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THE NUMBER SYSTEM CHAPTER 3 August 14 - 29
MS. SYLVESTER’S 7TH GRADE MATH
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INTRODUCTION TO INTEGERS August 14 - 15
August 14 – 15: Use as introduction to lesson, have student record notes (exactly as they are shown in the powerpoint) in their math journals. After daily notes, supplement with extra practice from the Chapter 3 textbook pages. What are integers and why/how do we use them? 7.NS.1.3
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TYPES OF REAL NUMBERS ADD EXAMPLES OF EACH TYPE AS YOU LEARN MORE ABOUT EACH TYPE:
RATIONAL NUMBERS IRRATIONAL NUMBERS August 14 – 15: Use as introduction to lesson, have student record notes (exactly as they are shown in the powerpoint) in their math journals. After daily notes, supplement with extra practice from the Chapter 3 textbook pages. INTEGERS WHOLE NUMBERS NATURAL NUMBERS
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WHAT IS A _____________ NUMBER?
NATURAL NUMBERS These are the numbers 1, 2, 3, … They are used for counting. WHOLE NUMBERS If we include zero then we get the whole numbers, 0, 1, 2, 3, …. INTEGERS The set of numbers …, −3, −2, −1, 0, 1, 2, 3, … (the whole numbers and their opposites) is called the integers. August 14 – 15: Use as introduction to lesson, have student record notes (exactly as they are shown in the powerpoint) in their math journals. After daily notes, supplement with extra practice from the Chapter 3 textbook pages.
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INTEGERS ON A NUMBER LINE
On a number line, whole numbers and their opposites are the same distance away from zero on a number line. The letter A represents the number 5 on the number line: The letter B represents the opposite of the number 5 on the number line: The letters A and B are the same distance away from zero the number line. They have same absolute value: A August 14 – 15: Use as introduction to lesson, have student record notes (exactly as they are shown in the powerpoint) in their math journals. After daily notes, supplement with extra practice from the Chapter 3 textbook pages. B A B A
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ABSOLUTE VALUE Absolute value is the distance a number is from zero. Absolute value is always positive, because distance is always positive. Think of an odometer on a car: I can drive to Circle K and back to Pryor and the mileage keeps going up. Although my position at the end of my trip is the same as when I started, the mileage has gone up. The symbols for absolute value looks like this ⎜⎟ Ex. ⎜4⎟ = 4 ⎜-11⎟ = ⎜6 - 3⎟ = ⎜3⎟ = ⎜- 23⎟ = 23 When there is a negative sign outside the absolute value symbols, it means take the opposite of: - ⎜7⎟ = ⎜-19⎟ = ⎜8 + 3⎟ = - ⎜11⎟ = ⎜7 - 6⎟ = - ⎜1⎟ = - 1 August 14 – 15: Use as introduction to lesson, have student record notes (exactly as they are shown in the powerpoint) in their math journals. After daily notes, supplement with extra practice from the Chapter 3 textbook pages.
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REVIEW INTEGERS ABSOLUTE VALUE NUMBER LINES
GUIDED PRACTICE What is the opposite of the number marked on the number line? A. B. Order these integers from least to greatest: C. { -8, 0, -3, 9, 7, 4, -4 } D. { 6, 1, -12, , 2, 3, 0 } Evaluate: E. ⎜- 8⎟ F. ⎜10⎟ G. ⎜5 + 6⎟ H. - ⎜-2⎟ Integers are all the whole numbers and their opposites—all the positive and negative whole numbers {…-3, -2, -1, 0, 1, 2, 3…} When represented on a number line, opposites are the same distance from zero. They have the same absolute value. August 14 – 15: Use as introduction to lesson, have student record notes (exactly as they are shown in the powerpoint) in their math journals. After daily notes, supplement with extra practice from the Chapter 3 textbook pages. B A 6 6
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INDEPENDENT PRACTICE INTEGERS & ABSOLUTE VALUE
Use what you know about integers to respond to the questions below: I. Are the mystery numbers on the number line opposites? How do you know? J. Compare the numbers below using the symbols < > = -5 ☐ 5 6 ☐ ☐ ☐ ☐ -8 K. What is absolute value? Why is the absolute value of a number positive? Give an example August 14 – 15: Use as introduction to lesson, have student record notes (exactly as they are shown in the powerpoint) in their math journals. After daily notes, supplement with extra practice from the Chapter 3 textbook pages.
