Pre-Algebra
Course Features
Course Details
Course Overview
The Pre-Algebra course is designed to help students become ready for algebra by ensuring they have a firm understanding of pre-algebra mathematical concepts.
Course topics include:
- Algebraic Expressions with Integers
- Rational Numbers and Exponents
- Applying Irrational Numbers to Pythagorean Theorem
- Transformations
- Angles and Pairs of Lines
- Volume of Circular Solids
- Linear Functions
- Systems of Linear Functions
- Scatter Plots
This course was developed by the International Academy of Science.
Learn More
Scope and Sequence
Unit 1 In this unit students study variables and expressions, coefficients, terms, and constants, evaluating algebraic expressions, and algebraic expressions with order of operations. They are introduced to equations, and learn to solve equations by adding and subtracting and by multiplying and dividing. They learn to solve two-step equations and multi-step equations. They learn to solve equations with distributive property and with variables on both sides, and they learn to solve special equations. Unit 2 In this unit students study rational numbers to decimal expansion, terminating decimals to rational numbers, repeating decimals to rational numbers, and percents to decimals. They explore exponents and bases, powers and exponents, multiplying powers with similar bases, multiplying powers with different bases, and dividing powers with similar bases. They learn about exponents of zero, negative exponents, converting exponential expressions, scientific notation, operations with scientific notation, and scientific notation formats. Unit 3 In this unit students learn about perfect squares, irrational numbers, and irrational numbers on the number line. They study cubes, cube roots, cube roots of negative numbers, and learn the Pythagorean Theorem with known legs, the Pythagorean Theorem with an unknown leg, proving the Pythagorean Theorem, and applying converse of Pythagorean Theorem. They further study PT determining right, acute and obtuse triangles, and using PT in the coordinate system. Unit 4 In this unit students explore dilations, translations, reflections, and rotations. They study combinations of transformations, congruent polygons, transformations and congruency, determining similarity with transformations, and similarity transformations. Unit 5 In this unit students learn about linear pairs of angles, and vertical angles. They explore corresponding angles and parallel lines, alternate interior angles and parallel lines, alternate exterior angles and parallel lines, same side interior angles and parallel lines, angles of parallel lines with algebra, angles and polygons, and similar figures and parallel lines. Following this unit students are presented with the Mid-Term Review and Exam. Unit 6 In this unit students study exact and approximate pi, area of circles, and volume of spheres, cylinders, cones, and composite shapes. They also study the Pythagorean Theorem in cones. Unit 7 In this unit students learn about relating graphs to events, functions, sequences, slope, unit rate as slope, and comparing proportional relationships. They study graphing linear equations with slope, slope formula, y-intercept, graphing lines with slope and y-intercept, special linear equations, independent versus dependent variables, and slopes of similar triangles. Unit 8 In this unit students learn about solving systems of equations, parallel lines, perpendicular lines, parallel slopes, and perpendicular slopes. They investigate solving systems of equations via elimination, solving RW systems of equations via elimination, solving systems of equations via substitution, and solving RW systems of equations via substitution. They study comparing linear functions, transforming linear functions, quadratic functions, exponential functions. Unit 9 In this unit students study clustering, linear association, positive versus negative association, outliers, and nonlinear association. They also learn about modeling data with lines, trend lines in scatter plots, correlation, interpolation vs. extrapolation, categorical data. Students are presented with the Final Review and Exam.#header {padding-top:15px;} #wrap h5 { font-family: Open Sans !important;} #wrap #header #nav > li > a { color:;} #wrap #header #nav > li > a:hover,.transparent-header-w.t-dark-w #header.horizontal-w.duplex-hd #wrap #header #nav > li:hover > a, .transparent-header-w #header.horizontal-w #wrap #header #nav > li:hover > a {color:;} #wrap #header #nav > li.current > a, #wrapv #header #nav li.current ul li a:hover, #wrap #header #nav > li.active > a {color:;} #wrap #scroll-top a {background-color:;} #wrap #scroll-top a:hover {background-color:;} #wrap.colorskin-custom .course-content .products li a.add_to_cart_button,.colorskin-custom .llms-notice a,.colorskin-custom .llms-checkout-section a,#wrap.colorskin-custom .wn-course-progress a:hover,.colorskin-custom .llms-access-plan-footer .llms-button-action.button,.colorskin-custom .llms-access-plan-restrictions ul li a,.colorskin-custom .w-single-event-phone:before,.colorskin-custom .courses-grid article .mc-content h5 a:hover,.colorskin-custom .courses-grid article .mc-price,.colorskin-custom .testimonials-slider-w.ts-penta .testimonial-content h4 q:before,.colorskin-custom .icon-box10:hover h4,.colorskin-custom .icon-box9 h4,.colorskin-custom .icon-box8 i,.colorskin-custom ul.check2 