MTEL Mathematics (63) case studies
MTEL Mathematics (63) · Put your knowledge to work in context.
The MTEL Mathematics (63) is a subject-matter licensure test within the Massachusetts Tests for Educator Licensure program, which the Massachusetts Department of Elementary and Secondary Education describes as part of a statewide education reform initiative for educators seeking PreK to grade 12 academic licenses. The MTEL system pairs a test of communication and literacy skills with tests of subject matter knowledge, and Mathematics (63) is the subject-matter test for candidates pursuing a mathematics teaching license. The MTEL Mathematics (63) case studies are 5 cases and about 4,137 words.
1Fair Game? Expected Value and a 40-Play Sample
Alvarez's seventh-grade class designed a carnival game for family night. A spinner has 8 equal sectors: 1 sector reads 'Win 3,' 2 sectors read 'Win 2,' and 5 sectors read 'Try again.' A play costs 1.
717 words, about 4 min2Reversible Steps: Losing, Creating, and Excluding Solutions
Okafor's algebra 2 class is solving equations, and he collects three exit slips. On item 1, 'Solve x² = 6x,' Leila writes x²/x = 6x/x, so x = 6, and boxes 6.
814 words, about 4 min3The Ambiguous Case: When Two Sides and an Angle Don't Determine a Triangle
In a geometry class, students are asked: 'In triangles ABC and DEF, AB = DE = 9 cm, BC = EF = 5 cm, and m∠A = m∠D = 30°. Must the triangles be congruent?' Jordan writes, 'Yes - two sides and an angle match, so the triangles are congruent by SAS.' Mr.
806 words, about 4 min4Four Error Patterns in Rational Number Sense
Brennan gives a four-item quiz to her sixth graders: (1) 0.4 × 0.3, (2) 1/2 ÷ 1/6, (3) 3 ÷ 1/2, (4) compare 0.7 and 0.65. Sorting responses, she finds four patterns.
860 words, about 4 min5Zero Average Rate of Change and a Model Past Its Domain
Duarte's precalculus class models a ball tossed from a balcony with h(t) = −16t² + 48t + 5, where h is height in feet and t is seconds after release. Ana computes the average rate of change on [0, 3] as (h(3) − h(0))/3 = (5 − 5)/3 = 0 ft/s and concludes, 'The ball didn't move between 0 and 3 seconds, so the model must be wrong.' Ben evaluates h(4) = −16(16) + 192 + 5 = −59 feet and says, 'At 4 seconds the ball is 59 feet below the balcony.' Mr.
940 words, about 5 min