Proficient Problem Solvers make sense
of problem situations, develop workable
solution plans, m odel the problem
situation w ith m athem atics,!
and communicate their
th in k in g clearly.
- AtiUimetk Sequences Uw; the arithmetic sequence 10,15,20.25a. Find the common difference of the sequence. __
b. Let x-the term uumbet, and let Graph the ordered pairs (x, y) for the first eight terms of the sequence. Draw a y- the corresponding term of the sequence.
c. Reasoning How is the slope of a Une from part (bl related to the common line through the points.
difference of the sequence?
( j | ChaHenge Do tite points in each set lie on the same line? Explain )our answer.50. Ml. 3). 8(4,2),q - 2 ,4) SI. G(3.S ),« -l.n«7.7) 52. D(-2, 3). Bfi. -1). Fft1)
S3. W. 2). « - 3. 2). 1H2, S) S4. 0(1. -2).W(-1. -5), US. 4) SS. S(-3.4). 7(0.2), «-3.0 )
Find the dope of the Bite that passes through each pair of points.S6. (a,-b),(-tl,-h) 57. (-m.n).(3m.-«) 58. (2o.M,(c.2d>
Apply Wiiaf You've learned MaumauucuPRACTICES
$ Apply What You've Learned
The table at the right shows the height of water in a glass when different numbers of marbles are dropped into it.
MAT HE MAT I CALPRACTICES
a. Find the rate of change in the water height with respect to die number of marbles from one row in the table to the next
What do you notice?^3 6.
b. For each marble you add to the glass, how much does the water level rise?^5 9 7.58.
c What can you conclude about the type of function that modelsthe relationship between the number of marbles and the water^14 17 102 11.
height? Explain. 23 12.
300 Chapter S Linear Function)
Throughout the chapter, you w i II Apply
What You've Learned to solve
problems that relate to the Performance Task.
You'll be asked to reason quantitatively and
model with mathematics.
Look back at your results from the Apply What You’ve Learned sections in Lessons 5-
and 5-4. Use the work you did to complete the following.
- Solve the problem in the Task Description on page 293 by predicting the number of
marbles you need to drop in the glass to raise the water level to the top of the glass.
Show all your work and explain each step of your solution.
- Reflect Choose one of the Mathematical Practices below and explain how you applied it
in your work on the Performance Task.
MP 1: Make sense of problems and persevere in solving them.
MP 2: Reason abstractly and quantitatively.
MP 4: Model with mathematics.
a. Predict the number of pieces of gravel Maria needs 10 drop In the glass <o raise the wafer level to the lop of the (daw. Justify yoin prediction.
b. Do you think your prediction from pan (a) will be more or leu accurate than the prediction your made when marble* were being dropped Into a glass? Explain.
In th e Pu l l It A l l To g et h er at
the e nd o f the c h a p te r, y o u w ill use the
concepts and skills presented throughout
the c h a p te r to solve the P e rform a nce
Task. Then yo u 'll have another Task to
solve On Yo ur Ow n.