Grade 7 Mathematics
= How could you model this problem using chips?
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
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?
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?
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?
Subtracting a Negative is the same as Adding
Example: What is 6 – (-3) ? = 99
Example: What is 14 – (-4) ? = 18
Subtracting a Positive or Adding a Negative is Subtraction
Example What is 5 + (-7) ? 5 – 7 = 22
Example What is 6 – (+3) ? 6 – 3 = 33
Rules: Two like signs become a positive sign. Two unlike signs become a negative sign.
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
You will understand and use the relationship between addition and subtraction to simplify computation by changing subtraction problems to addition or vice versa.
(+5) + (-3) = (+5) – (+3) = (+5) + (+3) = (+5) – (-3) =
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.
= 5 = 5 5 – 3 = 2 5 – 2 = 3
(-7) + (+2) = -5 (+2) + (-7) = -5 What is the next fact family? (-5) – (+2) = -7 What is the next fact family? (-5) – (-7) = +2
Develop and use algorithms for multiplying integers.
Two positives make a positive Example: 3 x 2 =
Two negatives make a positive Example: (-3) x (-2) =
A negative and a positive make a negative Example: (-3) x 2 =
A positive and a negative make a negative Example: 3 x (-2) =
Step 1: Multiply the top numbers (the numerators) Step 2: Multiply the bottom numbers ( the denominators) Step 3: Simplify the fraction if needed
Step 1: Convert to Improper Fractions Step 2: Multiply the fractions Step 3: Convert the result back to Mixed Fractions
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
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
Division is the opposite of multiplying Example: 3 x 5 = 15 Which means 15 / 3 = 5 Also, 15 / 5 = 3
Dividend ÷ Divisor = Quotient Example: 12 ÷ 3 = 4 12 = Dividend 3 = Divisor 4 = Quotient
Two positives make a positive Example: 8 ÷ 2 =
Two negatives make a positive Example: (-8) ÷ (-2) =
A negative and a positive make a negative Example: (-8) x 2 =
A positive and a negative make a negative Example: 8 ÷ (-2) =