move onto the next set of centers.  If they need more practice, have some additional physical egg problems ready, without supports.  I use 3/9 and 5/25, but I can also change the original stations by removing a few total eggs or replace broken eggs.

5) Second round of centers:  Put students into groups of 4.  Give them a picture of eggs and the corresponding cards.  Each group will record their answers on the second handout. [this center could also be done individually by giving each child their own handout]  Students will have to choose two or more cards that represent their picture of eggs (they can use the handout to draw pictures if they need it).  They must also explain their thinking.  Ask each group to explain to another group how they solved their problem.

 

6) Give each student finished with the second round of centers the second check in formative assessment.  Ask students to judge their knowledge on the bottom of the second check in sheet using the answer sheet.  If they feel very confident with their answer or just made a simple mistake, the students can move onto the next center.  There are additional problems on the part 2 picture handout for any students that would like to have more practice.

 

7) Third round of centers:   Students can work in groups or individually.  Students can either write their answers (if working in a group) on the part 3 picture handout or record their answers on a separate sheet or small whiteboard.  When the group (or student) is finished, they need to share their answer with another group (or student).  Note:  the most difficult are the cards with the bunny “Rolff,” because students will have to create a set that isn’t obvious – for example the card says ¼ so they will have to make a larger set like 8 objects.

8) Whole class closure & discussion:  Either hand out a copy of the compare both kinds of division handout to each person or show on a smart board.  Students can either write an answer in a journal or discuss in partners.  Discuss as a class.  Make sure that students discuss the difference between number of sets and how many in each set.

 

Assessment (Acceptable Evidence):  First check handout & answer sheetsecond check handout & answer sheet

 
Attached worksheets or documents:  part 1 pictures, part 2 pictures, part 3 pictures, first handout, second handout, first check handout, second check handout, compare both kinds of division handout

 
Cautionary notes/ misconceptions/additional connections:  For a fantastic website to learn comparison of fractions visit Greg Tang’s website: http://gregtangmath.com/play?game=satisfraction