BEGHI
1
We need your feedback to create the next version of this tool! Please complete this short form to help us create the best version of Brilliant for Educators.
3
Lesson With LinkEstimated Time (Mins)Related Standard(s)Topics covered in the lessonAdditional Wrap-up Question
4
Course: Solving Equations ⬇
5
Understanding Variables157.EE.4Finding unknown values in one and two-step linear equationsWhat is a variable used for in a [math statement] [equation] [expression]? Can you write an equation with a variable and solve for it?
6
Understanding expressions107.EE.4writing expressions, evaluating expressions when substituting values in for variablesIf we have the expression 10+2x+5y, choose numbers between 1-10 to give this expression the highest possible value. You may only use each number once. How did you decide which numbers to use?
7
Understanding Equations156.EE.5, 7.EE.4One step equations, two step equationsIf you have an equation that says 4c+10=130, draw a diagram that represents this balanced on a scale with c=circles. Show what steps you’d need to take to find a value for c which allows for the scales to be balanced.
8
Understanding Solutions207.EE.3, 8.EE.7.ADefinition of a solutionIf you have an equation where 3x+5=x+ [some unknown value] + 2x, can you come up with something for the unknown value that causes x to have no solutions? Infinite solutions?
9
Working Backward157.EE.3Solving two-step equations, multiple ways of solving an equation.Given the equation x/2 +5=11, there are 2 different ways to start it, one by subtracting and one by multiplying. Which do you prefer and why?
10
Isolating Variables207.EE.3, 7.EE.4Solving two step equationsIf your soup cools by 6 degrees, then you double it so that it tastes right, what was the original temperature. Soup should be served at 106-112º.
11
Isolating Expressions156.EE.5, 7.EE.3, 7.EE.2, 7.EE.4Cube roots, solving equations, working with variables with exponentsIf you were given x^4+3=19 could you make a substitution to simplify this problem? If so, what would you choose to replace? From there, are you able to solve for x?
12
Writing Equations207.EE.3, 7.EE.4Writing and solving equations from real life. Multistep equations with supporting visual diagrams.Blorb goes to the registry of Robot names because he wants his name to be longer. They charge him 100 credits for the application and 25 credits for each letter he wants to add. The equation 100+25L=325 represents Blorb’s cost. What variable does L represent in this statement? What value does L represent and what does that mean in the context of this situtation?
13
Adding signed numbers207.NS.1.AMagnitude and value, Drawing diagrams on the number line, Finding the sum of adding two integersHere are two numbers: 7 and -23. Which has a greater magnitude? Which has a greater value? What would you need to add to each to get back to zero?
14
More Operations on Signed Numbers257.EE.3, 7.NS.3Subtracting, multiplying, dividing negative numbersIf you are given the expression -3 - (-5), what are some ways that you could rewrite it to get the same answer? Also, what is the answer?
15
The Distributive Property107.NS.2.ADistributive property of multiplication over additionIf you wanted to solve the problem 312*5 in your head, what would be a good first step in terms of simplifying the problem so that you could solve it using the distributive property?
16
Applying the Distributive Property157.EE.1, 7.NS.2.A, 8.EE.7.BUsing the distributive property to solve equations, numerical and situationalIf you have the equation 3(c+6)=30, explain why subtracting 6 from both sides is not the correct first step. Then, give some options of things you could do for the first step.
17
Combining like terms107.NS.2.ARearranging like termsIf you had the expression that said 3x+2y - 5y -x and you decided to rearrange the terms to say 3x+x-2y-5y, is this correct? If not, what are the mistakes and how could you fix them?
18
Simplifying Equations157.EE.3Writing equations that have variables on both sides. Collect like terms and solve them.If you had the equation 4x + 10 +3x =31, what are two options you could do for first steps? Which one would be better and why?
19
Representing inequalities207.EE.4Introduction to inequalities, solving inequalities, Graphing inequalities.If you had the following two inequalities, x +1 ≥5 and x+2>6, name one value that is a solution to one of these but not the other. Why is that?
