Units

• LOGISTICS, RESOURCES, & REGISTRATION 
• Unit 1: Oper­a­tors Explore num­bers and basic oper­a­tions using the prop­er­ties of math­e­mat­ics. 2 weeks
  • § 1.1 — 1.5 : Oper­a­torsreview oper­a­tors includ­ing expo­nents as we pre­pare to study alge­bra. 1 hr
  • §1.6 — 1.9 : Order of Oper­a­tions & Dis­trib­u­tive Prop­er­tyExplore the order of oper­a­tions and expand­ing math expres­sions using the dis­trib­u­tive prop­er­ty. 45 min
  • §1 : ReviewA short review of the oper­a­tors cov­ered in unit 1. 45 min
• Unit 2: Func­tions & Graphs Explore basic func­tions and graphs and how they meet on the carte­sian plane. 2 weeks
  • § 2.1 — 2.3 : Func­tionsExplore the def­i­n­i­tion of a func­tion, how to visu­al­ize a func­tion on a coor­di­nate plane, and how to tell when a set of num­bers or a graph is a func­tion. 45 min
  • § 2.4 — 2.6 : Direct & Inverse Vari­a­tionWrap up the sec­ond half of unit 2 on func­tions by explor­ing diverse and inverse vari­a­tion. 1 hr
  • § 2 : ReviewReview func­tions includ­ing direct and inverse vari­a­tion. 30 min
• Unit 3: Inte­gers Explore inte­gers, both pos­i­tive and neg­a­tive, and their rela­tion­ships using the oper­a­tions and coor­di­nate plane. 2 weeks
  • § 3.1- 3.4 : Neg­a­tive Inte­gersExplore neg­a­tive inte­gers on the coor­di­nate plane. 40 min
  • § 3.5 — 3.7 : Prac­tice with Neg­a­tive Inte­gersTest your knowl­edge of oper­a­tions by com­plet­ing them with neg­a­tive inte­gers 30 min
  • § 3 : ReviewReview inte­gers includ­ing neg­a­tive and pos­i­tive on the coor­di­nate plane. 30 min
• Unit 4: Ratio­nal Num­bers Explore ratio­nal num­bers through def­i­n­i­tion and by explor­ing absolute val­ue and approx­i­ma­tions. 1 week
  • § 4 : Live ClassExplore ratio­nal num­bers through def­i­n­i­tion and absolute val­ue 30 min
  • § 4 : ReviewReview ratio­nal num­bers includ­ing def­i­n­i­tions, approx­i­ma­tion, and absolute val­ue. 45 min
• Jacobs’ Fall Semes­ter Assessments 
• Unit 5: Equa­tions in One Vari­able Work with equa­tions involv­ing one vari­able includ­ing inverse oper­a­tions, length and area con­ver­sions, and rate prob­lems. 3 weeks
  • § 5.1 — 5.3 : Sim­ple equa­tions with one vari­ableLearn the gold­en rule and inverse oper­a­tors to start solv­ing sim­ple equa­tions. 45 min
  • § 5.4 — 5.6 : Solv­ing equa­tions with one vari­ableReview alge­bra­ic prop­er­ties and how we use them to solve equa­tions with one vari­able. 30 min
  • § 5.7 — 5.8 : Rate Prob­lemsLearn how to solve rate prob­lems by fol­low­ing five sim­ple steps. 30 min
  • § 5 : ReviewReview equa­tions of one vari­able includ­ing rate prob­lems. 45 min
• Unit 6: Equa­tions in Two Vari­ables Explore the ins and outs of graph­ing equa­tions with two vari­ables. 2 weeks
  • § 6.1 — 6.3 : Equa­tions with Two Vari­ablesLearn about equa­tions with two vari­ables and how the graph shows the solu­tions. 30 min
  • § 6.4 — 6.6 : Inter­cept, Slope, & Graph­ingLearn how to graph an equa­tion using the slope and inter­cepts. 45 min
  • § 6 : ReviewReview solv­ing sys­tems of lin­ear ques­tions with sub­sti­tu­tion. 1 hr
• Unit 7: Simul­ta­ne­ous Equa­tions solve sys­tems of lin­ear equa­tions with two vari­ables. 2 weeks
  • § 7.1 — 7.4 : Simul­ta­ne­ous Equa­tionsLearn how to solve simul­ta­ne­ous equa­tions using addi­tion, sub­trac­tion, and graph­ing. 45 min
  • § 7.5 — 7.7 : Simul­ta­ne­ous Equa­tions part 2Learn how to solve simul­ta­ne­ous equa­tions using sub­sti­tu­tion 45 min
  • § 7 : ReviewReview solv­ing simul­ta­ne­ous equa­tions 1 hr
  • § 1 — 7 : Fall Review Ques­tion Ses­sionReview rate prob­lems and simul­ta­ne­ous equa­tions by com­plet­ing some exam­ples. 30 min
• Unit 8: Expo­nents Explore prop­er­ties of expo­nents and how to fol­low these prop­er­ties to sim­pli­fy a prob­lem. 2 weeks
  • § 8.1 — 8.4 : Expo­nentsReview expo­nents by work­ing through the three laws and dis­cov­er what the val­ues of 0 and neg­a­tive expo­nents are. 45 min
