How can we help?

# Content Update: Math and AP Special Edition (July 2020)

Updated

We know our teachers might be starting to plan for the new school year, so we wanted to give an update on some upcoming course updates.

We’re excited to share that we’ve made enhancements to an AP course and 11 Math courses. See our earlier article for specific information on how much updates to each course will impact your students’ Mastery percentages.

For courses that were significantly updated, we included more information on what changed and why so you can better understand the new course content. For all courses, you'll find a list of content that was added and removed during this update.

AP Biology

Algebra 1

Algebra 2

Arithmetic

Basic Geometry

Early Math

High School Geometry

Mathematics 1

Mathematics 2

Mathematics 3

Trigonometry

## AP Biology

### Changes to Exercises Content in AP Biology

 New Exercises, Quizzes, and Unit Test Artificial selection Population genetics Evidence of evolution Common ancestry and continuing evolution Speciation Extinction Variations in populations Origins of life on Earth Unit 6 Quiz 2 Unit 6 Quiz 3 Unit 7 Quiz 1 Unit 7 Quiz 2 Unit 7 Quiz 3 Unit 7 Quiz 4 Unit 7 Unit test

top^

The new and improved second grade course provides learners with a smooth progression through 2nd grade Common Core Standards. We added over 20 new exercises to the course to allow more depth and breadth of the standards. We also created new videos that engage the user in a quick and fun way.

• Engaging content: Our team worked hard to create items that use visuals, such as number lines, tape diagrams, base ten blocks, and ten frames to make our content more colorful and fun! We have also found ways to incorporate whimsy and even some characters you may know (like Elsa and Olaf!) in our content. Learning math may be challenging, but we also want to ensure that it is FUN!
• Aligned Instruction: We meticulously researched each standard to ensure that all standards are being appropriately addressed and assessed. As we built the course, we continuously considered the three CCSS shifts of focus, coherence, and rigor. Both the practice content and the instructional content are aligned to the CCSS.
• Conceptual Understanding: We have worked hard to put a focus on conceptual understanding throughout the course. We included scaffolded exercises, digital interactive tools, and visuals that will help solidify the conceptual piece of different standards.
• Hints: Every single practice question consists of custom hints that tackle misconceptions and make sure students understand the process to work through each individual problem. The hints were crafted to allow  a “productive struggle” for students by scaffolding the solution in a way that makes sense and is age appropriate.

### Changes to Article Content in 2nd Grade Math

 Removed Articles Comparing lengths Measuring lengths with different units

## Algebra 1

What's changed:

• In addition to the videos and exercises below, we added 12 new skills.
• New practice focuses on concepts and their application more than procedures.

top^

top^

## Algebra 2

What's changed:

• In addition to the videos and exercises below, we added 4 new skills.
• New practice focuses on concepts and their application more than procedures.

top^

top^

## Basic Geometry

### Changes to Exercise Content in Basic Geometry

 New Exercises Analyze shapes Analyze shapes by angles Classify shapes Equal parts of circles Equal parts of rectangles Partitioning rectangles

top^

top^

## High School Geometry

Here are some of the ways we're bringing the concepts of reasoning and justification—which in geometry means explaining why you are sure something is true—to the forefront and tightening our focus so students have just the right amount of support and challenge.

1. Timely, targeted support: Every unit begins with an article titled "Getting ready" that reviews key prerequisite skills from earlier courses. The embedded practice in the article offers students a low-stakes and lightweight way to gauge their own readiness for the unit with links for more practice as needed. Each article empowers students to identify and revisit unfinished learning and explains how the earlier skills tie into the unit's grade-level content.
2. Proofs and justification: Throughout the course, we will complete and evaluate proofs and informal justifications. Beyond selecting proof steps and explaining why they are valid, we will also determine intermediate goals for a proof, translate between symbolic statements and what they mean verbally about figures, and identify errors in sample work.
3. Conceptual depth: Geometry is about so much more than a list of formulas. We’ll explore how the building blocks of volume extend to more nuanced forms. We’ll also grapple with the relationships between angle measures and lengths, learning how one can give us clues about the other. And we’ll use the Pythagorean theorem and slope to relate visual representations of figures with their algebraic representations.
4. Visual sense-making: Are those lines definitely parallel, or could they intersect? Will the figure help us prove a property for all parallelograms or just for this particular one? We’ll sort out what's true from what's possible in diagrams and geometric constructions.

