A Supreme Court that has in recent days shown that it is sharply divided along ideological lines is poised to wrap up its work this week and to announce some of the biggest decisions of the term.

The justices pride themselves on reaching unanimous results, often publicizing their ability to find common ground in a surprisingly high number of cases. But in just the last week, seven of the nine decisions announced by the Supreme Court split the justices 6 to 3, with all Republican nominees in the majority and all Democratic nominees in dissent.

That familiar lineup is likely to hold in a number of the remaining eight rulings the court is set to issue on Monday and at least one other day this week, before the justices take their traditional summer break.

The divisive rulings illustrate how the court’s six Republican nominees are routinely controlling the outcome in decisions large and small this term, and moving the law steadily to the right.

There are blockbusters left to be decided: Can President Trump fire the leaders of independent agencies over policy differences and end the guarantee of birthright citizenship for babies born in the United States to illegal immigrants?

Another big decision will determine whether the president can oust Lisa D. Cook from the influential and independent Federal Reserve Board of Governors over unproven allegations of mortgage fraud. And the court will decide whether transgender female athletes can participate on girls’ and women’s sports teams.

The justices hinted at tensions among them in public appearances at law schools and judicial conferences this spring. That friction was briefly evident on the bench last Thursday, when the court sided with the Trump administration, 6 to 3, to allow officials to turn away asylum seekers at the U.S.-Mexico border who have not set foot on U.S.-soil.

After Justice Samuel A. Alito Jr. read a brief summary of his opinion, he seemed taken aback when Justice Sonia Sotomayor spent 10 minutes summarizing her dissent.

Justice Alito then departed from the court’s usual practice by responding and suggesting he had been unaware that his colleague had planned to dissent from the bench.

There is “much that I would have added,” Justice Alito said, going on to briefly defend the majority opinion.

On Friday, a court spokeswoman said the dust-up had been just a misunderstanding on the part of Justice Alito, who had been notified by Justice Sotomayor’s chambers that she planned to read a dissent from the bench.

To be sure, the court has issued two dozen unanimous opinions in its term, which began in October. All nine justices, for instance, agreed to narrow a federal gun control measure, siding with a marijuana user who had challenged a provision banning drug users from owning or possessing guns.

And there were unusual alliances when three of the court’s Republican nominees joined the liberal justices to invalidate the president’s sweeping tariffs on imports from nearly all U.S. trading partners.

But common ground has been in short supply in many of the cases decided this month, as is often the case when the court issues its final, most contentious decisions.

Other important decisions to come this week will set rules for financing political campaigns and counting mail-in ballots, and decide the fate of a popular law enforcement tool used to sweep up location data from cellphones to find suspects and witnesses near crime scenes.

Last week, all three liberal justices dissented when the majority cleared the Trump administration to strip deportation protections from hundreds of thousands of migrants.

The court’s decision signing off on the termination of humanitarian protections, known as Temporary Protected Status, was a long-sought victory for conservatives and has implications for 1.3 million T.P.S. holders in the United States who come from more than a dozen nations.

The 6 to 3 split emerged in other areas as well. The court’s conservative majority struck down a Hawaii law that required gun owners to get permission before carrying a concealed firearm onto private property like gas stations and grocery stores that are open to the public.

Even some of the court’s lower-profile rulings this term have revealed broader strains among the justices.

Justice Sotomayor dissented last week when the court ruled that members of the Falun Gong spiritual movement could not sue a U.S. company that they claimed helped facilitate the Chinese government’s efforts to target and torture them.

The court “closes the courthouse doors” not just to the Falun Gong members, but also “to virtually every future litigant seeking redress for a violation of international law” under the Alien Tort Statute, she wrote, joined in part by Justices Elena Kagan and Ketanji Brown Jackson.

The court’s conservative majority, she added, was seeking “yet another notch in its belt, unabashedly remaking the law in its preferred image.”

Abbie VanSickle contributed reporting.