diff --git a/htdocs/js/GatewayQuiz/gateway.js b/htdocs/js/GatewayQuiz/gateway.js
index 4aecb3f37e..365389560c 100644
--- a/htdocs/js/GatewayQuiz/gateway.js
+++ b/htdocs/js/GatewayQuiz/gateway.js
@@ -158,22 +158,20 @@
 
 		const remainingTime = serverDueTime - browserTime + timeDelta;
 
-		if (!timerDiv.dataset.acting) {
-			if (remainingTime <= 10 - gracePeriod) {
-				if (sessionStorage.getItem('gatewayAlertStatus')) {
-					sessionStorage.removeItem('gatewayAlertStatus');
-
-					// Submit the test if time is expired and near the end of grace period.
-					actuallySubmit = true;
-					submitAnswers.click();
-				}
-			} else {
-				// Set the timer text and check alerts at page load.
-				updateTimer();
+		if (!timerDiv.dataset.acting && remainingTime <= 10 - gracePeriod) {
+			if (sessionStorage.getItem('gatewayAlertStatus')) {
+				sessionStorage.removeItem('gatewayAlertStatus');
 
-				// Start the timer.
-				setInterval(updateTimer, 1000);
+				// Submit the test if time is expired and near the end of grace period.
+				actuallySubmit = true;
+				submitAnswers.click();
 			}
+		} else {
+			// Set the timer text and check alerts at page load.
+			updateTimer();
+
+			// Start the timer.
+			setInterval(updateTimer, 1000);
 		}
 	}
 
diff --git a/lib/WeBWorK/ConfigValues.pm b/lib/WeBWorK/ConfigValues.pm
index 24cb77116c..19f3172f38 100644
--- a/lib/WeBWorK/ConfigValues.pm
+++ b/lib/WeBWorK/ConfigValues.pm
@@ -529,7 +529,14 @@ sub getConfigValues ($ce) {
 				var  => 'permissionLevels{record_answers_when_acting_as_student}',
 				doc  => x('Can submit answers for a student'),
 				doc2 => x(
-					'When acting as a student, this permission level and higher can submit answers for that student.'),
+					'When acting as a student, this permission level and higher can submit answers for that student, '
+						. 'which includes starting and grading test versions.  This permission should only be turned '
+						. 'on temporarily and set back to "nobody" after you are done submitting answers for a '
+						. 'student, as it can interfere with tests.  If you have this permission and are viewing a '
+						. 'test version for a student that is also working on that version, your answers will be '
+						. 'saved for that student when moving between pages, which could reset or change the answers '
+						. 'entered in by the student.'
+				),
 				type => 'permission'
 			},
 			{
diff --git a/lib/WeBWorK/ContentGenerator/GatewayQuiz.pm b/lib/WeBWorK/ContentGenerator/GatewayQuiz.pm
index cfd6b4ab85..8d09e610e0 100644
--- a/lib/WeBWorK/ContentGenerator/GatewayQuiz.pm
+++ b/lib/WeBWorK/ContentGenerator/GatewayQuiz.pm
@@ -142,9 +142,12 @@ sub can_recordAnswers ($c, $user, $permissionLevel, $effectiveUser, $set, $probl
 
 	if ($user->user_id ne $effectiveUser->user_id) {
 		# If the user is not allowed to record answers as another user, return that permission.  If the user is allowed
-		# to record only set version answers, then allow that between the open and close dates, and so drop out of this
-		# conditional to the usual one.
-		return 1 if $authz->hasPermissions($user->user_id,  'record_answers_when_acting_as_student');
+		# to record an unsubmitted test, allow that.  If the user is allowed to record only set version answers, then
+		# allow that between the open and close dates, and so drop out of this conditional to the usual one.
+		return 1
+			if $authz->hasPermissions($user->user_id, 'record_answers_when_acting_as_student')
+			|| $c->can_gradeUnsubmittedTest($user, $permissionLevel, $effectiveUser, $set, $problem, $tmplSet,
+				$submitAnswers);
 		return 0 if !$authz->hasPermissions($user->user_id, 'record_set_version_answers_when_acting_as_student');
 	}
 
@@ -225,6 +228,15 @@ sub can_checkAnswers ($c, $user, $permissionLevel, $effectiveUser, $set, $proble
 	return 0;
 }
 
