 United States Court of Appeals
         FOR THE DISTRICT OF COLUMBIA CIRCUIT



Argued March 31, 2017                  Decided June 23, 2017

                         No. 16-7076

                         DL, ET AL.,
                         APPELLEES

                              v.

DISTRICT OF COLUMBIA, A MUNICIPAL CORPORATION, ET AL.,
                     APPELLANTS


        Appeal from the United States District Court
                for the District of Columbia
                    (No. 1:05-cv-01437)


    Lucy E. Pittman, Assistant Attorney General, Office of the
Attorney General for the District of Columbia, argued the cause
for appellants. With her on the briefs were Karl A. Racine,
Attorney General, Todd S. Kim, Solicitor General, and Loren
L. AliKhan, Deputy Solicitor General.

    Todd A. Gluckman argued the cause for appellees. With
him on the brief were Margaret A. Kohn, Cyrus Mehri, Carolyn
S. Pravlik, and Patrick A. Sheldon.

   Iris Y. González, Daniel B. Kohrman, Kelly R. Bagby,
Sharon Krevor-Weissbaum, Ira A. Burnim, Mary Nell
McGarity Clark, and Martha Jane Perkins were on the brief
                                2
for amici curiae AARP, et al. in support of appellees. Jon M.
Greenbaum entered an appearance.

   Before: TATEL, GRIFFITH and MILLETT, Circuit Judges.

   Opinion for the Court filed by Circuit Judge TATEL.

    TATEL, Circuit Judge: More than a decade ago, the parents
of six children, ages three to six, sued the District of Columbia,
alleging that it was violating the “Child Find” requirement of
the Individuals with Disabilities Education Act by failing to
provide special education to their children and hundreds of
other preschoolers with disabilities. The district court certified
the suit as a class action under Federal Rule of Civil Procedure
23, found the District liable, and entered a comprehensive
injunction designed to bring the District into compliance with
IDEA. On appeal, the District argues that the case has become
moot because the six named plaintiffs are no longer toddlers
with a stake in the requested relief. The District also challenges
the class certification and argues that the injunction exceeds the
district court’s authority. For the reasons set forth in this
opinion, we affirm in all respects.

                                I.
    For much of this nation’s history, children with disabilities
“were either totally excluded from schools or were sitting idly
in regular classrooms awaiting the time when they were old
enough to drop out.” Board of Education of Hendrick Hudson
Central School District v. Rowley, 458 U.S. 176, 179 (1982)
(alteration and internal quotation marks omitted). Faced with
this “pervasive and tragic academic stagnation,” Congress
passed the Education of the Handicapped Act of 1975 (EHA).
Endrew F. ex rel. Joseph F. v. Douglas County School District
RE-1, 137 S. Ct. 988, 999 (2017). That “ambitious” law,
Rowley, 458 U.S. at 179, which applied to public schools
                                3
receiving federal funds, sought to provide all children with
disabilities a “free appropriate public education . . . tailored to
[their] unique needs,” id. at 180.

    Fifteen years later, finding that EHA implementation had
“been impeded by low expectations” and resource constraints,
20 U.S.C. § 1400(c)(4)-(7), Congress strengthened the statute
and renamed it the Individuals with Disabilities Education Act
(IDEA), see Pub. L. No. 101-476, § 901, 104 Stat. 1103 (1990).
This time Congress drew on its authority under the Spending
Clause to offer states a deal: in exchange for additional federal
funding, they would “pledge[] to comply” with a series of
requirements designed to ensure that each student receives a
“free appropriate public education,” or FAPE. Endrew F., 137
S. Ct. at 993; see U.S. CONST., Art. I, § 8, cl. 1. Among the
most important of these requirements, the “Child Find”
provision obliges states to develop a “practical method” to
track which children are receiving special education services
and to ensure that all children “who are in need of special
education and related services . . . are identified, located, and
evaluated” within a timeframe set by the state—120 days in this
case. 20 U.S.C. § 1412(a)(3)(A); see 20 U.S.C.
§ 1414(a)(1)(C)(i)(I) (authorizing states to “establish[] a
timeframe within which the evaluation must be conducted”);
D.C. Code § 38-2561.02(a)(1) (requiring an evaluation “within
120 days from the date the student was referred for an
evaluation”). Another requirement, the “smooth and effective
transition” condition, obliges states to provide a seamless
transition when three-year-olds move from “early
intervention” programs (governed by IDEA Part C) to
preschool (governed by IDEA Part B). 20 U.S.C.
§§ 1412(a)(9), 1435(a)(8)(A), 1437(a)(9); 34 C.F.R.
§ 303.209. The transition between these programs qualifies as
“smooth and effective” if, among other things, it begins at least
ninety days before the child’s third birthday, delivers
                                 4
uninterrupted services, and involves both Part B and C
personnel. 20 U.S.C. § 1412(a)(9); 34 C.F.R. § 303.209. In the
District of Columbia, which IDEA defines as a state, see 20
U.S.C. § 1401(31), and which receives millions of dollars of
IDEA funding each year, early intervention programs are run
by the Office of the State Superintendent of Education and
preschool programs by the District of Columbia Public Schools
(DCPS).

