CONTENT SUMMARY
Each place on the place value chart represents a power of ten. As we move left of the decimal place, the numbers increase in value. The opposite happens when we move right of the decimal point. All digit to the left of the decimal point are whole numbers. Digits to the right of the decimal point are fractional numbers. Every digit has three values: the place, the face and the actual or true value. The place times the place gives the actual value.
The factors of a number are all the numbers that are able to completely divide a given number without leaving a remainder. One (1) is a universal factor.
Review what is meant by prime factorization, standard form, expanded form and exponent from. We are all going to play a quick game. You will all take a strip of paper from my basket. They all represent numbers written in expanded, standard, worded and exponential form. As soon as you have selected your paper, walk around and find your number family and stand beside them. (3ft apart) Afterwards we will decide if you are family or not.
EXPLORE
Let's just quickly use the place value mats to represent the number 4589 in expanded form.
Place each digit under their correct place. (4000 + 500 + 80 + 9 )
4000 = 4 x 1000
500 = 5 x 100
80 = 8 x 10
9 = 9 x 1
Today, we are going to write the expanded form of numbers in exponential form.
Let's watch this video clip so we can gain some insights as to how this is done.
Explain the steps involved in changing from expanded form to exponent form. Eg.
213 = 2 x 100 + 1 x 10 + 3 x 1
= 2 x 102 + 1 x 10 1 + 3 x 10 0
EXTEND/ELABORATE
1. State if each statement is true or false. They will justify their answers as they go along.
(a) 10 0 = 10
(b) In 648, 8 has the greatest value.
(c) 3 2 = 2 x 3
(d) 5 2 = 25
(e) 200 + 30 + 7 is referred to as exponential form
(f) The exponent tells how many times the base must be multiplied.
2. Complete the table below.
|
STANDARD FORM |
EXPANDED FORM |
WORDS |
EXPONENTIAL FORM |
|
|
30 + 6 |
|
2 2 x 3 2 |
|
81 |
|
Eighty one |
|
|
|
|
|
5 2 |
|
100 |
|
|
|
|
162 |
|
|
|
|
|
200 +40+ 5 |
|
|
|
|
|
One thousand |
|
Lesson Duration: 1 hour
Grade Level: 6
STEM Integrated
Focus Question:
How do I write numbers in the different number system?
Lesson Objectives:
By the end of the lesson, students should be able to:
-
Read, write and use numbers, using the principle of place value, in the Hindu-Arabic system of numeration.
-
Write numbers in exponential form.
-
Write composite numbers as a product of primes in exponential form.
Materials/Resources Needed:
-
Place value chart
-
Base-10 blocks (or digital simulation)
-
Chart showing Hindu-Arabic vs Exponential notation
-
Prime number cards (2–30)
-
Grid paper
-
STEM video (short clip)
-
Computers/tablets or calculator (optional)
-
Projector/Whiteboard
-
Differentiated task cards
5E Lesson Plan Breakdown
1. Engage (5–7 mins)
Activity:
Display the number 8,000 using base-10 blocks (or an image). Ask:
“Can anyone guess what this number means and how else we could write it using repeated multiplication?”
Then show:
8,000 = 10 × 10 × 10 × 8
Ask: “Is there a shorter way to write repeated multiplication?”
Bridge to lesson:
Introduce the concept of exponents and the Hindu-Arabic system.
2. Explore (10–12 mins)
Activity:
Divide class into small groups and give them the following to explore:
-
Write these numbers in Hindu-Arabic form:
-
4 thousands + 3 hundreds + 5 tens + 2 ones
-
-
Convert repeated multiplication to exponential form:
-
3 × 3 × 3 × 3 = ?
-
2 × 2 × 2 = ?
-
-
Use prime factor trees to break down composite numbers like 12, 18, and 36.
STEM Connection:
Students will watch a short animation showing how exponents are used in computer memory (bytes and bits) and in engineering to measure large/small values (e.g., nanometers in microchips).
3. Explain (10–15 mins)
Teacher-led explanation with visuals:
Concepts:
-
Hindu-Arabic System: Based on 10 digits (0–9) and place value.
-
Exponential Notation:
-
e.g., 2 × 2 × 2 = 2³ (read as “two to the power of three”).
-
Base = 2, Exponent = 3
-
-
Prime Factorization Using Exponents:
-
12 = 2² × 3
-
36 = 2² × 3²
-
Model these examples on the board using prime factor trees.
4. Elaborate (15–18 mins)
Differentiated Activities – Task Cards
| Tier | Task |
|---|---|
| Tier 1 (Support) | Use base-10 blocks and place value charts to write numbers in Hindu-Arabic and expanded form (e.g., 4,325 = 4000 + 300 + 20 + 5). |
| Tier 2 (On-Level) | Match repeated multiplication with exponential form and break down composite numbers into prime factors (without exponents). |
| Tier 3 (Advanced) | Complete prime factorization of large numbers and express in exponential form. Also solve real-life STEM problems like: "A computer stores 2⁵ bits in one packet. How many bits are in 4 packets?" |
Students rotate through stations or work independently based on their level.
5. Evaluate (5–8 mins)
Three-Tier Evaluation:
| Level | Task | Skills Assessed |
|---|---|---|
| Basic | Write the number 6,432 in Hindu-Arabic form and explain the place value of each digit. | Objective 1 |
| Proficient | Convert: 2 × 2 × 2 × 2 into exponential form. Then factor 18 into primes and write in exponential form. | Objectives 2 & 3 |
| Advanced | A number is written as 2³ × 3². Find the number. Then explain how exponents help in simplifying computer storage representations. | Objectives 2 & 3 + STEM connection |
Exit Ticket:
“How do exponents make writing and using large or repeated numbers easier?”
STEM Component
-
Science & Tech: Explore use of exponents in scientific notation and technology (e.g., data storage, power of ten in physics).
-
Engineering & Math: Use exponents in understanding scale and efficient computation (e.g., algorithms, building designs using repeated structures).
Differentiation Strategies:
-
Use visual aids and manipulatives for struggling students.
-
Challenge high achievers with real-world application problems.
-
Provide peer support/group work to encourage collaboration.
No comments:
Post a Comment