Grade 6 Mathematics · Unit 2: Understanding the World Around Us Through StatisticsStandard 6.NOS.3

Lesson 2.122.4–2.12 Catch-Up

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target I can show I am caught up on Lessons 2.4–2.12 by using each lesson's big idea in mixed practice.

Start hereWords for this lesson

Read each word before you begin. Say it out loud.

WordWhat it meansExample
Display Data with Box PlotsSpanish: Representar datos con diagramas de caja Show a data set's five-number summary in a box-and-whisker display. minimum | Q1 [ median ] Q3 | maximum
Box PlotSpanish: Diagrama de caja A graph that shows how data is spread using five key numbers. A box from Q1 to Q3 with a line at the median, and whiskers from min to max
MedianSpanish: Mediana The middle number when you put them in order. Data: 10, 15, 20, 25, 30 → median is 20 (the 3rd value)
QuartileSpanish: Cuartil Numbers that split the data into four equal parts. Data: 2, 4, 6, 8, 10, 12, 14 → Q1 = 4 (median of lower half), Q3 = 12 (median of upper half)
Interquartile RangeSpanish: Rango intercuartílico The spread of the middle half of the data (Q3 − Q1). If Q1 = 12 and Q3 = 20, then IQR = 20 − 12 = 8 — the middle 50% spans 8 units
Data distributionSpanish: Distribución de datos How the data looks: where it sits and how spread out it is. A box plot where the median is centered in the box shows symmetric distribution

How it worksWorked example

These numbers are not on your problems. The steps are. Follow them with your own numbers.

Lesson 2.4 — Represent and Describe Data in a Box Plot: The box always holds the middle 50% of the data, and the line inside the box is the median.

  1. Lesson 2.5 — Describe Data by Range and Interquartile Range: Range = greatest − least, and it covers every value. Interquartile range = Q3 − Q1, and it covers only the middle half, so one faraway value cannot stretch it.
  2. Lesson 2.6 — Divide Multi-Digit Numbers Using an Algorithm: Repeat the cycle Divide → Multiply → Subtract → Bring Down until no digits are left to bring down; what is left at the end is the remainder.
  3. Lesson 2.7 — Divide Decimals Using an Algorithm: Slide the decimal point the same number of places to the right in BOTH the divisor and the dividend. Write the answer's decimal point in the column directly above the dividend's point. Then repeat Divide → Multiply → Subtract → Bring Down.
  4. Lesson 2.8 — Describe Data Using the Mean: Mean = total of all the values ÷ how many values there are.
  5. Lesson 2.9 — Describe Data by Mean Absolute Deviation: MAD = the average of how far each number is from the mean (always a positive distance).
  6. Lesson 2.10 — Choose Appropriate Measures: Use the mean for data with no outliers; use the median when an outlier or a skewed shape would pull the mean away from typical.
  7. Lesson 2.11 — Add and Subtract Decimals: Line up the decimal points, add zeros so each number has the same number of decimal places, then add or subtract one column at a time.
  8. Lesson 2.12 — Multiply Decimals: Multiply like whole numbers, then the product has the SAME total of decimal places as both factors combined.

Now you trySame steps, your turn

The steps are the same as the worked example. The numbers are yours. Do the work.

From 2.4: New, smaller data set: 2, 5, 5, 8, 11. First, what is the median (the middle value)?

Answer:

Say it and write itSentence starters

Finish each sentence out loud with a partner. Then use them in your writing.

  • I estimated x by rounding to x = , which told me the product is than 20.

Word bank Display Data with Box PlotsBox PlotMedianQuartileInterquartile RangeData distributionestimaterounddecimal placesproductmultiplyreasonable

Watch outA common mistake

A common mistake in Multiply Decimals is counting decimal places from only one factor instead of adding the decimal places from BOTH factors. For example, in 0.4 × 0.06, a student multiplies 4 × 6 = 24, then places the decimal point using just one factor's place count (1 place), writing 0.24 instead of the correct answer: 0.4 has 1 decimal place and 0.06 has 2 decimal places, for a total of 3, so 24 becomes 0.024. Before you submit, count the decimal places in EACH factor separately and add them together — that total is how many decimal places belong in your final answer.

Grade 6 Mathematics · Unit 2: Understanding the World Around Us Through StatisticsStandard 6.NOS.3

Lesson 2.122.4–2.12 Catch-Up

Catch-UpSkill bridge

Mastery check☐ Exceeds☐ Meets target☐ Needs practice
Name Date Period

Learning target I can show I am caught up on Lessons 2.4–2.12 by using each lesson's big idea in mixed practice.

Part 1Understand the ideamodels and meaning
  1. 1Circle the letter of the best answer. Show how you know.

    (Lesson 2.4) On a box plot, what does the line inside the box represent?

    1. AThe mean
    2. BThe median
    3. CThe mode
    4. DThe range

    Hint Picture a box plot: a box with whiskers, and a line cutting through the box. That line marks the CENTER of the data.

    Show your work
Part 2Apply itreal-world problems
  1. 2Circle the letter of the best answer. Show how you know.

    (Lesson 2.4) A box plot shows: Min = 10, Q1 = 15, Median = 20, Q3 = 28, Max = 35. What is the interquartile range (IQR)?

    1. A10
    2. B13
    3. C20
    4. D25

    Hint You're given five numbers, but IQR only uses two of them: Q1 and Q3. Ignore the min, median, and max.

    Put the data in order
    Work
    1. 1OrderSmallest to largest.
    2. 2CountHow many values?
    3. 3LocateMiddle, or add and divide.
    4. 4AnswerSay which measure it is.
  2. 3Circle the letter of the best answer. Show how you know.

    (Lesson 2.5) A data set runs from a least value of 12 to a greatest value of 30. What is the range?

    1. A12
    2. B18
    3. C21
    4. D30

    Hint Range asks how far it is from one end of the data to the other.

    Put the data in order
    Work
    1. 1OrderSmallest to largest.
    2. 2CountHow many values?
    3. 3LocateMiddle, or add and divide.
    4. 4AnswerSay which measure it is.
  3. 4Circle the letter of the best answer. Show how you know.

    (Lesson 2.5) On a box plot, Q1 = 20 and Q3 = 36. What is the interquartile range?

    1. A16
    2. B28
    3. C36
    4. D56

    Hint The IQR is the width of the box on a box plot.

    Put the data in order
    Work
    1. 1OrderSmallest to largest.
    2. 2CountHow many values?
    3. 3LocateMiddle, or add and divide.
    4. 4AnswerSay which measure it is.
  4. 5Circle the letter of the best answer. Show how you know.

    (Lesson 2.6) What is 936 ÷ 12?

    1. A68
    2. B76
    3. C78
    4. D87

    Hint Estimate first: 12 × 70 = 840 and 12 × 80 = 960, so the quotient must land between 70 and 80.

    12936
    1. 1DivideHow many fit?
    2. 2MultiplyMultiply back.
    3. 3SubtractWhat is left?
    4. 4Bring downNext digit.

Explain your thinkingHow did estimating by rounding help you sort the products? How do you decide where to place the decimal in the exact product?

Sentence starter I estimated ___ x ___ by rounding to ___ x ___ = ___, which told me the product is ___ than 20.

How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help