    In 2005, the parents of six children, ages three to six, sued
the District, alleging a “pervasive and systemic” breakdown in
the school system’s Child Find program. D.L. v. District of
Columbia, No. 05-cv-1437, ECF No. 1, at 3 (D.D.C. July 21,
2005). According to the complaint, the District was failing to
identify large numbers of disabled children and delivering
inadequate and delayed services to many others. These
deficiencies, the parents argued, were depriving “hundreds” of
preschoolers of their right to a FAPE. Id.

    The district court, Judge Royce C. Lamberth, certified the
suit as a class action in 2006. D.L. v. District of Columbia, 237
F.R.D. 319 (D.D.C. 2006). The class definition was broad: “All
children [between three and five] who are or may be eligible
for special education and related services, who live in, or are
wards of, the District of Columbia” and whom the District had
failed or would fail to “identify, locate, evaluate or offer special
education and related services.” Id. at 324–25. Four years later,
the parties each moved for summary judgment. After reviewing
the record, the district court granted summary judgment to the
parents with respect to their claims up to and through 2007 and
scheduled a bench trial on all remaining claims. D.L. v. District
of Columbia, 730 F. Supp. 2d. 84, 95, 98 (D.D.C. 2010).
During that trial, the court heard two days of testimony from
statisticians, school district staff, and experts in education
policy and early childhood development.
                                5
    After trial but before the district court issued its decision,
the Supreme Court decided Wal-Mart Stores, Inc. v. Dukes,
which held that “one of the most expansive class[es] ever” was
too broad to meet the requirements of Federal Rule of Civil
Procedure 23. 564 U.S. 338, 342 (2011). Relying on Wal-Mart,
the District moved to decertify the class, arguing that it was
similarly overbroad. Although the parents insisted that the class
complied with Wal-Mart, they suggested that if the court had
any doubt it should recertify the class as four subclasses of
children whom the District had failed to (1) identify, (2) timely
evaluate, (3) offer a timely determination of eligibility for
special education and related services, and (4) provide a
smooth transition from early intervention programs to
preschool. D.L., ECF No. 271-2, at 7–8 (Aug. 18, 2011).
Satisfied that the certified class complied with Wal-Mart,
however, the district court deemed subclasses unnecessary.
D.L. v. District of Columbia, 277 F.R.D. 38, 46–47 (D.D.C.
2011).

    The court then found the District liable for violating its
Child Find obligations and failing to ensure a “smooth and
effective transition” for toddlers entering preschool. D.L. v.
District of Columbia, 845 F. Supp. 2d 1, 21–23 (D.D.C. 2011).
These violations, Judge Lamberth observed, deprived “some of
our most vulnerable citizens” of services in the “first few
years” of their lives, a “narrow window of opportunity in which
special education, tailored to the child’s particular needs, can
work a miracle.” Id. at 5. Based on these findings, the court
entered a comprehensive injunction that set compliance
benchmarks and required annual improvement in the numbers
of children identified as needing, evaluated for, and offered
special education and related services.

