WGU OOT2 GLM2 Tasks 1–3 – Mathematics Education – (Passed Task).
Task 1 (Technology) focuses on selecting digital tools (desmos, GeoGebra, TI
calculators) and justifying their use.
Task 2 (Lesson Plan) focuses on pedagogy, standards (NCTM), and student
engagement.
Task 3 (History) focuses on mathematicians, cultural contexts, and classroom
integration.
Part 1: Technology in Mathematics (Questions 1-60)
1. A math teacher wants students to visualize the effect of changing the slope and
y-intercept in real-time. Which technology tool is most specifically designed for
this purpose?
a) Microsoft Excel
b) Desmos Graphing Calculator
c) A digital camera
d) A word processor
Answer: b) Desmos Graphing Calculator
,Rationale: Desmos allows users to add sliders for variables like *m* (slope) and
*b* (y-intercept), instantly updating the graph to show the visual effect of
changes. Excel can graph, but sliders are not its native or easiest function.
2. Which of the following is the best justification for using a dynamic geometry
system (DGS) like GeoGebra over static paper diagrams when teaching triangle
congruence theorems (SSS, SAS, ASA)?
a) It allows students to check their answers faster.
b) It enables students to drag vertices and see which combinations of sides/angles
actually force congruence.
c) It automatically generates two-column proofs for the student.
d) It prevents students from making measurement errors.
Answer: b) It enables students to drag vertices and see which combinations of
sides/angles actually force congruence.
Rationale: The pedagogical power of DGS is the "drag test." Students can discover
that specific combinations (like SSS) create rigid, congruent triangles, while others
(like AAA) allow the shape to change size. This supports constructivist learning.
3. When integrating technology into a math lesson, the primary focus should
remain on:
,a) The number of different apps used.
b) The mathematical learning objective.
c) The students' typing speed.
d) The aesthetic design of the digital presentation.
Answer: b) The mathematical learning objective.
Rationale: Technology is a pedagogical tool, not the goal itself. Effective
integration requires that the technology directly supports students in achieving a
specific math standard (e.g., 8.F.3 or HSF.IF.C.7).
4. A teacher uses an online polling tool like Mentimeter during a lesson on
statistics. Students submit their predictions for the mean of a data set before
calculating it. This strategy primarily addresses which common misconception?
a) Forgetting to label axes.
b) The belief that the mean is always a whole number present in the data set.
c) Inability to sort numbers.
d) Confusing the mean with the mode.
Answer: b) The belief that the mean is always a whole number present in the data
set.
, Rationale: By polling predictions, the teacher surfaces student thinking before
instruction. It allows the class to see that the mean can be a decimal or a value
not in the original set, addressing the misconception directly through peer
comparison.
5. Which standard from the National Council of Teachers of Mathematics (NCTM)
is most directly supported by having students use spreadsheets to model
exponential growth (e.g., compound interest)?
a) Communication Standard
b) Connections Standard
c) Representation Standard
d) The "Sliders" Standard
Answer: c) Representation Standard
Rationale: The NCTM Representation Standard emphasizes using mathematical
representations (like formulas, tables, and graphs interchangeably) to model
phenomena. A spreadsheet allows students to represent a real-world situation in
a table and formula simultaneously.
6. In a "flipped classroom" model for high school algebra, what is the most
effective use of class time after students have watched a video on solving
quadratics at home?
Task 1 (Technology) focuses on selecting digital tools (desmos, GeoGebra, TI
calculators) and justifying their use.
Task 2 (Lesson Plan) focuses on pedagogy, standards (NCTM), and student
engagement.
Task 3 (History) focuses on mathematicians, cultural contexts, and classroom
integration.
Part 1: Technology in Mathematics (Questions 1-60)
1. A math teacher wants students to visualize the effect of changing the slope and
y-intercept in real-time. Which technology tool is most specifically designed for
this purpose?
a) Microsoft Excel
b) Desmos Graphing Calculator
c) A digital camera
d) A word processor
Answer: b) Desmos Graphing Calculator
,Rationale: Desmos allows users to add sliders for variables like *m* (slope) and
*b* (y-intercept), instantly updating the graph to show the visual effect of
changes. Excel can graph, but sliders are not its native or easiest function.
2. Which of the following is the best justification for using a dynamic geometry
system (DGS) like GeoGebra over static paper diagrams when teaching triangle
congruence theorems (SSS, SAS, ASA)?
a) It allows students to check their answers faster.
b) It enables students to drag vertices and see which combinations of sides/angles
actually force congruence.
c) It automatically generates two-column proofs for the student.
d) It prevents students from making measurement errors.
Answer: b) It enables students to drag vertices and see which combinations of
sides/angles actually force congruence.
Rationale: The pedagogical power of DGS is the "drag test." Students can discover
that specific combinations (like SSS) create rigid, congruent triangles, while others
(like AAA) allow the shape to change size. This supports constructivist learning.
3. When integrating technology into a math lesson, the primary focus should
remain on:
,a) The number of different apps used.
b) The mathematical learning objective.
c) The students' typing speed.
d) The aesthetic design of the digital presentation.
Answer: b) The mathematical learning objective.
Rationale: Technology is a pedagogical tool, not the goal itself. Effective
integration requires that the technology directly supports students in achieving a
specific math standard (e.g., 8.F.3 or HSF.IF.C.7).
4. A teacher uses an online polling tool like Mentimeter during a lesson on
statistics. Students submit their predictions for the mean of a data set before
calculating it. This strategy primarily addresses which common misconception?
a) Forgetting to label axes.
b) The belief that the mean is always a whole number present in the data set.
c) Inability to sort numbers.
d) Confusing the mean with the mode.
Answer: b) The belief that the mean is always a whole number present in the data
set.
, Rationale: By polling predictions, the teacher surfaces student thinking before
instruction. It allows the class to see that the mean can be a decimal or a value
not in the original set, addressing the misconception directly through peer
comparison.
5. Which standard from the National Council of Teachers of Mathematics (NCTM)
is most directly supported by having students use spreadsheets to model
exponential growth (e.g., compound interest)?
a) Communication Standard
b) Connections Standard
c) Representation Standard
d) The "Sliders" Standard
Answer: c) Representation Standard
Rationale: The NCTM Representation Standard emphasizes using mathematical
representations (like formulas, tables, and graphs interchangeably) to model
phenomena. A spreadsheet allows students to represent a real-world situation in
a table and formula simultaneously.
6. In a "flipped classroom" model for high school algebra, what is the most
effective use of class time after students have watched a video on solving
quadratics at home?
