1. Grade 7 Mathematics

2.  5 + 8 =  How could you model this problem using chips?

4.  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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6.  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?

8.  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?

10.  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?

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

13.  Subtracting a Negative is the same as Adding

14.  Example:  What is 6 – (-3) ?  6 + 3 = 99

15.  Example:  What is 14 – (-4) ?  14 + 4 =  18

16.  Subtracting a Positive or Adding a Negative is Subtraction

17.  Example  What is 5 + (-7) ?  5 – 7 = 22

18.  Example  What is 6 – (+3) ?  6 – 3 = 33

19.  Rules:  Two like signs become a positive sign.  Two unlike signs become a negative sign.

20.  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

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

22.  (+5) + (-3) =  (+5) – (+3) =  (+5) + (+3) =  (+5) – (-3) =

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

24.  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.

25.  3 + 2 = 5  2 + 3 = 5  5 – 3 = 2  5 – 2 = 3

26.  (-7) + (+2) = -5  (+2) + (-7) = -5  What is the next fact family?  (-5) – (+2) = -7  What is the next fact family?  (-5) – (-7) = +2

27.  Develop and use algorithms for multiplying integers.

28.  Two positives make a positive  Example:  3 x 2 =

29.  Two negatives make a positive  Example:  (-3) x (-2) =

30.  A negative and a positive make a negative  Example:  (-3) x 2 =

31.  A positive and a negative make a negative  Example:  3 x (-2) =

36.  Step 1: Multiply the top numbers (the numerators)  Step 2: Multiply the bottom numbers ( the denominators)  Step 3: Simplify the fraction if needed

39.  Step 1: Convert to Improper Fractions  Step 2: Multiply the fractions  Step 3: Convert the result back to Mixed Fractions

40.  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

42.  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

44.  Division is the opposite of multiplying  Example:  3 x 5 = 15  Which means 15 / 3 = 5  Also, 15 / 5 = 3

45.  Dividend ÷ Divisor = Quotient  Example:  12 ÷ 3 = 4  12 = Dividend  3 = Divisor  4 = Quotient

46.  Two positives make a positive  Example:  8 ÷ 2 =

47.  Two negatives make a positive  Example:  (-8) ÷ (-2) =

48.  A negative and a positive make a negative  Example:  (-8) x 2 =

49.  A positive and a negative make a negative  Example:  8 ÷ (-2) =