    The District appealed, and this court vacated the class
certification order. D.L. v. District of Columbia, 713 F.3d 120,
                                6
121 (D.C. Cir. 2013). Citing Wal-Mart, we held that a class
defined by reference “to the District’s pattern and practice of
failing to provide FAPEs speaks too broadly because it
constitutes only an allegation that the class members ‘have all
suffered a violation of the same provision of law.’” Id. (quoting
Wal-Mart, 546 U.S. at 350). We noted that the parents
“appeared to recognize [this] problem,” and had proposed
subclasses tied to failures in four distinct administrative
functions. Id. at 128. Rather than deciding whether those
subclasses satisfied Wal-Mart, we remanded to the district
court to consider that question in the first instance.

    The district court then certified the same four subclasses the
parents had proposed: (1) disabled three-to-five-year-olds
whom the District failed to identify for the purpose of offering
special education services; (2) disabled three-to-five-year-olds
whom the District failed to give an initial evaluation within 120
days of being referred for special education services; (3)
disabled three-to-five-year-olds whom the District failed to
give an “eligibility determination”—i.e., a decision as to
whether they qualify for IDEA services—within 120 days of
being referred; and (4) all children who transitioned from early
intervention to preschool programs, and whom the District
denied a “smooth transition” by age three. This court denied
the District’s petition for interlocutory review, In re District of
Columbia, No. 13-8009, Doc. No. 1477562 (D.C. Cir. Jan. 30,
2014), and the case once again advanced to summary
judgment, where the district court entered judgment for the
District on all claims concerning subclass two, and then on to
a bench trial. D.L. v. District of Columbia, 109 F. Supp. 3d 12,
36 (D.D.C. 2015). After considering testimony from seventeen
witnesses and reviewing hundreds of exhibits, the district court
issued a 130-page opinion finding the District liable for
violating IDEA. D.L. v. District of Columbia, 194 F. Supp. 3d
30 (D.D.C. 2016).
                                7
    The district court’s findings were stark. It found that the
District was failing to identify between 98 and 515 children a
month—some two percent of preschoolers with disabilities
who should have been located and offered special education
services. Id. at 48. This placed the District’s Child Find
performance below jurisdictions with comparable rates of
childhood disability, such as Arkansas, Kentucky, and Puerto
Rico. Id. at 48, 53. In addition, the court found that the District
was failing to provide a “smooth and effective transition” to
almost 30 percent of disabled toddlers, id. at 63, and despite
having the “longest period of time in the country” to decide
whether children qualify for special education services, was
missing the deadline for issuing eligibility determinations
approximately 20 percent of the time, id. at 58–59.

    Acknowledging that the District had improved its Child
Find program since 2007, when it had “the lowest percentage”
of special education enrollment in the United States, the court
stressed that “the District ha[d] yet to attain a period of
sustained compliance.” Id. at 78, 98. Indeed, the court
observed, the numbers of children receiving special education
had fallen by 15 percent in 2013 and 2014 when the District
lacked “an enrollment benchmark”—i.e., a target number of
children who should be enrolled in special education and
related services. Id. at 51. Given these deficiencies, the court
concluded that injunctive relief was necessary and, drawing on
its “broad authority to grant ‘appropriate’ relief,’” Forest
Grove School District v. T.A., 557 U.S. 230, 239 (2009)
(construing 20 U.S.C. § 1415(i)(2)(C)(iii)), crafted remedies
for the three remaining subclasses.

    For subclass one—children the District was failing to
identify—the court set an 8.5 percent enrollment target, a
figure drawn from national rates of special education
enrollment and expert testimony concerning risk factors unique
                                8
to Washington, D.C. To reach that target, the court required the
District to increase enrollment rates by half a percent each year.
For subclass three—children denied timely eligibility
determinations—the court ordered the District to meet the
statutory deadline 95 percent of the time and to improve its
performance annually until it reached that level. Similarly, for
subclass four—toddlers transitioning to preschool—the court
required annual improvement, with an ultimate goal of 95
percent compliance. The court also imposed a range of
“programmatic” remedies designed to improve the District’s
methods of finding and tracking children in its system. D.L. v.
District of Columbia, 194 F. Supp. 3d 30, 101–03. These
remedies included requirements that the District establish
databases, disseminate information to parents, and report its
progress to the court.

