Date Learning Target/s Classwork Homework Self-Assess Your Learning. and negative. Pg. 5-6: ATN 1.2- Extending the number line

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1 Accentuate the Negative: Investigation 1 Name: Per: Investigation 1: Extending the Number Line Date Learning Target/s Classwork Homework Self-Assess Your Learning Day 1 Students will locate and Pg. 2-3: ATN 1.1 Pg. 4: ATN compare numbers on a Using positive 1.2( Take number line, interpret and and negative notes with write number sentences, and find the difference between numbers EdPuzzle ) two numbers. Day 2 Day 3 Day 4 Students will estimate values of positive and negative points on a number line. They develop informal strategies for comparing, ordering, and locating numbers and their opposites on a number line. Students focus on both distance and direction as they describe changes in temperature and represent these changes with number sentences. Students explore relationships between addition and subtraction on chip-board displays. Pg. 5-6: ATN 1.2- Extending the number line Pg. 8-9: ATN 1.3- From Sauna to Snowbank Pg : ATN 1.4-Using the chip model Day 5 Extra Practice Pg. 14 and 15- Pizzaz puzzle Inv. 1 Pg. 7: ATN 1.3 ( Take notes with EdPuzzle ) Pg. 10: ATN 1.4a (Take notes with EdPuzzle) Pg. 13: ATN 1.4b (Take notes with EdPuzzle) Completed packet/ signed CCSS.MATH.CONTENT.7.NS.1: Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. a. Describe situations in which opposite quantities combine to make 0. b. Describe situations in which opposite quantities combine to make 0. For example, a hydrogen atom has 0 charge because its two constituents are oppositely charged. CCSS.MATH.CONTENT.7.E.E.4: b. Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem Student Signature: Due: Parent/Guardian Signature: Due: 1

2 Day 1 1.1: Playing Math Fever Using Positive and Negative Numbers A. At one point in a game of Math Fever, the scores are as follows: Super Brains (SB): -300 Rocket Scientists (RS): 150 Know-It-Alls (KIA): -500 Label each team s score on the number line below: Which team has the highest score? Which team has the lowest score? Explain how you decided. 2. Find the difference in points for each pair of teams. (Hint: Look at the number line.) SB and RS SB and KIA RS and KIA 3. Use number sentences to show two possible ways that each team reached its score (remember that questions are worth 50, 100, 150, 200, or 250 points). SB RS KIA B. Write a number sentence to represent each sequence of points after another round of the game. 1. Super Brains: Start with -300 points, then answer a 200-point question correctly, a 150-point question incorrectly, a 50-point question correctly, and a 50-point question correctly. What is their score now? 2. Rocket Scientists: Start with 150 points, then answer a 50-point question incorrectly, a 200-point question incorrectly, a 100-point question correctly, and a 150-point question incorrectly. What is their score now? 3. Know-It-Alls: Start with -500 points, then answer a 100-point question incorrectly, a 200-point question correctly, a 150-point question incorrectly, and a 50-point question incorrectly. What is their score now? 4. Label each team s new score on the number line below: 2

3 Which team has the highest score? Explain how you decided. C. Find the difference in points for each pair of teams. SB and RS SB and KIA RS and KIA D. The number sentences below describe what happens during a game of Math Fever. For each number sentence find the missing number and explain what the sentence tells about a team s performance and overall score. 1. BrainyActs: = 2. Xtremes: = 3. ExCells: = 4. AmazingMs: = -150 E. Sam forgot to record a score. Sam wrote this number sentence: = What score goes in the missing space? Explain how you know your answer makes sense. F. Find three different pairs of numbers that have a sum of G. Luisa answers a 300-point question correctly and a 400-point question incorrectly. Luisa and Sam use different methods to keep score. Who is correct? Explain your reasoning. Luisa s Method: = -100 Sam s Method: =

4 Day 1 Homework: ATN 1.2 Watch (EdPUzzle Video) Introduction to inequalities < or >=, Looks like when plotted on the number line. or =, looks like when plotted on the number line. Example 1: Graph: x<3 This says: any 3. What kind of dot will be plotted(circle)? Open closed Example 2: Graph: x -4 This says : any -4. What kind of dot will be plotted(circle)? Open closed Try: Complete the number plots below 1. X< x 4 3. x 5 4. x> 3 4

5 Day 2 Problem 1.2: Extending the Number Line A. Use the number line below: Estimate values for points A-E and their opposites. A = Opposite of A = B = Opposite of B = C = Opposite of C = D = Opposite of D = E = Opposite of E = 1. A thermometer can be thought of as part of a vertical number line on which values above zero are positive. Use the thermometer (vertical number line) at right and place the following temperatures on it. Explain to your group members how you decided where each temperature should be placed How do the number lines from parts (1) and (3) help you find which of two numbers is greater? B. For each pair of temperatures, identify which temperature is further from -2 F. Explain how you decided or or or -7 5

6 or 7 C. Identify the temperature that is halfway between each pair of temperatures. Explain your reasoning and and and and 8 D. Integers are also used in chemistry. For example, a hydrogen atom has one proton, which has a charge of +1, and one electron, which has a charge of -1. The total charge of a hydrogen atom is +1 and -1, or 0. Describe three more real-life situations in which opposite quantities combine to make 0. E. Recall that the graph of an inequality is a sketch on a number line on which possible answers are shaded. For each part, graph the possible solutions for x on a number line. 1. x is positive 2. x is less than or equal to x < x < x x F. Find the values of x that satisfy the inequality. Then graph the solutions. 1. x + 5 > 0 2. x x < 9 G. Describe how you drew your graphs for Questions E and F. 6