### Changes to Video Content in High School Geometry

 New Videos Removed Videos Using right triangle ratios to approximate angle measure Special right triangles intro (part 2) Using similarity to estimate ratio between side lengths Intro to the trigonometric ratios Multi-step word problem with Pythagorean theorem Special right triangles intro (part 1) Intro to the Pythagorean trig identity Pythagorean theorem II Pythagorean theorem in 3D Intro to the Pythagorean theorem Dilating in 3D Trig challenge problem: verify identities Cavalieri's principle in 3D Pythagorean theorem example Applying volume of solids Introduction to the Pythagorean theorem Volume of pyramids intuition Intro to the Pythagorean theorem 2 Volumes of cones intuition Pythagorean theorem word problem: carpet Using related volumes Pythagorean theorem word problem: fishing boat Radians as ratio of arc length to radius Radius, diameter, circumference & π Calculating angle measures to verify congruence Area of inscribed equilateral triangle Proving triangle congruence Vertical angles Geometric constructions: perpendicular line through a point not on the line Triangle angle challenge problem 2 Segment congruence equivalent to having same length Area of a quadrilateral on a grid Proving the SAS triangle congruence criterion using transformations Measures of angles formed by a transversal Angle congruence equivalent to having same measure Lines, line segments, & rays Geometric constructions: parallel line Area of a circle Proving the SSS triangle congruence criterion using transformations Area of a parallelogram Proving the ASA and AAS triangle congruence criteria using transformations Measuring angles in degrees Geometric constructions: congruent angles Kites as a geometric shape Exploring medial triangles Sum of interior angles of a polygon Rational equations intro Area of a triangle on a grid Proof: Parallel lines divide triangle sides proportionally Worked example: Triangle angles (diagram) Equation of a parabola from focus & directrix Area of trapezoids Intro to conic sections Measuring angles using a protractor Intro to focus & directrix Specifying planes in three dimensions Dilating triangles: find the error Proving angles are congruent Dilating shapes: shrinking Surface area using a net: rectangular prism Proving triangle medians intersect at a point Worked example: Triangle angles (intersecting lines) Classifying figures with coordinates Perimeter & area of composite shapes Radius, diameter, circumference & π Radius & diameter from circumference Measuring angles using a protractor 2 Equation practice with complementary angles Quadrilateral properties Area of kites Challenge problems: perimeter & area Intro to nets of polyhedra Equation practice with supplementary angles Area of composite shapes Quadrilateral types Intro to quadrilateral Area of a triangle Angles, parallel lines, & transversals Triangle inequality theorem Complementary & supplementary angles Equation practice with vertical angles Acute, right, & obtuse angles Missing angles with a transversal Perimeter & area Parallel & perpendicular lines Sum of the exterior angles of a polygon Dilating shapes: shrinking by 1/2

### Changes to Exercise Content in High School Geometry

 New Exercises Removed Exercises Relate ratios in right triangles Use Pythagorean theorem to find right triangle side lengths Pythagorean theorem in 3D Use Pythagorean theorem to find isosceles triangle side lengths Use ratios in right triangles Solid geometry word problems Apply Cavalieri's principle Inscribed quadrilaterals Volume of prisms and pyramids Vertical angles Apply volume of solids Radius and diameter Use related volumes Angle types Prove parallelogram properties Area of a circle Justify triangle congruence Surface area using nets Prove triangle congruence Circumference of a circle Justify constructions Area of composite shapes Prove triangle properties Triangle side length rules Prove theorems using similarity Shaded areas Rational equations intro Equation practice with vertical angles Prove triangle similarity Draw rays, lines, & line segments Equation of a parabola from focus & directrix Angle relationships with parallel lines Classify figures by coordinates Nets of polyhedra Proofs with transformations Finding angle measures between intersecting lines Surface area Area of trapezoids Equation practice with angles Area of parallelograms Areas of shapes on grids Angles of a polygon Quadrilateral types Quadrilateral angles Points, lines, and planes Finding angle measures using triangles Complementary and supplementary angles (visual) Equation practice with angle addition Identify points, lines, line segments, rays, and angles Area of triangles Measure angles

