Parabola lab day 1
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This document outlines a lab exploring how changing the numbers in a parabolic equation affects the graph of the parabola. Students are asked to graph various parabolas with different openings, vertices, stretches, and shifts both vertically and horizontally. They are also challenged to combine transformations to a base parabola y=x^2. The goal is for students to discover they can manipulate a parabola's graph through changes to the coefficients in the standard form quadratic equation.
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Quadratic function in standard form (y = ax^2 +bx + c
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Linear day 16
This document outlines a lesson plan to teach linear systems of equations through three parts: launching with an example of Gerardo's work, exploring how to save for a bike through a story problem, and summarizing with an exercise from page 199 problem 4.
Systemsday1
Students will learn to determine solutions to systems of linear equations. The lesson will begin with an introduction and launch activity to engage students. Students will then explore systems of linear equations through an investigation activity.
Linear day 10
This document outlines a lesson plan for September 23rd with the learning goal of understanding linear relationships in tables, graphs, and equations. It includes launching with examples A and B, exploring practice problems 3 through 11, and summarizing with problem 202 number 4. The plan also lists launching practice problem 152 number 2 ab.
Linear day 11
The document outlines a learning goal to understand linear relationships through tables, graphs and equations. It provides activities using scatter plots and linear plots to explore relationships, including exploring hamburger data and completing practice problems from pages 151-152 and 191 of a textbook.
Linear day 12
This document outlines a lesson plan focused on understanding linear relationships. The lesson will launch with an activity on population data, then have students explore linear relationships through a point-slope investigation and practice problems. Students will complete practice questions from their textbook to summarize the lesson.
Linear day 12a
This document outlines a learning goal to understand linear relationships in tables, graphs and equations. It provides instruction to explore linear plots through exercises on pages 210 problems 29a and 29b, as well as through exercises 1-2, 3 and 4 which involve creating and analyzing linear plots.
Linear day 13
This document provides a lesson plan for understanding linear relationships. The lesson will have students find the equations of lines through given points to explore slope and linear relationships represented in tables, graphs, and equations. Students will then solve practice problems and review the key concepts covered in the lesson.
Linear day 14
This document outlines a learning goal to understand linear relationships in tables, graphs and equations. It provides an agenda to launch an activity to determine rules, explore rule investigation through tables and graphs, and summarize with problems from page 219 numbers 1 and 3.
Linear day 15
This document outlines a learning goal to understand linear relationships in tables, graphs and equations. It lists activities for October 2nd including launching with solving equations, exploring a solving equations game, and summarizing with problems from page 221 numbers 4 and 6.
Intersections and inequalities day 14a
Students will learn to determine solutions to systems of linear equations. They will explore an investigation to solve systems of linear equations. The learning outcome is to understand how to find the solutions to systems of linear equations.
Intersections and inequalities day 17
This document discusses learning how to solve systems of linear inequalities. It provides examples and notes on determining solutions to systems of linear inequalities and has students investigate examples.
Intersections and inequalities day 11
This document outlines a lesson plan to revisit the concept of slope of a line. The lesson includes a launch, exploration through investigations and practice problems, and opportunities for students to work independently to reinforce their understanding of slope.
Intersections and inequalities day 12
This document outlines steps for students to learn how to determine the slope-intercept form of a line, including a launch, exploration through investigation and notes, and independent practice. Students will explore concepts and take notes to understand how to find the slope and y-intercept of a line and represent it in slope-intercept form.
Intersections and inequalities day 13
This document outlines steps for students to determine the slope-intercept form of a line, including a launch, investigation through exploration, taking notes during exploration, and working independently.
Intersections and inequalities day 14
Students will learn to determine solutions to systems of linear equations. The learning outcome is to understand how to solve multiple linear equations simultaneously by finding the point where their graphs intersect. An exploration activity is planned to reinforce the concepts.
Intersections and inequalities day 15
Students will learn to determine solutions to systems of linear equations. The lesson will begin with an introduction and launch activity to engage students. Students will then explore systems of linear equations through an investigation activity.
