ALEX Classroom Resource

  

Can You Solve This Pier Puzzle? | Physics Girl

  Classroom Resource Information  

Title:

Can You Solve This Pier Puzzle? | Physics Girl

URL:

https://aptv.pbslearningmedia.org/resource/pier-puzzle-physics-girl/pier-puzzle-physics-girl/

Content Source:

PBS
Type: Audio/Video

Overview:

This math brainteaser challenges you to find a simple, elegant solution to a seemingly complex problem! Students will use geometry principles and their knowledge about triangles to solve this puzzle. Can you figure it out?

Content Standard(s):
Mathematics
MA2015 (2016)
Grade: 9-12
Geometry
10 ) Prove theorems about triangles. Theorems include measures of interior angles of a triangle sum to 180o, base angles of isosceles triangles are congruent, the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length, and the medians of a triangle meet at a point. [G-CO10]


Alabama Alternate Achievement Standards
AAS Standard:
M.G.AAS.HS.10- Given a measure of a leg or base angle of an isosceles triangle, identify the measure of the other leg or other base angle.


Mathematics
MA2015 (2016)
Grade: 9-12
Geometry
16 ) Use the properties of similarity transformations to establish the angle-angle (AA) criterion for two triangles to be similar. [G-SRT3]

Mathematics
MA2015 (2016)
Grade: 9-12
Geometry
17 ) Prove theorems about triangles. Theorems include a line parallel to one side of a triangle divides the other two proportionally, and conversely; and the Pythagorean Theorem proved using triangle similarity. [G-SRT4]

Mathematics
MA2019 (2019)
Grade: 9-12
Geometry with Data Analysis
32. Use coordinates to prove simple geometric theorems algebraically.
Unpacked Content
Evidence Of Student Attainment:
Students:
  • Given coordinates and geometric theorems and statements defined on a coordinate system, use the coordinate system and logical reasoning to justify (or deny) the statement or theorem, and to critique arguments presented by others.
Teacher Vocabulary:
  • Simple geometric theorems
  • Simple geometric figures
Knowledge:
Students know:
  • Relationships (e.g. distance, slope of line) between sets of points.
  • Properties of geometric shapes.
  • Coordinate graphing rules and techniques.
  • Techniques for presenting a proof of geometric theorems.
Skills:
Students are able to:
  • Accurately determine what information is needed to prove or disprove a statement or theorem.
  • Accurately find the needed information and explain and justify conclusions.
  • Communicate logical reasoning in a systematic way to present a mathematical proof of geometric theorems.
Understanding:
Students understand that:
  • Modeling geometric figures or relationships on a coordinate graph assists in determining truth of a statement or theorem.
  • Geometric theorems may be proven or disproven by examining the properties of the geometric shapes in the theorem through the use of appropriate algebraic techniques.
Diverse Learning Needs:
Essential Skills:
Learning Objectives:
GEO.32.1: Apply formulas, and properties of polygons, angles, and lines to draw conclusions from the given information.
GEO.32.2: Identify properties of perpendicular and parallel lines, properties of polygons.
GEO.32.3: Illustrate polygons created by given coordinates on a coordinate plane.
GEO.32.4: Identify distance formula, circle formula, Pythagorean Theorem, midpoint.

Prior Knowledge Skills:
  • Define quadrant, coordinate plane, coordinate axes (x-axis and y-axis), horizontal, vertical, and reflection.
  • Demonstrate an understanding of an extended coordinate plane.
  • Draw and label a 4 quadrant coordinate plane.
  • Draw and extend vertical and horizontal number lines.
  • Interpret graphing points in all four quadrants of the coordinate plane in real-world situations.
  • Recall how to graph points in all four quadrants of the coordinate plane.
  • Define ordered pairs.
  • Name the pairs of integers and/or rational numbers of a point on a coordinate plane.
  • Demonstrate when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes.
  • Identify which signs indicate the location of a point in a coordinate plane.
  • Recall how to plot ordered pairs on a coordinate plane.
  • Identify the length between vertices on a coordinate plane.
  • Calculate the perimeter and area using the distance between the vertices.
  • Define a right angle, Pythagorean Theorem, converse, and proof.
  • Recognize examples of right triangles.
  • Demonstrate how to find square roots.
  • Solve problems with exponents.

Alabama Alternate Achievement Standards
AAS Standard:
M.G.AAS.10.31a When given an isosceles triangle and a measure of a leg or base angle, identify the measure of the other leg or base angle.
M.G.AAS.10.31b When given a parallelogram and the measure of one side or one angle, identify the measure of the opposite side or angle.