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WHERE ARE INTEGERS IN REAL LIFE?
Even though we don’t see negative numbers in real life very often, there are many situations in which we use negative numbers to describe things. Sometimes negative numbers can describe direction or a change in a situation, like the following examples: The temperature dropped 5°F Mary forgot her bag so we drove back 2 miles to go to her house Sean bought a pizza that cost $6.50 The sea-level decreased by 12 feet yesterday What negative numbers describe the situations above? Can you think of more situations that negative numbers could describe? August 14 – 15: Use as introduction to lesson, have student record notes (exactly as they are shown in the powerpoint) in their math journals. After daily notes, supplement with extra practice from the Chapter 3 textbook pages.
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POSITIVE & NEGATIVE KEY WORDS SOME WORDS SHOW US THAT NUMBERS ARE MEANT TO BE POSITIVE OR NEGATIVE—HERE ARE SOME EXAMPLES. ADD MORE AS YOU SEE THEM: POSITIVE NEGATIVE DEPOSITED / DEPOSIT ADDED WENT FORWARD/TOWARD ROSE / RISE / RAISED INCREASE / INCREASED IMPROVED GAINED WITHDREW / WITHDRAWAL REMOVED WENT AWAY FROM FELL / FALL / FALLEN DECREASE / DECREASED DROPPED LOST August 14 – 15: Use as introduction to lesson, have student record notes (exactly as they are shown in the powerpoint) in their math journals. After daily notes, supplement with extra practice from the Chapter 3 textbook pages.
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SITUATIONS DESCRIBED BY INTEGERS
Once we understand how key words tell us if numbers in the real-world are positive and negative, we can use the symbols we already know ( × ÷ ) to write expressions to explain more about what is happening in the situations. Ex. Becki had $30 in her bank account. Then she deposited $5.50. = 35.50 Becki has $35.50 in her bank account after making her deposit. Before we can look at writing expressions for situations that deal with negative numbers, we should discuss how to operate when using negative numbers. August 14 – 15: Use as introduction to lesson, have student record notes (exactly as they are shown in the powerpoint) in their math journals. After daily notes, supplement with extra practice from the Chapter 3 textbook pages.
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ADDING INTEGERS August 16 - 17
August 16 – 17: Use as introduction to lesson, have student record notes (exactly as they are shown in the powerpoint) in their math journals. After daily notes, supplement with extra practice from the Chapter 3 textbook pages. How do negative numbers affect addition? 7.NS.1.1 & 7.NS.1.3
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ADDING INTEGERS: SAME SIGNS
When adding integers, pay attention to the signs of the numbers you are working with. They determine how you operate with those numbers. ADDING INTEGERS WITH SAME SIGNS Add the integers Keep the sign Ex = 9 ⨁⨁⨁⨁⨁ ⨁⨁⨁⨁ ⨁⨁⨁⨁⨁⨁⨁⨁⨁ = -7 ⊖⊖⊖⊖⊖⊖ ⊖ ⊖⊖⊖⊖⊖⊖⊖ How can you describe what is happening when you add numbers with the same sign? August 16 – 17: Use as introduction to lesson, have student record notes (exactly as they are shown in the powerpoint) in their math journals. After daily notes, supplement with extra practice from the Chapter 3 textbook pages.
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ADDING INTEGERS: DIFFERENT SIGNS
Number that are opposites combine to make zero. This allows us to add integers with different signs: ADDING INTEGERS WITH DIFFERENT SIGNS Subtract the numbers Take the sign of the number with the higher absolute value Ex = ⊖⊖⊖⊖⊖⊖⊖⊖ 8 – 4 = ⊖⊖⊖⊖⊖⊖⊖⊖ ⨁⨁⨁⨁ ⨁⨁⨁⨁ ⎜-8⎟ = ⎜4⎟ = 4 -8 has a higher absolute value than 4, so there are more negatives that positives. When we subtract 4 from 8, we see there are 4 more negatives than positives, as shown in the diagram above. So, = - 4 How can you describe what is happening when you add numbers with different signs? August 16 – 17: Use as introduction to lesson, have student record notes (exactly as they are shown in the powerpoint) in their math journals. After daily notes, supplement with extra practice from the Chapter 3 textbook pages.
