6.DS.4 Lesson 2-8-group2 🟣 Group 2 · Set B
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

2.8 Small Group · Group 2

Second Challenge Form · Non-Routine Extension · Same Standard, New Problems

Visual Models · Mean · Average · Procedural Fluency

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: Push further — What is the mean?
1Mean = total of all the values ÷ how many values there are — and you can say why it is true, and where it would stop being true.
  • You already can do this. So we go up a level, not up a number: find what is always true, show it a second way, and be ready to defend it with a reason instead of an answer.
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.
3Second Model — Try it together — then prove it
  1. New data set: a dog walker earns $9, $11, $16, and $12 over 4 days. First, what is the total?
  2. Next, how many values are in the data set? That number is what we divide by.
  3. Last, divide the total by 4. Is your answer bigger than the smallest day and smaller than the biggest day? It should be.
  4. Now prove it: say why that move had to work at all — not just that it did.
  5. Sentence frame — convince a skeptic: "My method works because ___ . It would stop working if ___ ."
4Mathematical 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.
5Watch 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

    Miguel earned $60 walking dogs over 4 days. Ana says his mean daily earning is $15. Beto says you cannot know, because Miguel might have earned nothing on some days. Who is right?

    1. AAna — the mean spreads the total evenly and does not claim he earned $15 each day
    2. BBeto — a mean is meaningless when the daily amounts are unknown
    3. CBoth — the mean is $15 but it is not a useful number
    4. DNeither — the mean is $240
    ✏️ Workspace & Solution Steps
  2. 2 MULTIPLE CHOICE

    Claim: “The mean is always one of the values in the data set.” Always, sometimes, or never true?

    1. ASometimes — 3, 5, 7 has a mean of 5, but 4, 6, 8, 10 has a mean of 7, which is not in the set
    2. BAlways — the mean has to come from the data
    3. CNever — the mean is a calculation, so it cannot match a value
    4. DSometimes — it depends whether the count of values is odd
    ✏️ Workspace & Solution Steps
  3. 3 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
  4. 4 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
  5. 5 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. 6 ERROR ANALYSIS

    Fix our table's thinking

    1. 1The problem:Find the mean of: 4, 6, 8, 10
    2. 2A classmate at our table answered:8

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

    ✏️ Corrected Mathematical Work & Explanation
📐 CER MATHEMATICAL PROOF MATRIX (CER 2.0) SMP.3 / Proof & Justification

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

C Claim
State your direct mathematical answer/claim with units.
E Evidence
Cite exact numbers, calculations, dimensions, or graph data.
R Reasoning
Explain the mathematical theorem, property, or definition connecting evidence to claim.
Student Mastery Self-Assessment:
1 · Need More Support
2 · Getting Closer
3 · Got It / Solid
4 · Master / Can Teach It