2.8 Small Group · Group 1

Tier 2 Intervention · Concrete-Representational-Abstract (CRA) · Dual-Language Anchors

Mean · Average · Procedural Fluency · Real-World Applications

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

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.
Now I redistribute the 60 counters equally among the 4 days. Each of the 4 groups ends up with 15 counters.
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.
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 CONCEPTUAL UNDERSTANDING & VISUAL MODELS [Visual Modeling]

SECTION 2 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]

🗣️ MATHEMATICAL DISCOURSE & TALK MOVES SMP.3 / Construct Viable Arguments

Group Discussion Prompt: How does your visual model justify your mathematical solution?

🗣️ Partner A:
Partner A: "I modeled this by identifying the relationship and..."

👂 Partner B:
Partner B: "I agree with your step because the standard mathematical rule states..."

✍️ The Writing Revolution (TWR) · Sentence Expansion Because · But · So

Complete each sentence stem to demonstrate precise mathematical reasoning:

BECAUSE A question is statistical because it expects varied responses across different subjects rather than a single fixed value.

BUT A question might gather numbers, but it is not statistical if there is only one exact unchanging answer.

SO The researcher needed to understand group variation, so she collected data using a statistical survey question.

📐 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