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ADDING INTEGERS ON A NUMBER LINE
We can show an addition expression on a number line by using dots and arrows to demonstrate what is happening: If we wanted to show 3 + 4, we would start at the first number in the expression, 3: Then, we look at he symbol that follows the first number in the expression. Because we are adding a positive, we will move that many spaces to the right: When we moved four spaces to the right, we landed on 7. The number we have landed on is our answer: August 16 – 17: Use as introduction to lesson, have student record notes (exactly as they are shown in the powerpoint) in their math journals. After daily notes, supplement with extra practice from the Chapter 3 textbook pages.
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ADDING INTEGERS ON A NUMBER LINE
When you add a positive number, you move that many spaces to the RIGHT. Let’s see what that looks like: Ex We start at the first number in the expression, - 7: Then, we add a positive 5, so we move five spaces to the right: = We landed on – 2, so – = - 2 August 16 – 17: Use as introduction to lesson, have student record notes (exactly as they are shown in the powerpoint) in their math journals. After daily notes, supplement with extra practice from the Chapter 3 textbook pages.
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ADDING INTEGERS ON A NUMBER LINE
When you add a negative number, you move that many spaces to the LEFT. Let’s see what that looks like: Ex (-10) = We start at the first number in the expression, 8: 8 + (-10) = Then, we add a negative 10, so we move 10 spaces to the left: 8 + (-10) = -2 We landed on – 2, so 8 + (-10) = - 2 August 16 – 17: Use as introduction to lesson, have student record notes (exactly as they are shown in the powerpoint) in their math journals. After daily notes, supplement with extra practice from the Chapter 3 textbook pages.
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ADDING INTEGERS ON A NUMBER LINE
Now let’s trying adding two negative numbers: Ex. (-3) + (-2) = We start at the first number in the expression, - 3: (-3) + (-2) = Then, we add a negative 2, so we move 2 spaces to the left: (-3) + (-2) = -5 We landed on – 5, so (- 3) + (- 2) = - 5 August 16 – 17: Use as introduction to lesson, have student record notes (exactly as they are shown in the powerpoint) in their math journals. After daily notes, supplement with extra practice from the Chapter 3 textbook pages.
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REVIEW ADDING INTEGERS
GUIDED PRACTICE Write an addition expression that is shown by the number lines below: A. B. Evaluate the expressions: C. (-16) D. (- 8) + (- 12) E (- 14) F G. (-5 ) + (- 8) H (- 3) I (-7) J (-19) ADDING INTEGERS WITH SAME SIGNS Add the integers Keep the sign ADDING INTEGERS WITH DIFFERENT SIGNS Subtract the numbers Take the sign of the number with the higher absolute value ADDING INTEGERS ON A NUMBER LINE Start on the number left of the operation Go right if adding a positive Go left if adding a negative The number you stop on is your solution August 16 – 17: Use as introduction to lesson, have student record notes (exactly as they are shown in the powerpoint) in their math journals. After daily notes, supplement with extra practice from the Chapter 3 textbook pages.
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INDEPENDENT PRACTICE ADDING INTEGERS
Use what you know about integers to respond to the questions below: K. Describe an addition situation that could be represented by the expression shown on the number line below. Explain your reasoning. L. Write the integers or integer expressions that match the situations below: Angela deposits five hundred thirty four dollars in her bank account The temperature was 80°F this morning and increased by 5°F by nightfall Jared scored two goals in the first game, six goals in the second, and four in the third M. Compare the numbers below using the symbols < > = (-7) + 5 ☐ 5 + (-7) (-4) ☐ (-6) (-8) + (-2) ☐ (-9) + 4 August 16 – 17: Use as introduction to lesson, have student record notes (exactly as they are shown in the powerpoint) in their math journals. After daily notes, supplement with extra practice from the Chapter 3 textbook pages.