    On appeal, the District challenges none of the district
court’s basic findings: that it was failing to identify children
with disabilities, that it often missed the deadline for issuing
eligibility determinations, and that it was providing a rocky
transition to toddlers entering preschool. Instead, it argues that:
(1) the case is moot because by the time the district court
certified the subclasses in 2013 each named plaintiff was over
age five, (2) class certification was improper under Wal-Mart,
and (3) the injunction was unauthorized by IDEA and
unsupported by the evidentiary record.

    Before considering these arguments, we think it helpful to
note that the parents who brought this case are not the only ones
concerned with the District’s IDEA compliance. Since at least
1997, the U.S. Department of Education, which oversees state
performance under IDEA, has repeatedly warned the District
that it was neglecting its Child Find obligations. See id. at 72–
78 (documenting the Department’s correspondence with the
District since the mid-1990s); see also 20 U.S.C. § 1416(d)-(e)
                                9
(authorizing the Secretary of Education to review state IDEA
compliance and to withhold federal funds). In 1998, the
Department “entered into a Compliance Agreement with DCPS
mandating full compliance with the requirements of Part B of
the IDEA.” D.L., 194 F. Supp. 3d at 76. In the two decades
since, the Department has nonetheless regularly listed DCPS as
a school district that “needs intervention.” Id. at 73–79.
According to the Department, the District has been especially
deficient in its duty to timely evaluate children referred for
special education by a parent, teacher, or pediatrician. Id. at 73.
The Department even withheld a portion of the District’s
funding in 2009. Id. at 77. Although the record here reveals no
specific link between the Department’s actions and this case,
the subclass two complaints, which focus on the same problem
with timely evaluation, have been resolved. See D.L. v. District
of Columbia, 109 F. Supp. 3d 12, 36 (D.D.C. 2015) (granting
summary judgment as to subclass two). This case now involves
identification (subclass one), eligibility determinations
(subclass three), and transition to preschool (subclass four).

                                II.
    Beginning with mootness, we start from a point on which
the parties agree: when the district court certified subclasses,
the named plaintiffs’ individual claims for injunctive relief
were moot because, by that time, each child was older than five
and, according to the District, had received special education
services. The District argues that this rendered the dispute non-
justiciable. According to the parents, however, two exceptions
to the mootness doctrine apply: first, a “relation back”
exception, which permits class actions to proceed when a
named plaintiff’s individual claim becomes moot only after a
district court’s error; and second, the “inherently transitory”
exception, which applies to claims so fleeting that “the trial
court will not have even enough time to rule” on class
certification before the named plaintiff’s claim expires.
                               10
Genesis Healthcare Corp. v. Symczyk, 133 S. Ct. 1523, 1530–
31 (2013) (citation and internal quotation marks omitted).

    The Supreme Court articulated the first of these exceptions
in United States Parole Commission v. Geraghty, 445 U.S. 388
(1980). In that case, a prisoner challenged the constitutionality
of the federal parole guidelines, the district court erroneously
denied the prisoner’s request for class certification, and the
prisoner was released before the Third Circuit could correct the
error. Id. at 394. The Court held that where an action “would
have acquired the independent legal status” of a class action
“but for the district court’s erroneous denial of class
certification, a corrected ruling on appeal ‘relates back’ to the
time of the erroneous denial.” Genesis Healthcare, 133 S. Ct.
at 1530 (describing the rule in Geraghty).

    The parents argue that this case is just like Geraghty. We
agree. Here, the district court ruled that an overly broad class
satisfied Wal-Mart, an error this court corrected on appeal. See
supra 5–6. Like the plaintiffs in Geraghty, the parents had live
claims when they sought certification, and but for the district
court’s error, could have obtained proper class certification
before their individual claims became moot. Under Geraghty,
then, the case remains justiciable.