Mathematics
MA2019 (2019)
Grade: 9-12
Geometry with Data Analysis
34. Use congruence and similarity criteria for triangles to solve problems in real-world contexts.
Unpacked Content
Evidence Of Student Attainment:
Students:
Given a contextual situation involving triangles,
  • Determine solutions to problems by applying congruence and similarity criteria for triangles to assist in solving the problem.
  • Justify solutions and critique the solutions of others.

  • Given a geometric figure, establish and justify relationships in the figure through the use of congruence and similarity criteria for triangles
Teacher Vocabulary:
  • Congruence and similarity criteria for triangles
Knowledge:
Students know:
  • Criteria for congruent (SAS, ASA, AAS, SSS) and similar (AA) triangles and transformation criteria.
  • Techniques to apply criteria of congruent and similar triangles for solving a contextual problem.
  • Techniques for applying rigid motions and dilations to solve congruence and similarity problems in real-world contexts.
Skills:
Students are able to:
  • Accurately solve a contextual problem by applying the criteria of congruent and similar triangles.
  • Provide justification for the solution process.
  • Analyze the solutions of others and explain why their solutions are valid or invalid.
  • Justify relationships in geometric figures through the use of congruent and similar triangles.
Understanding:
Students understand that:
  • Congruence and similarity criteria for triangles may be used to find solutions of contextual problems.
  • Relationships in geometric figures may be proven through the use of congruent and similar triangles.
Diverse Learning Needs:
Essential Skills:
Learning Objectives:
GEO.34.1: Develop an equation from given information to prove congruence or similarity.
GEO.34.2: Illustrate congruence and similarity in geometric figures.
GEO.34.3: Apply proportional reasoning to real-world scenarios.
GEO.34.4: Solve proportions.

Prior Knowledge Skills:
  • Analyze an image and its dilation to determine if the two figures are similar.
  • Identify similar figures.
  • Define similar.
  • Identify congruent figures.
  • Identify attributes of two-dimensional figures.
  • Compare rotations to translations.
  • Compare reflections to rotations.
  • Compare translations to reflections.
  • Define congruent and sequence.
  • Apply the rule of proportional relationship to real-world context.
  • Recognize similar triangles.
  • Define similar triangles, intercept, slope, vertical, horizontal, and origin.
  • Demonstrate how to plot points on a coordinate plane using ordered pairs from table.
  • Analyze the graph to determine the rate of change.
  • Generate the slope of a line using given ordered pairs.
  • Graph a function given the slope-intercept form of an equation.
  • Identify the slope-intercept form (y=mx+b) of an equation where m is the slope and y is the y-intercept.
  • Graph a linear equation given the slope-intercept form of an equation.
  • Recognize that two sets of points with the same slope may have different y-intercepts.
  • Identify the slope-intercept form (y=mx+b) of an equation where m is the slope and y is the y-intercept.
  • Recall that for a relationship to be proportional, the graph must pass through the origin.
  • Demonstrate how to graph on a Cartesian plane.
  • Recall that for a relationship to be proportional, both variables must start at zero.
  • Identify the unit rate of two quantities.
  • Recall how to write a ratio of two quantities as a fraction.
  • Recall equivalent ratios and origin on a coordinate (Cartesian) plane.
  • Define proportional, independent variable, dependent variable, and unit rate.
  • Identify proportional relationships.
  • Locate/use scale on a map.
  • Define scale, scale drawings, length, area, and geometric figures.
  • Use a table or graph to determine whether two quantities are proportional.
  • Define equivalent ratios and origin.
  • Define unit rate, proportions, area, length, and ratio.
  • Recognize polygons. M. 6.3.4: Restate real-world problems or mathematical problems. M. 6.3.3: Calculate unit rate or rate by using ratios or proportions. M. 6.3.2: Create a ratio or proportion from a given word problem, diagram, table, or equation. M. 6.3.1: Define ratio, rate, proportion, percent, equivalent, input, output, ordered pairs, diagram, unit rate, and table. M. 6.3.16: Form a ratio. M. 6.3.15: Solve a proportion using part over whole equals percent over 100. M. 6.3.14: Identify a proportion from given information. M. 6.3.13: Calculate a proportion for missing information. M. 6.3.10: Create a proportion or ratio from a given word problem.

Alabama Alternate Achievement Standards
AAS Standard:
M.G.AAS.10.36 Use geometric shapes to describe real-world objects.


Tags: algebra, congruence, coordinates, geometric theorems, geometry, similarity, theorems, transformations, triangles
License Type: Custom Permission Type
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Author: Hannah Bradley