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SUBTRACTING INTEGERS August 18 - 21
August 18 – 21: Use as introduction to lesson, have student record notes (exactly as they are shown in the powerpoint) in their math journals. After daily notes, supplement with extra practice from the Chapter 3 textbook pages. How do negative numbers affect subtraction? 7.NS.1.1 & 7.NS.1.3
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SUBTRACTING INTEGERS: SAME & DIFFERENT SIGNS
When subtracting integers, think about adding the opposite. This rule applies whether the numbers have same or different signs: Keep the first number Change the subtraction sign to addition Change the sign of the number after the addition sign Follow the rules for adding integers (check the signs) Ex = = ⊖⊖⊖⊖⊖⊖⊖⊖ ⨁⨁⨁ ⊖⊖⊖⊖⊖⊖⊖⊖ ⊖⊖⊖ ⊖⊖⊖⊖⊖⊖⊖⊖⊖⊖⊖ Ex = = ⨁⨁ ⊖⊖⊖⊖⊖⊖⊖ ⨁⨁ ⨁⨁⨁⨁⨁⨁⨁ ⨁⨁⨁⨁⨁⨁⨁⨁⨁ August 18 – 21: Use as introduction to lesson, have student record notes (exactly as they are shown in the powerpoint) in their math journals. After daily notes, supplement with extra practice from the Chapter 3 textbook pages.
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SUBTRACTING INTEGERS: SAME & DIFFERENT SIGNS
Keep the first number Change the subtraction sign to addition Change the sign of the number after the addition sign Follow the rules for adding integers (check the signs) Ex = = ⊖⊖⊖⊖⊖ ⨁ ⊖⊖⊖⊖⊖ ⊖ ⊖⊖⊖⊖⊖⊖ Ex = = ⨁⨁⨁⨁⨁⨁ ⨁⨁⨁ ⨁⨁⨁⨁⨁⨁ ⊖⊖⊖ ⨁⨁⨁ How can you describe what is happening when you subtract integers with same/different signs? August 18 – 21: Use as introduction to lesson, have student record notes (exactly as they are shown in the powerpoint) in their math journals. After daily notes, supplement with extra practice from the Chapter 3 textbook pages.
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SUBTRACTING INTEGERS ON A NUMBER LINE
We can show a subtraction expression on a number line by using dots and arrows to demonstrate what is happening: If we wanted to show 5 - 4, we would start at the first number in the expression, 5: Then, we look at he symbol that follows the first number in the expression. Because we are subtracting a positive, we will move that many spaces to the left: When we moved four spaces to the left, we landed on 1. The number we have landed on is our answer: August 18 – 21: Use as introduction to lesson, have student record notes (exactly as they are shown in the powerpoint) in their math journals. After daily notes, supplement with extra practice from the Chapter 3 textbook pages.
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SUBTRACTING INTEGERS ON A NUMBER LINE
When you subtract a positive number, you move that many spaces to the LEFT. Let’s see what that looks like: Ex. (- 2) We start at the first number in the expression, - 2: (- 2) Then, we subtract a positive 5, so we move five spaces to the left: (- 2) - 5 = -7 We landed on – 7, so (– 2) - 5 = (- 7) August 18 – 21: Use as introduction to lesson, have student record notes (exactly as they are shown in the powerpoint) in their math journals. After daily notes, supplement with extra practice from the Chapter 3 textbook pages.
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SUBTRACTING INTEGERS ON A NUMBER LINE
When you subtract a negative number, you move that many spaces to the RIGHT. Let’s see what that looks like: Ex. 0 – (- 7) We start at the first number in the expression, 0: 0 – (- 7) Then, we subtract a negative 7, so we move seven spaces to the right: 0 – (- 7) = 7 We landed on – 7, so (– 2) - 5 = (- 7) August 18 – 21: Use as introduction to lesson, have student record notes (exactly as they are shown in the powerpoint) in their math journals. After daily notes, supplement with extra practice from the Chapter 3 textbook pages.
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REVIEW SUBTRACTING INTEGERS
GUIDED PRACTICE Write an subtraction expression that is shown by the number lines below: A. B. Evaluate the expressions: C D. (-10) - 6 E. (- 14) – (- 9) F G – H. (- 16) - 4 I J REVIEW SUBTRACTING INTEGERS SUBTRACTING INTEGERS WITH SAME SIGNS AND DIFFERENT SIGNS Keep the first number Change the subtraction sign to addition Change the sign of the number after the addition sign Follow the rules for adding integers (check the signs) ON A NUMBER LINE Follow subtraction rules for integers Go right if adding a positive Go left if adding a negative The number you stop on is your solution August 18 – 21: Use as introduction to lesson, have student record notes (exactly as they are shown in the powerpoint) in their math journals. After daily notes, supplement with extra practice from the Chapter 3 textbook pages.
