Unit 3 introduction
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This document provides an introduction to unit 3 on proportional relationships. It includes essential questions about solving real-life problems using proportions and the graphical representation of proportional relations. An example is given of using proportional reasoning to determine the number of buckets of water for a sand sculpture. The unit overview explains that students will analyze changes in representations of proportional relationships, including tables, equations, and graphs, to determine characteristics like a constant ratio between y- and x-coordinates. Students should have prior knowledge of graphs, tables, equations, and the coordinate plane. Key vocabulary is defined.
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- MAP testing will take place this week, with detailed information available in announcements
- Next week, students will begin working on their end-of-year projects
- This document provides information about bivariate data, scatter plots, and lines of best fit for a statistics and probability lesson
Parallel lines cut by a transversals
This week is the last week of Unit 2. Next week will include the Unit 2 test, so students should stay up to date on assessments and check any feedback. There will be a help session at 2:00 PM to assist with preparations.
Transversals
This document discusses an upcoming unit 2 test and lessons on transversals and the angles they create. It provides an overview of lesson 4 on transversals, which teaches how a transversal line intersecting two nonparallel lines determines different angle relationships. The lesson content and schedule are outlined, including identifying and finding measures of various angles like complementary, supplementary, vertical and adjacent that are created by a transversal.
Rotations (day 2)
The document discusses rotations and transforming figures using rotations. It provides examples of rotating a triangle 180 degrees about the origin by multiplying the coordinates by -1. It also lists some Virtual Nerd links on rotations for 90, 180, and 270 degrees around the origin. Finally, it asks if there are any questions after learning about rotations and mentions next steps like a shapes in motion activity and a quiz.
Rotations
The document discusses transformations of plane figures including translations, reflections, rotations, and dilations. It provides an example of graphing a 90 degree counterclockwise rotation of a triangle about the origin, showing that the y-coordinates remain the same while the x-coordinates change sign. Students are asked if they completed previous IXL questions and directed to complete additional questions to practice transformations.
Reflections (day 2)
Last week we finished Unit 2 Lesson 1 and started Lesson 2, which introduced different types of transformations including translations, reflections, rotations, and dilations. The document then focused on reflections, explaining that a reflection flips a figure across a line to create a mirror image. An example showed how to graph the reflection of triangle FGH across the x-axis by multiplying the y-coordinate of each vertex by -1. In conclusion, an IXL assignment was given to practice transformations using translations.
Reflections
The document discusses different types of transformations including translations, reflections, rotations, and dilations. It provides an example of graphing the reflection of a quadrilateral across the y-axis by multiplying the x-coordinates of each vertex by -1. The document encourages completing formative assessments and getting caught up on any missed work.
Translations (day 2)
The document discusses transformations of plane figures using translations. It provides examples of graphing translations of triangles and quadrilaterals on a coordinate plane by adding or subtracting values from the x- and y-coordinates of each vertex. Students are reminded to submit their formative assessments and that IXL Skill Q.3 on translations was assigned.
Translations (day 1)
This document discusses transformations of plane figures including translations, reflections, rotations, and dilations. It provides examples of transformations when riding amusement park rides and defines a transformation as a change in a figure's position or size. Students are instructed to practice transformations using translations on IXL skill Q.2 which involves graphing the image of translated figures.
Dilations (day 2)
This document provides instructions for a lesson on dilations. It asks the student if they completed independent work on dilations which included reading a section, watching a video, and completing two IXL skills. It then lists the learning objectives for the lesson which are to understand how dilations affect two-dimensional figures, graph dilated figures given scale factors, identify coordinates of dilated figures, and determine scale factors for dilations. It finishes by naming another IXL skill for dilations.
Dilations (day 1)
This document provides an overview of math lessons and assessments for geometry units 1 and 2. It asks if the unit 1 test and project have been completed and the unit 2 pretest. It then lists learning objectives for understanding dilation of two-dimensional figures through graphing and identifying coordinates. Recommended activities are included for learning dilation through reading, watching videos, and practicing skills on IXL.
Unit 2 introduction
This geometry unit teaches students about transformations of shapes, including enlarging, shrinking, flipping, and sliding shapes. Students will learn to translate, dilate, rotate, and reflect shapes on a coordinate plane. They will also learn the differences between similar and congruent shapes and understand transversals and the angles they create. The unit aims to help students understand geometry concepts through learning about transformations of shapes.
Writing an equation using a table (day2)
The document provides instructions for writing an equation for a linear function given its values in a table. It outlines a three step process: 1) Find the slope using two points from the table, 2) Find the y-intercept using the slope and a point, 3) Write the linear equation in slope-intercept form. It also includes examples of tables with x and y values that could be used to write the corresponding linear equations.
