Upcoming SlideShare
×

# 6 - mapping diagrams; functions as words & equations; input-output tables, review power point

1,411 views

Published on

0 Likes
Statistics
Notes
• Full Name
Comment goes here.

Are you sure you want to Yes No
• Be the first to comment

• Be the first to like this

Views
Total views
1,411
On SlideShare
0
From Embeds
0
Number of Embeds
8
Actions
Shares
0
4
0
Likes
0
Embeds 0
No embeds

No notes for slide
• 2198
1570
• 2198
1570
• Sophie 42
Diane 6
• Sophie 42
Diane 6
• Sophie 42
Diane 6
• Sophie 42
Diane 6
• ### 6 - mapping diagrams; functions as words & equations; input-output tables, review power point

1. 1. Sixth Grade Mapping Diagrams
2. 2. 6 -- Warm Up 9.1 Mapping Diagrams 6 3 9 57 2 5x + 7 < 92 9 – 2x ≥ 145 𝟒 𝟓 ÷ 𝟕 𝟗 145.2(21.5) ESSENTIAL QUESTION: What’s a mapping diagram? How can it be used to represent a function? COMMON CORE 6.EE.9
3. 3. 6 -- Warm Up [ANSWER KEY] 70 𝑢𝑛𝑖𝑡𝑠3 5x + 7 < 92 x = 17 9 – 2x ≥ 145 x = 68 𝟒 𝟓 ÷ 𝟕 𝟗 = 𝟑𝟔 𝟑𝟓 145.2(21.5) = 3,121.8 162 𝑢𝑛𝑖𝑡𝑠3
4. 4. Create a mapping diagram
5. 5. 6 -- Exit Slip Homework: Green WB pp194 Draw a Mapping Diagram of the ordered pairs List the ordered pairs in the Mapping Diagram Complete the Mapping Diagram. Describe a pattern algebraically. (1,5) (2,10) (3,10) (5, 20) (9, 6) (0, 0) (-9, -6) (-18, -12) 12 18 24 30 36 0 5 a b c 5 10 d 20 e 4 8 f
6. 6. 6 -- Exit Slip [ANSWER KEY] Homework: Green WB pp194 Draw a Mapping Diagram of the ordered pairs List the ordered pairs in the Mapping Diagram Complete the Mapping Diagram. Describe a pattern algebraically. (1,5) (2,10) (3,10) (5, 20) (9, 6) (0, 0) (-9, -6) (-18, -12) 12 18 24 30 36 0 5 10 15 20 5 10 15 20 2 4 8 10
7. 7. 6 -- Warm Up 9.2: Functions as Words & Expressions ESSENTIAL QUESTION: How do you describe a function with words & equations? COMMON CORE: 6.EE.9 -- Represent & analyze quantitative relationships between dependent & independent variables. Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent & independent variables using graphs & tables, & relate these to the equation. • Big Ideas Math Chapter Resource Book – Chapter Nine “Functions, Tables & Graphs” • 9.1 Practice A –Page 343 URL: http://www.mediafire.com/view/?qlixpb16ahbhb86
8. 8. 9.2 “Functions as Words & Expressions” Index Card Activity GROUPS OF THREE OR FOUR After each step cards should be passed to the student to the right. Step 1: Draw a polygon Step 2: Create a mapping diagram for their new card. Step 3: Write an equation that describes the function. Step 4: Check the work on the card
9. 9. 6 – Exit Slip 9.2: Functions as Words & Expressions • Big Ideas Math Chapter Resource Book – Chapter Nine “Functions, Tables & Graphs” • 9.2 Practice A – Page 349 1. y x = + 10 2. 2. y = 3x 3. y x = − 8 4. y x = 2 5. y = 4 6. y = 24 7. y = 39 8. y = 6 9. solution 10. not a solution 11. not a solution 12. solution 13 a. d h = 6 13 b. d = 12 miles 14 a. s a = − 4 14 b. s = \$3.50 14 c. a = \$6 URL: http://www.mediafire.com/view/?qlixpb16ahbhb86
10. 10. 6 – Warm Up 9.3: Input Output Tables ESSENTIAL QUESTION: How can you use a table to describe a function? COMMON CORE: 6.EE.9 • Big Ideas Math Chapter Resource Book – Chapter Nine “Functions, Tables & Graphs” • 9.2 Practice B – Page 350 URL: http://www.mediafire.com/view/?qlixpb16ahbhb86