Linear day 7
This document outlines a lesson plan focused on understanding linear relationships. The plan includes launching with exercise 3 on page 159, exploring exercises 6 on page 160 and 9 on page 175, and summarizing with exercise 10 on page 175. The overall learning goal is to understand linear relationships as expressed in tables, graphs, and equations.
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This document provides instructions for solving quadratic inequalities and graphing them on a number line. Learners are asked to solve four linear inequalities and graph the solutions on a number line. They are then introduced to solving quadratic inequalities and using graphs of quadratic functions to help determine the solution sets of inequalities involving quadratic expressions. Learners are asked to graph two quadratic functions and use colored pencils to show the solution regions for an inequality involving those functions.
Intersections and inequalities day 3b
This document outlines the learning outcomes and activities for a math lesson on interpreting functions and solving equations graphically. The lesson includes launching an activity to check understanding, exploring how to solve equations graphically through multiple activities, and solving quadratic inequalities by considering the graphs of two quadratic functions and using colored pencils to show answers.
Intersections and inequalities day 2
This document discusses solving inequalities graphically. It provides an example of solving an inequality related to ticket sales and profit. Learners are asked to determine the number of tickets that need to be sold to make exactly $2500 and more than $2500 based on the equation. The document guides students through exploring examples of finding solutions to inequalities and summarizes the key concepts.
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みなさんこんにちはこれ何文字まで入るの？40文字以下不可とか本当に意味わからないけどこれ限界文字数書いてないからマジでやばい文字数いけるんじゃないの？えこ...
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Parabola lab day 1
- 1. Sept 3rd Learning outcome: To discover what happens to a parabola’s graph when you change the numbers in the equation? Launch: 1. Graph your table from last week’s pattern 2. Do you recall what this type of graph is called? x 0 1 2 3 4 n y 0 1 4 9 16 n2
- 2. Explore: Parabola Lab 1.What happens to a parabola’s graph when you change the numbers in the equation? a. On graph paper, graph y = (x-2)(x-2). Labeling important points including the vertex (lowest point) and line of symmetry (line that cuts the graph in half). b. Use your graphing calculator to find the equations of 2 parabolas with different graphs that also open upward and still have a vertex at (2, 0). Use 2 different colored pencils to add the sketches along with the equations to the graph from #1.
- 3. Explore: Parabola Lab c. Use your calculator to find the equation of 2 different parabolas that open downward, each with its vertex on the x-axis at x = 2. Use 2 different colored pencils to add the sketches along with the equations to the graph from #1 a and b. d. Use your calcuator to find the equation of a parabola that opens downward with a vertex of (-4, 0). What is the equation of your parabola’s line of symmetry? e. Choose a new point on the x-axis and find at least 3 equations of parabolas that touch the x- axis only at that one point.
- 4. Explore: Parabola Lab part 2 2. Use your graph y = x2 from the launch to do the following: a. Find a way to stretch y = x2 vertically (make it narrower), but the vertex stays in the same place. Use a colored pencils to add the sketch along with the equations to the graph from the launch. b. Find a way to compress y = x2 vertically (make it flatter), but the vertex stays in the same place. Use a colored pencils to add the sketch along with the equations to the graph from the launch. c. Find a way to open y = x2 downward, but the vertex stays in the same place and is the same shape as y = x2. Use a colored pencils to add the sketch along with the equations to the graph from 2a.
- 5. Explore: Parabola Lab part 2 2d. Find a way to move y = x2 5 units down (but remain the same shape and size and vertex at (0,5)). Use a colored pencils to add the sketch along with the equations to the graph from the launch. 2e. Find a way to move y = x2 3 units to the right (but remain the same shape and size and vertex at (3,0)). Use a colored pencils to add the sketch along with the equations to the graph from the launch. 2f. Find a way to move y = x2 3 units left and stretch vertically Use a colored pencils to add the sketch along with the equations to the graph from the launch.
- 6. Parabola Lab challenge 3. Find a way to change the equation y = x 2 parabola vertically compressed, open down, move six units up and move two unites to the left. Where is the vertex of your new parabola?
- 7. Summary Now that you are a parabola expert can you write a general equation for a parabola that can be stretched or shifted any direction?