TOPIC 5-1: THE COORDINATE PLANE https://www.khanacademy.org/math/geometry/hs-geo-transformations/hs-geo-reflections/v/reflecting-points

10-30-2017 MONDAY TUESDAY WEDNESDAY THURSDAY FRIDAY WARM-UP MULTIPLICATION FACTS REVIEW Graph ordered pair for points, and identify quadrant it, the hexagon is shifted three units up and 6 units, the line segment   LESSON COORDINATE PLANE, RELATIONS, DOMAIN, RANGE, TRANSFORMATION USING PROBLEM-SOLVING STRATEGIES 5.1 USING PROBLEM-SOLVING STRATEGIES A translation is a geometric transformation  If the line segment is reflected over the x-axis, what would be the new coordinates for each Y point? If the hexagon is shifted three units up and 2 units left, what would be the new coordinates? Hexagon (root word) Transformation: Dilation, rotation, translation 5-2: RELATIONS, DOMAIN, & RANGE Project: Transformation 5.3 functions 5.4 Graphs and functions PRACTICE https://www.khanacademy.org/math/basic-geo/basic-geo-transformations-congruence/basic-geometry-translations/e/translations

Word Problems Solving Strategies GUESS, CHECK, AND REVISE Guessing and checking is helpful when a problem presents large numbers or many pieces of data, or when the problem asks students to find one solution but not all possible solutions to a problem. When students use this strategy, they guess the answer, test to see if it is correct and if it is incorrect they make another guess using what they learned from the first guess. In this way, they gradually come closer and closer to a solution by making increasingly more reasonable guesses. Students can also use this strategy to get started, and may then find another strategy which can be used. DRAW A PICTURE For some students, it may be helpful to use an available picture or make a picture or diagram when trying to solve a problem. The representation need not be well drawn. It is most important that they help students understand and manipulate the data in the problem. ACT IT OUT OR USE OBJECTS Some students may find it helpful to act out a problem or to move objects around while they are trying to solve a problem. This allows them to develop visual images of both the data in the problem and the solution process. By taking an active role in finding the solution, students are more likely to remember the process they used and be able to use it again for solving similar problems. MAKE AND USE AN ORGANIZED LIST, TABLE, CHART OR GRAPH Making an organized list, table, chart or graph helps students organize their thinking about a problem. Recording work in an organized manner makes it easy to review what has been done. Students keep track of data, spot missing data, and identify important steps that must yet be completed. It provides a systematic way of recording computations. Patterns often become obvious when data is organized. This strategy is often used in conjunction with other strategies. LOOK FOR A PATTERN A pattern is a regular, systematic repetition. A pattern may be numerical, visual, or behavioral. By identifying the pattern, students can predict what will "come next" and what will happen again and again in the same way. Sometimes students can solve a problem by recognizing a pattern, but often they will have to extend a pattern to find a solution. Making a number table often reveals patterns, and for this reason is frequently used in conjunction with looking for patterns. USE LOGICAL REASONING Logical reasoning is really used for all problem solving. However, there are types of problems that include or imply various conditional statements such as, "if.. then," or "if.. then.. else," or "if something is not true, then...” The data given in the problems can often be displayed in a chart or matrix. This kind of problem requires formal logical reasoning as a student works his or her way through the statements given in the problem. WORK BACKWARD To solve certain problems, students must make a series of computations, starting with data presented at the end of the problem and ending with data presented at the beginning of the problem. SOLVE A SIMPLER OR A SIMILAR PROBLEM Making a problem simpler may mean reducing large numbers to small numbers, or reducing the number of items given in a problem. The simpler representation of the problem may suggest what operation or process can be used to solve the more complex problem. GUESS, CHECK, AND REVISE DRAW A PICTURE ACT IT OUT OR USE OBJECTS MAKE AND USE AN ORGANIZED LIST, TABLE, CHART OR GRAPH LOOK FOR A PATTERN USE LOGICAL REASONING WORK BACKWARD SOLVE A SIMPLER OR A SIMILAR PROBLEM