11. 11. 9.3: Input Output Tables The output (y) is twice the input (x) x 0 4 8 12 y The output (y) is two times plus 4 the input (x) x 0 4 8 12 y The output (y) is five less than the input (x) x 0 4 8 12 y The input (x) is 6 more than the input (y) x y 12 18 24 30 DIRECTIONS: Write an equation for the function. Then complete the table, Use separate paper! x 3 6 9 y 9 36 81 x 1 6 10 x 3 4 4 5 9 10 20 20 y 3 18 30 y 3.75 4.00 4.50 5 DIRECTIONS: Write an equation for the table. Use separate paper! File Name: F:TeachingNorth East Carolina Prep SchoolLesson PlansMathAssigments6 – Input Output Tables x 0 5 10 x 1 7 13 19 y 1 16 31 y 4.5 31.5 58 1 2 92 + 4.5 DIRECTIONS: Complete the table. Make a mapping diagram as well. Use separate paper! URL
12. 12. Seventh Grade Volume of Prisms; Cylinder; Pyramid; Cones V = 1 3 𝜋𝑟2 (ℎ) V = 1 3 (𝑏)(ℎ) V = (a)(b)(c) V = 𝜋𝑟2 (ℎ) V = 5 2 (𝑎)(𝑏)(ℎ)
13. 13. 7 – Warm Up 7.0: Chapter Opener 7 – Multiplying 3 Digits by Two Digits DOCX URL Essential Question: N/A Common Core: N/A URL: http://www.scribd.com/doc/134235140/7-%E2%80%93-Multiplying-3-Digits-by-Two-Digits
14. 14. 7 – Warm Up 7.0: Chapter Opener [ANSWER KEY] 1) 11,988 6) 9384 11) 63,456 2) 11,592 7) 27579 12) 18,102 3) 23,791 8) 11,616 13) 24,852 4) 40,313 9) 70,176 14) 16,360 5) 33,733 10) 59,414 15) 12,350 URL: http://www.scribd.com/doc/134235140/7-%E2%80%93-Multiplying-3-Digits-by-Two-Digits 7 – Multiplying 3 Digits by Two Digits DOCX URL
15. 15. 7 -- Exit Slip 7.0 Chapter Opener 1. Molly and Lucy went to lunch at a cafe. They ordered a spinach salad for \$8.00, a tuna sandwich for \$6.60, and 2 glasses of lemonade for \$0.70 each. The tax was \$1.60. They gave the waiter \$20.00. How much change should they have received? 2. James had 13 green marbles. Then he bought 9 bags of blue marbles. There were 10 marbles in each bag. How many marbles does James have now? 3. Laura needs 100 cupcakes for a birthday party. She already has 34 chocolate cupcakes and 18 vanilla cupcakes. How many more cupcakes should Laura buy? HW: Finish Red Workbook pp 161 & 162 URL
16. 16. 7 -- Exit Slip 7.0 Chapter Opener [ANSWER KEY] 1. Molly and Lucy went to lunch at a cafe. They ordered a spinach salad for \$8.00, a tuna sandwich for \$6.60, and 2 glasses of lemonade for \$0.70 each. The tax was \$1.60. They gave the waiter \$20.00. How much change should they have received? \$2.40 2. James had 13 green marbles. Then he bought 9 bags of blue marbles. There were 10 marbles in each bag. How many marbles does James have now? 103 3. Laura needs 100 cupcakes for a birthday party. She already has 34 chocolate cupcakes and 18 vanilla cupcakes. How many more cupcakes should Laura buy? 48
17. 17. 7 – Warm Up 7.1: Volume of Prisms 7 – Multiplying Decimals 1 DOCX & URL ESSENTIAL QUESTION: How can you find the volume of a prism? COMMON CORE 7.G.6: Solve real-life & mathematical problems involving angle measure, area, surface area, & volume. Solve real-world & mathematical problems involving area, volume & surface area of two- & three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, & right prisms. URL: http://www.scribd.com/doc/134237433/7-%E2%80%93-Multiplying-Decimals-1
18. 18. 7 – Warm Up 7.1: Volume of Prisms [ANSWER KEY] 7 – Multiplying Decimals 1 DOCX & URL URL: http://www.scribd.com/doc/134237433/7-%E2%80%93-Multiplying-Decimals-1 1) 1,589.19 6) 569.95 11) 5,847.27 2) 2,448.3 7) 6496.55 12) 3,243.71 3) 320.93 8) 1,107.52 13) 1,033.82 4) 1,479.56 9) 1,833.01 14) 879.73 5) 2,404.87 10) 2,496.23 15) 1,507.51
