6.DS.4 Lesson 2-8-group1 🟡 Group 1 · Set B
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

2.8 Small Group · Group 1

Second Practice Form · Re-Teach, Homework or Retake · Same Standard, New Problems

Mean · Average · Procedural Fluency · Real-World Applications

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ CONCEPT SUMMARY & GUIDED NOTES: Let's build it together — What is the mean?
1Mean = total of all the values ÷ how many values there are.
  • The mean, or average, is a measure of center that describes a whole data set with one number. It is what every value would be if the total were leveled out and shared equally. We'll walk through a worked example, try one together, then you'll try a few with hints right there when you need them.
2Worked Example — Watch me
  1. Miguel's 4 days of earnings are shown with counters. When I combine all of the counters, there are 60 of them, which means Miguel earned $60 in all.
  2. Now I redistribute the 60 counters equally among the 4 days. Each of the 4 groups ends up with 15 counters.
  3. The arithmetic does exactly the same thing: I find the total, 60, and divide it by the number of days, 4. So 60 ÷ 4 = 15.
  4. We can use $15 to describe Miguel's typical daily earnings. That leveled value is the mean.
3Mathematical Word Bank
  • Mean (Media) — The average of a data set. Add all the values, then divide by how many values there are.
  • Average (Promedio) — Another word for the mean — the amount each value would be if the total were shared equally.
  • Measure of center (Medida de centro) — A single number used to describe the middle, or typical value, of a whole data set.
  • Balance point (Punto de equilibrio) — The value where the total distance of the data above it equals the total distance below it. The mean is the balance point.
  • Data set (Conjunto de datos) — The whole collection of values that were gathered or measured.
4Watch out
  • The most common mistake with the mean is adding correctly and then dividing by the wrong number — or not dividing at all. Students report the total (for 8, 10, 6, 12 they say the mean is 36) or they divide by a count that does not match the data, such as dividing a 4-value total by 5, or skipping a zero when counting the values. Before you finish, do two things: count the values in the data set out loud, and check that your mean lands between the smallest and largest value. A mean of 36 for data that never goes above 12 is impossible.
SECTION 1 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 1 MULTIPLE CHOICE

    Sofia wants to average 15 points per game over 10 games. How many points does she need in all 10 games combined?

    1. A150 points
    2. B15 points
    3. C25 points
    4. D1.5 points
    per 1
    1. 1LabelWrite what each column is.
    2. 2Find per 1Divide to get one.
    3. 3ScaleMultiply up to what is asked.
    4. 4CheckDoes the size make sense?
  2. 2 MULTIPLE CHOICE

    Sofia's points in games 1 through 9 were 12, 20, 16, 11, 17, 14, 15, 10, and 18. How many points has she scored so far?

    1. A133 points
    2. B123 points
    3. C150 points
    4. D15 points
    ✏️ Workspace & Solution Steps
  3. 3 MULTIPLE CHOICE

    Sofia has 133 points after 9 games and needs 150 points in all to average 15 over 10 games. How many points must she score in game 10?

    1. A17 points
    2. B15 points
    3. C13 points
    4. D283 points
    ✏️ Workspace & Solution Steps
SECTION 2 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 4 ERROR ANALYSIS

    The Mean Mistake (forgot to divide)

    1. 1Data set:Points scored in 4 games: 8, 10, 6, 12
    2. 2Goal:Find the MEAN number of points per game.
    3. 3Add the values:8 + 10 + 6 + 12 = 36
    4. 4Answer:Mean = 36 points

    Which step contains the error? Explain the mathematical misconception and write the correct calculation below.

    ✏️ Corrected Mathematical Work & Explanation
  2. 5 ERROR ANALYSIS

    The Wrong Divisor

    1. 1Data set:Points in 4 games: 6, 11, 9, 14
    2. 2Goal:Find the MEAN number of points per game.
    3. 3Add the values:6 + 11 + 9 + 14 = 40
    4. 4Divide:The student divides by 5: 40 ÷ 5 = 8, so the mean is 8.

    Which step contains the error? Explain the mathematical misconception and write the correct calculation below.

    ✏️ Corrected Mathematical Work & Explanation
  3. 6 OPEN RESPONSE

    Sofia realized she made an error: she actually scored 12 points in Game 8, not 10. Her other games are unchanged (12, 20, 16, 11, 17, 14, 15, and 18). How does this change the number of points she needs in Game 10 to average 15 points per game? Show how you know.

    💬 Sentence Starter: Her new total after 9 games is ___ points. To average 15 over 10 games she still needs ___ points in all, so Game 10 must now be ___ points. That is ___ points fewer than before, because ___.
    ✏️ Mathematical Justification & Response
📐 CER MATHEMATICAL PROOF MATRIX (CER 2.0) SMP.3 / Proof & Justification

Writing Task: Justify why your mathematical solution is accurate and complete.

C Claim
Starter: My mathematical claim is that the solution is...
E Evidence
Starter: The evidence from the model/table demonstrates that...
R Reasoning
Starter: This proves my answer because the standard mathematical definition of...
Student Mastery Self-Assessment:
1 · Need More Support
2 · Getting Closer
3 · Got It / Solid
4 · Master / Can Teach It