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INDEPENDENT PRACTICE SUBTRACTING INTEGERS
Use what you know about integers to respond to the questions below: K. Describe a subtraction situation that could be represented by the expression shown on the number line below. Explain your reasoning. L. Write the integers or integer expressions that match the situations below: Kennah withdraws six hundred fifty four dollars from her bank account The temperature was 75°F this morning and dropped 20°F by nightfall Sarah missed 24 points on her test, which had a highest possible score of 100 M. Compare the numbers below using the symbols < > = (-6) – (-3) ☐ 9 - (-2) (-9) ☐ (-7) (-10) - (-22) ☐ (-25) – (-13) August 18 – 21: Use as introduction to lesson, have student record notes (exactly as they are shown in the powerpoint) in their math journals. After daily notes, supplement with extra practice from the Chapter 3 textbook pages.
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CHAPTER 3, PART 1 QUIZ REVIEW August 18 - 21
August 18 – 21: Use as introduction to lesson, have student record notes (exactly as they are shown in the powerpoint) in their math journals. After daily notes, supplement with extra practice from the Chapter 3 textbook pages. COVERING STANDARDS 7.NS.1.1 & 7.NS.1.3
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MULTIPLYING INTEGERS August 23
August 23: Use as introduction to lesson, have student record notes (exactly as they are shown in the powerpoint) in their math journals. After daily notes, supplement with extra practice from the Chapter 3 textbook pages. How do negative numbers affect multiplication? 7.NS.1.2 & 7.NS.1.3
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MULTIPLYING INTEGERS: SAME SIGNS
When multiplying integers with the same signs, the answer is always POSITIVE: Ex × = [⨁⨁] [⨁⨁] [⨁⨁] = 6 Two positives in three equal groups is six positives. Ex × = -[⊖⊖⊖⊖] -[⊖⊖⊖⊖] = 8 Four negatives in two equal groups is eight positives. August 23: Use as introduction to lesson, have student record notes (exactly as they are shown in the powerpoint) in their math journals. After daily notes, supplement with extra practice from the Chapter 3 textbook pages. +2 +2 +2 -(-4) -(-4)
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MULTIPLYING INTEGERS: DIFFERENT SIGNS
When multiplying integers with different signs, the answer is always NEGATIVE: Ex. 3 × = [⊖⊖] [⊖⊖] [⊖⊖] = - 6 Two negatives in two equal groups is six negatives. Ex × 5 = [⊖] [⊖] [⊖] [⊖] [⊖] = - 5 Four negatives in two equal groups is eight positives. August 23: Use as introduction to lesson, have student record notes (exactly as they are shown in the powerpoint) in their math journals. After daily notes, supplement with extra practice from the Chapter 3 textbook pages. -2 -2 -2 -1 -1 -1 -1 -1
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REVIEW MULTIPLYING INTEGERS
GUIDED PRACTICE Evaluate the expressions: A. (-12) × 3 B. (-1) × (-30) C. 5 × (-6) D × 0 E. (-8) × (-7) F × (-2) G × (-4) H. (-9) × 2 Write an expression that describes the following: I. Lilly bought 4 pairs of blue jeans at $32 each How much money did she pay the clerk? J. Maggie owes the candy store $35. Each of 5 friends will help her pay off her debt. How much will each friend pay? REVIEW MULTIPLYING INTEGERS MULTIPLYING INTEGERS WITH SAME SIGNS WHEN YOU MULTIPLY INTEGERS WITH THE SAME SIGNS, THE ANSWER IS ALWAYS POSITIVE. MULTIPLYING INTEGERS WITH DIFFERENT SIGNS WHEN YOU MULTIPLY INTEGERS WITH THE SAME SIGNS, THE ANSWER IS ALWAYS NEGATIVE. August 23: Use as introduction to lesson, have student record notes (exactly as they are shown in the powerpoint) in their math journals. After daily notes, supplement with extra practice from the Chapter 3 textbook pages.