---------------------------------------------------------------------------------------------- GUESS, CHECK, AND REVISE DRAW A PICTURE ACT IT OUT OR USE OBJECTS USE LOGICAL REASONING LOOK FOR A PATTERN WORK BACKWARD SOLVE A SIMPLER OR A SIMILAR PROBLEM MAKE AND USE AN ORGANIZED LIST, TABLE, CHART OR GRAPH GUESS, CHECK, AND REVISE DRAW A PICTURE ACT IT OUT OR USE OBJECTS USE LOGICAL REASONING LOOK FOR A PATTERN WORK BACKWARD SOLVE A SIMPLER OR A SIMILAR PROBLEM MAKE AND USE AN ORGANIZED LIST, TABLE, CHART OR GRAPH

Monday

http://www. mathsisfun. com/algebra/word-questions-addition http://www.mathsisfun.com/algebra/word-questions-addition.html MONDAY WARM-UP Sofia had 6 mice and was given 7 more, how many mice does she have now? Patrick lost 7 dollars, and now has only 3 dollars. How many did he have before? Jill gives a woman 3 pens. A woman already had 3 pens. So how many does a woman have now? Sofia was carrying balloons but the wind blew 7 away. She has 5 balloons left. How many did she start with? DEMONSTRATE: THE PROBLEM SOLVING STRATEGIES AND KEEP THE NOTES IN YOUR FOLDER. GUESS, CHECK, AND REVISE Guessing and checking is helpful when a problem presents large numbers or many pieces of data, or when the problem asks students to find one solution but not all possible solutions to a problem. When students use this strategy, they guess the answer, test to see if it is correct and if it is incorrect they make another guess using what they learned from the first guess. In this way, they gradually come closer and closer to a solution by making increasingly more reasonable guesses. Students can also use this strategy to get started, and may then find another strategy which can be used. DRAW A PICTURE For some students, it may be helpful to use an available picture or make a picture or diagram when trying to solve a problem. The representation need not be well drawn. It is most important that they help students understand and manipulate the data in the problem.

An ordered pair is a pair of numbers that describes a ______________ on the coordinate plane. Is it a function __________________ Write the coordinates in order from least to greatest on the map and “t” chart. REVIEW EXAMPLES: Graph the ordered pair for each point, and tell which quadrant it is located in. A(5, -1) _______ E(0,-3) _______ B(1, 3.5) _______ F(0, 2) _______ C(-3, 0) _______ G(-1/2, 1) _______ D(-6, 7) _______ H(5, 0) _______ MAPPING “t” chart X Y x y

EXAMPLES: Plot the following points: A translation is a is a geometric transformation that moves every point of a figure or a space by the same amount in a given direction that moves the graph to a new position ____________________ and/or ____________________ on the coordinate plane. A reflection _______________ a figure over a line of reflection. TOPIC 5-1: THE COORDINATE PLANE Label the following parts of the coordinate plane: x-axis _______ y-axis ______ Origin ______ Quadrants 1. ______ 2. ______ 3. ______ 4. ______ A E D B C F G

A man lost 2 times as many mice as he has. He has only 8 mice now A man lost 2 times as many mice as he has. He has only 8 mice now. How many did he have before? A man lost 4 times as many mice as he has. He has only 6 mice now. How many did he have before?

Tuesday Follow the directions for the following story problems. Read through the problem. Circle #s, box important words and build a house around the independent part of the problem. What problem-solving strategy could you use? ______________________ Set up the equation. ___________________________________________

https://www. khanacademy https://www.khanacademy.org/math/basic-geo/basic-geo-transformations-congruence/basic-geometry-translations/e/translations TUESDAY REVIEW

DEMONSTRATE: THE PROBLEM SOLVING STRATEGIES AND KEEP THE NOTES IN YOUR FOLDER. Cut out the hexagons to use with the coordinate quadrants. If the hexagon is shifted three units up and 2 units left, what would be the new coordinates of the following points:   A__________; D__________ X If the segment is reflected over the x-axis, what would be the new coordinates for each Y point?   X__________; Y__________   What would they be if it was reflected over the y-axis?  X__________; Y__________