### Changes to Article Content in High School Geometry

 New Articles Removed Articles Getting ready for right triangles and trigonometry Triangle angles review Side ratios in right triangles as a function of the angles Area of triangles Volume of a pyramid or cone Reflections review Cavalieri's principle in 2D Rotations review Cavalieri's principle in 3D Translations review Volume of composite figures Solid geometry vocabulary Getting ready for solid geometry Arcs, ratios, and radians Getting ready for circles Properties of congruence and equality Getting ready for congruence Getting ready for similarity Angle-angle triangle similarity criterion Parabola focus & directrix review Getting ready for conic sections Getting ready for performing transformations Getting ready for analytic geometry Getting ready for transformation properties

top^

## Mathematics 1

### Changes to Exercise Content in Mathematics 1

 New Exercises Removed Exercises Classify figures by coordinates Rate problems 2 Find angles in isosceles triangles Justify constructions Justify triangle congruence Line and angle proofs Proofs with transformations Prove parallelogram properties Prove triangle congruence Prove triangle properties Reasoning with linear equations Reasoning with systems of equations Rotational symmetry of 2D shapes Sequences and domain Using inequalities to solve problems

### Changes to Article Content in Mathematics 1

 New Articles Removed Articles Getting ready for analytic geometry Reflections review Getting ready for congruence Rotations review Getting ready for performing transformations Translations review Getting ready for transformation properties Properties of congruence and equality

top^

## Mathematics 2

### Changes to Video Content in Mathematics 2

 New Videos Removed Videos Applying volume of solids Pythagorean theorem II Area of a circle intuition Intro to the Pythagorean theorem Cavalieri's principle in 3D Pythagorean theorem example Dilating in 3D Introduction to the Pythagorean theorem Exploring medial triangles Intro to the Pythagorean theorem 2 Factoring completely with a common factor Pythagorean theorem word problem: carpet Factoring quadratics with a common factor Pythagorean theorem word problem: fishing boat Interpret a quadratic graph Special right triangles intro (part 1) Interpret quadratic models: Factored form Special right triangles intro (part 2) Interpret quadratic models: Vertex form Trig challenge problem: verify identities Interpreting a parabola in context Intro to the trigonometric ratios Multi-step word problem with Pythagorean theorem Radius, diameter, circumference & π Multiply monomials by polynomials: Area model Area of inscribed equilateral triangle Proof: Parallel lines divide triangle sides proportionally Proof: parallel lines have the same slope Proof: perpendicular lines have opposite reciprocal slopes Pythagorean theorem in 3D Pythagorean theorem with isosceles triangle Radians as ratio of arc length to radius Rational equations intro Solve by completing the square: Integer solutions Solve by completing the square: Non-integer solutions Strategy in solving quadratic equations Using related volumes Using right triangle ratios to approximate angle measure Using similarity to estimate ratio between side lengths Volume of pyramids intuition Volumes of cones intuition

### Changes to Exercise Content in Mathematics 2

 New Exercises Removed Exercises Apply Cavalieri's principle Inscribed quadrilaterals Apply volume of solids Solid geometry word problems Interpret parabolas in context Use Pythagorean theorem to find right triangle side lengths Interpret quadratic models Prove theorems using similarity Prove triangle similarity Pythagorean theorem in 3D Rational equations intro Relate ratios in right triangles Solve equations by completing the square Strategy in solving quadratics Use ratios in right triangles Use related volumes Volume of prisms and pyramids

top^

top^

## Trigonometry

### Changes to Video Content in Trigonometry

 New Videos Removed Videos Interpreting trigonometric graphs in context Intro to the trigonometric ratios Using right triangle ratios to approximate angle measure Trig challenge problem: verify identities Using similarity to estimate ratio between side lengths

top^

top^