19. 19. 7 Exit Slip 7.1 Volume of Prisms a = 4 b = 6 h = 12 HW: Red Workbook pp 166
20. 20. 7 Exit Slip 7.1 Volume of Prisms [ANSWER KEY] 24 𝑚𝑒𝑡𝑒𝑟𝑠3 36 𝑓𝑒𝑒𝑡3 1,920 𝑢𝑛𝑖𝑡𝑠3 720 𝑢𝑛𝑖𝑡𝑠3 a = 4 b = 6 h = 12
21. 21. 7 – Warm Up 7.2: Volume of Cylinders ESSENTIAL QUESTION: How can you find the volume of a cylinder? • 7.G.4: Solve real-life & mathematical problems involving angle measure, area, surface area, & volume. Know the formulas for the area & circumference of a circle & use them to solve problems; give an informal derivation of the relationship between the circumference & area of a circle. • 7.G.6: Solve real-life & mathematical problems involving angle measure, area, surface area, & volume. Solve real-world & mathematical problems involving area, volume & surface area of two- & three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, & right prisms • 8.G.9: Solve real-world & mathematical problems involving volume of cylinders, cones, & spheres. Know the formulas for the volumes of cones, cylinders, & spheres & use them to solve real-world & mathematical problems Big Ideas Math Chapter Resource Book – Chapter Seven “Volumes of Solids” • 7.1 Practice A –Page 291
22. 22. 7 – Warm Up 7.2: Volume of Cylinders [ANSWER KEY] Big Ideas Math Chapter Resource Book – Chapter Seven “Volumes of Solids” • 7.1 Practice A –Page 291 1) 𝟑𝟔 𝒊𝒏𝒄𝒉𝒆𝒔 𝟑 5) 𝟏𝟓 𝒊𝒏𝒄𝒉𝒆𝒔 𝟑 2) 𝟏𝟑𝟓 𝒎𝒆𝒕𝒆𝒓𝒔 𝟑 6) 𝟑𝟎𝟎 𝒎𝒆𝒕𝒆𝒓𝒔 𝟑 3) 𝟏𝟐𝟎 𝒄𝒆𝒏𝒕𝒊𝒎𝒆𝒕𝒆𝒓𝒔 𝟑 7) 𝟖 𝒊𝒏𝒄𝒉𝒆𝒔 𝟑 4) 𝟏𝟔 𝒚𝒂𝒓𝒅𝒔 𝟑 8) 𝟓, 𝟐𝟖𝟎 𝒊𝒏𝒄𝒉𝒆𝒔 𝟑 9. 8.7 gallons
23. 23. 7 – Exit Slip 7.2 Volume of Cylinders HW: Red Workbook pp 170 URL 10 7 feet 5 10 inches
24. 24. 7 – Exit Slip 7.2 Volume of Cylinders [ANSWER KEY] HW: Red Workbook pp 170 URL 10 7 5 10 2,198 𝑓𝑒𝑒𝑡3 1,570 𝑖𝑛𝑐ℎ𝑒𝑠3
25. 25. 7 – Warm Up 7.3: Volume of Pyramids • ESSENTIAL QUESTION: How can you find the volume of a pyramid? • 7.G.6: Solve real-life & mathematical problems involving angle measure, area, surface area, & volume. Solve real-world & mathematical problems involving area, volume & surface area of two- & three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, & right prisms Glencoe McGraw Hill Homework Practice Workbook Pre Algebra Chapter 12.3: Skills Practice “Volume of Cylinders” Page 167 URL: https://docs.google.com/file/d/0ByTURXvBusNWMXpZUkgxTTlxeGc/edit?usp=sharing
26. 26. 7 – Warm Up 7.3: Volume of Pyramids [ANSWER KEY] Glencoe McGraw Hill Homework Practice Workbook Pre Algebra Chapter 12.3: Skills Practice “Volume of Cylinders” Page 167 URL: https://docs.google.com/file/d/0ByTURXvBusNWMXpZUkgxTTlxeGc/edit?usp=sharing 1) 7) 13) 2) 8) 14) 3) 9) 15) 4) 10) 16) 5) 11) 17) 6) 12) 18)
27. 27. 7 – Warm Up 7.4: Volume of Cones • ESSENTIAL QUESTION: How can you find the volume of a cone? • 7.G.4: Solve real-life & mathematical problems involving angle measure, area, surface area, & volume. Know the formulas for the area & circumference of a circle & use them to solve problems; give an informal derivation of the relationship between the circumference & area of a circle. • 7.G.6: Solve real-life & mathematical problems involving angle measure, area, surface area, & volume. Solve real-world & mathematical problems involving area, volume & surface area of two- & three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, & right prisms • 8.G.9: Solve real-world & mathematical problems involving volume of cylinders, cones, & spheres. Know the formulas for the volumes of cones, cylinders, & spheres & use them to solve real-world & mathematical problems 7 – Volume of Pyramid 1 PDF & URL