li:before,.colorskin-custom li.check2:before,.colorskin-custom .cer-online2 .student-name,#wrap.colorskin-custom ul.check li:before, #wrap.colorskin-custom li.check:before,.transparent-header-w.t-dark-w .colorskin-custom #header.horizontal-w #nav>li:hover>a,.transparent-header-w.t-dark-w .colorskin-custom #header.horizontal-w #nav>li.current>a,.colorskin-custom .widget.buddypress div.item-options a ,.colorskin-custom #buddypress a,.colorskin-custom #buddypress a:visited,.colorskin-custom span.bbp-breadcrumb-sep , .colorskin-custom .bbp-body a,.colorskin-custom .bbp-body a:visited , .colorskin-custom .bbp-single-topic-meta a , .colorskin-custom .blog-post a:hover,.colorskin-custom .blog-author span,.colorskin-custom .blog-line p a:hover , .colorskin-custom h6.blog-date a:hover,.colorskin-custom h6.blog-cat a:hover,.colorskin-custom h6.blog-author a:hover , .colorskin-custom .blog-line:hover h4 a , .colorskin-custom a.readmore , .colorskin-custom #commentform input[type="submit"] , .colorskin-custom .blgtyp1 .au-avatar-box h6:after , .colorskin-custom .w-next-article:hover a:before,.colorskin-custom .w-prev-article:hover a:before,.colorskin-custom .w-next-article a:after,.colorskin-custom .w-prev-article a:after , .colorskin-custom .w-next-article:hover a, .w-prev-article:hover a , .colorskin-custom .single-event .event-tag, .colorskin-custom .date-box:hover h3 , .colorskin-custom .faq-toggle .acc-trigger a:before , .colorskin-custom .button.bordered-bot.theme-skin , .colorskin-custom .button.bordered-bot.gold , .colorskin-custom .w-table a:hover , .colorskin-custom .courses-grid article .mc-content h6 a:hover , .colorskin-custom .modern-cat:hover a, .modern-cat:hover i , .colorskin-custom .modern-grid .llms-title a:hover , .colorskin-custom .modern-grid .llms-price-wrapper .llms-price , .colorskin-custom .course-list-content h5 a:hover , .colorskin-custom .w-course-list .course-list-price , .colorskin-custom .w-course-list .course-list-meta i , #wrap.colorskin-custom .um-icon-android-checkbox-outline , #wrap.colorskin-custom .wpb_accordion .wpb_accordion_wrapper .ui-state-active a, #wrap.colorskin-custom .wpb_accordion .wpb_accordion_wrapper .wpb_accordion_header a:hover , .colorskin-custom .testimonials-slider-w.ts-hexa .testimonial-content h4 q:before ,.colorskin-custom .testimonials-slider-w.ts-hexa .testimonial-content h4 q:after, #wrap.colorskin-custom .testimonials-slider-w.ts-hexa .w-crsl .owl-buttons div:after , #wrap.colorskin-custom .crsl .owl-buttons .owl-prev , #wrap.colorskin-custom .crsl .owl-buttons .owl-next , .colorskin-custom .contact-info i , .colorskin-custom ul.check li:before, li.check:before , .colorskin-custom .acc-trigger a:hover,.colorskin-custom .acc-trigger.active a,.colorskin-custom .acc-trigger.active a:hover , .colorskin-custom .w-pricing-table1 .plan-title , .colorskin-custom .w-pricing-table2 .plan-price , .colorskin-custom .w-pricing-table2 .price-footer a.readmore , .colorskin-custom .events-clean .event-article:hover .event-title , .colorskin-custom .events-minimal .event-date , .colorskin-custom .events-minimal a.magicmore:hover , .colorskin-custom .a-course h4 a:hover , .colorskin-custom .teaser-box2 .teaser-subtitle , .colorskin-custom .teaser-box7:hover h4 , .colorskin-custom .latestnews2 .ln-item .ln-content .ln-button:hover , .colorskin-custom .latestposts-one .latest-title a:hover , .colorskin-custom .latestposts-two .blog-line p.blog-cat a , .colorskin-custom .latestposts-two .blog-line:hover h4 a , .colorskin-custom .latestposts-three h3.latest-b2-title a:hover , .colorskin-custom .latestposts-three h6.latest-b2-cat a, .latestposts-three .latest-b2-metad2 span a:hover, .colorskin-custom .latestposts-six .latest-title a:hover , .colorskin-custom .latestposts-six .latest-author a:hover , .colorskin-custom .latestposts-seven .wrap-date-icons h3.latest-date , .colorskin-custom .latestposts-seven .latest-content .latest-title a:hover , .colorskin-custom .latestposts-seven .latest-content .latest-author a , .colorskin-custom .latestposts-seven .latest-content .latest-cat a:hover , .colorskin-custom .tribe-events-list-separator-month span , .colorskin-custom .tribe-events-list .type-tribe_events h2 a:hover , .single-tribe_events .colorskin-custom .w-event-meta dd a:hover , #wrap.colorskin-custom #tribe-events .tribe-events-button , .single-tribe_events .colorskin-custom .w-single-event-organizer i,.single-tribe_events .colorskin-custom .w-tribe-events-meta-date i, .colorskin-custom .w-single-event-date:before,.colorskin-custom .w-single-event-time:before,.colorskin-custom .w-single-event-location:before,.colorskin-custom .w-single-event-category:before,.colorskin-custom .w-tribe-event-cost:before,.colorskin-custom .w-tribe-event-website:before, .colorskin-custom .tribe-events-list-separator-month span , .colorskin-custom #tribe-events-content-wrapper .tribe-events-sub-nav a , .colorskin-custom .events-grid .event-article .event-title:hover , .colorskin-custom .events-grid2 .event-article .event-title:hover , .colorskin-custom .goals .goal-content .goal-title:hover , .colorskin-custom .goals .goal-content .donate-button , .colorskin-custom .goals .goal-progress .vc_pie_chart_value, .colorskin-custom .blox .widget_search input[type="submit"]#searchsubmit.btn, .max-hero .widget_search input[type="submit"]#searchsubmit.btn , .colorskin-custom .course-main .w-category a ,.colorskin-custom .course-main .course-postmeta span, #wrap.colorskin-custom .course-content .llms-button , .colorskin-custom .course-content .container .llms-message a , .colorskin-custom .button#llms_review_submit_button , .colorskin-custom .llms-lesson-preview.is-complete .llms-lesson-link,.colorskin-custom .llms-lesson-preview .llms-lesson-link.free , .colorskin-custom .w-course-price , .colorskin-custom .llms-lesson-preview .llms-lesson-link:hover .lesson-tip:hover i:before, .colorskin-custom .llms-parent-course-link a , .colorskin-custom .blgt1-top-sec a:hover , .colorskin-custom .llms-lesson-preview.prev-lesson.previous:hover h5,.colorskin-custom .llms-lesson-preview.prev-lesson.previous span,.colorskin-custom .llms-lesson-preview.next-lesson.next:hover h5,.colorskin-custom .llms-lesson-preview.next-lesson.next span , .colorskin-custom .llms-lesson-preview.prev-lesson.previous:hover a:before,.colorskin-custom .llms-lesson-preview.prev-lesson.previous a:after,.colorskin-custom .llms-lesson-preview.next-lesson.next:hover a:before,.colorskin-custom .llms-lesson-preview.next-lesson.next a:after , .colorskin-custom .llms-lesson-preview .llms-widget-syllabus .done.llms-free-lesson-svg,.colorskin-custom .llms-widget-syllabus .lesson-complete-placeholder.done,.colorskin-custom .llms-widget-syllabus .llms-lesson-complete.done,.colorskin-custom .llms-widget-syllabus .llms-lesson-preview .done.llms-free-lesson-svg , .colorskin-custom .llms-quiz-result-details ul li a , .colorskin-custom .llms-template-wrapper h4 span , .colorskin-custom .questions-total , .colorskin-custom .llms-checkout-wrapper .llms-checkout .llms-title-wrapper h4 a, #wrap.colorskin-custom .author-carousel .owl-buttons div:hover,.colorskin-custom .author-carousel .owl-buttons div:active, .colorskin-custom .filter-category-dropdown.nice-select:after , #wrap.colorskin-custom .filter-category .course-category.active ul li.active a,#wrap.colorskin-custom .filter-category .course-category.active ul li.active > a i,#wrap.colorskin-custom .filter-category .course-category.active ul li.active a span , .colorskin-custom a.btn.btn-default.btn-sm.active,.colorskin-custom a.btn.btn-default.btn-sm.active:hover , .colorskin-custom .footer-contact-info i , #wrap.colorskin-custom .enrolment-wrap .enrolment-item:nth-of-type(odd) h4:after, #wrap.colorskin-custom .enrolment-wrap .enrolment-item:nth-of-type(even) h4:after, .colorskin-custom .enrolment-wrap .enrolment-item:hover span , #wrap.colorskin-custom .answer-questions.about-us input[type="submit"]:hover , #wrap.colorskin-custom .wpcf7 .instructor p:hover:before , .colorskin-custom .contac-info a , .colorskin-custom .switch-field input:checked+label , .colorskin-custom .course-sorting-wrap .nice-select:after , .colorskin-custom .blox.dark .icon-box2 i , .colorskin-custom .blox.dark .icon-box2:hover h4 , .colorskin-custom .icon-box4 i , .colorskin-custom .icon-box4:hover i , .colorskin-custom .icon-box7 , .colorskin-custom .icon-box7 i , .colorskin-custom .icon-box7 a.magicmore:hover , .colorskin-custom .icon-box8 a.magicmore , .colorskin-custom .icon-box9:hover a.magicmore , .colorskin-custom .icon-box11 i , .colorskin-custom .icon-box11 .magicmore , .colorskin-custom .icon-box12 i , .colorskin-custom .blox.dark .icon-box13:hover i , .colorskin-custom .icon-box14 i , .colorskin-custom .icon-box14 p strong , .colorskin-custom .icon-box15 i , .colorskin-custom .icon-box16 i,.colorskin-custom .icon-box16 img , .colorskin-custom .icon-box20 i , .colorskin-custom.dark-submenu #nav ul li a:hover , .colorskin-custom.dark-submenu #nav ul li.current a , #wrap.colorskin-custom.dark-submenu #nav ul li ul li.current a , #wrap.colorskin-custom.dark-submenu #nav ul li ul li:hover a , .colorskin-custom #header-b .course-category-box2:hover a span , .transparent-header-w .colorskin-custom #header.horizontal-w #nav > li:hover > a, .transparent-header-w .colorskin-custom #header.horizontal-w #nav > li.current > a , .colorskin-custom .footer-in h5.subtitle,.colorskin-custom .toggle-top-area h5.subtitle , .colorskin-custom .breadcrumbs-w i , .colorskin-custom.online-t .top-bar .inlinelb.topbar-contact:hover , .colorskin-custom.online-t #footer .widget ul li:before , .colorskin-custom.online-t #footer .widget ul li a:hover , .colorskin-custom.online-t #footer .widget-subscribe-form input[type="text"] , .colorskin-custom.online-t #footer .widget-subscribe-form button , .colorskin-custom.online-t #footer .widget-subscribe-form button:before , .colorskin-custom.online-t #tribe-events-content-wrapper .tribe-events-calendar div[id*=tribe-events-daynum-] , .colorskin-custom .widget ul li.cat-item:hover a , .colorskin-custom .widget ul li.cat-item a:before , .colorskin-custom .widget ul .recentcomments:hover:before , .colorskin-custom .widget-tabs .tabs li.active a , #wrap.colorskin-custom .review-result-wrapper .review-result i , .colorskin-custom .course-search-form .nice-select:after , .colorskin-custom .widget .course-categories li a i , .colorskin-custom .widget .course-categories li a:hover,.colorskin-custom .widget .course-categories li a:hover span , #wrap.colorskin-custom .w-crsl .owl-buttons div:hover,.colorskin-custom .our-clients-wrap.w-crsl .owl-buttons div:active, #wrap.colorskin-custom .widget .owl-buttons div:after , .colorskin-custom .llms-widget-syllabus .lesson-title.active a , .colorskin-custom .llms-widget-syllabus .lesson-title.done:before , .colorskin-custom .widget.buddypress div.item-options a , .woocommerce .colorskin-custom div.product .woocommerce-tabs ul.tabs li.active , .woocommerce .colorskin-custom ul.products li.product .price , .woocommerce .colorskin-custom div.product form.cart button.single_add_to_cart_button:hover , .woocommerce .colorskin-custom .star-rating span:before , .woocommerce .colorskin-custom .myaccount_user a,.woocommerce .colorskin-custom .col-1.address .title a , .colorskin-custom .pin-box h4 a:hover,.colorskin-custom .tline-box h4 a:hover , .colorskin-custom .pin-ecxt h6.blog-cat a:hover , .colorskin-custom .pin-ecxt2 p a:hover , .colorskin-custom .blog-single-post .postmetadata h6.blog-cat a:hover , .colorskin-custom h6.blog-cat a , .colorskin-custom .blgtyp3.blog-post h6 a, .blgtyp1.blog-post h6 a, .blgtyp2.blog-post h6 a, .blog-single-post .postmetadata h6 a, .blog-single-post h6.blog-author a , .colorskin-custom .blgtyp3.blog-post h6 a:hover,.colorskin-custom .blgtyp1.blog-post h6 a:hover,.colorskin-custom .blgtyp2.blog-post h6 a:hover,.colorskin-custom .blog-single-post .postmetadata h6 a:hover,.colorskin-custom .blog-single-post h6.blog-author a:hover , .colorskin-custom .blog-post p.blog-cat a,.colorskin-custom .blog-line p.blog-cat a , .colorskin-custom .about-author-sec h3 a:hover , .colorskin-custom .blog-line:hover .img-hover:before , .colorskin-custom .rec-post h5 a:hover , .colorskin-custom .rec-post p a:hover , .colorskin-custom a.magicmore , .colorskin-custom .rec-post h5 a:hover , .colorskin-custom .blgtyp3.blog-post h6 a,.colorskin-custom .blgtyp1.blog-post h6 a,.colorskin-custom .blgtyp2.blog-post h6 a,.colorskin-custom .blog-single-post .postmetadata h6 a,.colorskin-custom .blog-single-post h6.blog-author a ,.colorskin-custom .blgtyp1.blog-post h6.blog-comments a , .colorskin-custom .blgtyp3.blog-post h6 a:hover,.colorskin-custom .blgtyp1.blog-post h6 a:hover,.colorskin-custom .blgtyp2.blog-post h6 a:hover,.colorskin-custom .blog-single-post .postmetadata h6 a:hover,.colorskin-custom .blog-single-post h6.blog-author a:hover ,.colorskin-custom .blgtyp1.blog-post h6.blog-comments a:hover , #wrap.colorskin-custom .colorf, #wrap.colorskin-custom .hcolorf:hover , .colorskin-custom .faq-minimal a:hover h4 , .colorskin-custom .faq-minimal .faq-icon , .colorskin-custom .circle-box p strong, #wrap.colorskin-custom .wpb_accordion .wpb_accordion_wrapper .ui-state-active .ui-icon:before , .colorskin-custom .our-team h5 , .colorskin-custom .testimonials-slider-w .testimonial-brand h5 , #wrap.colorskin-custom .vc_carousel.vc_carousel_horizontal.hero-carousel h2.post-title a:hover , #wrap.colorskin-custom .wpb_gallery_slides .flex-caption h2.post-title a:hover , .colorskin-custom .events-clean2 .event-article:hover .event-title , .colorskin-custom #tribe-events-content .tribe-events-tooltip h4,.colorskin-custom #tribe_events_filters_wrapper .tribe_events_slider_val, .single-tribe_events .colorskin-custom a.tribe-events-gcal, .single-tribe_events .colorskin-custom a.tribe-events-ical , #wrap.colorskin-custom .hebe .tp-tab-title , .colorskin-custom .latestposts-one .latest-author a:hover , .latestposts-two .blog-post p.blog-author a:hover , .colorskin-custom .latestposts-two .blog-line:hover .img-hover:before , .colorskin-custom .latestposts-four h3.latest-b2-title a:hover , .colorskin-custom .latestposts-five h6.latest-b2-cat a , .colorskin-custom .latestposts-six .latest-content p.latest-date , .colorskin-custom .a-post-box .latest-title a:hover , .colorskin-custom .tribe-events-list .tribe-events-read-more , .colorskin-custom .tribe-events-list .type-tribe_events h2 a:hover , .colorskin-custom .goal-box .goal-sharing .goal-sharing-icon , .colorskin-custom .goal-box .goal-sharing .goal-social a:hover , .colorskin-custom .button.llms-next-lesson , .colorskin-custom .w-llms-my-certificates h3 i,.colorskin-custom .w-llms-my-achievements h3 i,.colorskin-custom .w-llms-my-courses h3 i,.colorskin-custom .w-llms-my-memberships h3 i , .colorskin-custom .w-contact-sidebar .icon-box i , .colorskin-custom .icon-box1 a.magicmore , .colorskin-custom #nav a:hover,.colorskin-custom #nav li:hover > a , .colorskin-custom #nav > li.current > a,.colorskin-custom #nav > li > a.active , .colorskin-custom #header.sticky #nav-wrap #nav #nav > li:hover > a , .colorskin-custom.dark-submenu #nav li.mega ul.sub-posts li a:hover , .colorskin-custom .nav-wrap2 #nav > li:hover > a, .top-links #nav > li:hover > a , .colorskin-custom .nav-wrap2.darknavi #nav > li > a:hover,.colorskin-custom .nav-wrap2.darknavi #nav > li:hover > a , .colorskin-custom .nav-wrap2 #nav > li.current > a , .colorskin-custom #header.sticky .nav-wrap2.darknavi #nav > li > a:hover , .w-header-type-12 .colorskin-custom #nav > li:hover > a , .colorskin-custom #header.horizontal-w.w-header-type-10 #nav > li:hover > a,.transparent-header-w .colorskin-custom #header.horizontal-w.w-header-type-10 #nav > li.current > a,.colorskin-custom #header.horizontal-w.w-header-type-10 #nav > li.current > a , .colorskin-custom .header-bottom #header-b li:hover a i , .colorskin-custom #header-b li.mega ul[class^="sub-"] ul li:hover a, .colorskin-custom #nav > li:hover > a,.colorskin-custom #nav li.current > a,.colorskin-custom #nav li.active > a, .colorskin-custom #header.res-menu #menu-icon:hover i,.colorskin-custom #header.res-menu #menu-icon.active i , .transparent-header-w .colorskin-custom #header.horizontal-w.duplex-hd #nav > li:hover > a, .transparent-header-w .colorskin-custom #header.horizontal-w.duplex-hd #nav > li.current > a , .colorskin-custom .top-links a:hover , .colorskin-custom .top-bar h6 i , .colorskin-custom .online-learning-contact .row:hover .icon , .colorskin-custom .online-t-contact .row:hover .icon , .colorskin-custom.online-t #tribe-events-content .tribe-events-tooltip h4,.colorskin-custom.online-t #tribe_events_filters_wrapper .tribe_events_slider_val, .single-tribe_events .colorskin-custom.online-t a.tribe-events-gcal, .single-tribe_events .colorskin-custom.online-t a.tribe-events-ical , .colorskin-custom .toggle-top-area .widget ul li a:hover ,.colorskin-custom #footer .widget ul li a:hover , .woocommerce .colorskin-custom nav.woocommerce-pagination ul li a , .woocommerce .colorskin-custom ul.products li.product:hover a.add_to_cart_button:hover , .woocommerce .colorskin-custom ul.cart_list li a:hover,.woocommerce .colorskin-custom ul.product_list_widget li a:hover { color: #2d5c88} #wrap.colorskin-custom .course-content .products:hover li .product-inner h3,.colorskin-custom .llms-checkout-wrapper .llms-form-heading,.colorskin-custom .llms-button-action,#wrap.colorskin-custom .wn-course-progress a,#wrap.colorskin-custom .llms-access-plan:hover .llms-access-plan-title,.colorskin-custom .llms-access-plan:hover .llms-access-plan-footer .llms-button-action.button,.colorskin-custom .wn-button.llms-button-primary,.woocommerce .colorskin-custom .button,.colorskin-custom .flip-clock-wrapper ul li a div div.inn,.colorskin-custom #header .woo-cart-header .header-cart span,.colorskin-custom .llms-purchase-link-wrapper .llms-button,.colorskin-custom #header.res-menu #menu-icon span.mn-ext1,.colorskin-custom #header.res-menu #menu-icon span.mn-ext2,.colorskin-custom .w-pricing-table3.featured .ptcontent > span,.colorskin-custom .icon-box10:hover i,.colorskin-custom .icon-box9:hover i,.colorskin-custom .subscribe-flat .subscribe-box-input .subscribe-box-submit,.colorskin-custom .max-hero h5:before,.colorskin-custom .teaser-box4 .teaser-title,.colorskin-custom .teaser-box4 .teaser-subtitle ,.colorskin-custom .wpcf7 .wpcf7-form input[type="submit"],.colorskin-custom .wpcf7 .wpcf7-form input[type="reset"],.colorskin-custom .wpcf7 .wpcf7-form input[type="button"],#wrap.colorskin-custom.school-t .top-bar,.colorskin-custom #buddypress .comment-reply-link,.colorskin-custom #buddypress .generic-button a,.colorskin-custom #buddypress a.button,.colorskin-custom #buddypress button,.colorskin-custom #buddypress input[type=button],.colorskin-custom #buddypress input[type=reset],.colorskin-custom #buddypress input[type=submit],.colorskin-custom #buddypress ul.button-nav li a,.colorskin-custom a.bp-title-button,.colorskin-custom a.readmore:after , .colorskin-custom h4.comments-title:after , #wrap.colorskin-custom #commentform input[type="submit"]:hover , .colorskin-custom .commentbox h3:after , .colorskin-custom .post-format-icon , .colorskin-custom .date-box .ln-date .ln-month , .colorskin-custom .button.theme-skin , .colorskin-custom .button.bordered-bot.theme-skin:hover , .colorskin-custom .button.bordered-bot.gold:hover , .colorskin-custom .esg-filter-wrapper span:hover , .colorskin-custom .esg-navigationbutton.esg-filterbutton.esg-pagination-button.selected , .colorskin-custom .esg-navigationbutton.esg-filterbutton.esg-pagination-button:hover, .colorskin-custom .w-table th , .colorskin-custom .wsingleblog-post .postmetadata .blog-cat a:hover , #wrap.colorskin-custom .um-button , .colorskin-custom .sub-title:after , .colorskin-custom #social-media.active.other-social , #wrap.colorskin-custom .ts-tri.testimonials-slider-w .w-crsl .owl-buttons div:hover:after , #wrap.colorskin-custom .testimonials-slider-w.ts-deca .owl-theme .owl-controls .owl-page.active span , #wrap.colorskin-custom #w-h-carusel.w-crsl .owl-buttons div:hover:after , .colorskin-custom .w-callout , .colorskin-custom .callout a.callurl , .colorskin-custom .w-pricing-table1 .price-footer a:hover , .colorskin-custom .w-pricing-table2 .price-footer a.readmore:after , .colorskin-custom .w-pricing-table2:hover.w-pricing-table2 .price-header h5 , .colorskin-custom .w-pricing-table2.featured .price-header h5 , .colorskin-custom .subscribe-bar1 .subscribe-box-input .subscribe-box-submit , .colorskin-custom #tribe-events-content-wrapper .tribe-events-calendar td:hover , .colorskin-custom .countdown-w.ctd-simple .block-w , .colorskin-custom .countdown-w.ctd-modern .block-w .icon-w , .colorskin-custom .tribe-events-list .booking-button , .colorskin-custom .tribe-events-list .event-sharing > li:hover , .colorskin-custom .tribe-events-list .event-sharing .event-share:hover .event-sharing-icon , .colorskin-custom .tribe-events-list .event-sharing .event-social li a , .colorskin-custom #tribe-events-pg-template .tribe-events-button , .single-tribe_events .colorskin-custom .booking-button , #wrap.colorskin-custom #tribe-events .tribe-events-button:hover , .colorskin-custom .tribe-events-list .event-sharing .event-share:hover .event-sharing-icon,.colorskin-custom .tribe-events-list .event-sharing .event-social li a,.colorskin-custom .tribe-events-list .event-sharing > li:hover , .colorskin-custom .events-grid2 .event-grid-head , #wrap.colorskin-custom .course-content .llms-button:hover , .colorskin-custom .course-content .course-titles:after , .colorskin-custom .course-content #old_reviews h3:after , .colorskin-custom .button#llms_review_submit_button:hover , .colorskin-custom .instructor-box h5 , #wrap.colorskin-custom .llms-lesson-complete-placeholder.free i , #wrap.colorskin-custom .llms-lesson-button-wrapper .button ,#wrap.colorskin-custom .llms-lesson-button-wrapper .llms-button-action, .colorskin-custom .llms-parent-course-link a:hover , .colorskin-custom .llms-quiz-results h3:after ,.colorskin-custom .quiz-description h4:after, .colorskin-custom #llms_start_quiz, .colorskin-custom #llms_answer_question,.colorskin-custom #llms_prev_question , #wrap.colorskin-custom .llms-clear-box.llms-center-content .llms-button , .single-llms_membership #wrap.colorskin-custom .llms-purchase-link-wrapper a.llms-button , .colorskin-custom .author-courses .course-title:after,.colorskin-custom .author .post-title:after , .colorskin-custom .filter-category h3:after , .colorskin-custom .filter-category .course-category.active , .colorskin-custom .llms-pagination ul li .page-numbers:hover , .colorskin-custom .enrolment-wrap .enrolment-item h4 , .colorskin-custom .enrolment-wrap .enrolment-item span , #wrap.colorskin-custom .enrolment-wrap .enrolment-item:hover p , .colorskin-custom .events-grid3 .event-grid3-header , .colorskin-custom .events-grid3 .event-grid-head , .colorskin-custom .events-grid3 .event-grid3-footer .event-sharing > li:hover , .colorskin-custom .events-grid3 .event-grid3-footer .event-sharing .event-social li a , #wrap.colorskin-custom .events-grid3 .event-grid3-footer .booking-button:hover , .colorskin-custom .events-grid3 .event-grid3-footer .booking-button:hover , .colorskin-custom .advancedlist > span , .colorskin-custom .our-curriculum .our-curriculum-content-wrap , .colorskin-custom .our-curriculum .our-curriculum-header , .colorskin-custom .icon-box6 i , .colorskin-custom .icon-box11 i:after , .colorskin-custom .icon-box14:hover i , .colorskin-custom .icon-box15:hover i , .colorskin-custom .icon-box21 .iconbox-rightsection .magicmore , .colorskin-custom .header-bottom #searchsubmit , .colorskin-custom #pre-footer .footer-social-items a:hover i, .colorskin-custom #pre-footer .footer-subscribe-submit, .w-modal .colorskin-custom .wpcf7 .wpcf7-form input[type="submit"],.w-modal .colorskin-custom .wpcf7 .wpcf7-form input[type="reset"],.w-modal .colorskin-custom .wpcf7 .wpcf7-form input[type="button"],#w-login #wp-submit, .colorskin-custom .wpcf7 .wpcf7-form .online-learning-contact input[type="submit"] , .colorskin-custom.online-t .footer-in h5.subtitle:after , .colorskin-custom.online-t #tribe-events-content-wrapper .tribe-events-calendar td:hover , .colorskin-custom.online-t .tribe-events-thismonth.tribe-events-future.tribe-events-has-events.mobile-trigger.tribe-events-right:hover,#wrap.colorskin-custom.online-t .tribe-events-thismonth.tribe-events-future.tribe-events-has-events.mobile-trigger.tribe-events-right:hover div[id*=tribe-events-daynum-],.colorskin-custom.online-t .tribe-events-thismonth.tribe-events-present.tribe-events-has-events.mobile-trigger:hover, .colorskin-custom.online-t .tribe-events-thismonth.tribe-events-present.tribe-events-has-events.mobile-trigger:hover div[id*=tribe-events-daynum-] , .colorskin-custom.school-t #footer .widget_nav_menu ul li:hover , .colorskin-custom .sidebar .widget h1:after,.colorskin-custom .sidebar .widget h4:after , .colorskin-custom #footer .tagcloud a:hover,.colorskin-custom .toggle-top-area .tagcloud a:hover , .colorskin-custom .widget-subscribe-form button , #wrap.colorskin-custom #footer .widget .owl-buttons div:after , .colorskin-custom .llms-widget-syllabus .lesson-title.active:before , .colorskin-custom .widget.widget_display_search #bbp_search_submit , .woocommerce .colorskin-custom a.button.alt,.woocommerce .colorskin-custom button.button.alt,.woocommerce .colorskin-custom input.button.alt,.woocommerce .colorskin-custom #respond input#submit.alt , .woocommerce .colorskin-custom .widget_price_filter .ui-slider .ui-slider-handle , .colorskin-custom .a-course .media-links , .colorskin-custom #tribe-events-content-wrapper .tribe-events-sub-nav a:hover , #wrap.colorskin-custom #tribe-events-content-wrapper #tribe-bar-form .tribe-events-button , .colorskin-custom .events-grid .event-detail , .colorskin-custom .goals .goal-content .donate-button:hover , .colorskin-custom .goals.goals-list .goal-content .goal-sharing a , .colorskin-custom .goal-box .donate-button , .colorskin-custom .blox .widget_search input[type="submit"]#searchsubmit.btn,.colorskin-custom .max-hero .widget_search input[type="submit"]#searchsubmit.btn , .colorskin-custom #menu-icon:hover,.colorskin-custom #menu-icon.active , .colorskin-custom .top-bar .topbar-login , .colorskin-custom #scroll-top a:hover , .colorskin-custom.online-t .top-bar .inlinelb.topbar-contact , .colorskin-custom .modal-title , .colorskin-custom.online-t #tribe-events-content-wrapper .tribe-events-calendar td:hover div[id*=tribe-events-daynum-] , .colorskin-custom.school-t .wuser-menu .wuser-smenu , .single .colorskin-custom .woo-template span.onsale, .woocommerce .colorskin-custom ul.products li.product .onsale , .woocommerce .colorskin-custom .button , .colorskin-custom .widget_shopping_cart_content p.buttons a.button , #wrap.colorskin-custom .blog-social a:hover , .colorskin-custom .commentlist li .comment-text .reply a:hover , #wrap.colorskin-custom .colorb, #wrap.colorskin-custom .hcolorb:hover , .colorskin-custom .latestposts-one .latest-b-cat:hover , .colorskin-custom .latestposts-seven .latest-img:hover img , #wrap.colorskin-custom .colorb, #wrap.colorskin-custom .hcolorb:hover , .colorskin-custom .latestposts-one .latest-b-cat:hover , .colorskin-custom .latestposts-seven .latest-img:hover img , .colorskin-custom .woocommerce-message a.button, .colorskin-custom .pin-ecxt2 .col1-3 span,.colorskin-custom .comments-number-x span , .colorskin-custom #tline-content:before , .colorskin-custom .tline-row-l:after,.colorskin-custom .tline-row-r:before , .colorskin-custom .tline-topdate , .colorskin-custom .port-tline-dt h3 , .colorskin-custom .postmetadata h6.blog-views span , #wrap.colorskin-custom .w-contact-p input[type="submit"]:hover , .colorskin-custom p.welcomebox:after , #wrap.colorskin-custom .ts-hepta.testimonials-slider-w .owl-theme .owl-controls .owl-page.active span , #wrap.colorskin-custom .vc_carousel.vc_carousel_horizontal.hero-carousel .hero-carousel-wrap .hero-metadata .category a , .colorskin-custom .our-process-item i:after , .colorskin-custom .events-clean2 .event-article:hover .event-date, #wrap.colorskin-custom .ls-slider1-a , .colorskin-custom .latestposts-four .latest-b2 h6.latest-b2-cat , .colorskin-custom .a-post-box .latest-cat , .colorskin-custom .llms-lesson-preview .llms-lesson-complete, .colorskin-custom .llms-button-wrapper .button.llms-next-lesson:hover , .colorskin-custom .llms-question-label input[type="radio"]:checked:before,.colorskin-custom .llms-question-label input[type="radio"]:hover:before , .colorskin-custom #header.res-menu #menu-icon span.mn-ext3 , .colorskin-custom .footer-in .tribe-events-widget-link a:hover,.colorskin-custom .footer-in .contact-inf button:hover , #wrap.colorskin-custom .socialfollow a:hover , #wrap.colorskin-custom .wp-pagenavi a:hover , .colorskin-custom .side-list li:hover img , .colorskin-custom .subscribe-bar1 .subscribe-box-input .subscribe-box-submit { background-color: #2d5c88} #wrap.colorskin-custom .course-content .products li a.add_to_cart_button,#wrap.colorskin-custom .course-content .products:hover,.colorskin-custom .llms-notice,.colorskin-custom .llms-checkout-section,#wrap.colorskin-custom .wn-course-progress a,#wrap.colorskin-custom .wn-course-progress a:hover,.colorskin-custom .llms-access-plan:hover .llms-access-plan-content,.colorskin-custom .llms-access-plan:hover .llms-access-plan-footer,.colorskin-custom .llms-access-plan-footer .llms-button-action.button,.colorskin-custom .widget-title:after,.colorskin-custom .widget-title:after,.colorskin-custom #header.w-header-type-10,.colorskin-custom .icon-box13, .transparent-header-w .colorskin-custom #header.w-header-type-10,#wrap.colorskin-custom #tribe-events .tribe-events-button,.colorskin-custom .tline-row-l,.colorskin-custom .tline-row-r, .colorskin-custom .big-title1:after, .colorskin-custom .max-title5:after,.colorskin-custom .max-title2:after,.colorskin-custom .max-title4:after, .colorskin-custom .subtitle-four:after, .colorskin-custom .max-counter.w-counter:before, .colorskin-custom .max-counter.w-counter:after, .colorskin-custom h6.h-sub-content, .colorskin-custom .teaser-box7 h4:before, .colorskin-custom .tribe-events-list-separator-month span, .colorskin-custom .tribe-events-list .tribe-events-event-meta, .colorskin-custom #header.box-menu .nav-wrap2 #nav > li.current, .colorskin-custom #header.box-menu .nav-wrap2 #nav > li > ul, .colorskin-custom .our-clients-wrap.w-crsl ul.our-clients img:hover, .colorskin-custom .woocommerce-info,.colorskin-custom #buddypress .comment-reply-link,.colorskin-custom #buddypress .generic-button a,.colorskin-custom #buddypress a.button,.colorskin-custom #buddypress button,.colorskin-custom #buddypress input[type=button],.colorskin-custom #buddypress input[type=reset],.colorskin-custom #buddypress input[type=submit],.colorskin-custom #buddypress ul.button-nav li a,.colorskin-custom a.bp-title-button,.colorskin-custom a.readmore:hover , #wrap.colorskin-custom .ts-hepta.testimonials-slider-w .owl-theme .owl-controls .owl-page.active span , .colorskin-custom .our-process-item:hover i , .colorskin-custom .w-pricing-table2:hover.w-pricing-table2 .ptcontent , .colorskin-custom .w-pricing-table2.featured .ptcontent , .colorskin-custom .llms-checkout-wrapper .llms-checkout , #wrap.colorskin-custom .author-carousel .owl-buttons div:hover, .author-carousel .owl-buttons div:active, .colorskin-custom .enrolment-wrap .enrolment-item p , #wrap.colorskin-custom .enrolment-wrap .enrolment-item:hover p , #wrap.colorskin-custom.kids-t .crsl .owl-buttons div:hover, #wrap.colorskin-custom.kids-t .our-clients-wrap.crsl .owl-buttons div:active, #wrap.colorskin-custom .wpcf7 .instructor p input:hover, #wrap.colorskin-custom .wpcf7 .instructor p textarea:hover , .colorskin-custom .icon-box20 span:before, .icon-box20 span:after , .colorskin-custom #pre-footer .footer-social-items a:hover i, #wrap.colorskin-custom .wp-pagenavi a:hover , .colorskin-custom.school-t #footer .socialfollow a:hover , #wrap.colorskin-custom .w-crsl .owl-buttons div:hover,.colorskin-custom .our-clients-wrap.w-crsl .owl-buttons div:active, #wrap.colorskin-custom #footer .widget .owl-buttons div:after , .colorskin-custom .commentlist li .comment-text .reply a:hover , #wrap.colorskin-custom .colorr, #wrap.colorskin-custom .hcolorr:hover , .colorskin-custom .blox.dark .vc_separator .vc_sep_holder .vc_sep_line , #wrap.colorskin-custom #w-h-carusel.w-crsl .owl-buttons div:hover:after , .colorskin-custom .events-clean2 .event-article:hover .event-date, .single-tribe_events .colorskin-custom .tribe-event-tags a:hover , .colorskin-custom #header.box-menu .nav-wrap2 #nav > li:hover , .colorskin-custom a.readmore , .colorskin-custom .button.bordered-bot.theme-skin , #wrap.colorskin-custom .um-form .um-button.um-alt , .colorskin-custom .our-team3:hover figure img , .colorskin-custom .testimonials-slider-w.ts-tetra .testimonial-brand img , .colorskin-custom .countdown-w.ctd-modern .block-w , .colorskin-custom #tribe-events-content-wrapper .tribe-events-sub-nav a , #wrap.colorskin-custom .course-content .llms-button , .colorskin-custom .button#llms_review_submit_button , .colorskin-custom .button.llms-next-lesson , .colorskin-custom .llms-question-label input[type="radio"] , .colorskin-custom .icon-box14 i , .colorskin-custom .side-list img , .colorskin-custom .widget-subscribe-form button , .colorskin-custom .llms-widget-syllabus .lesson-title.active:before { border-color: #2d5c88} .colorskin-custom .tp-caption.Fashion-BigDisplay { color:#2d5c88 !important;} .colorskin-custom .Button-Style { background-color:#2d5c88 !important;} .colorskin-custom .eg-item-skin-2-element-11 { background-color: ;} .colorskin-custom .woocommerce div.product .woocommerce-tabs ul.tabs li.active { border-top-color:#2d5c88 !important;} .llms-form-field.type-radio input[type=radio]:checked+label:before { background-image: -webkit-radial-gradient(center,ellipse,#2d5c88 0,#2d5c88 40%,#fafafa 45%); background-image: radial-gradient(ellipse at center,#2d5c88 0,#2d5c88 40%,#fafafa 45%);} .colorskin-custom #header.box-menu .nav-wrap2 #nav > li.current { border-bottom-color:#2d5c88; } .colorskin-custom h4.h-subtitle {border-bottom-color:#2d5c88; } .colorskin-custom .vc_progress_bar .vc_single_bar .vc_bar.animated {background-color: #2d5c88 !important;} #wrap.colorskin-custom .course-category-box-o .course-category-box:hover .ccb-hover-content.colorb { background-color: rgba(45,92,136,0.76); } .single-tribe_events .colorskin-custom .w-single-event-organizer i, .single-tribe_events .colorskin-custom .w-tribe-events-meta-date i { color: #2d5c88 !important; } #wrap.online-t.colorskin-custom .tribe-events-thismonth.tribe-events-future.tribe-events-has-events.mobile-trigger.tribe-events-right:hover div[id*=tribe-events-daynum-], .colorskin-custom .woocommerce-message a.button, .colorskin-custom .top-bar .inlinelb.topbar-contact, .online-t.colorskin-custom .tribe-events-thismonth.tribe-events-future.tribe-events-has-events.mobile-trigger.tribe-events-right:hover, .online-t.colorskin-custom .tribe-events-thismonth.tribe-events-present.tribe-events-has-events.mobile-trigger:hover, .online-t.colorskin-custom .tribe-events-thismonth.tribe-events-present.tribe-events-has-events.mobile-trigger:hover div[id*=tribe-events-daynum-]{ background-color: #2d5c88 !important; } .colorskin-custom .filter-category .course-category.active:after,.colorskin-custom .llms-lesson-preview.is-complete .llms-lesson-link, .colorskin-custom .llms-lesson-preview .llms-lesson-link.free, .colorskin-custom.online-t .tribe-events-thismonth.tribe-events-present.tribe-events-has-events.mobile-trigger:before { border-left-color: #2d5c88 ;} .colorskin-custom .woocommerce-message,.woocommerce .colorskin-custom div.product .woocommerce-tabs ul.tabs li.active { border-top-color: #2d5c88 ;} .colorskin-custom.online-t #footer .widget-subscribe-form input[type="text"]::-webkit-input-placeholder { color: #2d5c88;} .colorskin-custom.online-t #footer .widget-subscribe-form input[type="text"]:-moz-placeholder { color: #2d5c88;} .colorskin-custom.online-t #footer .widget-subscribe-form input[type="text"]::-moz-placeholder { color: #2d5c88;} .colorskin-custom.online-t #footer .widget-subscribe-form input[type="text"]:-ms-input-placeholder { color: #2d5c88;} .w-modal .colorskin-custom .wpcf7 .wpcf7-form input[type="submit"], .w-modal.colorskin-custom .wpcf7 .wpcf7-form input[type="reset"], .w-modal .colorskin-custom .wpcf7 .wpcf7-form input[type="button"], #w-login .colorskin-custom #wp-submit { background-color: #2d5c88 ;} #wrap #commentform input[type="submit"]:hover ,#wrap .w-llms-my-courses .course-link a, #wrap .top-bar .inlinelb.topbar-contact:hover, #wrap #tribe-events .tribe-events-button:hover, #wrap .llms-purchase-link-wrapper .llms-purchase-button.llms-button:hover, #wrap .w-course-list .llms-button { color: #fff ; } #wrap .w-course-list .llms-button:hover { background: #424242 !important;} #wrap.college-t .top-bar .inlinelb.topbar-contact { background-color: #4a4a4a; } #wrap .widget h1:after,#wrap .widget h4:after { border-right-color: #fff;border-left-color: #fff; } #wrap .button.theme-skin:hover { background: #333; border-color: #333; } .button.bordered-bot.theme-skin {background-color:transparent;} .button.bordered-bot.theme-skin:hover ,.goals .goal-content .donate-button:hover{color:#fff;} .course-grid-t .modern-content .llms-price-wrapper { display: none;} .course-titles { display: none;} .llms-syllabus-wrapper { display: none;} .modern-grid .modern-viewers { display: none;} .course-single-post .course-take-rate { display: none;} .modern-grid .modern-duration { display: none;} .llms-price-wrapper { display: none;} .llms-purchase-link-wrapper { display: none;} .modern-viewers { display: none;} .switch-field { display: none;} .top-links a:hover {background-color: #ffffff; border:1px solid #4a4a4a; padding:8px;} .top-links a {border:1px solid #4a4a4a; padding:8px;} .postmetadata { display: none;} .modern-grid .modern-rating { display: none;}
More Courses by this Instructor
Full Year 
Mark Rogers
Micro Course - 5 Units Long 