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Unit 10 · Final Applications and ReviewLesson

Day 139Connecting Models and Explanations

LearnClassworkAnswer keyPDF packet ↗
Standards 6.G.A.16.G.A.26.G.A.46.SP.A.26.SP.A.36.SP.B.5a6.SP.B.5b6.SP.B.5c6.SP.B.46.SP.B.5d
LEARNING TARGET

I can select models and explain geometric and statistical results.

01 · LEARN

Build the idea

Read the requested quantity first and identify the relevant model. Two matching triangles form a parallelogram, so A = (base × perpendicular height)/2. A slanted side is not necessarily the height. Label area in square units. Explain why the units and the final value fit the situation.

WORKED EXAMPLE 1

A rectangular prism has edges 2, 3, and 4 cm. Sketch it and find its volume.

24 cm³

B = 2 × 3 = 6 cm²; V = B × 4 = 24 cm³.

WORKED EXAMPLE 2

Reading times in minutes are 3, 4, 4, 5, 6, 15. Find the five-number summary and draw a labeled box plot. State the IQR.

(3, 4, 9/2, 6, 15); IQR 2 min

Box runs from 4 to 6, median line at 9/2, whiskers to 3 and 15.

02 · PRACTICE

Your turn

Work in order. Start with the foundations, then build toward explanation and application.

  1. Sketch a triangle with base 16 cm and perpendicular height 5 cm. Find its area.

  2. A rectangular prism has edges 5, 2 1/2, and 2 cm. Sketch it and find its volume.

  3. A 5 cm by 4 cm base and 5 cm height form a closed box. Draw its net and find the material area. Ignore tabs and overlap.

  4. Reading times in minutes are 6, 9, 9, 12, 12, 15. Describe a typical value, range, shape, and any striking value.

  5. Reading times in minutes are 6, 9, 9, 12, 12, 15. Report n, units, and mean.

  6. Reading times in minutes are 8, 13, 13, 18, 18, 23. Find Q1, Q3, IQR, and range.

  7. Reading times in minutes are 6, 7, 7, 8, 9, 18. Calculate the mean and MAD. Show all absolute deviations. Interpret MAD in a sentence.

  8. Reading times in minutes are 2, 3, 3, 4, 5, 14. Find the five-number summary and draw a labeled box plot. State the IQR.

  9. Reading times (min): Group A [6, 7, 7, 8, 9, 18], Group B [8, 9, 9, 10, 11, 20]. Compare median and IQR. Which group reads longer typically? Which is more consistent?

  10. Reading times in minutes are 2, 3, 3, 4, 5, 14. Write a summary with count, attribute, units, center, variability, shape, and a justified choice of measures.

03 · CHECK

Answers and reasoning

Reveal the teacher answer key
  1. 40 cm²

    A = bh/2 = 16 × 5 ÷ 2 = 40. Two such triangles make a parallelogram.

  2. 25 cm³

    B = 5 × 5/2 = 25/2 cm²; V = B × 2 = 25 cm³.

  3. 130 cm²

    Closed surface area = 2(20+25+20) = 130.

  4. Center near 21/2 min; range 9 min; roughly symmetric; no isolated extreme

    The values balance around the middle. Range = 15 - 6.

  5. n = 6; minutes; mean 21/2 min

    Sum = 63; mean = 63 ÷ 6 = 21/2.

  6. Q1 13, Q3 18; IQR 5 min; range 15 min

    Lower half [8, 13, 13] has median 13; upper half [18, 18, 23] has median 18. Subtract Q1 from Q3.

  7. Mean 55/6 min; MAD 53/18 min; a typical distance from the mean is 53/18 min

    Distances: 19/6, 13/6, 13/6, 7/6, 1/6, 53/6; sum 53/3; divide by 6 = 53/18.

  8. (2, 3, 7/2, 5, 14); IQR 2 min

    Box runs from 3 to 5, median line at 7/2, whiskers to 2 and 14.

  9. A median 15/2, B median 19/2 min; both IQR 2 min. B is typically 2 min higher; equal middle-half variability.

    Adding 2 shifts all values and the median by 2, but does not change Q3 - Q1.

  10. 6 observations of reading time in minutes. Median 7/2 min, IQR 2 min; right-skewed with a high value 14 min, so median/IQR resist that value.

    Calculate the center and spread before interpreting them in context. Other accurate, justified summaries are acceptable.

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