20
Handling Negatives207.EE.4Solving inequalities with negative coefficientsIf you’re trying to solve the inequality -3k < -15, tell why k <5 is the wrong answer? What step is missing in the process and how should it be fixed?
21
Solving Inequalities157.EE.4Solving inequalities that use positive coefficientsIf you have an equalty that said 5k ≤ 30, what is the first thing you would do if you were going to represent the solution on a numberline? What other steps would you need to take to find the answer? How would you know if you’re correct?
22
Solving More Inequalities157.EE.4Writing and solving inequalitiesBlorg learns that pineapple juice is now available for a flat monthly fee or 100 credits. He can also get a refillable cup for 12 credits and buy each cup for 4 credits. Could you write an inequality to show when Blorg would spend less per month buying them individually? What is your solution to this problem and explain what your answer means.
23
Course: Understanding Graphs ⬇
24
Seeing Solutions158.EE.8.CWhat does it mean to be a solution to an equation, especially if it has 2 variables. There are an infinite number of solutions to a two variable (linear) equationIf you had an equation that said y+12=3x+12, could you find a value of x that makes it true? If x was 5, what would y be? What if x was 6? How many solutions in the form (x,y) would make this true?
25
Intercepts15HSF-IF.7.ADefinition of intercept, using intercepts to graph from standard form, extending to intercepts in quadratics.Think about the line 2x + 3y = 12. What are the intercepts? Visualize these points and use them to determine if the line has a positive or negative slope. How do you know?
26
Revealing Patterns15Make tables to graph non-linear equations.If you were going to graph the equation y= 12/x+5, what are 3 good values to choose for x if you were going to make a table? What’s one that would be more difficult? Why?
27
Graphing Equations158.EE.2Non-linear equations, finding values of 2nd variableConsider the graph y=x^3 (use a calculator or just go back in the lesson). If x=1/2, is y more or less than 1/2? Is that what you expected? How do you know this from the graph?
28
Up and Down15graphing xy=k, graphing with abs value.Given the graph y= x + abs(x), what would the shape of this graph be? When would it be increasing? Decreasing? Staying the same?
29
Minimums and Maximums10HSF-IF.7.ALocal extremaUse a graphing calculator to graph the following: y=((x-3)^2)(x+1)^2)-1. When is the graph increasing? Decreasing? What are the minimum and maximum values?
30
Graph Gallery15HSF-IF.7.B, HSF-IF.7.Dboundaries (extreme x, y values), asymptotes, greatest integer functions (ceiling functions)In the graph y=4/((x-2)(x+3)) +1, there are two different x values where the graph doesn’t have a y value. What are they? Why doesn’t y exist here?
31
The Y-intercept158.F.3Writing equations of a line in the form of y=mx+bThere’s a point at (3,1) on a line that has a slope of 2. It crosses the y axis at the point (0,b). What’s b? Write the equation of this line in the form y=mx+b. Then, name three other points that are on this line.
32
Steepness157.RP.2.B, 8.EE.5writing proportional relationships, definition of slopeYou are given two lines, one with a slope of two and one with a slope of negative 4. What are some differences you’ll think about when you graph these lines? Discuss which way they’ll go up (or down) as you read left to right and which is steeper and what that means.
33
Parameters158.F.4vertical translations of proportional relationships, y=mx+bIf a “super bonsai” tree grows at a rate of 6cm and is 40 cm tall after 5 years, what can you say about this tree when it was planted? Write an equation that models its growth using y for height and x for years in the form y=mx+b. What do the parameters y and b represent in this equation? How tall will it be after 9 years total?
34
Equations and Lines158.F.3Define horizontal and vertical lines, zero and undefined slopes. Define linear relationship as constant slope.Three lines form a triangle, y=4, x=2, and y=1/2x. Sketch this in your notebook and use it to answer the following questions:
a. What are the slopes of these lines?
b. Is this a right triangle?
c. Do you have enough information to find the area of this triangle? If so, tell what it is and how you found it.