Writing an equation using a table
This document discusses completing lessons for a math unit. It asks if the previous lesson's quiz was finished and informs that this is the last lesson of the unit. It also lists learning objectives involving interpreting rate of change from a function table and constructing an equation from two (x,y) values using a table.
Rate of change comparing functions
Formative assessments make up 20% of the overall grade. Students should check feedback and resubmit assessments as needed. The document schedules conferences which students can request by sending a coursemail. It then provides an example comparing the rate of change of two functions to determine which one has a greater rate of change, defining rate of change as the ratio comparing the amount of change in a dependent variable to the change in an independent variable.
Rate of change graphs & tables
The document discusses introducing the concept of rate of change in mathematics. It defines rate of change as a ratio that compares the amount of change in a dependent variable to the amount of change in an independent variable. Examples are provided to demonstrate identifying rates of change from sets of data where the rates may vary or remain constant. The document encourages completing any questions or examples to understand the definition and application of rates of change.
Rate of change tables, points, and equations
The document discusses rates of change and identifying slopes. It provides examples of finding the slope of lines passing through ordered pairs. The agenda is to understand rates of change through tables, ordered pairs, equations, and questions. A rate of change compares the amount of change in a dependent variable to the amount of change in an independent variable, and rates can be variable or constant.
Rate of change graphs (day 1)
Last week's lesson discussed evaluating functions and included a quiz. This lesson aims to help understand the rate of change by defining it as a ratio that compares the amount of change in a dependent variable to the amount of change in an independent variable. Rates can be constant or variable depending on the data. Examples are provided to identify constant and variable rates of change from graphs and data sets.
Evaluating functions basic rules (day 3)
This document discusses evaluating functions by replacing variables with given numbers in function rules. It provides examples of evaluating functions f(4), f(3), f(-5), and g(7) based on the function rules provided. Formatives like IXL skills, journal activities, and lesson quizzes make up 20% of the grade, while summatives like unit tests make up the remaining 80%. The first semester closes today and all grades will be converted to a letter grade.
Evaluating functions basic rules (day 2)
The document discusses evaluating functions by replacing variables with numbers in function rules. It provides examples of evaluating functions g(-5), g(-4), and f(-10) and reminds the reader of important rules like exponents, adding/subtracting integers, and order of operations when evaluating functions. More practice evaluating functions is offered.
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Unit 3 introduction
- 1. Last week, we finished unit 2 and you should have completed the summative assessment. Next week – No Live Class!! Questions?
- 2. Goal…. Unit 3 Introduction Agenda…. Essential Questions Real Life Connections Overview Prior Knowledge Vocabulary Scale Questions
- 5. Essential Questions: • What types of real life problems can be solved using proportions? • What does the graph of a proportional relation look like?
- 6. Real Life Connections: You can apply proportional reasoning to many everyday applications. For example, sand artists often use a ratio of 1 part water to 8 parts sand when building their sculptures. By using proportional reasoning, an artist can determine that the number of buckets of water required for 40 buckets of sand.
- 7. Unit Overview: Proportional reasoning is the ability to think about and compare multiplicative relationships between quantities. In this unit, you will analyze changes in tables, equations, and graphs of lines to determine proportionality. You will determine characteristics of proportional relationships given in multiple representations, such as verbal, numerical, algebraic, and graphical. You will explore how a change in one representation affects another representation. You will determine that a relationship is proportional if the ratio of the y-coordinate to the x- coordinate for each point on a line stays the same and the line goes through the origin.
- 8. Prior Knowledge: To be successful in this unit, you need to have worked with graphs, tables, and equations. You should be familiar with the coordinate plane and how to plot ordered pairs on a coordinate plane. You should also be able to make a table and graph given an equation.
- 9. Vocabulary: Cross product Proportional Non-Proportional Rate Ratio Unit Rate Slope Constant of Proportionality
- 11. • You know and understand the vocabulary • You can identify the graphical features of a proportional relationship • You can display all of the possibilities in a proportional relationship by graphing • You can state in words the proportional relationship shown in a graph • You can calculate the unit rate of a graph
- 12. • You can compare proportional relationships displayed in different forms
- 13. Goal…. Unit 3 Introduction Agenda…. Essential Questions Real Life Connections Overview Prior Knowledge Vocabulary Scale Questions
- 14. Complete the Unit 2 summative IXL Skills: • Ration Tables – 6th Grade: R.2 • Equivalent Ratios – 6th Grade: R.4 • Equivalent Ratios: Word Problems – 6th Grade: R.5 • Compare Ratios: Word Problems – 6th Grade: R.6 • Coordinate Graphs Review – 6th Grade: W.1