If the hexagon is shifted three units up and 6 units left, what would be the new coordinates of the following points:   A_________; D_________ X What would they be if it was reflected over the y-axis? X_________;Y________

Wednesday 1-1 Variables and Expressions Variable Algebraic Expression English Math

http://www. mathsisfun. com/algebra/word-questions-addition http://www.mathsisfun.com/algebra/word-questions-addition.html WEDNESDAY REVIEW "A man was carrying balloons but the wind blew 5 times as many away. He has 6 balloons left. How many did he start with?" Yesterday you saw 5 robins on the grass, and 2 flying past. How many robins did you see altogether? Jasmine has 3 mice and plans to get 3 more tomorrow. How many will she have then? Henry gives Mr. Edwards 10 pens. Mr. Edwards already had 4 pens. So how many does Mr. Edwards have now? DEMONSTRATE: THE PROBLEM SOLVING STRATEGIES AND KEEP THE NOTES IN YOUR FOLDER.

A #4-1 Independent and Dependent Variables INDEPENDENT VARIABLE – ____ value, on the ___-axis. DEPENDENT VARIABLE - ____ value, on the ___ - axis. The value of the DEPENDENT VARIABLE ________ on the value of the INDEPENDENT VARIABLE. The DEPENDENT VARIABLE is a ______________ the INDEPENDENT VARIABLE.

Follow the directions for the following story problems.   Read through the problem. Circle #s, box important words and build a house around the independent part of the problem. What problem-solving strategy could you use? ______________________ Set up the equation. ___________________________________________ On average, Jay can ride his bike 12 miles in one hour. The function m = 12h represents the number of miles, “m”, he can ride in “h” hours. Input variable ____________ What goes inside of the house? ______ Output variable___________ What is outside of the “house”? ______ What is independent? _____ What is dependent? _______________ Which quantity is this relationship is the dependent quantity? _______ Which quantity is this relationship is the independent quantity? ______ Which of the following statements is true? The number of hours depends on the number of miles. The number of miles depends on the number of hours. On average, Jay can ride his bike 12 miles in one hour. The function m=12h, he can ride in h hours. After work, Jay only has 4 hours to ride his bike before it gets dark. What domain and range are reasonable for this situation? D: ______________________ R: _____________________ a._________________ b._________________ c._________________ d._________________ e._________________ f._________________

Follow the directions for the following story problems. Read through the problem. Circle #s, box important words and build a house around the independent part of the problem. What problem-solving strategy could you use? ______________________ Set up the equation. ___________________________________________ Paul pays a $27.00 fee and $15 each hour he uses the sailboat. Let “c” represent the total cost of renting the sailboat for “h” hours.   Write the equation __________________. Write in function notation ___________________________. Which quantity in this relationship is the independent quantity? _________ Which quantity in this relationship is the dependent quantity? _________ Paul has a budget of #$200 to spend on renting the sailboat. What domain and range are reasonable for this situation? Nickname for Domain, Range and x,y. ___________ a._________________ b._________________ c._________________ d._________________ e._________________ f._________________

Follow the directions for the following story problems. Read through the problem. Circle #s, box important words and build a house around the independent part of the problem. What problem-solving strategy could you use? ______________________ Set up the equation. ___________________________________________ Katie’s mom gave her $15 to send flowers to her friend for her birthday. To determine the total cost of the flowers, T, the equation T = 0.60L + 7.50 can be used, where L represents the number of lilies used in the arrangement. Which quantity in this relationship is the dependent quantity? ________ Which quantity in this relationship is the independent quantity? _______   Nickname for Domain, Range and x,y. ___________ a._________________ b._________________ c._________________ d._________________ e._________________ f._________________

5-2: RELATIONS, DOMAIN, & RANGE   A RELATION is a set of __________ ____________. Relations can be expressed in five different ways: 1) _________________________________ 2) ________________________________ 3) _________________________________ 4) ________________________________ 5) _________________________________ If the line segment is reflected over the x-axis, what would be the new coordinates for each Y point?   X________; Y________   What would they be if it was reflected over the y-axis? https://sites.google.com/a/csisd.org/amchsalgebra1/unit-4/4-1-independent-and-dependent