35
Problem Solving with Lines158.F.4finding additional points in a linear relationship, finding y intercept, change slope of a line to find solution to contextual problemA football field is about 5900 square meters. If Lawnbot has two settings, 230 sq meters/hour and 400 sq meters/hour, write two different equations that represent the amount of uncut lawn remaining related to the amount of time spent working. Then, tell the difference in how many hours faster it would be working at high speed compared to low speed.
36
Multiplying equations25HSF-IF.8.ACreating parabolas by multiplying two linear equations, identifying intercepts, introducing quadraticsGiven the two linear equations y=x+3 and y=x-1, predict what will happen if you multiply them. What will the x-intercepts be and what does this mean? What will the y-intercept be and what does that mean? Are you able to multiply it out and put into standard quadratic form y=ax^2+bx+c? If so, tell what it is.
37
Parabola Features20HSF-IF.8.AMin/max of parabolas, vertex, axis of symmetryA parabola has an x-intercept of (-4,0) and minimum output of -6, and a line of symmetry that occurs at x=1. What are the coordinates of the minimum? What is the other x intercept? Does this parabola appear to open up or open down? How do you know?
38
Shaping Parabolas25HSF-IF.8.Avertical/horizontal shift of parabolas,A parabola is symmetric about the y-axis and has an x intercept at (3,0). If the vertex is at (0,18), what’s the a value? Write the equation of parabola. Then, name the other x-intercept and two more points on the curve.
39
Building Quadratics20HSF-IF.8.Avertex form y=a(x-h)^2+k, students will get to see what different parameters do to the graph.If you look at two parabolas, f(x)=3(x-2)^2+4 and g(x)=-5(x-2)^2+1, what are some differences you’d notice if you graph them? What are the similarities?
40
Course: Systems of Equations ⬇
41
Systems of Equations158.EE.8.Csystems of equations: writing two equations, solve with substitutionYou order m mugs and s sweatshirts online from Math-a-zon, the company that puts equations on the outside of your package. The mugs weigh 120 grams and the sweatshirts weigh 200 grams and m = number of mugs and s= number of sweatshirts. You know there are 7 items in the package and it weighs 1160 grams. What are the equations written on the package?
42
Making Substitutions158.EE.8.B,8.EE.8.Cformally introduces substitution. Rewrite system of equations using substitution in one variable. Use substitution to find both variables.If you had a system of equations that said y=3x+1 and 2x+5y=57, what would your first step be when rewriting it in one variable using substitution? Where do you think the most common mistake would occur when students in your class tried to do this?
43
Elimination208.EE.8.B,8.EE.8.CElimination, Add/subtract one line, multiply one line by a constantIf you had a system of equations

3x-5y=-1
6x+15y=48

What would be your first step if you wanted to eliminate one of the variables? Is there more than one option? After you’ve done this step, what would you do next?
44
Linear Systems208.EE.8.Asolving systems graphically, definition solution and intersectionIf you had a system of equations with two lines, y=2x+4 and y=ax+b, Can you give values of a and b so that:
1. The system has one solution?
2. The system has no solution?
3. The system has an infinite number of solutions?
45
Systems with Quadratics15HSA-REI.7Manipulating quadratics to create 0, 1, or 2 solutions.You’re going to need your graphing calculator to do this. If you have a parabola y=-2x^2+5, chose a and b in y=ax+b so that the system has
a. one solution
b. two solutions
c. no solutions

do not use horizontal lines. (since you’re using y=mx+b, you can’t make a vertical line anyway)
46
Speed, Distance, and Time20Distance rate time, literal equationsIf you have the equation d=r*t (distance= rate* time), rewrite it so that r is isolated. Then, rewrite it do that t is isolated. What are these two other forms of the equation useful for?
47
Direct and Joint variation156.RP.3.D,7.RP.3,HSA-CED.2y=kx, writing equations using direct variation, ratios.If Yolanda can mow k lawns in one hour, then y=kx represents the y lawns she mows in x hours. If she works 2.5 times as fast and works for twice as long as normal, how many lawns would she mow? Express your answer in terms of y and explain how you got it.