7 Day 2 Homework: ATN 1.3 Take Notes through ED puzzle One horizontal number line can show the same information as the two thermometers. 1) What does n represent? 2) What does the number sentence 120+n=-20 tell you? 3) What does the number sentence -20+n=120 tell you? The national weather service keeps records of temperature changes. The world record for the fastest rise in outside air temperature occurred in Spearfish, South Dakota, on January 22, The temperature rose from -4 F to 45 F in two minutes. 4) What was the temperature change over those 2 minutes? 5) How could you show this change on a number line? From -4 F to 0 F is a change of +4 F. From 0 F to 45 F. The total change is +49 F. The following number sentence shows this: 4 + n = = 45 The sign of the change in temperature shows the direction of the change. In this case +49 means the temperature increase 49 F. If the temperature had instead dropped 10 F from -4 F you would write the change as -10 F. The final temperature would be -14 F. Number sentence: Try! If the current temperature is 5 F, what change in temperature would result in a final temperature of -25 F? Write an number sentence to represent the scenario. 7

8 Day 3 Problem 1.3: From Sauna to Snowbank Using a Number Line A. A person goes from a sauna at 115 degrees F to an outside temperature of -30 degrees F. What is the change in temperature? Sketch a number line and write a number sentence. B. The temperature reading on a thermometer is 25 degrees F at noon. During the afternoon, the temperature changes. What is the new reading for each temperature change? Sketch a number line and write a number sentence for each scenario. 1. Rises 10 degrees F 2. Falls 2 degrees F 3. Falls 30 degrees F C. The temperature reading on a thermometer is -15 degrees F. What is the new reading for each temperature change? Sketch a number line and write a number sentence for each scenario degrees F degrees F degrees F D. What is the change in the temperature when the thermometer reading moves from the first temperature to the second temperature? Sketch a number line and write a number sentence for each scenario degrees F to -10 degrees F 8

9 degrees F to -10 degrees F degrees F to 10 degrees F degrees F to -20 degrees F degrees F to 10 degrees F degrees F to 20 degrees F 7. Describe a strategy for finding the difference of two temperatures. E. The temperature was -5 degrees F when Sally went to school on Monday. The temperature rose 20 degrees F during the day, but fell 25 degrees F during the night. A heat wave increased the temperature 40 degrees F on Tuesday, but then an arctic wind overnight decreased the temperature 70 degrees F. What was the temperature on Wednesday? Write a number sentence and explain how you found your answer. Sally s work for finding Monday s temperature changes for the problem above is shown below. Do you agree with Sally s computation? Explain your reasoning. 9

10 Day 3 Homework-ATN 1.4A (Take Notes with EDPUZZLE) A. Black chip = Red chip= negative +positive= Using the chip model, what are some ways to show a total value of zero? Julia changes the chip board by adding one red chip and one black chip. By how much has Julia changed the total value? B. Use the chip board as the STARTING VALUE FOR EACH NUMBER, write a number sentence to show the total value on the chip board for each move. 1. Original chip board 2. Add 5 black chips 3. Remove 5 red chips 4. Remove 3 black chips 5. Add 3 red chips C. Find the missing part for each chip problem. Write a number sentence for each problem 10

11 Day 4: Problem 1.4: In the Chips Using a Chip Model A. Use this chip board as the starting value for each part: Find the value of the original chip board. Draw a diagram and write a number sentence to show the total value on the chip board for each move. Start With Rule End With Diagram Number Sentence Add 5 black chips Remove 5 black chips Remove 3 black chips Add 3 red chips What patterns do you see? B. Start with the original chip board from Question A. Find three number sentences that create each value. Start End Number Sentence 1 Number Sentence 2 Number Sentence 3 With With C. Give three combinations of red and black chips (using at least one of each color) that will equal each value. Value Combination 1 Combination 2 Combination

12 D. Find the missing part for each chip problem. Write a number sentence for each problem. Start With Rule End With Diagram Number Sentence 3 red chips Add 5 black chips 2 red chips and 1 black chip Subtract 3 red chips 6 red chips 2 red chips Subtract 3 red chips 4 black chips E. Describe a chip board diagram that matches each number sentence. Find the missing value in each case = Diagram: = Diagram: (-2) = Diagram: = 1 Diagram: = Diagram: 6. - (-2) = 6 Diagram: F. Nadie has a chip board with 4 red chips. She needs to subtract 2 black chips, but there are no black chips on the board. Nadie says, It is impossible to subtract 2 black chips. There are none on the board! What can Nadie do to the chip board so that she can subtract 2 black chips? Explain your reasoning. 12

13 Day 4: Homework ATN 1.4B - (Take notes through EdPuzzle) Directions: Write a number sentence and determine the final position. You may use the number line OR the online chip model. Example 1: Start at 8. Add -7 Number sentence: Example 2: Start at -3. Subtract 5. Number sentence: Try! 1. Start at -7. Add 7 2. Start at -2. Add 12. Number sentence: Number sentence: 3. Start at 3. Subtract Start at -2. Subtract 2. Number sentence: Number sentence: 5 Start at 4. Subtract Start at 0. Subtract 5. Number sentence: Number sentence: Find the value for each labeled point on the number line. Then use the values to calculate each change. Example 3: A to B= Example 4: C to A= Try! 7. A to C= 8. B to A 9. C to B 10. B to C 13

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