CCSS.Math.Content.7.SP.C.8b
The Standard
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.
Common Core State Standards for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students show every possible result of a compound chance process using an organized list, table, or tree diagram. They select the outcomes that match an event stated in everyday words.
What Mastery Looks Like
- Students create a complete, organized list, table, or tree diagram without missing or repeating outcomes. They identify exactly which outcomes satisfy an event described in words.
Common Misconceptions
- Students often leave out outcomes, repeat outcomes, or treat order as irrelevant when it matters. They may also confuse one outcome, such as 6 then 6, with the full event being described.
How to Assess It
- Give this exit ticket: “Flip a coin and roll a four-sided die. Show the sample space, then circle all outcomes with tails or an even number.”
Lesson moves
Ways to Teach It
Give pairs two coins and a numbered spinner to test outcomes, then have them build a table matching their results.
Ask students to explain in writing why “a sum greater than 8” includes several outcomes when rolling two number cubes.
Play Sample Space Match by having students pair event cards with organized lists, tables, or tree diagrams that show the correct outcomes.
Use a lunch menu with three sandwiches and two drinks, then list every meal and identify meals containing juice.
Free download
Printable 7.SP.C.8b Worksheet
A ready-to-print activity worksheet aligned to CCSS.Math.Content.7.SP.C.8b, with an answer key for the teacher on its own page. No account needed.
PDF, US Letter, prints cleanly in black and white.
Download the worksheetLearning progression
Where This Standard Sits
Before This Standard
If students are struggling here, check these first.
- CCSS.Math.Content.7.SP.C.7
Understanding probability models, events, and observed outcomes supports listing compound-event sample spaces and selecting outcomes that match an event.
- CCSS.Math.Content.7.SP.C.5
Interpreting compound event outcomes needs the idea that events have likelihoods between 0 and 1, but listing sample spaces can begin without quantifying them.
What This Unlocks
Mastery here sets students up for these next.
- CCSS.Math.Content.7.SP.C.8c
Simulation requires defining possible outcomes and which outcomes count as the compound event before tallying frequencies.
- CCSS.Math.Content.HSS-CP.A.1
Listing sample spaces and matching everyday events to outcomes supports describing events as subsets, unions, intersections, and complements.
- CCSS.Math.Content.HSS-CP.B.9
Listing outcomes and matching events to them prepares students to count outcomes efficiently with permutations and combinations.
Keep exploring
Related Standards
- CCSS.Math.Content.7.SP.C.8a
Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event oc...
- CCSS.Math.Content.HSS-MD.A.1
(+) Define a random variable for a quantity of interest by assigning a numerical value to each event in a sample space; graph the corresponding probability dist...
- CCSS.Math.Content.7.SP.C.8
Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.
Turn this exact standard into a lesson
Grade, subject, topic, and the complete standard are prefilled. Create one free, no account needed.