  • § 8.5 — 8.7 : Sci­en­tif­ic Nota­tion, Expo­nent lawsExplore expo­nents fur­ther by learn­ing two more laws and prac­tic­ing with sci­en­tif­ic nota­tion 45 min
  • § 8 : ReviewReview prop­er­ties of expo­nents and how to fol­low them. 45 min
• Unit 9: Poly­no­mi­als Explore poly­no­mi­als by defin­ing mono­mi­als, bino­mi­als, and apply­ing the dis­trib­u­tive prop­er­ty. 2 weeks
  • §9.1–9.4 : Mono­mi­als, Bino­mi­als, Adding, & Mul­ti­ply­ingIntro­duc­ing mono­mi­als, bino­mi­als, poly­no­mi­als, adding like terms, and mul­ti­ply­ing all in one! 45 min
  • § 9.5−9.7 : Squar­ing & Divid­ing Poly­no­mi­alsReview mul­ti­ply­ing and learn how to divide poly­no­mi­als 45 min
  • § 9 : ReviewReview poly­no­mi­als by defin­ing mono­mi­als, bino­mi­als, and poly­no­mi­als 1 hr
• Unit 10: Fac­tor­ing Fac­tor mono­mi­als, bino­mi­als, and poly­no­mi­als includ­ing rec­og­niz­ing spe­cial pat­terns. 2 weeks
  • §10.1 — 10.4 : Fac­tor­ingJoin me as we start to look at fac­tors of poly­no­mi­als 45 min
  • § 10.5 — 10.8 : Fac­tor­ing Squares & more!Work with more pat­terns in fac­tor­ing poly­no­mi­als 45 min
  • § 10 : ReviewReview fac­tor­ing mono­mi­als, bino­mi­als, and poly­no­mi­als 1 hr
• Unit 11: Frac­tions Explore the arith­metic of frac­tions and then apply those laws to frac­tions con­tain­ing poly­no­mi­als. 2 weeks
  • § 11.1 — 11.4 : Alge­bra­ic Frac­tionsBasic Intro­duc­tion to alge­bra­ic frac­tions by start­ing with what we know. 30 min
  • § 11.5 — 11.8 : Com­plex Alge­bra­ic Frac­tionsLearn the three step process to sim­pli­fy­ing com­plex alge­bra­ic frac­tions 45 min
• Unit 12: Rad­i­cals Study the ori­gin of the rad­i­cal and how the prop­er­ties of rad­i­cals can be used with vari­ables. 2 weeks
  • § 12.1 — 12.4 : Square RootsReview the basics of square roots and learn how to apply a root as an expo­nent for clar­i­fi­ca­tion. 45 min
  • § 12.5 — 12.7 : Prop­er­ties of RootsPrac­tice work­ing with rad­i­cals by apply­ing prop­er­ties 45 min
  • § 12 : ReviewReview the ori­gin and prop­er­ties of rad­i­cal. 45 min
• Unit 13: Qua­drat­ic Equa­tions Solv­ing qua­drat­ic equa­tions by graph­ing, fac­tor­ing, com­plet­ing the square, also solv­ing high­er expo­nen­tial poly­no­mi­als. 3 weeks
  • § 13.1 — 13.3 : Graph­ing Qua­drat­icsStart solv­ing qua­drat­ic equa­tions by learn­ing how to graph them using tables. 1 hr
  • § 13.4 ‑13.6 : Solv­ing by Fac­tor­ing, etc.Learn the three main meth­ods that we use to solve qua­drat­ics using alge­bra 45 min
  • §13.7 — 13.9 : Qua­drat­ic For­mu­laLearn the ori­gin of the qua­drat­ic for­mu­la and how to use it to solve for a qua­drat­ic. 45 min
  • § 13 : ReviewReview solv­ing qua­drat­ic by var­i­ous means 1 hr 30 min
• Unit 14: Real Num­bers Exam­ine the set of real num­bers by look­ing at its sub­sets: irra­tional and ratio­nal num­bers. 1 week
  • § 14.1 — 14.5 : Real Num­bersExplore real num­bers and focus on con­vert­ing ratio­nal num­bers from dec­i­mal to quo­tients, espe­cial­ly num­bers with a repeat­ing dec­i­mal 45 min
  • § 14 : ReviewReview the set of real num­bers by explor­ing its sub­sets, ratio­nal and irra­tional num­bers. 40 min
• Unit 15: Frac­tion­al Equa­tions Solve equa­tions that con­tain ratios and pro­por­tions. 1 week
  • § 15.1 — 15.5 : Alge­bra­ic Frac­tionsReview ratios and explore solv­ing alge­bra­ic frac­tions 60 min
  • § 15 : ReviewReview solv­ing prob­lems that include ratios and pro­por­tions. 40 min
• Unit 16: Inequal­i­ties Explore mean­ing behind inequal­i­ties, and how to graph them and solve for x. Also, brief intro­duc­tion to solv­ing for x with­in an absolute val­ue. 1 week
  • § 16 : ReviewReview the mean­ing behind inequal­i­ties includ­ing graph­ing and solv­ing for x. 40 min
• Unit 17: Num­ber Sequences Explore arith­metic and geo­met­ric num­ber sequences includ­ing find­ing terms and com­put­ing the sum of terms. 1 week
  • § 17 : ReviewReview arith­metic and geo­met­ric num­ber sequences includ­ing find­ing terms and com­put­ing the sums of terms. 30 min
• Jacobs’ Year End Review 1 hour