28. 28. 7 – Warm Up 7.4: Volume of Cones [ANSWER KEY] 7 – Volume of Pyramid 1 PDF & URL 1) 𝟔𝟒 𝒚𝒂𝒓𝒅𝒔 𝟑 6) 𝟕𝟐 𝒄𝒆𝒏𝒕𝒊𝒎𝒆𝒕𝒆𝒓𝒔 𝟑 2) 𝟐𝟏 𝒎𝒆𝒕𝒆𝒓𝒔 𝟑 7) 𝟏𝟔 𝒎𝒊𝒍𝒆𝒔 𝟑 3) 𝟕𝟐 𝒚𝒂𝒓𝒅𝒔 𝟑 8) 𝟑𝟕 𝒊𝒏𝒄𝒉𝒆𝒔 𝟑 4) 𝟏𝟎 𝒎𝒆𝒕𝒆𝒓𝒔 𝟑 9) 𝟑𝟐𝟎 𝒊𝒏𝒄𝒉𝒆𝒔 𝟑 5) 𝟗𝟔 𝒇𝒆𝒆𝒕 𝟑 10) 𝟖𝟖 𝒎𝒊𝒍𝒆𝒔 𝟑
29. 29. 8th Grade Linear Equations Word Problems 04.08 – 04.12.2013
30. 30. 8 – Warm Up 3.4 :Real Life Linear Equations 8 – Two Step Equations 1 DOCX & URL ESSENTIAL QUESTION: How can you use linear equations with two variables to solve real life situations? COMMON CORE 8.EE.6: Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b. 8.F.4: Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values URL: http://www.scribd.com/doc/134324541/8-Two-Step-Equations-1
31. 31. 8 – Warm Up 3.4 :Real Life Linear Equations [ANSWER KJEY] 8 – Two Step Equations 1 DOCX & URL URL: http://www.scribd.com/doc/134324541/8-Two-Step-Equations-1 1) x= 5 5) x= 9 9) x= 0 2) x= 9 6) x= 7 10) x= 0 3) x= (-9) 7) x= 5 11) x= 1 4) x= 10 8) x= 5 12) x= (-6)
32. 32. 8 – Exit Slip 3.4 :Real Life Linear Equations Sophie reads 21 pages per hour. After a total of 2 hours of reading this week, how many pages will Sophie have read in all? Diane learns to perform 2 vocal pieces during each week of lessons. After 3 weeks of voice lessons, how many pieces will Diane be able to sing, in total? HW: 8 – Linear Equation Word Problems 5
33. 33. 8 – Exit Slip 3.4 :Real Life Linear Equations [ANSWER KEY] Sophie reads 21 pages per hour. After a total of 2 hours of reading this week, how many pages will Sophie have read in all? 42 Diane learns to perform 2 vocal pieces during each week of lessons. After 3 weeks of voice lessons, how many pieces will Diane be able to sing, in total? 6
34. 34. 8 – Warm Up 3.4 :Real Life Linear Equations 8 -- Systems of Linear Equations Multiplication Solve by Elimination Homework 12 ESSENTIAL QUESTION: How can you use linear equations with two variables to solve real life situations? COMMON CORE 8.EE.6: Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b. 8.F.4: Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values URL:
35. 35. 8 – Warm Up 3.4 :Real Life Linear Equations [ANSWER KEY] 8 -- Systems of Linear Equations Multiplication Solve by Elimination Homework 12 URL: 69) x = 3y - 5 3x - y = 9 answer: x = 4, y = 3 70) y = - 5x - 3 - 4x = - 3 - y answer: x = 0, y = -3 71) x = - 4y + 44 x + 2y = 26 answer: x = 8, y = 9 72) - 5y + 2x = 34 y = 3x - 12 answer: x = 2, y = -6 73) 4x = - 5y - 77 x = - 5y - 53 answer: x = -8, y = -9 74) 2y - x = - 3 y = - 2x - 24 answer: x = -9, y = -6 75) x = - y - 11 x = - 2y - 18 answer: x = -4, y = -7 76) x = - y - 7 - 4x + 2y = 40 answer: x = -9, y = 2
36. 36. 8 – Exit Slip 3.4 :Real Life Linear Equations Sophie reads 47 pages per hour. After a total of 3 hours of reading this week, how many pages will Sophie have read in all? Diane learns to perform 9 vocal pieces during each week of lessons. After 7 weeks of voice lessons, how many pieces will Diane be able to sing, in total? HW: 8 – Linear Equation Word Problems 6