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INDEPENDENT PRACTICE MULTIPLYING INTEGERS
Use what you know about integers to respond to the questions below: K. Use multiplication symbols, grouping symbols, and the numbers in the set { - 1, 3, -5, 4, -2} to make the numbers below. Show your work: 60 - 24 24 30 -40 L. Compare the numbers below using the symbols < > = (-10) × 2 ☐ 4 × (-5) (-8) × (-9) ☐ (-3) × (-7) 4 × (-6) ☐ (-1) × 15 August 23: Use as introduction to lesson, have student record notes (exactly as they are shown in the powerpoint) in their math journals. After daily notes, supplement with extra practice from the Chapter 3 textbook pages.
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DIVIDING INTEGERS August 24
August 24: Use as introduction to lesson, have student record notes (exactly as they are shown in the powerpoint) in their math journals. After daily notes, supplement with extra practice from the Chapter 3 textbook pages. How do negative numbers affect division? 7.NS.1.2 & 7.NS.1.3
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DIVIDING INTEGERS: SAME SIGNS
When dividing integers with the same signs, the answer is always POSITIVE: Ex ÷ = [⨁⨁⨁] [⨁⨁⨁] [⨁⨁⨁] = 3 Positive nine split into three groups is positive three. Ex ÷ = [⊖⊖⊖⊖ ] [⊖⊖⊖⊖ ] = 2 Eight negatives divided by negative four is two. 3 3 3 August 24: Use as introduction to lesson, have student record notes (exactly as they are shown in the powerpoint) in their math journals. After daily notes, supplement with extra practice from the Chapter 3 textbook pages. (-4) (-4)
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DIVIDING INTEGERS: DIFFERENT SIGNS
When dividing integers with different signs, the answer is always NEGATIVE: Ex ÷ = -1 Five negatives split into five equal groups shows negative one in each group. Ex ÷ = [⊖⊖⊖] [⊖⊖⊖] = - 5 Six positives split by negative three results in two equal groups. -1 -1 -1 -1 -1 August 24: Use as introduction to lesson, have student record notes (exactly as they are shown in the powerpoint) in their math journals. After daily notes, supplement with extra practice from the Chapter 3 textbook pages. -3 -3
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REVIEW DIVIDING INTEGERS
GUIDED PRACTICE Evaluate the expressions: A. 45 ÷ (-9) B. (-63) ÷ (-3) C. (-70) ÷ D. 81 ÷ (-18) E. (-24) ÷ (-8) F. 77 ÷ (-7) G. (-19) ÷ (-1) H. (-36) ÷ 12 Write an expression that describes the following: I. A person has a debt of $200. Five friends offer to pay off all of the debt. How much does each person need to pay in order to pay off the debt? J. A sprinkler was -8 feet below ground level. Mr. S has a machine that digs - 2 feet at a time. How many digs does he need to make in order to reach the sprinkler? REVIEW DIVIDING INTEGERS DIVIDING INTEGERS WITH SAME SIGNS WHEN YOU DIVIDE INTEGERS WITH THE SAME SIGNS, THE ANSWER IS ALWAYS POSITIVE. DIVIDING INTEGERS WITH DIFFERENT SIGNS WHEN YOU DIVIDE INTEGERS WITH THE SAME SIGNS, THE ANSWER IS ALWAYS NEGATIVE. August 24: Use as introduction to lesson, have student record notes (exactly as they are shown in the powerpoint) in their math journals. After daily notes, supplement with extra practice from the Chapter 3 textbook pages.
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INDEPENDENT PRACTICE DIVIDING INTEGERS
Use what you know about integers to respond to the questions below: K. Use division symbols, grouping symbols, and the numbers in the set {-100,150, -5, 2, -3, 6, -4} to make the numbers below. Show your work: 10 -5 -1 -30 -7 L. Compare the numbers below using the symbols < > = (-21) ÷ (-7) ☐ (-44) ÷ (11) (-39) ÷ 3 ☐ 90 ÷ (-9) ÷ 6 ☐ (-60) ÷ (-3) August 24: Use as introduction to lesson, have student record notes (exactly as they are shown in the powerpoint) in their math journals. After daily notes, supplement with extra practice from the Chapter 3 textbook pages.
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CHAPTER 3 TEST REVIEW August 25-28
August 25-28: Use as introduction to lesson, have student record notes (exactly as they are shown in the powerpoint) in their math journals. After daily notes, supplement with extra practice from the Chapter 3 textbook pages. COVERING STANDARDS 7.NS.1.1, 7.NS.1.2 & 7.NS.1.3 TEST ON AUGUST 29
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