Lesson Plan

The Numbers We Know

Grade Level: 6-12

Length: 1-15 minutes

DE Domain: TP

Students use a number line to capture the probabilities that feel most natural to use in everyday communications.

For most students (and adults!) using numbers rather than words to convey likelihoods, probabilities, or degrees of confidence is not intuitive. To bring more numeracy and probabilistic thinking to classroom conversations, it is helpful for students to shine a spotlight on the numerical values that may already feel intuitive to them. This short activity guides students into discovering and naming those familiar probabilistic values so that they can begin referencing them more regularly.

TP.2 – Strategically apply appropriate numeracy and probability techniques

Lesson:

Display a blank number line for the whole group to see.

Ask students a series of questions to help them identify and fill in the most common values that likely feel somewhat intuitive to them (0%, 25%, 50%, 75%, and 100%).

Use your own prompts or consider using or modifying the suggested ones below:

Suggested Prompts and Language:

  • How likely is it for a purple furry fish to come walking through our classroom door? There is a 0% likelihood this will happen. [add 0 to the number line]. We can say with total certainty this will not happen.
  • How likely is it that you will see someone you know before the end of the day? Since you are at school, there is a 100% likelihood this will happen. [add 100 to the number line]. We can say with total certainty that this will happen.
  • If I flip this coin, how likely is it that it will land on tails? In a fair coin flip, there is a 50% likelihood this will happen. [add 50 to the number line]. One way to think about this is if there are two worlds, in one world the coin will land on tails and in the other it won’t.
  • If I spin this spinner (available here), how likely is it that the arrow will land on the white space? There is a 1 in 4 chance, which means 25%. [add 25 to the number line]. One way to think about this is if there are four worlds, in one world the arrow will land on the white space and in the others it won’t.
  • If I spin this spinner, how likely is it that the arrow will land on a black space? There is a 3 in 4 chance, which means 75%. [add 75 to the number line]. One way to think about this is if there are four worlds, in three worlds the arrow will land on a blank space and in the other it won’t.


Keep the number line posted, so throughout your lesson or over time, you can refer students to it when asking them how confident they are in their answers, beliefs, or predictions.

Differentiation:

Depending on students’ readiness, consider starting with just 0, 50, and 100, or starting with more than 5 numbers.

Allow for hands-on experimentation with the spinners and coin toss so students can begin to track if over time, their spins and tosses approach 25% and 75% (spinners) or 50% (coin toss).

Optional extensions:

As students begin to use the numerical values more regularly in the classroom, revisit the number line to see if there are other numbers they are ready to add. If 75% feels intuitive, for example, after a while, perhaps other numbers (80%, 90%) maye begin to fee useful.

Consider having each student maintain their own number line so that they can individualize their own additions over time.

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