    Resisting this conclusion, the District argues that Geraghty
applies only when a court erroneously denies class
certification. In support, the District points out that the
Supreme Court stated in Geraghty that its holding was “limited
to the appeal of the denial of the class certification motion.”
Geraghty, 445 U.S. at 404. The District reads too much into the
word “denial.” The point in Geraghty was that claims relate
back when a trial court’s error prevents a class from gaining
independent status under Rule 23. Whether that error is the
erroneous denial of class certification (as in Geraghty) or the
                               11
erroneous certification of an excessively broad class (as here)
makes no difference. What matters is that the named plaintiffs’
claims became moot—and their class therefore never
“acquired . . . independent legal status,” Genesis Healthcare,
133 S. Ct. at 1530—due to the district court’s mistake. In other
words, but for the district court’s error—certifying an overly
broad class—the parents’ claims would not have become moot.
There is no legally relevant difference between this case and
Geraghty.

    The District insists that the parents could have avoided this
entire problem by finding new toddler-plaintiffs in 2013 when
this court remanded the case to the district court. This misses
the point: when the relation back doctrine applies, as it does
here, named plaintiffs have no obligation to find new class
representatives even if they could.

     Permitting relation back in this case is also consistent with
Rule 23’s purpose. As the Supreme Court explained in
Geraghty, the “justifications that led to the development of the
class action include . . . the provision of a convenient and
economical means for disposing of similar lawsuits[] and the
facilitation of the spreading of litigation costs among numerous
litigants with similar claims.” 445 U.S. at 402–03 (citing
Advisory Committee Notes on Fed. R. Civ. P. 23). Those
interests are served by a rule allowing class claims to proceed
when a district court erroneously certifies too broad a class
while plaintiffs’ claims are live, only to be reversed and
instructed to consider smaller subclasses containing exactly the
same children. By contrast, Rule 23’s purpose would be
disserved by a rule, advocated by the District, requiring parents
to find new named plaintiffs at every turn of inevitably
protracted class litigation.
                                12
    Ultimately, the District’s argument runs counter to the
Supreme Court’s instruction in Geraghty that “Art[icle] III
mootness doctrine” has a “flexible character.” Id. at 400.
Mootness is a pragmatic doctrine meant to limit “judicial
power to disputes capable of judicial resolution.” Id. at 396; cf.
Campbell-Ewald Co. v. Gomez, 136 S. Ct. 663, 669 (2016) (“A
case becomes moot . . . ‘only when it is impossible for a court
to grant any effectual relief whatever to the prevailing party.’”
(quoting Knox v. Service Employees, 132 S. Ct. 2277, 2287
(2012))). In this case, the mootness issue stems neither from
the lack of real dispute nor from any deficiency in the parents’
advocacy, but rather from judicial error. The separation of
powers concerns that animate justiciability jurisprudence are
absent in this context. In Geraghty, the Court emphasized that
the two elements of a justiciable controversy—“sharply
presented issues in a concrete factual setting and self-interested
parties vigorously advocating opposing positions”—can “exist
with respect to . . . class certification . . . notwithstanding the
fact that the named plaintiff’s claim on the merits has expired.”
445 U.S. at 403. Both elements remain present here.

    Citing Genesis Healthcare, 133 S. Ct. at 1523, the District
argues that “[n]o exception to the mootness doctrine allowed”
certification in 2013. Appellants’ Br. 30. The question in
Genesis Healthcare was whether the relation back doctrine
applied when an individual claim under the Fair Labor
Standards Act (FLSA) expired before certification of a
“collective action,” an opt-in procedure established by FLSA
for litigating multiple claims. See 29 U.S.C. § 216(b). The
Court held that it did not and that the action was therefore non-
justiciable. Genesis Healthcare, 133 S. Ct. at 1530–32. In
reaching this conclusion, however, the Court relied not just on
relation back cases, but “[m]ore fundamentally” on the
distinction between FLSA collective actions, which do not
“produce a class with an independent legal status,” and Rule 23
                                13
class actions, which do. Id. at 1530. The outcome in Genesis
Healthcare thus hinged on the unique features of the FLSA
cause of action. In this case, by contrast, we are clearly in Rule
23-land and guided by Geraghty.

     Having concluded that the relation back doctrine applies,
we have no need to consider whether the parents’ claims also
fall under the “inherently transitory” exception to mootness. Id.
at 1530–31. We thus turn to the District’s challenge to class
certification.

