Free Printable WorksheetMathGrade 8Math Curriculum8.SP.A.3

8.179 Evaluating the Reasonableness of Predictions and Extrapolation Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Grade 8 Math worksheet provides structured practice on 8.179 Evaluating the Reasonableness of Predictions and Extrapolation. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

8.179 Evaluating the Reasonableness of Predictions and Extrapolation - Which statement correctly judges whether the prediction is reasonable and whether it is interpolation or extrapolation? (CCSS 8.SP.A.3; CA 8.SP.A.3; MA 8.SP.A.3)

Whether you are an educator preparing classroom handouts, a tutor reinforcing weekly topics, or a parent supporting homeschool learning, this printable resource gives students the deliberate practice required to achieve subject fluency and master state standards.

Grade

Grade 8

Subject

Math

Domain

Math Curriculum

Formats

PDF & DOCX

Sample Practice Problems

Preview the types of problems and questions covered in this worksheet

Below are sample questions representative of the exercises included on this worksheet and related 8.179 Evaluating the Reasonableness of Predictions and Extrapolation skill assessments:

Problem 1Difficulty: Hard

A coach recorded free-throw practice rounds and free-throw percent. The model y = 6.7x + 19.9 came from data with number of practice rounds values from 1 to 7 rounds. It predicts about 73.5% when number of practice rounds is 8 rounds. Ava says this is interpolation because the predicted y-value seems similar to the data values. Which response is best? Remember that the data points fit the line closely in the observed range.

AAva should check the x-value first. Because 8 is just outside the observed x-range, the prediction is extrapolation, but it can still be reasonable here because the value is nearby and the trend is steady.

BAva is correct because interpolation and extrapolation depend on whether the predicted y-value is near the other y-values.

CThe prediction should be classified only by the predicted y-value, not by whether 8 is in the x-range.

DAva is correct because any value that comes from a line of best fit is automatically reasonable.

Solution & Explanation:A prediction is extrapolation when its x-value is outside the observed range. Here, 8 is just beyond the range, so it is extrapolation. Because the value is nearby and the pattern is strong, the estimate of 73.5% can still be judged reasonable.

Problem 2Difficulty: Medium

A class tracked cans collected and total dollars donated by a recycling sponsor. A line of best fit is y = 21.9x + 14.1. The original data used number of cans collected values from 4 to 8 cans. Jasper uses the model when number of cans collected is 9 cans. Which choice correctly analyzes the use of the model?

AThe model gives about $214.6, so the prediction is a reasonable interpolation.

BThe model gives about $214.2, so the prediction is interpolation but not reasonable.

CThe model gives about $211.2, and since 9 is just outside 4 to 8 cans, the prediction is a reasonable extrapolation.

DThe model gives about $207.1, so the prediction is a reasonable extrapolation.

Solution & Explanation:Substituting 9 into y = 21.9x + 14.1 gives about $211.2. Since 9 is just outside the x-range used for the model, the prediction is extrapolation, but it is still reasonable for a nearby value.

Problem 3Difficulty: Hard

A cooler recorded draining time and liters left in a 30-liter cooler. The model y = -0.8x + 21.9 was created from draining time values from 3 to 10 minutes. Sana says a prediction at 10.5 minutes should be judged by checking whether the x-value is inside or outside the data range. Ivy says the y-value alone decides whether it is interpolation or extrapolation. Which option is correct?

ASana is correct because 10.5 is just outside the observed x-range, so the prediction is extrapolation, and it can still be reasonable for a nearby value.

BBoth students are correct because every prediction from a linear model is reasonable.

CIvy is correct because interpolation and extrapolation depend only on the predicted y-value.

DNeither student is correct because you never use the x-range to judge predictions.

Solution & Explanation:A prediction is extrapolation when its x-value is outside the observed range. Here, 10.5 is just beyond the range, so it is extrapolation. Because the value is nearby and the pattern is strong, the estimate of 13.5 liters can still be judged reasonable.

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QWhat grade level and standards does this worksheet align with?

This worksheet is designed specifically for Grade 8 Math students. It aligns with educational standard 8.SP.A.3 (Primary standard selected for prompt fields: CCSS 8.SP.A.3. Skill statement: Which statement correctly judges whether the prediction is reasonable and whether it is interpolation or extrapolation? Associated standards listed with this skill: CCSS 8.SP.A.3; CA 8.SP.A.3; MA 8.SP.A.3. Use this embedded wording as the best available supporting standard description for this workflow.).