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.

Why This Matters Missed a lesson — or just want a refresher? This catch-up station reviews Lessons 2.4–2.12: 2.4 Represent and Describe Data in a Box Plot, 2.5 Describe Data by Range and Interquartile Range, 2.6 Divide Multi-Digit Numbers Using an Algorithm, 2.7 Divide Decimals Using an Algorithm, 2.8 Describe Data Using the Mean, 2.9 Describe Data by Mean Absolute Deviation, 2.10 Choose Appropriate Measures, 2.11 Add and Subtract Decimals, 2.12 Multiply Decimals. Work one example from each lesson, then prove you're caught up in the mixed practice.

Start hereWords for this lesson

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

WordWhat it meansExample
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
VariabilitySpanish: Variabilidad How spread out the numbers are. Small IQR = low variability in the middle 50%. Large IQR = high variability

How it worksWorked example

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

Find the five numbers for a box plot of this data: 2, 5, 5, 8, 11.

  1. Find the median, the middle value: 2, 5, 5, 8, 11 → 5
  2. Find Q1, the middle of the lower half: (2 + 5) ÷ 2 = 3.5
  3. Find Q3, the middle of the upper half: (8 + 11) ÷ 2 = 9.5
  4. Find the least and greatest values: 2 and 11
  5. Least 2, Q1 3.5, median 5, Q3 9.5, greatest 11.
  6. Class A's box plot shows: least 62, Q1 74, median 81, Q3 87, greatest 90. Find the range and the IQR.
  7. Subtract the least from the greatest: 90 − 62 = 28
  8. Subtract Q1 from Q3: 87 − 74 = 13
  9. The range is 28 and the IQR is 13.
  10. Find 384 ÷ 8.
  11. Divide 38 by 8. Multiply and subtract: 38 ÷ 8 → 4; 4 × 8 = 32; 38 − 32 = 6
  12. Bring down the 4. Repeat with 64: 64 ÷ 8 → 8; 8 × 8 = 64; 64 − 64 = 0
  13. Check by multiplying: 8 × 48 = 384
  14. 384 ÷ 8 = 48
  15. Find 8.4 ÷ 2.1.
  16. Move both points 1 place right: 2.1 → 21; 8.4 → 84
  17. Divide the whole numbers: 84 ÷ 21 = 4
  18. Check by multiplying: 2.1 × 4 = 8.4
  19. 8.4 ÷ 2.1 = 4
  20. A dog walker earns $9, $11, $16 and $12 in 4 days. Find the mean amount per day.
  21. Add all the values: 9 + 11 + 16 + 12 = 48
  22. Divide by the number of values: 48 ÷ 4 = 12
  23. The mean is $12 per day.
  24. Find the MAD of this data set: 6, 8, 10, 12.
  25. Find the mean: 36 ÷ 4 = 9
  26. Find each distance from the mean: 3, 1, 1, 3
  27. Find the mean of the distances: 3 + 1 + 1 + 3 = 8; 8 ÷ 4 = 2
  28. The MAD is 2.
  29. Which measure better shows a typical value for this data set: 4, 5, 6, 7, 40?
  30. Look for an outlier: 40
  31. Find the mean and the median: 62 ÷ 5 = 12.4; median → 6
  32. Choose the one close to most values: 6
  33. The median, 6, better shows a typical value.
  34. Add 12.45 and 7.8.
  35. Write a zero so both numbers have hundredths: 7.8 = 7.80
  36. Line up the decimal points and add: 12.45 + 7.80 = 20.25
  37. The sum is 20.25.
  38. Multiply 0.4 × 0.7.
  39. Multiply like whole numbers: 4 × 7 = 28
  40. Add the decimal places in both factors: 1 + 1 = 2
  41. Put the point 2 places from the right: 28 → 0.28
  42. 0.4 × 0.7 = 0.28

Now you trySame steps, your turn

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

Here are 7 values in order: 1, 3, 4, 7, 9, 10, 12. What is Q3?

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 Box PlotMedianQuartileInterquartile RangeData distributionVariabilityestimaterounddecimal placesproductmultiplyreasonable

Watch out!A 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

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.

