Grade 7 Mathematics. 5 + 8 = How could you model this problem using chips?

Unit 1Grade 7 Mathematics

Introducing Addition of Integers

5 + 8 = How could you model this problem

using chips?

Chip Board

Introducing Addition of Integers

At a desert weather station, the temperature at sunrise was 10°c. It rose 25°c by noon.

The temperature at noon was 10°c + 25°c = 35°c

Number Line

Introducing Subtraction of Integers

Kim had 9 CDs. She sold 4 CDs at a yard sale. How many CDs does she have left?

How could you model this problem using chips?

Chip Board

Introducing Subtraction of Integers

Otis earned $5 babysitting. He owes Latoya $7. He pays her the $5, how much does he owe her now?

How could you model this problem using chips?

Chip Board

Introducing Subtraction of Integers

The Arroyo family just passed mile 25 on the highway. They need to get to the exit at mile 80. How many more miles do they have to drive?

Number Line

Chip Board Manipulatives

http://nlvm.usu.edu/en/nav/grade_g_2.html

Adding & Subtracting Integers Subtracting a

Negative is the same as Adding

Adding & Subtracting Integers

Example: What is 6 – (-3) ?

6 + 3 =

9

Adding & Subtracting Integers

Example: What is 14 – (-4) ?

14 + 4 =

18

Adding & Subtracting Integers Subtracting a

Positive or Adding a Negative is Subtraction

Adding & Subtracting Integers

Example What is 5 + (-7) ?

5 – 7 =

2

Adding & Subtracting Integers

Example What is 6 – (+3) ?

6 – 3 =

3

Adding & Subtracting Integers

Rules: Two like signs become a positive

sign. Two unlike signs become a negative

sign.

Adding & Subtracting Integers

Common Sense Explanation:

A friend is +, an enemy is – + + = +, a friend of a friend is my

friend + - = -, a friend of an enemy is my

enemy - + = -, an enemy of a friend is my

enemy - - = +, an enemy of an enemy is my

friend

“+/-” Connection

You will understand and use the relationship between addition and subtraction to simplify computation by changing subtraction problems to addition or vice versa.

“+/-” Connection

(+5) + (-3) =

(+5) – (+3) =

(+5) + (+3) =

(+5) – (-3) =

Chip Board Manipulatives

http://nlvm.usu.edu/en/nav/grade_g_2.html

Fact Families

You will understand and use the relationship between addition and subtraction found in fact families

Fact families are built based on the relationship between addition and subtraction

Definition: A fact family is a group of numbers that are related to each other in that those numbers can be combined to create a number of equations.

Fact Families

3 + 2 = 5

2 + 3 = 5

5 – 3 = 2

5 – 2 = 3

Fact Families

(-7) + (+2) = -5

(+2) + (-7) = -5

What is the next fact family? (-5) – (+2) = -7 What is the next fact family? (-5) – (-7) = +2

Multiplication of Integers

Develop and use algorithms for multiplying integers.

Multiplication of Integers Two positives

make a positive

Example: 3 x 2 =

Multiplication of Integers

Two negatives make a positive

Example: (-3) x (-2) =

Multiplication of Integers A negative and a

positive make a negative

Example: (-3) x 2 =

Multiplication of Integers

A positive and a negative make a negative

Example: 3 x (-2) =

Multiplication of Integers

Multiplication of Integers

Multiplication of Integers

Multiplication of Integers

Multiplication of Fractions

Step 1: Multiply the top numbers (the numerators)

Step 2: Multiply the bottom numbers ( the denominators)

Step 3: Simplify the fraction if needed

Multiplication of Fractions

Multiplication of Fractions

Multiplication of Mixed Numbers

Step 1: Convert to Improper Fractions

Step 2: Multiply the fractions Step 3: Convert the result back to

Mixed Fractions

Multiplication of Mixed Numbers

Converting a mixed number to improper fraction

Step 1: Multiply the denominator by the whole number

Step 2: Then add that to the numerator

Step 3: Then write the result on top of the denominator

Multiplication of Mixed Numbers

Multiplication of Mixed Numbers

Converting an improper fraction to a mixed number

Step 1: Divide the numerator by the denominator

Step 2: Write down the whole number answer

Step 3: Then write down any remainder above the denominator

Multiplication of Mixed Numbers

Division of Integers

Division is the opposite of multiplying

Example: 3 x 5 = 15 Which means 15 / 3 = 5 Also, 15 / 5 = 3

Division of Integers

Dividend ÷ Divisor = Quotient

Example: 12 ÷ 3 = 4 12 = Dividend 3 = Divisor 4 = Quotient

Division of Integers

Two positives make a positive

Example: 8 ÷ 2 =

Division of Integers

Two negatives make a positive

Example: (-8) ÷ (-2) =

Division of Integers

A negative and a positive make a negative

Example: (-8) x 2 =

Division of Integers

A positive and a negative make a negative

Example: 8 ÷ (-2) =