Keeping Track of All Possible Outcomes

10 min

Narrative

The purpose of this Warm-up is to elicit methods students are already using to organize their understanding of different outcomes. In this lesson, students are asked to use different structures to think about the different combinations that are possible from selecting one item from each of three categories.

Monitor for groups who use different strategies to organize their thinking about the different combinations, such as:

  • List several options and count them.
  • Group several options together and multiply.
  • Draw links between some of the options.
This activity uses the Compare and Connect math language routine to advance representing and conversing as students use mathematically precise language in discussion.

Launch

Arrange students in groups of 2. Tell students they should organize their work so it can be understood by others. Give students 1 minute of quiet think time, 3 minutes for partner discussion, and follow up with a whole-class discussion. 

Ask students if they have looked at the jewelry part of a store. Then ask what options are available for different bracelets.

Tell students that many Native American tribes, such as Navajo (NA-vah-hoh) and Hopi (HOH-pee), craft jewelry such as bracelets for trade, status, and fashion. The bracelets are often made with different types of featured stone, have designs, and come in different sizes. In their own language, the Navajo people call themselves Diné (di-NEH).

Select students who used each strategy described in the Activity Narrative to share later. Aim to elicit both key mathematical ideas and a variety of student voices, especially from students who haven’t shared recently.

Student Task

Bracelets made by a tribe of Native American jewelers in Arizona and New Mexico are available with several different options. How many different bracelets are possible if each one includes 1 stone, 1 design, and 1 size?

Silver bracelet with large turquoise stone in the center

stones

  • turquoise
  • pink coral
  • lapis lazuli

designs

  • animal
  • floral

sizes

  • small
  • medium
  • large

Sample Response

There are 18 different bracelets (3⋅2⋅3=183 \boldcdot 2 \boldcdot 3 = 18). 

Synthesis

The goal of this discussion is for students to share their methods for organizing their thoughts about the different bracelets that are possible.

Display 2–3 approaches/representations from previously selected students for all to see. If time allows, invite students to briefly describe their approach, then use Compare and Connect to help students compare, contrast, and connect the different approaches. Here are some questions for discussion:

  • “How did you know that you counted all of the different possible bracelets?” (We began with the turquoise option and wrote out all of the bracelets that have turquoise and animal designs, then all the bracelets that have turquoise and floral designs. We knew that there would be the same number of bracelets that had pink coral or lapis lazuli instead of turquoise, so we multiplied that by 3.)
  • “How did you know you didn’t repeat any bracelets?” (By carefully keeping the different options separate and going through them systematically, we made sure we didn’t repeat.)
Standards
Addressing
  • 7.SP.8.b·Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (e.g., "rolling double sixes"), identify the outcomes in the sample space which compose the event.
  • 7.SP.C.8.b·Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (e.g., “rolling double sixes”), identify the outcomes in the sample space which compose the event.

15 min

10 min