Finish Strong

The students are undoubtedly excited for the summer break, but they need to successfully navigate through this final week first. Please encourage them to study hard for their exams and finish strong. They have received a review sheet.

Last Week of Algebra I

We are almost to summer! It has been a pleasure to work with all the students this year. This week the students started reviewing for their final exam. We will continue to review for the exam on Monday and Tuesday with the Final on Thursday. They should be working on their final review packet and reviewing their notes to study for the final. As this is their last weekend of the semester, please remind them that their test corrections and any late work is due on Tuesday, May 24th.


Wall Challenge Problem Answers:

Problem #29 – The Game of 24 (1, 1, 6, 9)

Problem #29 Solutions – 9(1+1)+6


Problem #30 – The Game of 24 (7, 14, 14, 18)

Problem #30 Solutions – (7+18)-(14/14)


Problem #31 – The Game of 24 (1, 4, 18, 24)

Problem #31 Solution – 4(24-18)*1; 24/4+(1*18)

The Crisis of the Third Century

Historians of the Roman Empire refer to the period following the death of Alexander Severus in 235 AD to the accession of Diocletian to the imperial throne in 284 AD as the “Crisis of the Third Century.” There were five reasons for this crisis:

  1. Invasions from Germanic barbarians east of the Rhine and north of the Danube and from Sassanid Persians to the Roman Empire’s easternmost border.
  2. The so-called “barracks emperors”—commoners, often from the outskirts of the Roman Empire, who had ascended the ranks of the military and garnered (temporarily) support from the troops—died in battle or were killed by the disenchanted troops who had put them in office. There were twenty-six emperors in this fifty year period.
  3. As a result of civil war, the Roman Empire was divided into three competing empires—the Western Gallic, the Central Roman, and the Eastern Palmyrene.
  4. Given that there had been no expansion since the reign of Hadrian (117-138 AD), the Roman Empire had lost a significant source of its income: conquest. This was compounded by the economic problems of barracks emperors being forced to pay the military to stay in power, paying off barbarian invaders, the expenses of the bread and circuses, inflation as a result of devaluing the denarius, and a decrease in trade.
  5. Plague struck in 250 AD, killing, it was said, 5,000 a day in Rome.


Last week, the students learned how to multiply and divide all types of polynomials. This week, they will have two unusual days and then finishing up their polynomial unit. On Monday, they will be taking a readiness test for next year. Tuesday and Thursday, the students will be reviewing for unit test. Wednesday the students will be going on a field trip to the Science Museum. Friday, the students will be taking their unit test on polynomials. They will need to be able to simplify polynomials, add polynomials, subtract polynomials, multiply polynomials, and divide polynomials.

First Jewish-Roman War

Since 63 BC, Judaea had been a client-state ruled by a local king chosen by the Romans. When Augustus took the provinces that bordered the non-Roman world into his own care, they were garrisoned with Roman legions and governed by a deputy appointed by the emperor. Judaea officially became an imperial province in 6 AD. As the name of the province suggests, it was heavily populated by Jews.

There were two primary sources of tension between the Jews and their Roman overlords. First, the Jews were monotheists who were increasingly troubled by the imposition of the Roman imperial cult. Second, they perceived the Roman system of taxation as unjust and oppressive. In 66 AD, Nero, in need of money, ordered Gessius Florus, procurator in Judaea, to take it from the temple in Jerusalem. Things became violent, the Jews revolted, and the Roman general Vespasian, with his son Titus, launched a military campaign to bring them back into subjection. Jerusalem was sacked and its temple destroyed in 70 AD.

The Julio-Claudian Dynasty

The Julio-Claudian dynasty (27 BC-68 AD) refers to the first five emperors—Augustus, Tiberius, Caligula, Claudius, and Nero—during the period of the Roman Principate. After the death of Augustus, whatever nobility and restraint that had characterized the Roman Republic was all but lost. Individual Julio-Claudians, men and women both, conspired and murdered their way to place themselves, their own immediate family members, or their lovers to positions of power. Once in power, these individuals gave themselves over to all sorts of depravity and licentiousness. The chief historian of this period, Suetonius (c. 71-c. 135), describes acts that are so wicked that they are at times even difficult to believe.


This week the students took their test on right triangles and radicals. Overall the students were very successful on this test. They received their test back on Thursday and have until next Monday (May 9th) to complete test corrections if they choose. I recommend that each student who earned lower than a C complete the test corrections. We then started our unit on polynomials. The students discussed how to add and subtract polynomials and multiply and divide when one of the polynomials is a monomial. Next week, the students are going to be taking their final Galileo benchmark test and continuing the polynomial unit. They will be discussing how to multiply and divide all polynomials, not just monomials.


Challenge Problem Answers:

HW #106 – #16) -19; #17) Start with 5, multiply by x, subtract 2, multiply by x, add 4, multiply by x, add 7, multiply by x, subtract 9

HW #107 – #18) 3y^2-9y-4; #19) p-9p-1; #20) –z^2-2z+4

HW #108 – #25) -125a^21; #26) [81b^8]/16


Wall Challenge Problem Answers:

No Wall Challenge Answers this week as we are keeping the three problems up for next week.

Augustus Caesar

Be advised: the students have their chapter test this coming Tuesday, April 26.

Gaius Octavius (63 BC-14 AD), better known to posterity as Augustus Caesar or simply Augustus, had learned from the mistakes of his adopted father Julius Caesar. He knew that to move too quickly, too abruptly, and too radically in the direction of autocracy would result in his own death—perhaps, like Caesar, in a pool of his own blood. Following the defeat of Mark Antony and Cleopatra at Actium in 31 BC, he directed his energies at slowly consolidating his own power and working within the contours of what remained of the Republican system. The Senate could not be brazenly marginalized. If he were to be in effect dictator perpetuo, dictator for life, he could never claim such a title for himself.

Right Triangles and Intro to Polynomials

This week the students finished up the unit on right triangles and radicals and started reviewing for their test on Monday, April 25. Please remind your student to study over this weekend and review the trigonometric and special right triangle ratios. Next week, we are going start our unit on polynomials. We will be discussing what makes an expression a polynomial and use the basic operations (addition, subtraction, multiplication, and division) with polynomials.


Challenge Problem Answers:

HW #102 – #10) x = 6.2


Wall Challenge Problem Answers:

Problem #23 – The Game of 24 (2, 5, 6, 8)

Problem # 23 Solutions – (2*5)+6+8; (5*6)-8+2; (6-5+2)*8; [(8-2)*5]-6


Problem #24 – The Game of 24 (2, 4, 11, 11)

Problem #24 Solutions – 11+11+4-2; 4/2+11+11


Problem #25 – Divisibility by 10

Problem #25 Solution – It is not true.


Senatus Populusque Romanus. The Senate and the Roman People. The Latin motto was meant to designate the symbiotic relationship between the Senate (or more broadly, the conservative aristocratic elite) and the Roman people—the dual sources of institutional power—working together toward the greater good of the Roman Republic. But in the final years of the Republic, this symbiotic relationship broke down into mutual antagonism. Following the failed efforts for land reform legislation of the brothers Tiberius and Gaius Gracchus (133-121 BC), the Republic became divided into two political factions—the optimates, who favored the senatorial aristocracy, and the populares, who favored the masses—that would ultimately lead its demise and transition into the Empire.