The Supreme Court begins a new term next week with a docket of cases that could have sweeping implications for religious freedom, jury deliberations and congressional redistricting.

Whether the court will be able to resolve all of its cases remains to be seen. The justices deadlocked several times last term, with the court evenly split between the conservative and liberal wings after the death in February of Justice Antonin Scalia.

{mosads}“You can see they were trying hard to come to consensuses when possible,” said Carrie Severino, chief counsel and policy director of the conservative Judicial Crisis Network. “They only had four cases come down 4-4.”

Severino cited Zubik v. Burwell as an example of the justices working toward consensus. In that case, the court ordered the Obama administration to work out a compromise with religious groups over how to meet the Affordable Care Act’s birth control mandate.

Experts are expecting Chief Justice John Roberts to keep pushing his colleagues to find common ground.  

The court has agreed to hear 31 cases in the new term and is likely to accept more at its fall conference Monday.

Among the petitions to watch is Gloucester County School Board v. G.G., which could prove to be a blockbuster case on transgender rights.

The term is also opening in the middle of a contentious presidential election that could swing the balance of the court to the left, should Hillary Clinton win the White House, or keep it firmly to the right, should Donald Trump triumph.

Here are five of the most interesting cases before the court. 

1. Trinity Lutheran Church of Columbia Inc. v. Pauley

This case centers on a Missouri program that gives schools money to buy recycled tires to resurface playgrounds.

Trinity Lutheran Church of Columbia requested funding for a playground on church property that’s used by its licensed preschool and daycare, called the Learning Center.

The Missouri Department of Natural Resources denied that request, citing state constitutional policy prohibiting public funds supporting churches.

Both the district court and the 8th Circuit Court of Appeals sided with the state.

The justices are being asked whether religious schools can be denied equal access to government benefits. Trinity additionally argues the rejection is a violation of both the First Amendment’s religious freedom clause and the 14th Amendment’s promise of equal protection under the law.

Court watchers note that the court accepted this case before Scalia died.

2. Peña Rodriguez v. Colorado

In 2007, a jury found Miguel Angel Peña Rodriguez guilty of attempting to sexually assault two teenage girls in the bathroom of a horse race track.

About two weeks after the trial ended, two jurors told Peña Rodriguez’s attorney that some of the jurors expressed a bias against him and his alibi witness because he is Hispanic. In sworn affidavits, the jurors recalled one juror specifically saying, “I think he did it because he’s Mexican, and Mexican men take whatever they want.”

Peña Rodriguez moved for a new trial, arguing that he was denied his constitutional right to an impartial jury. The lower courts, however, said the affidavits were inadmissible, citing a longstanding rule prohibiting jurors from testifying about anything that occurs during the course of jury deliberations.

The justices must now decide if jurors can be questioned after a verdict to prove a racial bias.

3. Samsung Electronics Co. v. Apple

The case stems from a lawsuit Apple brought against Samsung in April 2011 for infringing on the look and feel of its iPhone design.

A jury awarded Apple $399 million — the total profits from various Samsung smartphone models that infringed on Apple’s design.

Samsung is appealing to the Supreme Court, arguing that the award should have only been a portion of the products’ profits since the patent designs only applied to one component of each device. 

4. Fry v. Napoleon Community Schools

The case centers on Ehlena Fry, a Michigan girl with cerebral palsy who has had a service dog since the age of five. According to court documents, the dog assists her in daily activities like retrieving dropped items, opening and closing doors, turning on and off lights and taking her coat off, but the Napoleon Community Schools and Jackson County Intermediate School District refused to let her bring the dog to school.

The issue in this case, however, is not about whether the goldendoodle named Wonder should have been allowed — it’s whether Fry’s parents should have exhausted all state administrative remedies under the Individuals with Disabilities Education Act and the Rehabilitation Act before suing the school for damages under the Americans with Disabilities Act. 

The justices have been asked to settle a circuit court split on the issue.

5. McCrory v. Harris

This is one of two racially charged redistricting cases the court has agreed to hear this term. The other, Bethune-Hill v. Virginia State Board of Elections, challenges the way state House districts were drawn in Virginia.

In McCrory v. Harris, North Carolina Gov. Pat McCrory is challenging a lower court ruling that held the state’s Congressional Districts 1 and 12 were unconstitutional racial gerrymanders.

Rep. G.K. Butterfield (D) represents District 1, and Rep. Alma Adams (D) represents District 12.