+# If user can use the problem grader, and the test is past due and has not been submitted, allow them to submit.
+sub can_gradeUnsubmittedTest ($c, $user, $permissionLevel, $effectiveUser, $set, $problem, $tmplSet, $submitAnswers = 0)
+{
+	return
+		!$submitAnswers
+		&& $c->can_showProblemGrader($user, $permissionLevel, $effectiveUser, $set, $problem, $tmplSet)
+		&& (after($set->due_date + $c->ce->{gatewayGracePeriod}) && !$set->version_last_attempt_time);
+}
+
 sub can_showScore ($c, $user, $permissionLevel, $effectiveUser, $set, $problem, $tmplSet) {
 	return
 		$c->authz->hasPermissions($user->user_id, 'view_hidden_work')
@@ -642,7 +654,8 @@ async sub pre_header_initialize ($c) {
 			if (
 				($currentNumAttempts < $maxAttemptsPerVersion)
 				&& ($effectiveUserID eq $userID
-					|| $authz->hasPermissions($userID, 'record_set_version_answers_when_acting_as_student'))
+					|| $authz->hasPermissions($userID, 'record_set_version_answers_when_acting_as_student')
+					|| $authz->hasPermissions($userID, 'record_answers_when_acting_as_student'))
 				)
 			{
 				if (between($set->open_date(), $set->due_date() + $ce->{gatewayGracePeriod}, $c->submitTime)) {
@@ -741,6 +754,7 @@ async sub pre_header_initialize ($c) {
 		checkAnswers          => $c->can_checkAnswers(@args),
 		recordAnswersNextTime => $c->can_recordAnswers(@args, $c->{submitAnswers}),
 		checkAnswersNextTime  => $c->can_checkAnswers(@args, $c->{submitAnswers}),
+		gradeUnsubmittedTest  => $c->can_gradeUnsubmittedTest(@args, $c->{submitAnswers}),
 		showScore             => $c->can_showScore(@args),
 		showProblemScores     => $c->can_showProblemScores(@args),
 		showWork              => $c->can_showWork(@args),
@@ -755,6 +769,11 @@ async sub pre_header_initialize ($c) {
 	$c->{can}  = \%can;
 	$c->{will} = \%will;
 
+	# Issue a warning if a test has not been submitted, but can still be graded by the instructor.
+	$c->addbadmessage(
+		'This test version is past due, but has not been graded. You can still grade the test for this user.')
+		if $can{gradeUnsubmittedTest} && $userID ne $effectiveUserID;
+
 	# Set up problem numbering and multipage variables.
 
 	my @problemNumbers;
diff --git a/templates/ContentGenerator/GatewayQuiz.html.ep b/templates/ContentGenerator/GatewayQuiz.html.ep
index ce8719b0fb..414dd4e6f8 100644
--- a/templates/ContentGenerator/GatewayQuiz.html.ep
+++ b/templates/ContentGenerator/GatewayQuiz.html.ep
@@ -235,7 +235,7 @@
 % # Remaining output of test headers.
 % # Display timer or information about elapsed time, output link, and information about any recorded score if not
 % # submitAnswers or checkAnswers.
-% if ($c->{can}{recordAnswersNextTime}) {
+% if ($c->{can}{recordAnswersNextTime} || $c->{can}{gradeUnsubmittedTest}) {
 	% my $timeLeft = $c->{set}->due_date - int($submitTime);    # This is in seconds
 	%
 	% # Print the timer if there is less than 24 hours left.
@@ -269,11 +269,13 @@
 		) =%>
 	% }
 	%
-	% if ($timeLeft < 60 && $timeLeft > 0 && !$authz->hasPermissions($userID, 'record_answers_when_acting_as_student')) {
+	% if ($timeLeft < 60 && $timeLeft > 0 && !$c->{can}{gradeUnsubmittedTest}
+			% && !$authz->hasPermissions($userID, 'record_answers_when_acting_as_student')) {
 		<div class="alert alert-danger d-inline-block mb-2 p-1">
 			<strong><%= maketext('You have less than 1 minute to complete this test.') %></strong>
 		</div>
-	% } elsif ($timeLeft <= 0 && !$authz->hasPermissions($userID, 'record_answers_when_acting_as_student')) {
+	% } elsif ($timeLeft <= 0 && !$c->{can}{gradeUnsubmittedTest} &&
+			% !$authz->hasPermissions($userID, 'record_answers_when_acting_as_student')) {
 		<div class="alert alert-danger d-inline-block mb-2 p-1">
 			<strong>
 				<%= maketext('You are out of time!')
@@ -653,11 +655,16 @@
 		%
 		<div class="submit-buttons-container col-12 mb-2">
 			<%= submit_button maketext('Preview Test'), name => 'previewAnswers', class => 'btn btn-primary mb-1' =%>
-			% if ($c->{can}{recordAnswersNextTime}) {
+			% if ($c->{can}{checkAnswersNextTime}
+					% && (!$c->{can}{recordAnswersNextTime} || $c->{can}{showProblemGrader})) {
+				<%= submit_button maketext('Check Test'), name => 'checkAnswers', class => 'btn btn-primary mb-1' =%>
+			% }
+			% if ($c->{can}{recordAnswersNextTime} || $c->{can}{gradeUnsubmittedTest}) {
 				<%= tag('input',
 					type  => 'submit',
 					name  => 'submitAnswers',
-					value => maketext('Grade Test'),
+					value => $effectiveUserID ne $userID
+						? maketext('Grade Test for [_1]', $effectiveUserID) : maketext('Grade Test'),
 					class => 'btn btn-primary mb-1',
 					$c->{set}->attempts_per_version
 					? (
@@ -687,9 +694,6 @@
 					: ()
 				) =%>
 			% }
-			% if ($c->{can}{checkAnswersNextTime} && !$c->{can}{recordAnswersNextTime}) {
-				<%= submit_button maketext('Check Test'), name => 'checkAnswers', class => 'btn btn-primary mb-1' =%>
-			% }
 		</div>
 		% if ($numProbPerPage && $numPages > 1 && $c->{can}{recordAnswersNextTime}) {
 			<p><em><%= maketext('Note: grading the test grades all problems, not just those on this page.') %></em></p>