CCSS.Math.Content.HSF-IF.B.4
The standard
For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship.
Common Core State Standards for Mathematics
What this standard means
Students need to read a graph or table as a story about two quantities. They should identify intercepts, increasing and decreasing intervals, where outputs are positive or negative, maximums, minimums, symmetry, end behavior, and repeated patterns when they appear.
Mastery means students can explain what each feature means in context, not just name it. They can also sketch a reasonable graph from a verbal description. Students often mix up x-intercepts and y-intercepts, describe intervals with y-values instead of x-values, and give answers without units or context.
Ways to teach it
- Hands-on activity: Give pairs a motion sensor graph or printed temperature graph and have them label intercepts, peaks, valleys, and increasing intervals.
- Discussion prompt: Ask, “What does the highest point mean in this situation, and why is it not just the biggest y-value?”
- Quick assessment: Show one graph with labeled axes and ask students to write three contextual statements about its key features.
- Real-world connection: Use a phone battery graph from morning to night and have students sketch when it charges, drains, and reaches low points.
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