Integrated Math 1
GeoGebra materials used in teaching Integrated Math 1 (8th grade). Sequence and materials adapted from Mathematics Vision Project, Secondary 1 ([url]http://www.mathematicsvisionproject.org/[/url]) with some help from EngageNY Algebra 1 and Geometry curricula ([url]https://www.engageny.org[/url])
Table of Contents
- Unit 1: Linear equations and inequalities
- Unit 2: Systems of linear equations and inequalities
- Too Big, or Not Too Big
- All For One, One For All
- Pet Sitters Feasible Region
- Unit 3: Sequences
- Unit 4: Linear and Exponential Functions
- Unit 5: Features of Functions
- IM1.5.1 Function basics
- IM1.5.1 Exit Ticket
- IM1.5.2 Model
- IM1.5.2 Pool Party!
- IM1.5.4 Intervals
- IM1.5.4 Alonzo and Maria
- IM1.5.4 Sierra's Comments
- IM1.5.4 Exit Ticket
- IM1.5.5 Exit Ticket
- IM1.5.6 Exit Ticket
- IM1.5.7 Calculator Skills
- IM1.5.7 Exit Ticket
- IM1.5.8 Exit Ticket
- IM1.5.9 Explore function transformations 1: Range
- IM1.5.9 Explore Transformations 2: Domain
- IM1.5.9 Exit Ticket
- IM1.5.10 Exit Ticket
- Unit 6: Congruence and Constructions
- Leaping Lizards
- Unit 7: Connecting Algebra and Geometry
- Unit 8: Modeling Data
- IM1.8.1 Texting by the numbers (MVP)
- IM1.8.2 Exit Ticket
- IM1.8.3
- IM1.8.3 Exit Ticket
- IM1.8.4 Relative Frequencies
- IM1.8.4 (2)
- IM1.8.4 (3)
- IM1.8.4 After School Activities (1)
- IM1.8.4 Exit Ticket
- IM1.8.4 RF Exit Ticket
- IM1.8.5 Correlation Coefficient 1
- IM1.8.5 CC 2
- IM1.8.5 Exit Ticket
- IM1.8.6 Exit Ticket
- IM1.8.7 Residuals 1
- IM1.8.7 Residuals 2
- IM1.8.7 Exit Ticket
Too Big, or Not Too Big
Enter the equation of one of the Pet Sitter constraints in the form of ac + bd = t, where c represents the number of cats, d represents the number of dogs, and t represents the total space, total cost, or total time. Pick a specific number of cats and dogs and decide if that number of cats and dogs would be "too big," "not too big," or "just right" for the constraint. Enter the coordinates of the point in the appropriate boxes and press the button corresponding with your prediction to plot the point. If your prediction was correct, the point will be plotted in the correct color: green, orange, or red. If not, the point will be plotted in black. Try to avoid getting black points while you are trying to plot at least five points of each of the other colors.
Too Big, or Not Too Big
IM1.5.1 Function basics
Fill in the blanks as you listen to your teacher.[br][br]1. A function is a rule that takes an _______________, does something to it, and produces an _______________.
2. ________________ are all around us. For example, your computer is full of functions. When we use our computers, we are providing the computer with ________________ by pressing keys or using the trackpad or mouse; the computer then provides ________________ by displaying letters, moving cursors, opening programs, and many other actions.
3. In mathematics, functions can be rules, formulas, _____________, _____________, tables of values, or even verbal descriptions that relate one set of input numbers to another set of output numbers. We call the input numbers the ____________________ of the function, and the output numbers the ______________________ of the function.
4. You might be asking yourself right now, “_________________? We already know how to use equations and formulas and graphs and tables of values. Why do we have to complicate things with this new idea of a _________________?” That’s a really great question, and the answer is that when we call a relationship a function, we are saying something very _____________________ and precise about the way it relates the numbers in the ________________ to the numbers in the __________________.
