Powers (Potenser)

Ämne / Topic

The meaning of power, exponent, and base.

Writing in Expanded and exponent form.

Calculating simple exponents.

Inlärningsmål / Learning Goals

After this lesson you should know / understand....

Whiteboard: I know... I understand...I can do... 

Define power, exponent, and base.

Writing in Expanded and exponent form.

Calculating simple exponents / powers.

Google Slides & Videos

Lektionssteg / Steps in the lesson: 

1. Lektionsuppvärmning / Lesson warm up / Hook / Review from previous lesson

Powers Race.

Equipment: Game board, 10 sided dice, a regular dice, calculators and game markers.

Number of participants: 2 - 3

Instructions:

• Player 1 starts by throwing both dice. 

  • The 10 sided dice shows the base of the number.

  • The regular dice shows the power (exponent).

    • i.e 10 sided dice shows 8 and the regular dice shows 4, the number made will be 8⁴.

• Calculate the value of the power (Calculators may be used if needed).

• If the value you calculated ends up within the range of the first ring, you jump there, otherwise you do not move.Then its the turn of the next player.

• All players continue to go in the same order. 

• The player who reaches the end first, wins.

2. Introduktion till lektionen / Introduction to the lesson content 

• Define power, exponent, and base.

• Writing in Expanded and exponent form (see worksheet at added files).

• Calculating simple exponents / powers (see worksheet at added files).

• Teacher will review the "parts" that make up powers.

• Learners will watch a video on exponents.

• Learners will work in groups to discuss the video and come up with their own conclusion on exponents and how to use them.

• Learners, with the help of the video and interaction with teacher will complete questions based on:

• Rewriting each exponent form in expanded form.Rewrite each expanded form in exponent form.Simple exponent calculations.

• Exit ticket - Once the learners have completed the worksheets, the teacher will give the learners, the opportunity to go up to the board and explain how they solved the question. 

3. Aktiviteter / Key Activities 

How to Write Exponents

An exponent is a valuable mathematical tool for showing repeated multiplication. 

To use exponents, you need to know several mathematical rules about interpreting their meaning.

A special numerical system that uses exponents is scientific notation, which is useful in expressing very large or very small numbers. 

When you use exponents or scientific notation in print or programming, you need to learn various ways to express the exponent. 

These will differ for different programs or typing formats.

Indices Rule 1: The Multiplication Law

The multiplication law states that when you multiply similar terms, you add the powers as shown, 

a² x a³ = a²⁺³

This multiplication law applies to all terms with powers (positive or negative): e.g.

b⁻⁵ x b² = b⁽⁻⁵⁾ ⁺ ²

Indices Rule 2: The Division Law

The division law is when you divide similar terms and in doing so, you subtract the powers:

a² ÷ a³ = a² ⁻ ³

The division law applies to all numbers, negative numbers and fractional powers,

b⁶ ÷ b² = b⁶ ⁻ ²

Indices Rule 3: Multiple Powers Law

The multiple powers law is when you raise one power to another, i.e. the power of a power. When this happens the powers are multiplied

A basic example shows how the multiple powers law works with numbers:

(a²)³ = 2 x 3 = a⁶

Indices Rule 4: Power 0 Law

Anything to the power 0=1

a⁰ = 1

The power 0 law applies to everything: 100⁰ = 1

Indices Rule 5: Power 1 Law

Anything to the power 1 is just itself.

a¹ = a

The power 1 law applies to everything: 100¹ = 100.

Indices Rule 6: The 1 Law

1 to the power anything = 1 e.g.

This works for any power: 1¹⁰⁰ = 1, 1⁻⁵ = 1

Indices Rule 7: The Fraction Law

The power of a fraction applies to both the top and bottom of the fraction.

(a/b)² = a² / b²

This also applies to mixed factions. 

4. Kolla vad eleverna kan / Check for understanding / Exit ticket

Speaking with students throughout class.

The way learners answer questions posed to them by the teacher on exponents.

Once the learners have completed the worksheets, the teacher will give the learners, the opportunity to go up to the board and explain how they solved the question. 

Exit ticket.

5.  Avslutning / Closure / Summary of lesson

Review difference between power, exponent, and base.

"What did I learn today?"

Learners will have turns coming up to the board and writing down what they learnt. Once a learner has gone, they will pass the pen onto another learner of their choosing.

The learners may not write down what another learner has already written. This will help learners really reflect on what they learnt in the lesson.

Resurser & Materiel / Resources & Materials

Textbook activities

ETT pg. 25 no. 1061 abc, 1062 abc, 1064.

TVÅ pg. 26 no. 1069 abc, 1070 abcd, 1071 abc, 1072.

TRE pg. 27 no. 1076 abc, 1077 abc, 1079 abc, 1080.

FYRA pg. 27 no. 1082 ab, 1083 ab, 1084 ab, 1086 ab, 1087 ab.

https://www.chilimath.com/lessons/intermediate-algebra/rules-of-exponents/