Write the equation and make a function box with mapping, “t” chart, and graph the information. Use the problem-solving strategies. Michelle took the train due south from the airport, heading to the end of the line. At the same time, Sheng also left home and started driving due north to the end of the line, where he would pick Michelle up. Michelle's train traveled 42 miles per hour, and Sheng drove 51 miles per hour. They started out 49 miles apart and arrived at the station at the same time. How long did it take them to meet? ACT IT OUT OR USE OBJECTS Some students may find it helpful to act out a problem or to move objects around while they are trying to solve a problem. This allows them to develop visual images of both the data in the problem and the solution process. By taking an active role in finding the solution, students are more likely to remember the process they used and be able to use it again for solving similar problems. MAKE AND USE AN ORGANIZED LIST, TABLE, CHART OR GRAPH Making an organized list, table, chart or graph helps students organize their thinking about a problem. Recording work in an organized manner makes it easy to review what has been done. Students keep track of data, spot missing data, and identify important steps that must yet be completed. It provides a systematic way of recording computations. Patterns often become obvious when data is organized. This strategy is often used in conjunction with other strategies.

If the line segment is reflected over the x-axis, what would be the new coordinates for each Y point?   X________; Y________   What would they be if it was reflected over the y-axis?

What is the RANGE? ______________ Nickname for x, y, domain and range. _______________________________

KEY D = 2,3,6,-1 R = 4,5,3 FUNCTION: YES(NO REPEATING X) D = 1, -2, -4, 2 R = 9,5,6,-3,8 FUNCTION: NO (REPEATING X)

Thursday

DEMONSTRATE: THE PROBLEM SOLVING STRATEGIES AND KEEP THE NOTES IN YOUR FOLDER. http://www.mathsisfun.com/algebra/word-questions-addition.html Write the equation and make a function box with mapping, “t” chart, and graph the information. Use the problem-solving strategies. Sofia had 63 mice and was given 7 more, how many mice does she have now? Yesterday you saw 20 seagulls on the grass, and 6 times as many flew past. How many seagulls did you see altogether? Jill gives a woman 23 pens. A woman already had 3 pens. So how many does a woman have now? Patrick has 17 sparkle markers and plans to get 4 more tomorrow. How many will he have then?

X Y -1 1

KEY DOMAIN RANGE X Y 2, 12; 2, -3; 1, 5; 0, 0 NOT A FUNCTION

KEY

DEMONSTRATE: THE PROBLEM SOLVING STRATEGIES AND KEEP THE NOTES IN YOUR FOLDER. GUESS, CHECK, AND REVISE Guessing and checking is helpful when a problem presents large numbers or many pieces of data, or when the problem asks you to find one solution but not all possible solutions to a problem. When you use this strategy, guess the answer, test to see if it is correct and if it is incorrect they make another guess using what they learned from the first guess. In this way, they gradually come closer and closer to a solution by making increasingly more reasonable guesses. You can also use this strategy to get started, and may then find another strategy which can be used. Josh has 7 sparkle markers and plans to get 7 more tomorrow. How many will he have then? Mrs. Jones was carrying balloons but the wind blew 6 away. She has 7 balloons left. How many did she start with?

Friday

Write the equation and make a function box with mapping, “t” chart, and graph the information. Use the problem-solving strategies. Sam has mice and plans to get three times as many as he has now minus 8. How many will he have then? Sam has several mice and plans to get twice as many as he has now. How many will he have then?

