Teske lived in the Grand Rapids, Michigan suburb of Grandville until he was 10 and his family moved to Medina, Ohio. Teske was as a high school freshman and as a sophomore before eclipsing as a junior for Medina High School. Among Teske's advisors on his recruitment was his maternal grandfather, Jim Zuidema. On August 7, 2014, he committed to Michigan via Twitter. Teske signed his National Letters of Intent on November 11, 2015 on the same day as future teammates Austin Davis, Ibi Watson and Zavier Simpson. Simpson, Watson and Teske were all named to the 2015–16 Associated Press Ohio high school Division I boys basketball all-state 1st team.
In November 2018, Teske twice posted 5 blocked shots in a game: On November 10 against Holy Cross and November 28 against North Carolina 84-67 in the ACC–Big Ten Challenge. Teske first posted 17 points and made a three-point shot on November 18 in a win against Providence in the Hall of Fame Tip Off tournament championship game. Teske again posted 17 points on December 1, against Purdue in Michigan's Big Ten Conference season opener. On December 4, Michigan defeated Northwestern 62-60. When Teske experienced his first foul trouble of the season Michigan saw a comfortable win turn into a nailbiter as Northwestern posted a 13-2 run after Teske joined teammate Charles Matthews on the sidelines with three fouls. On January 10, 2019, Michigan defeated Illinois as Teske added 13 points and 11 rebounds, for his third career double-double, and first of the season. With the win, the Wolverines improved to 16–0 on the season, matching the 2012–13 and 1985–86 teams for the school's best start to a season. On January 13, Michigan defeated Northwestern to establish a school record for best start at 17-0 and tied the 1984–85 team's school record 17-game win streak on the strength of a career-high tying 17 points by Teske, who posted his second consecutive double-double. Teske tied his career high of 17 points again in wins against Wisconsin on February 9 and on February 21 against Minnesota when he again posted five blocks. On February 24, Teske posted 10 points and 11 rebounds, for his fourth double-double of the season in a loss to Michigan State. On February 28, Teske posted a then career-high 22 points and 10 assists, for his second consecutive double-double and fifth of the season, in a win against Nebraska. On March 3, Teske posted 11 points and 10 rebounds, for his third consecutive game with a double-double and sixth of the season in a win against Maryland. Following the season, he was a 2019 All-Big Ten honorable mention selection. Teske's 75 blocked shots in 37 games, finished second in the Big Ten to Purdue's Matt Haarms who had 79 blocks in 36 games.
Senior season
Prior to the season, Teske was named to the preseason Abdul-Jabbar Award 20-man watchlist. The team began the season unranked but received votes in the national polls. On November 5, 2019, in a game against Appalachian State, Teske posted 17 points and a career-high 13 rebounds, for his 11th career double-double. During the November 27 - 29. 2019, Battle 4 Atlantis, Michigan defeated Iowa State, North Carolina, and Gonzaga to win the tournament. In the championship game, Teske added 19 points, a career-high 15 rebounds and four blocks and was named tournament MVP. Teske's three double-digit scoring games and 10-block/29-rebound tournament earned him co-Big Ten Player of the Week. His performance helped Michigan tie the 1989–90 Kansas Jayhawks for the largest jump in the history of the AP Poll as they jumped from unranked to number 4 in the 2019–20 basketball rankings. On December 5, Teske was one of six Big Ten athletes named to the Oscar Robertson Trophy Watch List. On December 29, Teske posted a career-high 25 points in a win against UMass Lowell.
Personal life
Teske is from a family of tall athletes. His father, Ben, is and his mother, Julie, is. His older sister, Hannah, and younger sister, Abby, are both at least. Both his parents played basketball for Grace College and his sisters played high school sports. His maternal grandparents remained in the Grand Rapids area after the family moved to Medina and Teske continued to visit Grand Rapids often while in college.