Commentary and solution can be found in attached document.
Assessment of CCSS-Math
Discussion the summative and formative assessment of 5-11 grade of assessment of CCSS-Math.
F.LE Patterns to Quadratic Equations
Common Core State Standards
CCSS.MATH.CONTENT.HSF.LE.A.2
CCSS.MATH.CONTENT.HSA.CED.A.1
Task
Generalize the pattern by finding an explicit quadratic equation for the number of shapes that make up any given term, n, in the sequence. Let Tn represent the number of shapes that make up the nth term. Show your reasoning, then find Tn for the next term, then draw it to check your answer.
1.
n=1 n=2 n=3
2.
n=1 n=2 n=3 n=4
Commentary and solutions are available on the original document
here: IM Task
CCSS.Math.Content.HSN.Q. Work it harder, Make it better, Do it faster, Makes us stronger.
Alignment to Content Standards
CCSS.MATH.CONTENT.HSN.Q.A.1
Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.
CCSS.MATH.CONTENT.HSN.Q.A.2
Define appropriate quantities for the purpose of descriptive modeling.
CCSS.MATH.CONTENT.HSN.Q.A.3
Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.
Tasks
Both of the guys from Daft Punk are supposed to go onstage in 20 minutes but first they need to clean their helmets. It would take one of them 50 minutes to clean both helmets by himself and it would take the other 35 minutes to clean them both by himself. Using your knowledge of algebra, ratios, and unit analysis, determine how long it will take them to clean the helmets if they work together. Will their concert be able to start on time?
See the following file for the assessment task, commentary, and solution for this problem:
G.SRT Calculating the Area of a Traffic Sign
Alignment to Content Standards
HSG.SRT.C.6 Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.
HSG.SRT.C.8 Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.*
Task
Yield signs are traffic signs shaped like an equilateral triangle. Estimate the area of the sign assuming that the triangle is an equilateral triangle (round to the nearest hundredth). Explain how you got to your conclusion.
The full task, including commentary and solution, can be found here.
HSG.C – Math 101: How to Pick Up Chicks
Alignment to Content Standards
CCSS.Math.Content.HSG.CO.D.12
Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line.
CCSS.MATH.CONTENT.HSG.C.A.4
(+) Construct a tangent line from a point outside a given circle to the circle.
CCSS.MATH.CONTENT.HSG.CO.A.1
Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc
Tasks
Scheme:
- Using the above circle A and point B draw segment AB.
- Construct the Perpendicular Bisector of AB and label the point of intersection M.
- What is point M in relation to segment AB?
- What can you say about segments AM and BM?
- Construct a new circle centered at M with radius BM and label the points of intersection between circles A and M, as Q and R.
- Draw segments BQ and BR.
- What can you say about the length of segments BQ and BR? Explain with specifics.
Below is the full assignment with answer key
HS.F.IF.A.1 Finding the Domain of a Given Function
Alignment to Content Standards:
CCSS.Math.Content.HSF.IF.A.1
Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x).
Task:
Given the function,
- Find solutions for f(9) and f(5), and show your work writing out every step.
- Explain your steps from solving the function for each of the above x-values and list the operations used. Explain any restrictions that resulted from solving f(9) and f(5).
- Give a possible domain for f(x).
The commentary and solution for the above task can be found in the document attached below.
GPE.B.4- Square; IM Assessment
Alignment to Content Standards:
Use coordinates to prove simple geometric theorems algebraically. For example, prove or disprove that a figure defined by four given points in the coordinate plane is a rectangle; prove or disprove that the point (1, √3) lies on the circle centered at the origin and containing the point (0, 2).
Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point).
Tasks
Plot these points on an x/y coordinate plane: A(4, 0), B(0, 3), C(-3, -1), and D(1, -4)
1) Find the length of segment AB.
2) Find the slope of segments AB and CB.
3) Join the sides of quadrilateral ABCD. Prove that quadrilateral ABCD is a square. How do the answers in question 2 aid in this proof?
For the full commentary and solution to the task, open the following attachment:
CCSS.MATH.CONTENT.8.G.B.7 I can identify a right triangle!
Alignment to Content Standards: Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.
Tasks:
The following rectangle, measuring 15 inches by 12 inches, has been divided into four triangles. The figure below has been filled in with a few other dimensions.
There are three right triangles surrounding a fourth shaded triangle. Using the Pythagorean Theorem
1) Find the missing lengths in the diagram
2) Prove whether the shaded triangle is a right triangle or not.
The commentary and solutions for this task are included in document link below.
S-ID Texting Champion
Task
A student in Ms. Smith’s class claimed that girls text faster than boys. Naturally, the boys disagreed. Therefore, Ms. Smith’s statistics class did an activity where each student calculated the average words per minute they could text. The data is recorded below.
1. Sketch two side by side box plots to compare the average words per minute of girls and boys. Make sure to include the minimum, maximum, first and third quartiles, and median. Additionally, calculate the mean for each data set.
2. Why is the mean less than the median in both boys and girls?
3. Compare and contrast the two box plots. What does this mean when we are comparing words per minute between boys and girls?
4. If I was trying to describe the center of these distributions, would the mean or median be more appropriate?
5. Based upon the data presented above, which gender texts faster? Support your answer with statistical data.
An assessment commentary and solution is on the attached document: IM problem