5. If we think about the example of a computer being a set of functions, imagine what would happen if the people who made computers weren’t so interested in being _____________________. What if you couldn’t be sure what would happen when you press the “a” key? What if there were two __________________ things that could happen when you pressed the space bar, and you just had to live with whatever happened?
6. So the thing that makes functions special relationships is that functions always assign ____________________________________________________________________. That way we can be sure what is going to happen when we apply a function to a set of numbers.
Leaping Lizards
Do the following for each of the following transformations:[br]1. Plot the anchor points in the correct locations.[br]2. Create a “tool” that will trace the image of the lizard after the transformation. The tool should be a geometric figure such as a line segment, a circle, or some combination of the two, so that when you drag one point on the “tool” around the lizard’s perimeter another point on the “tool” will trace out the lizard in the correct location.[br][br]HINT: To trace a point, right click the point you want to trace, then select "Trace on." To stop tracing a point, right click the point and click "Trace on" again. To erase previously made traces, press the orange "Erase traces" button.[br][br]Lazy Lizard: Translate the original lizard so the point at the tip of its nose is located at (24, 20), making the lizard appears to be sunbathing on the rock.[br][br]Lunging Lizard: Rotate the lizard 90° about point A (12,7) so it looks like the lizard is diving into the puddle of mud.[br][br]Leaping Lizard: Reflect the lizard about given line so it looks like the lizard is doing a back flip over the cactus.
IM1.8.1 Texting by the numbers (MVP)
Task 1: Entering and displaying data with GGB
Technology changes quickly and yet has a large impact on ourlives.
Recently, Rachel was busy chatting with her friends via text message when her mom was trying to also have a conversation with her. Afterward, they had a discussion about what is an appropriate amount of texts to send each day. Since they could not agree, they decided to collect data on the number of texts people send on any given day. [br][br]They each asked 24 of their friends the following question:“What is the average number of texts you SEND each day?” The data representing all 48 responses are below: [br]Data:[br]{150, 5.5, 6, 5, 3, 10, 150, 15, 20, 15, 6, 5, 3, 6, 0, 5,12, 25, 16, 35, 5, 2, 13, 5, 130, 145, 155, 150, 162, 80, 140, 150, 165, 138,175, 275, 85, 137, 110, 143, 138, 142, 164, 70, 150, 36, 150, 150}[br][br] 1. Enter the data in Row 1 of your spreadsheet below (you can copy and paste).[br][br]2. Select Row 1 and do a One Variable Analysis [icon]/images/ggb/toolbar/mode_onevarstats.png[/icon] of the data. You should get a histogram.
Here's my histogram
3. Can you make your histogram look like mine? (Hint: you may need to move the pane dividers to make your histogram bigger). [br][br]4. Change the display from “Histogram” to “Dot Plot”. How is this view similar or[br]different? [br][br]5. Change the display from “Dot Plot” to “Box Plot”. [b] [/b]How is this view similar or different? [br][br][b]Answer these questions below.[/b][br]6. What does a box plot show that a histogram and a dot plot do not?[br][br]7. What do a histogram and a dot plot show that a box plot does not?
Rachel's Box Plot
Prior to talking about the data with her mom, Rachel had created a box plot using her own data she collected and it looked quite different than when they combined their data. [br][br]8. Looking at Rachel's box plot, which of the following data sets is Rachel's, and which is her mother's? How do you know?[br][br]Set A: {150, 5.5, 6, 5, 3, 10, 150, 15, 20, 15, 6, 5, 3, 6, 0, 5, 12, 25, 16, 35, 5, 2, 13, 5}[br][br]Set B: {130, 145, 155, 150, 162, 80, 140, 150, 165, 138, 175, 275, 85, 137, 110, 143, 138, 142, 164,70, 150, 36, 150, 150} [br][br]
9. Create a box plot of the data from Rachel's mother in the spreadsheet below.[br]
10. Rachel wants to continue sending her normal number of texts (average of 100 per day) and her mom would like her to decrease this by half. Present an argument for each side, using mathematics and the box plots to justify each person’s request.