Integrated Math 3
GeoGebra materials used in teaching Integrated Math 3 (10th grade). Sequence and materials adapted from Mathematics Vision Project, Secondary 3 (http://www.mathematicsvisionproject.org/) with some help from EngageNY Algebra 2 and Geometry curricula (https://www.engageny.org)
Table of Contents
- Unit 1: Inverse Functions
- IM3.1.1 Inverse Linear Functions
- Unit 2: Logarithms
- Unit 3: Polynomials
- Unit 4: Rational Functions
- Unit 5: 3D Geometry, Δ Trigonometry
- Unit 6: Trigonometric Functions
- IM3.6.1 Exit Ticket
- IM3.6.2 Exit Ticket
- Unit Circle
- IM3.6.3 More Ferris Wheels
- IM3.6.3 More Ferris Wheels
- IM3.6.3 Exit Ticket
- IM3.6.4 Exit Ticket
- IM3.6.5 Tangent 1
- IM3.6.5 Tangent 2
- IM3.6.5 Tangent 3
- IM3.6.5 Exit Ticket
- IM3.6.6 Radians 1
- IM3.6.6 Exit Ticket
- IM3.6.7 Exit Ticket
- IM3.6E: Modeling temperature
- Unit 7A: Probability
- IM3.7.1 Probability Basics
- IM3.7.2 Two way tables (TWT)
- IM3.7.2 Exit Ticket
- IM3.7.3 TWT and CP
- IM3.7.3 Exit Ticket
- IM3.7.4 ET
- IM3.7.5 Probability Rules
- IM3.7.6 Basics
- IM3.7.6 Shape
- IM3.7.6 Exit Ticket
- IM3.7.7 Normal Distribution
- IM3.7.7 Standard Normal
- IM3.7.7 Exit Ticket
- IM3.7.8 Standard Normal Applications
- IM3.7.8 Exit Ticket
- Unit 7B: Statistics
- IM3.7B.2 Exit Ticket
- IM3.7B.1 Exit Ticket
- IM3.7B.3 MOE
- IM3.7B.3 Exit Ticket
IM3.1.1 Inverse Linear Functions
Looking online, Carlos found a company that will sell 8 pounds of Brutus Bites for $6 plus a flat $5 shipping charge for each order. The company advertises that they will sell any amount of food at the same price per pound.[list][*]Model the relationship between the price and the amount of food using Carlos’ approach (where the number of pounds is the input). (Graph the relationship by writing the function in the input pane below. Make sure to label your axes.)[/*][/list]
[list][*]Model the relationship between the price and the amount of food using Clarita's approach (where the number of dollars is the input). (Graph the relationship by writing the function in the input pane below. Make sure to label your axes.)[/*][/list]
[list=1][*]What is the relationship between these two functions? How do you know?[br][/*][*]Use function notation to write the relationship between the functions.[br][/*][*]Should Clarita and Carlos buy their Brutus Bites from this company or the one we looked at in class? Why?[br][/*][/list]
IM3.6.1 Exit Ticket
Using the given information for right triangle ABC, with C=90°, find the measure of angle A. Round all answers to three significant figures if necessary.
a=3, c=5
Using the given information for right triangle ABC, with C=90°, find the measure of angle A. Round all answers to three significant figures if necessary.
a=5, c=10
Using the given information for right triangle ABC, with C=90°, find the measure of angle A. Round all answers to three significant figures if necessary.
a=9.1, c=12.3
Using the given information for right triangle ABC, with C=90°, find the measure of angle A. Round all answers to three significant figures if necessary.
a=14.1, c=18
Using the given information for right triangle ABC, with C=90°, find the measure of angle A. Round all answers to three significant figures if necessary.
a=9.7, c=12.7
Using the given information for right triangle ABC, with C=90°, find the measure of angle A. Round all answers to three significant figures if necessary.
a=14.6, c=20.3
IM3.7.1 Probability Basics
Tools
Use the following tools open in separate tabs to complete this worksheet.[br]Coin Flip: https://www.geogebra.org/material/simple/id/131714[br]Card deal: https://www.geogebra.org/material/simple/id/111564[br]Dice roll: https://www.geogebra.org/material/simple/id/138167
Let's say I make up a "game" where each player takes a turn by flipping a coin, drawing a card from the deck and noting whether it's red or black, and rolling a die and noting whether it's even or odd.[br]1. List all the possible turns, or [b]events[/b], in this game, or [b]chance experiment[/b]. This is called the [b]sample space [/b]of the chance experiment.[br]2. Find the probabilities of the following events:[br]a. HBO[br]b. TRE[br]c. T(R or B)O
Make your own game
In the game above, all of the events in the sample space are equally likely. [br]a. Make up your own game where the events are not equally likely. Describe the rules in detail, clearly stating which event (or events) are "winners".[br]b. Calculate the probability of winning your game.This calculated probability is called the [b]theoretical probability[/b].[br]c. Play your game at least 10 times, keeping track of how many times you won and lost. Calculate the [b]experimental probability[/b] of winning based on your experiment.[br]d. Compare your theoretical and experimental probabilities.
IM3.7B.2 Exit Ticket
A class of 28 eleventh graders wanted to estimate the proportion of all juniors and seniors at their high school with part-time jobs after school. Each eleventh grader took a random sample of juniors and seniors and then calculated the proportion with part-time jobs. Following are the sample proportions.[br][br]0.7,0.8,0.57,0.63,0.7,0.47,0.67,0.67,0.8,0.77,0.4,0.73,0.63,0.67,0.6,0.77,0.77,0.77,0.53,[br]0.57,0.73,0.7,0.67,0.7,0.77,0.57,0.77,0.67[br]Construct a dot plot of the sample proportions below by [br]1. entering the values in column A[br]2. Selecting all of the values and choosing One Variable Analysis [icon]/images/ggb/toolbar/mode_onevarstats.png[/icon][br]3. Change "Histogram" to "Dot plot"
A. Describe the shape of the distribution[br]B. Find the mean and standard deviation of the sample proportions using the "show statistics" button (ask your teacher).[br]C. Do you think that the proportion of all juniors and seniors at the school with part-time jobs could be 0.7? Do you think it could be 0.5? Justify your answers based on your dot plot.D. a. Suppose the eleventh graders had taken random samples of size 60. How would the distribution of sample proportions based on samples of size 60 differ from the distribution for samples of size 30?