37. 37. 8 – Exit Slip 3.4 :Real Life Linear Equations [AK] Sophie reads 47 pages per hour. After a total of 3 hours of reading this week, how many pages will Sophie have read in all? 141 Diane learns to perform 9 vocal pieces during each week of lessons. After 7 weeks of voice lessons, how many pieces will Diane be able to sing, in total? 63 HW: 8 – Linear Equation Word Problems 6
38. 38. 8 – Warm Up 3.5 :Real Life Systems of Linear Equations 8 -- Systems of Linear Equations Multiplication Solve by Elimination Homework 13 ESSENTIAL QUESTION: How can you use a system of linear equations with two variables to solve real life situations? COMMON CORE • 8.EE.8a • 8.EE.8b • 8.EE.8c URL:
39. 39. • Peak Valley MS has 1,200 students; decreasing by 30 per year • Southern Tier MS has 500 students; increasing by 40 students per year – In how many years will the schools have the same enrollment? Year (x) Peak Valley P Southern Tier S 0 1,200 500 1 2 3 4 5 6 7 8 9 10 Activity 3: Writing a System
40. 40. Activity 3: Writing a System • Peak Valley MS has 1,200 students; decreasing by 30 per year • Southern Tier MS has 500 students; increasing by 40 students per year – In how many years will the schools have the same enrollment? Year (x) Peak Valley P Southern Tier S 0 1,200 500 1 1,170 540 2 1,140 580 3 1,110 620 4 1,080 660 5 1,050 700 6 1,020 740 7 990 780 8 960 820 9 930 860 10 900 900
41. 41. Activity 3: Writing a System • Peak Valley MS has 1,200 students; decreasing by 30 per year • Southern Tier MS has 500 students; increasing by 40 students per year – In how many years will the schools have the same enrollment? • Peak Valley y = mx + b y = 30x + 1,200 • Southern Tier y = mx + b y = ____x + _____
42. 42. Activity 3: Writing a System • Peak Valley MS has 1,200 students; decreasing by 30 per year • Southern Tier MS has 500 students; increasing by 40 students per year – In how many years will the schools have the same enrollment? • Peak Valley y = mx + b y = -30x + 1,200 • Southern Tier y = mx + b y = 40x + 500
43. 43. Activity 4: Writing a System YOU • NECP has 400 students; increasing by per year 500 • ECPS has 7,400 students; decreasing by 400 students per year – In how many years will the schools have the same enrollment? Year (x) NECP ECPS 0 400 7,400 1 7,000 2 1,400 3 6,200 4 5,800 5 6 5,000 7 5,400 8 9 10
44. 44. Activity 4: Writing a System • NECP has 400 students; increasing by per year 500 • ECPS has 7,400 students; decreasing by 400 students per year – In how many years will the schools have the same enrollment? (if possible) Year (x) NECP ECPS 0 400 7,400 1 900 7,000 2 1,400 6,600 3 1,900 6,200 4 2,400 5,800 5 2,900 5,400 6 3,400 5,000 7 3,900 4,600 8 4,300 4,200 9 4,800 3,800 10
45. 45. Activity 4: Writing a System • NECP has 400 students; increasing by per year 500 • ECPS has 7,400 students; decreasing by 400 students per year – In how many years will the schools have the same enrollment? (if possible) • YOU • NECP y = mx + b y = _____x + _______ • ECPS y = -mx + b y = -_____x + _______
46. 46. Activity 4: Writing a System • NECP has 400 students; increasing by per year 500 • ECPS has 7,400 students; decreasing by 400 students per year – In how many years will the schools have the same enrollment? (if possible) • YOU • NECP y = mx + b y = 500x + 400 • ECPS y = -mx + b y = -400x + 7,400
47. 47. • Blue Workbook – 71 – 73 – HW: Blue WB 74