Write the equation and make a function box with mapping, “t” chart, and graph the information. Your teacher has 5 sparkle markers and plans to get 9 more tomorrow. If a student borrows 3, how many will she have tomorrow? DEMONSTRATE: THE PROBLEM SOLVING STRATEGIES AND KEEP THE NOTES IN YOUR FOLDER. http://www.mathsisfun.com/algebra/word-questions-addition.html Mrs Jones was carrying balloons but the wind blew 6 away. He has 7 balloons left. How many did he start with?

f(1) + g(3) = _______________   e) 2[g(-2)] + 3[f(2)] = __________

KEY g*(-2) [5 – (3*-2)] F* (2) 2 * [5 - (3 * -2)] = [22 + (4 * 2)] 2 * [5 - (3 * -2)] = 2 * [5 + (-3*-2)] = 2 * [5 + 6] = 2 * [11] = 22 F* (2) [22 + (4 * 2)] * [22 + (4 * 2)] = 3 * [4 + 8 ]= 3 * [12] = 36 2 [ 5 - ( 3 * - 2) ] + [ 3 [2]2 + (4 * 2)] 2[5 - (3 * - 2)] + 3[2]2 + (4 * 2) 2[5 - (-6)] + 3[2]2 + (8) 2[5 + 6] + 3 * [ 4 + (8)] 2[11] + 3[ 12] 22 + 36 = 58 DEMONSTRATE: THE PROBLEM SOLVING STRATEGIES AND KEEP THE NOTES IN YOUR FOLDER.

Monday

USE LOGICAL REASONING Logical reasoning is really used for all problem solving. However, there are types of problems that include or imply various conditional statements such as, "if.. then," or "if.. then.. else," or "if something is not true, then...” The data given in the problems can often be displayed in a chart or matrix. This kind of problem requires formal logical reasoning as you work your way through the statements given in the problem.

LOOK FOR A PATTERN A pattern is a regular, systematic repetition. A pattern may be numerical, visual, or behavioral. By identifying the pattern, students can predict what will "come next" and what will happen again and again in the same way. Sometimes you can solve a problem by recognizing a pattern, but often you will have to extend a pattern to find a solution. Making a number table often reveals patterns, and for this reason is frequently used in conjunction with looking for patterns.

MAKE AND USE AN ORGANIZED LIST, TABLE, CHART OR GRAPH Making an organized list, table, chart or graph helps students organize their thinking about a problem. Recording work in an organized manner makes it easy to review what has been done. You keep track of data, spot missing data, and identify important steps that must yet be completed. It provides a systematic way of recording computations. Patterns often become obvious when data is organized. This strategy is often used in conjunction with other strategies.

ACT IT OUT OR USE OBJECTS You may find it helpful to act out a problem or to move objects around while you are trying to solve a problem. This allows you to develop visual images of both the data in the problem and the solution process. By taking an active role in finding the solution, you are more likely to remember the process you used and be able to use it again for solving similar problems. 30

REVIEW AND ASSESSMENT Tuesday

“t” chart

https://sites. google. com/a/csisd https://sites.google.com/a/csisd.org/amchsalgebra1/unit-4/4-5-graphing-y-mx-b-and-linear-parent-function

Directions: Use at least one of your problem solving strategies. Write the equation and make a function box with mapping, “t” chart, and graph the information. Use the problem-solving strategies. Michelle took the train due south from the airport, heading to the end of the line. At the same time, Shell also left home and started driving due north to the end of the line, where she would pick Michelle up. Michelle's train traveled 59 miles per hour, and Shell drove 42 miles per hour. They started out 49 miles apart and arrived at the station at the same time. How long did it take them to meet?

KEY g*(-2) [5 – (3*-2)] F* (2) 2 * [5 - (3 * -2)] = [22 + (4 * 2)] 2 * [5 - (3 * -2)] = 2 * [5 + (-3*-2)] = 2 * [5 + 6] = 2 * [11] = 22 F* (2) [22 + (4 * 2)] * [22 + (4 * 2)] = 3 * [4 + 8 ]= 3 * [12] = 36 2 [ 5 - ( 3 * - 2) ] + [ 3 [2]2 + (4 * 2)] 2[5 - (3 * - 2)] + 3[2]2 + (4 * 2) 2[5 - (-6)] + 3[2]2 + (8) 2[5 + 6] + 3 * [ 4 + (8)] 2[11] + 3[ 12] 22 + 36 = 58

Write the equation and make a function box with mapping, “t” chart, and graph the information. Use the problem-solving strategies. Sam has mice and plans to get three times as many as he has now minus 8. How many will he have then? Sam has several mice and plans to get twice as many as he has now. How many will he have then?