                               III.
   Federal Rule of Civil Procedure 23 requires plaintiffs to
show that:

    (1) the class is so numerous that joinder of all members
        is impractical;

    (2) there are questions of law or fact common to the
        class;

    (3) the claims or defenses of the representative parties
        are typical of the claims or defenses of the class;
        and

    (4) the representative parties will fairly and adequately
        protect the interests of the class.

If the action satisfies these prerequisites, plaintiffs must then
demonstrate that their proposed class falls into one of the
categories of class actions listed in Rule 23(b). In this case, the
district court certified subclasses under Rule 23(b)(2), which
applies when the defendant “has acted or refused to act on
grounds that apply generally to the class, so that final injunctive
relief or corresponding declaratory relief is appropriate
                                14
respecting the class as a whole.” Courts may certify classes
under this provision “only when a single injunction or
declaratory judgment would provide relief to each member of
the class.” Wal-Mart, 564 U.S. at 360.

    The Supreme Court interpreted these requirements in Wal-
Mart, in which named plaintiffs seeking to represent 1.5
million women sued the retail giant Wal-Mart under Title VII
of the Civil Rights Act of 1964, alleging endemic sex
discrimination in pay and promotions across the company’s
“approximately 3,400 stores.” Id. at 342. The district court
certified a class of “all women employed at any Wal-Mart
domestic retail store at any time [in the prior thirteen years]
who [had] been or may be subjected to” the company’s
challenged policies and practices. Id. at 346 (alterations and
internal quotation marks omitted).

    Explaining that the class lacked commonality, the Court
reversed. “Commonality requires the plaintiff to demonstrate
that the class members have suffered the same injury,” the
Court observed. Id. at 349–50 (citation and internal quotation
marks omitted). Yet there are multiple theories of Title VII
liability—that statute can, “for example, . . . be violated . . . by
intentional discrimination, or by hiring and promotion criteria
that result in disparate impact, and by the use of these practices
on the part of many different superiors in a single company.”
Id. at 350. Given this, the Court concluded, the assertion that
Wal-Mart had violated Title VII in one way or another as to
each employee did not demonstrate “that all their claims
[could] productively be litigated at once.” Id. Instead, plaintiffs
needed a “common contention . . . of such a nature that it is
capable of classwide resolution—which means that
determination of its truth or falsity will resolve an issue that is
central to the validity of each one of the claims in one stroke.”
Id.
                               15
    As mentioned above, our court has already considered Wal-
Mart’s applicability to this case. We rejected the first certified
class, which included all three-to-five-year-olds allegedly
denied a FAPE, because it spanned “different policies and
practices at different stages of the District’s Child Find and
FAPE process.” D.L., 713 F.3d at 127. “For some plaintiffs,”
we explained, “the alleged harm suffered is due to the failure
of the District to have an effective intake and referral process;
for others the alleged harm is caused by the District’s failure to
offer adequate and timely education placements . . . ; for still
others, the cause is the absence of a smooth and effective
transition . . . .” Id. at 128. Seeming to agree that narrower
subclasses could resolve the commonality problem, the District
argued that the class violated Wal-Mart because it “cover[ed]
failures in four distinct administrative functions: (1)
identification of a child . . . , (2) location of that child, (3)
evaluation for potential services, and (4) if necessary, provision
of services.” Id. (quoting Appellant’s Br. 29).

    On remand, the district court addressed just this defect,
certifying subclasses tied to separate phases of the Child Find
process. Three of those subclasses consist of three-to-five-year-
olds whom the District had failed to (1) identify, (2) evaluate
within 120 days of referral, and (3) provide an eligibility
determination within 120 days of referral. The fourth subclass
contains all children with disabilities denied smooth transitions
from early intervention to preschool programs. Although these
four subclasses appear responsive to both our 2013 opinion and
the District’s concerns, this time around the District argues that
they too are insufficient under Wal-Mart. Once again, then, we
review the district court’s certification order for abuse of
discretion. Hartman v. Duffey, 19 F.3d 1459, 1471 (D.C. Cir.
1994) (“[W]e review a class certification decision
conservatively only to ensure against abuse of discretion or
erroneous application of legal criteria.”). We find none.
                               16
    The three subclasses at issue here (recall that the court
resolved subclass two claims before trial) are each defined by
reference to a “uniform policy or practice” governing a specific
stage of the special education process. D.L., 713 F.3d at 127.
Whereas before the parents’ claims were united only by a
shared allegation of IDEA liability, now the suit has subclasses
cast around “common harm[s],” id. at 128, susceptible to
common proof, and curable by a “single injunction,” Wal-
Mart, 564 U.S. at 360.

