Run sheet

Prime Factorization and Exponential Notation — Exponential Notation

Grade 7 · Lesson 5 · 23 slides · blocked practice

The big idea

Exponential notation is a shorter way to write a prime factorization — and it makes the structure of the number visible at a glance.

Slide by slide

#	On the screen	What you say
1	Today — WARM-UP	Point at the five parts. Name where we are.
2	Write 40 as a product of primes.	Boards up on three. This is yesterday's work — Prime Factorization. Do not help each other; I need to see what each of you kept.
3	2 × 2 × 2 × 5 answer — own slide	Show me. Everyone at once. Check your own board against this.
4	Today — I DO	We are at I DO. Boards down and flat.
5	Exponential notation is a shorter way to write a prime factorization — and it makes the structure of the number visible at a glance.	Read this out. Do not explain it yet — the example explains it.
6	72 = 2 × 2 × 2 × 3 × 3 build 1 of 5	The prime factorization of 72.
7	72 = 2 × 2 × 2 × 3 × 3 three 2s, two 3s build 2 of 5	Count how many of each prime.
8	72 = 2 × 2 × 2 × 3 × 3 three 2s, two 3s 2³ build 3 of 5	Three 2s is 2³.
9	72 = 2 × 2 × 2 × 3 × 3 three 2s, two 3s 2³ 2³ × 3² build 4 of 5	Two 3s is 3².
10	72 = 2 × 2 × 2 × 3 × 3 three 2s, two 3s 2³ 2³ × 3² 72 = 2³ × 3² build 5 of 5	Same number, and now the structure is visible.
11	Write the prime factorization of 48 in exponential notation.	Now the same thing on a new one. Watch — nothing on your boards.
12	48 = 2 × 2 × 2 × 2 × 3. Four 2s and one 3. 2⁴ × 3 answer — own slide	I say every step aloud as I write it. The board keeps all of it.
13	Today — WE DO	We are at WE DO. Boards up.
14	Write the prime factorization of 100 in exponential notation.	Factorize first, then count each prime. Boards up.
15	100 = 2 × 2 × 5 × 5 2² × 5² answer — own slide	Boards up. Everyone at once — check yours against this.
16	Write the prime factorization of 54 in exponential notation.	One prime appears once. Decide how to write it.
17	54 = 2 × 3 × 3 × 3 2 × 3³ answer — own slide	Boards up. Everyone at once — check yours against this.
18	Today — YOU DO	We are at YOU DO. Boards down, books open.
19	Dimensions 7A — page 7	Open your books to this page. Wait — do not start yet.
20	Do — page 7	These are the book's own problems, same type as the three we have just done. Work them in the book.
21	Today — CLOSURE	Last part. Answers up.
22	“How many of each prime — and does a single one need an exponent?”	This is the question to ask yourself every time, not just today.
23	Write 24 in exponential notation.	One last board. Then we are finished.

Mini whiteboards, by segment

Segment	MWB	Time	Boards	What to hold
WARM-UP	retrieval	3-5 min	BOARDS UP	Question up, boards up on the count. Everyone shows at once — a child who waits to see a neighbour's board has not retrieved anything.
I DO	none — they watch	3-4 min	boards down	Boards DOWN and flat. This segment is watching, and a child writing is not watching. Say so once at the start of the year and then hold it.
WE DO	primary use	5-6 min	BOARDS UP	One step, then boards up. Do not let them run ahead to the answer — the point is that everybody is on the same step at the same time.
YOU DO	on the sheet	4-5 min	boards down	Boards down. This is the book's problems, worked where the work will be kept.
CLOSURE	answers displayed	2-3 min	boards down	Answers on the board, children check their own. Mark nothing here.

Watch for
A prime appearing once is written plainly, not as 2¹. Both are correct and the convention is the plain form; say so rather than marking it wrong. Grade 6's 4² = 8 error also returns here — check it.