Why This Matters Missed a lesson — or just want a refresher? This catch-up station reviews Lessons 2.4–2.12: 2.4 Represent and Describe Data in a Box Plot, 2.5 Describe Data by Range and Interquartile Range, 2.6 Divide Multi-Digit Numbers Using an Algorithm, 2.7 Divide Decimals Using an Algorithm, 2.8 Describe Data Using the Mean, 2.9 Describe Data by Mean Absolute Deviation, 2.10 Choose Appropriate Measures, 2.11 Add and Subtract Decimals, 2.12 Multiply Decimals. Work one example from each lesson, then prove you're caught up in the mixed practice.

Part 1Practice the skillshow every step
  1. 1Complete each step, then write the final answer.

    What is 945 ÷ 7?

    Show your work

    Hint Start with 9. Then repeat: divide, multiply, subtract, bring down.

    Final answer:
  2. 2Complete each step, then write the final answer.

    What is 672 ÷ 4?

    Show your work

    Hint Start with 6. Bring down one digit at a time.

    Final answer:
  3. 3Complete each step, then write the final answer.

    Find 4.2 ÷ 0.6.

    Show your work

    Hint Move both points 1 place right. Then find 42 ÷ 6.

    Final answer:
  4. 4Complete each step, then write the final answer.

    Find 12.5 ÷ 2.5.

    Show your work

    Hint Move both points 1 place right. Then find 125 ÷ 25.

    Final answer:
  5. 5Complete each step, then write the final answer.

    Find 3.2 + 4.65.

    Show your work

    Hint Write 3.2 as 3.20. Line up the decimal points. Then add.

    Final answer:
  6. 6Complete each step, then write the final answer.

    Find 0.5 × 0.7.

    Show your work

    Hint 5 × 7 = 35. The factors have 2 decimal places in all.

    Final answer:
  7. 7Complete each step, then write the final answer.

    Find 1.3 × 2.1.

    Show your work

    Hint 13 × 21 = 273. Each factor has 1 decimal place.

    Final answer:
Part 2Apply itreal-world problems
  1. 8Complete each step, then write the final answer.

    Here are 5 values in order: 1, 4, 6, 9, 10. What is Q1?

    Show your work

    Hint The median is 6. The lower half is 1 and 4.

    Final answer:
  2. 9Complete each step, then write the final answer.

    Here are 7 values in order: 2, 4, 5, 8, 11, 12, 15. What is Q3?

    Show your work

    Hint The median is the 4th value. Q3 is the middle of the 3 values after it.

    Final answer:
  3. 10Complete each step, then write the final answer.

    A box plot shows: least 3, Q1 7, median 10, Q3 14, greatest 18. What is the range?

    Show your work

    Hint The range uses the least and greatest values.

    Final answer:
  4. 11Complete each step, then write the final answer.

    A box plot shows: least 20, Q1 24, median 29, Q3 33, greatest 41. What is the IQR?

    Show your work

    Hint The IQR uses Q1 and Q3.

    Final answer:
  5. 12Complete each step, then write the final answer.

    Find the mean of 2, 4, 6, 8.

    Show your work

    Hint Add the four values. Then divide the total by 4.

    Final answer:
  6. 13Complete each step, then write the final answer.

    Find the mean of 10, 20, 15, 25, 30.

    Show your work

    Hint Add the five values. Then divide the total by 5.

    Final answer:
  7. 14Complete each step, then write the final answer.

    Find the MAD of this data set: 1, 4, 7.

    Show your work

    Hint The mean is 4. Find how far 1, 4 and 7 are from 4.

    Final answer:
  8. 15Complete each step, then write the final answer.

    Find the MAD of this data set: 5, 6, 10, 11.

    Show your work

    Hint The values add to 32. Find the mean, then each distance from it.

    Final answer:
  9. 16Complete each step, then write the final answer.

    Which measure better shows a typical value for 5, 6, 7, 6, 30: the mean or the median?

    Show your work

    Hint Is one value far from the rest? An outlier pulls the mean toward it.

    Final answer:
  10. 17Complete each step, then write the final answer.

    Which measure should you use for 2, 4, 6, 8, 10: the mean or the median?

    Show your work

    Hint Look for a value far from the rest. If there is none, use the mean.

    Final answer:
  11. 18Complete each step, then write the final answer.

    Find 8.75 − 2.4.

    Show your work

    Hint Write 2.4 as 2.40. Line up the decimal points. Then subtract.

    Final answer:

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.

3-Point Exit Checklist: ☐ 1. Units & Labels Verified ☐ 2. Mathematical Reasoning Stated ☐ 3. Calculations Double-Checked
How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help