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Activity 1

Standards Alignment

Building On

Addressing

Instructional Routines

None

Materials

To Copy (from Blackline Masters)

Secret Fraction Stage 1 Cards

Secret Fraction Stage 1 Directions

Activity Narrative

The purpose of this activity is for students to learn Stage 1 of the Secret Fractions center. Students practice building non-unit fractions from unit fractions. Each partner starts with three “secret” non-unit fraction cards and five unit fraction cards. On their turn, students choose either to ask their partner for a unit fraction or to trade one of their secret fractions for a new secret fraction card. If the student has the requested secret fraction, they give it to their partner. If they do not have the requested unit fraction, they tell their partner to pick a unit-fraction card from the stack. After building each secret fraction, students reveal the secret fraction and explain how they made that fraction. For example, to complete a secret fraction card with , students need 3 cards with . A diagram is available in the blackline master that students can use to explain their thinking. The first student to build all three secret fractions wins. The Activity Synthesis highlights strategies students used to build their non-unit fractions.

Folders or other objects can be used to keep students’ work hidden.

Engagement: Develop Effort and Persistence. Check in and provide each group with feedback that encourages collaboration and community. Consider checking in with partners after the second round of Secret Fractions.
Supports accessibility for: Social-Emotional Functioning

Launch

Groups of 2
Give each group a set of cards, directions, and access to a folder, or something similar, to keep their cards hidden.
“We’re going to play a game called Secret Fractions. Let’s read through the directions and play 1 round together.”
Read through the directions with the class and play a round against the class, displaying the cards and thinking through decisions aloud.
If needed, show students how to place an object, such as a folder, between them to obstruct the view of the other player.

Activity

“Now, play Secret Fractions with your partner.”
10–15 minutes: partner work time
Monitor for students who:
- Trade their secret fractions for new ones because most of their unit fractions have a different denominator.
- Keep track of the unit fractions they have as they try to make their non-unit fractions.

The goal of the game is to be the first to build 3 secret fractions with unit fractions.

Make 2 stacks of cards: 1 for secret fractions and 1 for unit fractions. Place all cards face down.
Each player:
- Pick 3 secret-fraction cards without showing your partner. These are the fractions you are trying to make with your unit fractions.
- Pick 5 unit-fraction cards and hold them in your hands without showing your partner.
Partner A, you can either:
- Ask your partner if they are holding a unit-fraction card that you need.
- Trade 1 of your secret-fraction cards for the secret-fraction card at the top of the stack. (Place your traded card at the bottom of that stack.)
Partner B:
- If you have the unit-fraction card your partner asked for, give it to your partner. If you have more than 1, only give your partner 1.
- If you do not have the unit-fraction that was asked for, tell your partner to pick a card from the top of the unit-fraction stack and keep it in their hand.
Partner A: If you have enough unit fractions to make 1 of your secret fractions, show the secret-fraction card and explain how you made that fraction with your unit-fractions cards. Then set all your used unit-fraction cards aside.
Switch roles and repeat.
The first player to make 3 secret fractions wins.

If you run out of unit-fraction cards, mix up the used cards and place them in a stack face down.

Activity Synthesis

“What strategies did you find helpful for building your secret fractions?” (When was my secret fraction, I was keeping track of how many cards I had to make . When I had as a secret fraction, I knew I needed cards, but I had a bunch of cards, so I traded for a different secret fraction.)

Activity 2

Standards Alignment

Building On

Addressing

Instructional Routines

None

Materials

To Gather

Materials for creating a display

Activity Narrative

The purpose of this activity is for students to use diagrams to represent situations that involve non-unit fractions. The Activity Synthesis focuses on how students partition and shade the diagrams and how the end of the shaded portion could represent the location of an object. When students interpret the different situations in terms of the diagrams, they reason abstractly and quantitatively (MP2).

MLR8 Discussion Supports. Synthesis: During group presentations, invite students who are not speaking to follow along and point to the corresponding parts of the display.
Advances: Speaking, Representing

Launch

Groups of 2
“What are some games that you like to play with friends?”
Share responses.
“Pilolo (PIH-loh-loh) is a game played in Ghana (GAH-nah). One player hides sticks, rocks, or pennies. The other players have to find one of the objects and be the first to reach the finish line to get a point. Look at the picture of some children playing Pilolo and think about some strategies you might use if you played this game.” (I would try to hide the objects in a good hiding spot. I would run fast to be the first person to the finish line.)
30 seconds: quiet think time
Share responses.
“We’re going to represent some situations about students playing Pilolo.”

Activity

“In the activity, each strip represents the length of a street where Pilolo is played.”
“Work independently to represent each situation on a diagram.”
3–5 minutes: independent work time
“With a partner, choose one of the situations and make a poster to show how you represented the situation with a fraction strip. You may want to include details, such as notes, drawings, labels, and so on, to help others understand your thinking.”
Give students materials for creating a display.
5–7 minutes: partner work time

Here are 4 situations about playing Pilolo (PIH-loh-loh) and 4 diagrams. Each diagram represents the length of a street where the game is played.

Represent each situation on a diagram. Be prepared to explain your reasoning.

Children in Ghana playing a game of Pilolo.

A student walks of the length of the street and hides a rock.
A student walks of the length of the street and hides a penny.
A student walks of the length of the street and hides a stick.
A student walks of the length of the street and hides a penny.
This diagram represents the location of a hidden stick.
About what fraction of the length of the street did the student walk to hide it? Be prepared to explain your reasoning.

Student Response

to access Student Response.

Advancing Student Thinking

If students partition into sixths or eighths by creating 6 or 8 parts, respectively, but the parts aren’t equal, consider asking:

“How did you partition the strip into sixths? Into eighths?”
“How could you use thirds to partition into sixths? Or use fourths to partition into eighths?”

Activity Synthesis

Display posters around the room.
“As you look at each poster, discuss how each situation was shown on the diagram.” (The diagram was partitioned into 6 equal parts. 5 of the equal parts were shaded.)
2–3 minutes: partner discussion
Share responses.
“What part of each diagram would represent where the object was hidden?” (The end of the shaded part.)

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Lesson 4

Build Fractions from Unit Fractions

Warm-up

Instructional Routines

Materials

Activity Narrative

Launch

Activity

Student Response

Advancing Student Thinking

Activity Synthesis

Activity 1

Standards Alignment

Building On

Addressing

3.NF.A.1

Instructional Routines

Materials

To Copy (from Blackline Masters)

Activity Narrative

Launch

Activity

Activity Synthesis

Activity 2

Standards Alignment

Building On

Addressing

3.NF.A.1

Instructional Routines

Materials

To Gather

Activity Narrative

Launch

Activity

Student Response

Advancing Student Thinking

Activity Synthesis

Lesson Synthesis

Student Section Summary

Standards Alignment

Building On

Addressing

3.OA.B.5

3.OA.C.7

Building Toward

Student Response

Advancing Student Thinking

Building Toward

Building Toward

3.NF.A.2