48
Inverse variation15HSA-CED.2Writing Inverse variation equations, problem solving with them.If you have 60 minutes to do p math problems and each one takes you m minutes, write an equation that shows this relationship. Then, tell what happens if your teacher gives you 1.5 times as many problems. What will need to happen to your speed?
49
Mixing Problems158.EE.8.COrganize info from a word problem that involves two missing quantities using only 1 variable.You buy 10 random items from uselessrandomjunk.com. You get x of the $1.50 items. Write an expression for the number of $2.10 items in terms of x. Then, write an equation showing the total of your order was $18.60. Solve and tell how many of each item you purchased.
50
Scalings15HSA.CED.2scaling similar solids, k^2 for the scaling of 2d corresponding measurements, k^3 for the scaling of 3d corresponding measurementsYour box of stuff from uselessrandomjunk.com is a cube and has a side length of c cm.

a. Find the surface area and volume of the box.
b. If you double length c, what’s the new surface area and volume?
c. If you multiply the length by m, give the new surface area and volume in terms of m and c.
51
Course: Reasoning with Algebra ⬇
52
Balancing Scales308.EE.8Systems of linear equations; balancing equations; substitution in linear equations.How would you find the solution to a system of linear equations in an equation versus in a coordinate graph?
53
Elimination308.EE.8.ASystems of linear equations by elimination; simplifying linear equations.How does using the elimination method on a balance scale compare to using the same method with computation by hand?
54
Substitution348.EE.8SubstituionHow do you know when you can substitute one expression for another in both a balance scale and in an equation.
55
Graphing Rates308.F.B.4Slope, proportional relationships, equivalent fractions.How do the triangles that demonstrate rise/run on the graphs in the lesson represent equivalent fractions? For example, a rise of 6 and a run of 3 graph a point on the same line as a rise of 2 and a run of 1.
56
Equations of Lines60HSA.SSE.2Slope, y-intercept, slope-intercept form, standard form of linear equations.How can we use graphs and tables to help us see that equivalent expressions represent the same line?
57
Special Lines30HSA.GPE.B.7Slope, parallel lines, perpendicular lines, undefined slopes, positive/negative slopes.How could you use the properties of parallel and perpendicular slope relationships in lines to graph a quadrilateral, like a rectangle, on an x-y axis?
58
From Scales to Graphs25HSA.REI.C.6Systems of linear equations.When equations are set equal to each other and each expression in the equation is graphed, a system of linear equations is the relationship created where the lines intersect on a graph. How do you know when a pair of coordinate points represent a solution to a system of linear equations in an equation?
59
Number of Solutions258.EE.C.7.ASystems of equations: types of solutions. One, none, or infinite.Write the equations for and graph the following systems of linear equations in context: if you and a friend worked the same number of hours at the same summer job, and earned the same hourly pay (p), but your friend ended the summer with and income (I) of $100 dollars more than you, would your system of linear equations have one, infinitely many, or no solutions? Why?
60
Problem Solving 140HSA.REI.C.6Systems of Linear equations; using SOLE to find the area of a triangle, using SOLE in a real-world context.In the linear system y=2x+4 and y=6x-2, why is it that you can set 2x+4 equal to 6x-2 and solve for x that way?
61
Exponent Properties208.EE.A.1Product and Quotient properties of exponents.Why do you simplify exponents differently than how you simplify coefficients in an exponential expression?
62
Powers of Products and Powers308.EE.8.APowers of powers with products and quotients.Why is it that when we raise a power to a power, such as we did in this lesson, we multiply the exponents, where before, when we simply multiplied powers, we added exponents?
63
Zero and Negative Exponents308.EE.8Zero and Negative exponentsHow could you help yourself remember that the value of an expression with a negative exponent is a fraction?
64
Fractional Exponents and Radicals25HSN.RN.A.1Fractional exponents and radicalsWhen writing a fractional exponent in it’s equivalent radical form, where do you place the numerator and denominator of fractional exponent and what operations do you perform on them?
