CCSS.Math.Content.HSS-CP.A.4
The Standard
Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities.
Common Core State Standards for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students organize paired categorical data in a two-way frequency table. They use table counts to find conditional probabilities and decide whether two events appear independent.
What Mastery Looks Like
- Students build a correctly labeled table with row, column, and grand totals. They choose the right denominator for a conditional probability. They compare conditional and overall proportions to support an independence claim.
Common Misconceptions
- Students often divide by the grand total instead of the total for the given condition. They may reverse probabilities such as P(A given B) and P(B given A). Some assume similar counts prove independence without comparing proportions.
How to Assess It
- Give this exit ticket: Of 40 bus riders, 18 play a sport; of 60 non-bus riders, 27 play a sport. Find P(sport given bus) and decide whether the events appear independent.
Lesson moves
Ways to Teach It
Students place anonymous sticky notes on a class grid showing two traits, then calculate row totals, column totals, and conditional probabilities.
Ask students to explain why the denominator changes when finding P(A) versus P(A given B), using one table cell as evidence.
Give pairs cards showing tables, probability questions, ratios, and independence claims, then have them match each complete set.
Use cafeteria survey data to compare drink choice by grade level and predict preferences across the school.
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Printable HSS-CP.A.4 Worksheet
A ready-to-print activity worksheet aligned to CCSS.Math.Content.HSS-CP.A.4, with an answer key for the teacher on its own page. No account needed.
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Where This Standard Sits
Before This Standard
If students are struggling here, check these first.
- CCSS.Math.Content.HSS-CP.A.1
Two-way tables require viewing category combinations as events in a sample space, including intersections and complements.
- CCSS.Math.Content.8.SP.A.4
Students extend two-way table counts and relative frequencies to conditional probability and independence judgments.
- CCSS.Math.Content.HSS-CP.A.3
Students use the formula and independence test from A.3 to interpret table entries as conditional probabilities and independence evidence.
What This Unlocks
Mastery here sets students up for these next.
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Related Standards
- CCSS.Math.Content.HSS-CP.A
Understand independence and conditional probability and use them to interpret data
- CCSS.Math.Content.8.SP.A.1
Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as cl...
- CCSS.Math.Content.HSS-ID.B.5
Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal,...
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