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Activity 1

Standards Alignment

Building On

Addressing

Building Toward

Instructional Routines

None

Materials

To Gather

Markers Paper Paper clips Tape (painter's or masking)

Activity Narrative

The purpose of this activity is for students to use their understanding of benchmark fractions and equivalent fractions to play a game that involves fractions on the number line. They toss paper clips on a game board that is a number line, and then write fractions to label the locations where the paper clips land. In previous lessons, students labeled fractions on a number line with premade tick marks. This activity gives students an opportunity to label them independently. Before playing the game, students prepare the game board and materials.

Representation: Access for Perception. Synthesis: Begin by demonstrating one round of the paper clip tossing game in order to support understanding of the context.
Supports accessibility for: Memory, Social-Emotional Functioning

Launch

Groups of 2
Give each group strips of paper, markers, paper clips, and tape.
“Work with your group to make the game board. Fold your paper strip in half and then in half again. Carefully tape it down to your workspace (desk or floor can work) and label the benchmark fractions.”
5 minutes: partner work time

Activity

“Work with your group to play the paper clip tossing game. To play the game, you will decide on a target fraction, toss some paper clips, and use fractions to label where they land. As you are playing, determine the best spot to stand and how to toss the paper clips.”
Monitor for students who:
- Use benchmark fraction strategies and numerical strategies for finding equivalent fractions to label the fractions.
- Consider what to do with paper clips that do not land on the strip.
5 minutes: partner work time

Let’s prepare a gameboard and figure out how to toss paper clips and record the results.

Make your gameboard:
- Fold your paper strip in half, then in half again.
- Tape the paper strip to your workspace and label the benchmark fractions 0, , 1, , and 2.
Play the game:
- Decide on which benchmark fraction you'll try to land. This is the target fraction.
- Take turns tossing the paper clips.
- Label the fraction where each paper clip lands.
- If you land on the target fraction, name an equivalent fraction to get a point.
- The player with the most points at the end of the game wins.

Be prepared to share your strategies for:

tossing the paper clips
finding out the fraction for each clip’s location on the gameboard
naming equivalent fractions for the target fractions

Activity Synthesis

Invite previously selected students to share their strategies for tossing and labeling the locations of the paper clips.
“Where was the best spot to stand? What did you think about when you tossed?”
“Take a look at all the fractions you recorded on your number line. What do you notice?” (They are ordered from least to greatest. We used lots of sixths and eighths. There are lots of different denominators.)
“What did you do if a paper clip landed in a location where it was difficult to name the fraction?” (I found the closest fraction that was easy to find and used that to help. I used equivalent fractions.)

Activity 2

Standards Alignment

Building On

Addressing

Building Toward

Instructional Routines

None

Materials

To Gather

Markers Paper Paper clips Tape (painter's or masking)

Activity Narrative

The purpose of this activity is for students to use what they have learned about comparing fractions to design a game. Students are given some constraints around what the game must involve, but have to come up with their own rules and the objective for winning the game. When students consider assumptions about information not given in a situation, they model with mathematics (MP4).

Launch

Groups of 2
Give each group strips of paper, markers, paper clips, and tape.
“Think about the game we played in the last activity. What were some good things about the game? What was something you would change about the game?” (The game had a clear way to win. I would change it so there were clear rules about where you are supposed to stand when you toss the paper clips.)
1 minute: quiet think time
Share responses.
“In this activity, your group is going to use your materials to design a game. You can use the strip from the first game or the new strip your group received. What are some things your group needs to think about when you’re making up the rules for the game?” (How someone wins the game. How you get points in the game. Rules for the game.)
Share and record responses for all to see.

Activity

10 minutes: partner work time
Monitor for groups that:
- Use one of the listed constraints.
- Come up with clear rules for their game.
- Come up with a clear way to win their game.

Invent your own game.

Make a list with the rules of your game. Your game should include at least one of the following:
- comparing fractions
- finding equivalent fractions
- using common denominators
- using benchmark fractions like or
Play your game, paying close attention to the rules.
Revise and clarify your game rules, if necessary.

Student Response

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Advancing Student Thinking

Activity Synthesis

Invite previously selected groups to share their game.
Consider asking:
- “How did you come up with the rules you chose?”
- “What parts of the rules make the game fair for both players?”
- “How do you win the game?”