65
Problem Solving 2308.EE.8Simplifying exponential and radical expressions in a problem-solving context.How does understanding the properties of exponents help reduce the time needed to solve problems with very large and very small numbers?
66
Patterns30HSF.IF.A.3Sequences and patterns.When first looking at a mathematical pattern of sequences, what operations do you notice are used frequently between terms?
67
Describing Sequences30HSF.LE.A.2Recursive, Explicit, and describing sequences by property.What is the difference between describing a sequence by property, as a recursive sequence, or as an explicit sequence?
68
Arithmetic Sequences30HSF.LE.A.2Arithmetic SequencesHow are the patterns for arithmetic sequences related to a linear function’s slope formula?
69
Geometric Sequences30HSF.LE.A.2Geometric SequencesArithmetic sequences work with repeated addition/subtraction while Geometric sequences work with repeated multiplication/division. Which do you think you would use to calculate interest rates?
70
Course: Functions and Quadratics ⬇
71
What is a Function?30HSF-IF.1Domain and Range; FunctionsWhy is it important that a function be defined so that each element in the domain have one and only one element in the range?
72
Tables and Graphs30F.IF.9Functions in tabular, graphical, and numeric format.To verify a solution to a function in a table of values, the x-value must be plugged into the function and the output f(x), needs to match the f(x) value in the given table. In the case of a graph, how can you tell if a coordinate pair is a solution to the function?
73
Domain and Range30HSF-IF.A.1Domain and RangeIn a function, each element in the domain is always paired with exactly one element in the range. Describe how you can determine that on a graph versus computing it with the function rule.
74
Rigid Transformations35HSG-CO.A.2Rigid transformations: function translationWhen a function is shifted vertically, the signs that accompany the shift are pretty straightforward, such as adding a positive number to shift up and a negative number to shift down. However, when a function is shifted horizontally, the signs are the opposite of the direction of the shift. For example, f(x)= (x-2)^2 shifts two units to the right. Why do you think that is?
75
Vertical Stretch and Shrink35HSF-F.B.3Functions: stretching and shrinking vertically; reflectionsWhen transforming functions, what effect does changing the sign on the a value of a function have on its resulting graph?
76
Horizontal Stretch and Shrink30HSF-F.B.3Function transformation: horizontal stretch and shrink, reflection over vertical axis.When you reflect f(x) over the vertical axis, why does it transform into f(-x)? How is that reflected in the specific quadrant that the transformed function lands?
77
Intro to Quadratics25F.IF.7.AQuadratics functions; Key characteristics of parabolas.Another way to create a quadratic function is to multiply two linear functions, such as (x+1) and (x+2). The original linear function graph two separate straight lines. When you graph the resulting quadratic function, your graph is now a parabola, which curves. Why do you think the graph becomes curved? (Hint, look at a table of values for the original functions versus the resulting function.)
78
Factored Form50HSA-SSE.A.2Quadratics; Factored Form: Difference of Squares: area model method; slip and slide factoring method.How do you use factored form to find the roots of a quadratic function?
79
Finding Roots35HSA-SSE.3.AQuadratics; roots; factored formHow can you determine the roots of a quadratic function in a graph versus in a table or an equation?
80
Intro to Complex Numbers40HSN-CN.A.1Complex numbers, imaginary unit, i. complex solutions to quadratic functionsWhy is it that the imaginary unit, i, which equals the square root of -1, is equal to positive 1 when it is squared? What pattern do you notice with the types of exponent values that occur each time you raise i to the next consecutive power?
81
Intro to Polynomials35F.IF.7C,HSA-APR.A.1Polynomials, end behavior, turns, negative and positive exponents, degreesWhy is it that a polynomials with odd exponent degrees have one of their tails in quadrants where y or f(x) is negative? And why is it that polynomials with even exponent degrees will only have their tails in quadrants where y or f(x) is negative only when the leading coefficient is negative?
82
Arithmetic and Finding Roots85HS-A.APR.A.1Polynomial addition, subtraction, multiplication, division; Factoring (Grouping), Rational Root TheoremHow is polynomial long division similar and how is it different from long division with integers?
