## Unit Representing Fractions using Sets: Pre-Activity Junior Grades

 MO 10 min A 10 min C/D 5 min 25 min Math Learning Goals Students will: represent fractions as parts of a set or parts of a whole connect the part-whole meanings of fractions to representations based on measure (distance, area, volume) and set communicate criteria used to determine what can be represented by a fraction Materials A variety of manipulatives (could include measuring cups) Minds On... Individual Activating Prior Knowledge Activity Ask students to construct representations of a fraction of their choice. Students record each representation and label it with the fraction in symbolic form. Whole Class Discussion Ask students to share their fraction and their representation. Have other students share their fraction if they can connect it in some way to the previous fraction. Fractions could be similar because the student used the same type of model (in which case you could ask other students who used the same type of model to represent different fractions to share); the same type of representation, such as an area model or a set model; the same fraction represented using a different model. Curriculum expectations/observation/mental note: Ask students to explain the connections between their representation and the symbolic form. Student examples could be recorded on whiteboards or displayed via document camera to ease sharing. Action! Pairs Discussion Share BLM 1 with the students. Ask pairs to identify what fraction of the balloons are orange? What assumptions are they making about the balloons? About the fraction? As the students make connections to the fraction language in the sidebar, formalize the language on the word wall. Whole Class Discussion Ask four students to move to the front of the room. Use an appropriate fraction to describe the group (e.g., one half is boys). Ask the students if it is appropriate to use a fraction even though the people are not connected (as were the pieces in an area model. Fraction language: Set model Area model Distance model Volume model Part Whole Equal measure Same colour Same attribute Consolidate/ Debrief Individual Math Log Students respond to the prompt: Fractions can be represented using measurement models (such as distance, area, volume) or set models. Explain how these models are similar and how they are different. Home Activity or Further Classroom Consolidation

## Unit Representing Fractions using Sets: Lesson 1 Junior Grades

 MO 10 min A 10 min C/D 5 min 25 min Math Learning Goals Students will: reason about the meaning of the denominator of the fraction for set models connect the part-whole meaning of fractions represented using sets Materials A number of lollipops Minds On... Think/Pair Activity Tape four markers in two different colours randomly on the blackboard. Ask students to first individually think about the following questions: Do the markers represent a fraction? What fraction do you see first? What other fraction can you see? Have students pair and discuss their responses. Differentiate content based on student engagement/interest: Provide a set of markers including three different colours to generate as many fractions as possible. Action! Whole Class Discussion Ask one pair to record one of the fractions on the board. Ask how many other pairs identified this fraction. Have another pair record on the board a different fraction they identified. Ask how many pairs saw this fraction. Continue until two equivalent fractions based upon the same attribute have been generated. Select one pair of equivalent fractions. Engage students in consideration of equivalent fractions using the following prompts: Are these two fractions the same? If so, how? If not, why not? What does the denominator represent in each of these fractions? What does the numerator represent in each of these fractions? How do fractions created from sets relate to fractions created from measurement models, such as an area model? It is important to record fractions with the attribute used. E.g., 2⁄4 purple; 1⁄2 purple. Consolidate/ Debrief Individual Exit Card Create a set of anything and represent it using a drawing. Write the fraction that it represents. Home Activity or Further Classroom Consolidation

## Unit Representing Fractions using Sets: Lesson 3 Junior Grades

 MO 5 min A 40 min C/D 15 min 60 min Math Learning Goals Students will: Represent a number of fractions using sets Reason about how changing the whole changes the fraction Materials Bags with 10 animal cards in each (randomly selected from BLM 3.1), 1 bag per group Minds On... Individual Activity Provoke student thinking with a prompt which involves changing the whole to make the fraction true (e.g., Show 3 shaded rectangles and 5 unshaded rectangles and ask them how the set would need to be changed to represent 1⁄3 of the rectangles are shaded or to represent 1⁄2 of the rectangles are unshaded) Action! Small Group Activity Distribute a cluster of animal cards (10) to each group. Ask groups to use their animal cards to represent the following fractions (move others aside as necessary): half the set has to be land animals; two-fourths must be water animals; one-third must have antlers two fractions (or more) of your own creation Students record solutions in their notebook. Whole Class Discussion Call on a variety of students to share their fractions. Lead a discussion to highlight how the same fraction can represent very different sets (e.g., half the set are land animals, and half the set are water animals), and how equivalent fractions can be used for the same attribute (e.g., for the land animals the fractions could be 5⁄10 or 1⁄2 which are equivalent. Consolidate/ Debrief Whole Group Consolidation Students record the fractions created in the large group. Encourage them to make connections between the fractions (e.g. , same attribute, equivalent fractions) and record their fractions accordingly. Home Activity or Further Classroom Consolidation

## Unit Representing Fractions using Sets: Lesson 4 Junior Grades

#### BLM 4.1

Consider the following group of shapes.

Write at least four different fractions which could be used to describe the set. Be sure to explain how you are creating the fraction.

## Unit Representing Fractions using Sets: Lesson 5 Junior Grades

 MO 10 min A 10 min C/D 5 min 25 min Math Learning Goals Students will: reason about the connections and distinctions between set and area representations Materials Copies of BLM 5.1 Minds On... Whole Class Shared Writing Activity Share the following letter with the class and engage them in a shared writing activity to craft a response. Dear Ms. Fraction, In class yesterday Devon created the fraction 3/8 for the shapes we were given. The only way I could see that fraction was by considering the fraction of the shapes that had four sides but Devon said she looked at shapes that have four or more sides and are shaded in. I thought you could only consider one characteristic when creating a fraction, such as shape, and not two, such as shape and colour. Can you help me understand what Devon is thinking? Signed, Out of Shapes in Ontario Action! Small Groups Preparation for Discussion Assign Each group one of the letter in BLM 5.1, ensuring that each of the three letters is addressed by multiple groups. Pairs prepare a response to the letter they were assigned. Consolidate/ Debrief Larger Groups Collaborative Activity Cluster pairs of students according to the letter they were assigned. Each pair presents their ideas to the larger group. The larger group reviews responses of their peers and establish, as a group, a ‘complete’ response. Remind each member of this larger group that they should be ready to present to the whole class. Whole Class Sharing Select three representatives of each of the three larger groups to share their thinking with the entire class. Encourage Math Talk Learning Community. Home Activity or Further Classroom Consolidation

#### BLM 5.1

Dear Ms. Fraction,

Last night my Dad baked 12 Pumpkin Spice muffins. After my brothers and sisters had eaten some, my Dad said that there was one-third left. I think that there were four muffins left. So, now I don’t really know whether my Dad or I is correct (but I hope it is me!).

Signed Hungry in Hamilton

Dear Ms. Fraction,

This girl in my class, Brooke, really thinks I’m cool. At least she thought I was cool. Then she offered to split her candies with me. Well, Ms. Fraction, I forgot what I was doing and ate 56 of the candies. That made Brooke angry. She said I am worse than her brother, Dawson, who ate 78 of the candies they were sharing.

So who’s worse, Dawson or me?

Signed Stumped Skittles Snacker

Dear Ms. Fraction,

Today in Math class, my teacher asked us to write a fraction to represent the green part in this model.

Liam said that it showed one fifth.

Sam argued that it was six tenths.

My teacher said that both were correct but I don’t understand why.

Are you smarter than my teacher? Can you help me?

Signed Konfused in Kawartha