Assignment #2: Microteaching

Group: Manjeet Mahal, Tam Tran, Kevin Greene

Microteaching: Integer Arithmetic

Math 8

Time: 15 minutes

I. Teaching Objectives:

• To demonstrate to students how to add, subtract, multiply, and divide integers using examples that are relevant to everyday life
• To have students become comfortable dealing with integers
• To have students understand how integer arithmetic works
• To engage students in the lesson

II. Learning Objectives:

• Students will be able to add, subtract, multiply, and divide integers
• Students will be able to understand how the integer rules were formulated
• Students will be able to relate addition and subtraction of integers to the thermometer
• Students will be able to visualize the process of adding and subtracting integers

III. Bridge/ Pre-test: 1 minute

Ask students which of the following numbers are integers: ½, 0.65, 10, squr(8), and -31.

IV. Participatory Activities: 10 minutes

Addition and Subtraction of Integers (4 minutes)

• Tam will start off by explaining addition and subtraction to the students by relating it to the thermometer
• Each time we add 1 cup of hot water the thermometer will go up 1°C.
• Each time we add 1 ice cube the thermometer will go down 1°C.
• During her lesson, Tam will be involving the students by asking them questions and by having volunteers demonstrate on the board using the thermometer to derive the answer. Tam will also involve students by having them discuss other ways they can arrive at the same answer.
• Examples:

1. Adding negative number: 8+(-6) = __
2. Subtracting positive number: 7-3 = __
3. Subtracting negative number: 9-(-4) = __

Instead of taking away 4 ice cubes to get 13°C, what else can we do?

How else can we rewrite 9-(-4)?

This leads to our general statement:

Taking away a negative number is the same as adding a positive number.

Eg. 9-(-4)=13 is the same as 9+4 =13

Now let’s try to solve this question by using the thermometer analogy:

4 + (-5) – (+2) + (-6)

Multiplication of Integers (3 minutes)

· Kevin will start the multiplication of integers by using the hot water and ice cubes analogy

· He will involve students by asking them questions as he explains the topic

· Positive and Positive:

· I’m going to take a container, and fill it to the top with 10 cups of hot water

§ Draw container with +10 inside

o How much hot water would I have if I had 2 such containers?

§ Wait for answer, ask how they got it, draw 2^nd container

§ (+10) + (+10) = (+20)

§ Include multiplying only if stated

o What if I had 3 such containers? 7? 12?

§ Ask how they got the answer, search for multiplying

§ ___ x (+10) = (+___)

o Now we’re going to use a container that can only hold 5 cups of water.

§ Draw container with +5 inside

o How much hot water do I have if I fill 3 of these containers?

§ How did they get the answer?

§ (+5) + (+5) + (+5) = (+15)

§ 3 x (+5) = (+15)

· Negatives:

· So what about ice? I’ll draw a bag, and you guys tell me how many ice cubes I can fit inside it.

§ Draw a bag with the number inside

o So if I had 6 of these bags, how many ice cubes would I have?

§ 6 x (-___) = (-___)

§ Ask for another number of bags

· General:

· Now I’m going to change a few things. Let’s see if you guys can get some answer

§ 4 x (-6) =

§ 9 x (-2) =

§ 5 x (+4) = Note the sign change!

§ 11 x (+12) =

o If needed still, explain how 6 is the same as +6

§ (+6) x (+10) =

§ (+10) x (-4) = Refer above if needed

§ (-2) x (+6) =

o Now let’s take a step back and see if we can notice a pattern

§ + + With reference

§ + - With reference

o So when the two signs are the same, we get a positive. When the two signs are different, we get a negative.

§ Diagram with partitions

o Who wants to guess the pattern if I put up another two signs that are the same?

§ - -

§ (-5) x (-2) =

Dividing Integers (3 minutes)

· Manjeet will discuss division of integer

· She will involve the class by having students participate in finding the solutions to the examples that she provides

· Example #1: Dividing positive numbers

· Find the value of ? for the following questions:

1. 7 × ? = 21

· ? = 3 – ask students how they got this

· Find ? by doing 21 ÷ 3 = 7

2. ? × 5 = 15

· ? = 3

· Find ? by doing 15 ÷ 5 = 3

· Example #2: Dividing Numbers that have different signs

· Find the value of ? for the following questions:

1. ? × 2 = -4

· ? = -2

· Therefore, (-2) × 2 = -4

· So, find ? by doing (-4) ÷ 2 = -2

2. (-3) × ? = 9

· ? = -3

· Find ? by doing 9 ÷ (-3) = -3

· Example #3: Dividing two negative numbers

· Find the value of ? for the following questions:

1. (-3) × ? = (-9)

· ? = 3

· Find ? by doing (-9) ÷ (-3) = 3

2. ? × (-10) = -100

· ? = (-100) ÷ (-10) = 10

· Additional Examples:

1. 81 ÷ 9 = ? ? = 9 Check: 9 × 9 =81

2. (-8) ÷ 2 = ? ? = -4 Check: (-4) × 2 = -8

3. 24 ÷ (-8) = ? ? = -3 Check: (-3) × (-8) = 24

4. (-50) ÷ (-10) = ? ? = 5 Check: 5 × (-10) = -50

V. Post-test: (3 minutes)

· Manjeet will do a little review of what has been taught by asking the students a few questions about integer arithmetic

o Give 2 solutions to the following problems:

· __ ÷ __ = -9

· __ × __ = -13

· __ - __ = -2

VI. Conclusion: (1 minute)

· Students will now have a better understanding of integers