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Grade 7 Mathematics
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5 + 8 = How could you model this problem using chips?
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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
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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?
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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?
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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?
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http://nlvm.usu.edu/en/nav/grade_g_2.html http://nlvm.usu.edu/en/nav/grade_g_2.html
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Subtracting a Negative is the same as Adding
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Example: What is 6 – (-3) ? 6 + 3 = 99
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Example: What is 14 – (-4) ? 14 + 4 = 18
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Subtracting a Positive or Adding a Negative is Subtraction
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Example What is 5 + (-7) ? 5 – 7 = 22
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Example What is 6 – (+3) ? 6 – 3 = 33
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Rules: Two like signs become a positive sign. Two unlike signs become a negative sign.
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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
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You will understand and use the relationship between addition and subtraction to simplify computation by changing subtraction problems to addition or vice versa.
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(+5) + (-3) = (+5) – (+3) = (+5) + (+3) = (+5) – (-3) =
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http://nlvm.usu.edu/en/nav/grade_g_2.html http://nlvm.usu.edu/en/nav/grade_g_2.html
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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.
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3 + 2 = 5 2 + 3 = 5 5 – 3 = 2 5 – 2 = 3
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(-7) + (+2) = -5 (+2) + (-7) = -5 What is the next fact family? (-5) – (+2) = -7 What is the next fact family? (-5) – (-7) = +2
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Develop and use algorithms for multiplying integers.
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Two positives make a positive Example: 3 x 2 =
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Two negatives make a positive Example: (-3) x (-2) =
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A negative and a positive make a negative Example: (-3) x 2 =
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A positive and a negative make a negative Example: 3 x (-2) =
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Step 1: Multiply the top numbers (the numerators) Step 2: Multiply the bottom numbers ( the denominators) Step 3: Simplify the fraction if needed
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Step 1: Convert to Improper Fractions Step 2: Multiply the fractions Step 3: Convert the result back to Mixed Fractions
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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
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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
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Division is the opposite of multiplying Example: 3 x 5 = 15 Which means 15 / 3 = 5 Also, 15 / 5 = 3
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Dividend ÷ Divisor = Quotient Example: 12 ÷ 3 = 4 12 = Dividend 3 = Divisor 4 = Quotient
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Two positives make a positive Example: 8 ÷ 2 =
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Two negatives make a positive Example: (-8) ÷ (-2) =
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A negative and a positive make a negative Example: (-8) x 2 =
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A positive and a negative make a negative Example: 8 ÷ (-2) =
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