1.2 — Growing Dots

Supplement for Mathematics Vision Project (MVP) curriculum · Secondary Math I, Module 1, Section 1.2
Independently created to support students using MVP Math. Not official publisher material and not affiliated with or endorsed by the Mathematics Vision Project.

Human review completed October 15, 2026.

1. In class: A Develop Understanding Task

Work through “Growing Dots,” Main 1–4, on pages 6–7 of your MVP packet with your class.

2. Ready

In your MVP packetReady · 1–12 · pages 8

Worked example — Ready 3

Original problem: Find \(f(-4)\) for \(f(n)=8n-3\).

\[f(-4)=8(-4)-3=-32-3=-35.\]

The input is −4; the output is −35. Parentheses help keep the negative sign attached to the input.

Check your work — Ready 1–12

Problem	Answer
1	37
2	5
3	-35
4	-22
5	-3
6	-10
7	5
8	-7

Problem	Missing values in order	Pattern
9	64, 128, 256	Multiply by 2
10	2, −14, −30, −46	Subtract 16
11	10, 5, 2.5, 1.25	Divide by 2
12	19, 26, 33, 40	Add 7

3. Set

In your MVP packetSet · 13–16 · pages 9

Check your work — Set 13–16

13 — Draw the next two figures

Step 4 has a four-tile tower and three tiles on either side. Step 5 has a five-tile tower and four tiles on either side.

Problem	Match	Reason
14	(c)	\(n=s+2(s-1)\) counts tower and two arms.
15	(b)	\(n=3s-2\) matches Sally’s rule.
16	(a)	\(n=(2s-1)+(s-1)\) counts the base, then the tiles above it.

All three expressions equal \(3s-2\), but the requested matches reflect each student’s way of seeing the figure.

4. Go

In your MVP packetGo · 17–28 · pages 10

Check your work — Go 17–28

Problem	Exponent form
17	\(6^5\)
18	\(4^3\)
19	\(15^4\)
20	\((\frac13)^2\)

Problem	A — Expanded form	B — Value
21	\(7\)	7
22	\(3\times3\)	9
23	\(5\times5\times5\)	125
24	\(10\times10\times10\times10\)	10000
25	\(7\times2\times2\times2\)	56
26	\(10\times8\times8\)	640
27	\(3\times5\times5\times5\times5\)	1875
28	\(16\times\frac12\times\frac12\times\frac12\)	2

Additional learning resources

Resource	What it helps with and scope
Khan Academy — Evaluating functions given their formula	Close match for substituting inputs into function rules in Ready. The course label is Algebra II, but this video’s evaluation method fits this work.
Khan Academy — Intro to arithmetic sequence formulas	Explains recursive and explicit arithmetic rules and how the initial term affects the formula.

Teacher/parent review of the source packet

No substantial mathematical errors were found in the student exercises. The teacher’s guide discussion mentions a disagreement between 100 and 101 for the 100-minute count; the displayed pattern actually gives 401. The count is one center dot plus four arms of 100 dots each.

Prompts and data adapted from Mathematics Vision Project, Secondary Mathematics I, Module 1 student packet, Section 1.2, pages 6–10, licensed under CC BY 4.0. Explanations and diagrams prepared for this supplement.

Last updated October 15, 2026.