83
Direct and Inverse Variation30HSA.CED.A.2,HSA.CED.A.4Direct and Inverse Variation; FunctionsHow can we use the rules of Algebra to solve for y in the direct variation equation k=y/x? To solve for x in k=y/x? Why would that knowledge be useful?
84
Variation with Powers25HSA.CED.A.2Direct and Inverse Variation with PowersWhy do you think that the function for light intensity,$ I=k/d^2$ as a graph that shows light intensity approaching zero the further the distance from the light is, but never equaling zero?
85
Rational Functions and Domain30HSA-APR.D.7Rational Functions; Holes in functions (undefined points).What does a hole mean in a function? How can you use computation to determine if your x-coordinate represents a hole in the function?
86
End Behavior35F-IF.7D,HSA-APR.D.7Horizontal, Vertical, and Slant Asymptotes of Rational FunctionsWhy will a graph never cross a vertical asymptote?
87
Problem-Solving20F.IF.7DProblem-solving with asymptote equations.Why is it that a rational function can only have one horizontal asymptote?
88
Absolute Value20F.IF.7BAbsolute Value FunctionWhy is it that the parent function $f(x)=|x|$ graphs lines only in quadrants 1 and 2 and not 3 and 4?
89
Piecewise Functions20F.IF.7BPiecewise Functions, Domain, RangeGiven this scenario, would a piecewise function model it well? Why or why not? A car wash charges a minimum fee of $5.00 for five minutes and then charges $.50 per minute after that.
90
Floor and Ceiling Functions35F.IF.7DPiecewise functions; floor and ceiling functionsHow can you determine whether a point is on a graph in a ceiling or floor function?
91
Problem Solving35F.IF.7DPiecewise and Absolute Value with Floor and Ceiling Functions; applications thereof.We use piecewise functions to represent rule changes within a situation. Many businesses use this model to price their products. What is an example from your experience purchasing a product where you have seen a product that might have been priced using a piecewise function?
92
Course: Measurement ⬇
93
Angles in Polygons158.G.5, HSG.CO.A.1, HSG.CO.A.4, HSG.CO.C.9, HSG.CO.C.10Interior Angles, Exterior AnglesHow are internal angles and external angles related to each other? How are internal and external angles related to a straight line? What is necessary to turn an angle or a set of angles into a polygon?
94
Polygon Angle Relationships10HSG.CO.C.9, HSG.CO.C.10Interior Angle Sum of Triangles and PolygonsHow is the internal angle sum of a triangle different than the internal angle sum of a quadrilateral? How are they the same? What can you say about a shape if you only know about their total internal angle sum?
95
Angles Made by Lines15HSG.CO.C.9Angles from Parallel Lines Cut by a TransversalWhat are the two main types of angle relationships amongst parallel lines cut by a transversal?
96
Triangle Sides and Angles20HSG.CO.C.10Exterior Angle Theorem, Isoceles and Equilateral TrianglesIf you know an exterior angle of a triangle, what else do you know about that triangle? How are side lengths and angles related to each other in a triangle?
97
Perimeters157.EE.A, HSG.GPE.B.7, HSG.GMD.A.1PerimeterExplain in your own words what perimeter means to you.
98
Circumference and Arc Lengths207.G.4, HSG.C.A.1, HSG.GMD.A.1, HSG.C.5Circumference and Arc LengthWhat do all circles have in common? Why do we need a symbol like Pi to create a relationship between the circumference and diameter of a circle? Is there an analog to arc length for polygons? Why or why not?
99
Scaling Shapes107.G.1, HSG.SRT.A.2Similarity BasicsWhen you scale an image up or down, what stays the same? What changes?
100
Scaling Lengths20HSG.SRT.A.1Similarity, Scale Factors, and ProportionsWhat does it mean for two images to be similar to each other? What are some ways you could prove that two images had to be similar?
101
Reasoning About Area154.MD.3, 6.G.1, G.GPE.B.7Area BasicsWhat are some strategies you can employ to find the area of complicated or irregular spaces?