6.DS.4 Lesson 2-8-part2 Apply Day · Version A
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

2.8 · Part II

Supported Application · Guided Entry to Today's Problem

Mean · Average

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ CONCEPT SUMMARY & GUIDED NOTES: 2.8 · Part II
1Measures of Center: Mean
2Strategy Model — step by step
  1. Add all data values together to find the total sum
  2. Divide the sum by the count of data values
  3. Concept: The mean represents the fair share or balance point of the data
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.
  1. 1 MULTIPLE CHOICE

    In her first 4 games, Sofia scored 12, 20, 16, and 11 points. What is her mean points per game so far?

    1. A14.75
    2. B59
    3. C15
    4. D20
    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?
📐 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
6.DS.4 Lesson 2-8-part2 Apply Day · Version B
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

2.8 · Part II

On-Level Application · Standard Rigor

Mean · Average

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: 2.8 · Part II
1Measures of Center: Mean
2The Structural Procedure
  1. Add all data values together to find the total sum
  2. Divide the sum by the count of data values
  3. Concept: The mean represents the fair share or balance point of the data
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.
  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
  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
📐 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
6.DS.4 Lesson 2-8-part2 Apply Day · Challenge
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

2.8 · Part II

Extension & Non-Routine Application

Mean · Average

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: 2.8 · Part II
1Measures of Center: Mean
2The Structural Procedure
  1. Add all data values together to find the total sum
  2. Divide the sum by the count of data values
  3. Concept: The mean represents the fair share or balance point of the data
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.
  1. 1 MULTIPLE CHOICE

    Find the mean of this data set: 6, 10, 14, 8, 12.

    1. A10
    2. B12
    3. C8
    4. D50
    Put the data in order
    Work
  2. 2 MULTIPLE CHOICE

    A data set has a mean of 20. Every value in the data set is then increased by 4. What is the new mean?

    1. A24
    2. B20
    3. C80
    4. D5
    Put the data in order
    Work
  3. 3 MULTIPLE CHOICE

    A data set of 5 numbers has a mean of 12. A sixth value of 12 is added. What happens to the mean?

    1. AIt stays 12 — adding a value equal to the mean cannot pull it either way
    2. BIt rises, because the total went up
    3. CIt falls, because there are more values to divide by
    4. DThere is not enough information without the original five numbers
    ✏️ Workspace & Solution Steps
📐 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