    Take subclass one, children with disabilities whom the
District failed to find. These children identified a common
harm, namely, denial of a FAPE due to a deficient and poorly
implemented Child Find policy. This contention, as is evident
from the district court’s findings, is subject to common proof:
after reviewing the evidence, the court found that the District
was failing to identify 98 to 515 children a month. This
violation of the statute can, as is also evident from the district
court’s decision, be remedied by a single order, i.e., an
injunction requiring the District to identify 0.5 percent more
children each year until it reaches 8.5 percent enrollment.

    As with subclass-one parents, the parents of subclass-three
children allege a common harm: contrary to the District’s own
policy, their children had not received eligibility
determinations within 120 days of being referred for a
disability evaluation. Again, this contention can be proved with
common facts, as the district court demonstrated: it found that
20 percent of preschoolers referred for a disability evaluation
received an eligibility determination after the statutory
deadline, if it all. And here, too, a single injunction can remedy
the harm: the court required the District to meet its statutory
deadline 95 percent of the time and to improve its performance
by 10 percent in the first year and 5 percent each year
thereafter.
                               17
    The same goes for subclass four, toddlers denied smooth
and effective transitions to preschool. Those children claimed
that the District’s policies and practices prevented them from
entering preschool by age three without interruption in their
special education services. This is a common allegation,
provable by evidence showing that the District failed to provide
smooth transitions to 30 percent of toddlers, and remediable by
a single injunction requiring annual improvement.

    We have no need to belabor the point. These three
subclasses are far more precise than the class this court vacated
in 2013, whose members shared only the contention that they
had been denied FAPEs at some point in their experiences with
the District’s special education programs.

    Relying on Wal-Mart, 564 U.S. at 352, in which the
Supreme Court observed that female employees had failed to
show common reasons for their managers’ decisions about
promotions and pay, the District argues that even if its policies
run afoul of IDEA, “there are many different reasons” it might
have denied a particular child a FAPE. Appellants’ Br. 39. For
example, the District explains that it may have deprived some
children of special education because of “insufficient outreach”
and others due to “insufficient staff” or “documentation
errors.” Id. Accordingly, the District claims, even the three
subclasses lack “common contention[s]” whose “truth or
falsity” can be resolved “in one stroke.” Wal-Mart, 564 U.S. at
350.

    There is, however, a significant distinction between Wal-
Mart and this case. As the Court pointed out in Wal-Mart, “[i]n
resolving an individual’s Title VII claim, the crux of the
inquiry is ‘the reason for a particular employment decision.’”
Id. at 352 (quoting Cooper v. Federal Reserve Bank of
Richmond, 467 U.S. 867, 876 (1984) (emphasis added)). The
                                18
fact that Wal-Mart supervisors might have had different
reasons for “literally millions of employment decisions” was
therefore fatal to the commonality of the plaintiffs’ Title VII
claims. Id. By contrast, IDEA requires the District to find and
serve all children with disabilities as a condition of its funding.
See, e.g., 20 U.S.C. § 1412(a)(3)(A). Unlike Title VII liability,
IDEA liability does not depend on the reason for a defendant’s
failure and plaintiffs need not show why their rights were
denied to establish that they were. They need only show that
the District in fact failed to identify them, failed to provide
them with timely eligibility determinations, or failed to ensure
a smooth transition to preschool. Wal-Mart’s analysis of
commonality in the Title VII context thus has limited relevance
here.

    Citing a Seventh Circuit decision, Jamie S. v. Milwaukee
Public Schools, 668 F.3d 481 (7th Cir. 2012), the District
argues that the parents in this case alleged only a “superficial
violation of the same provision of law.” Appellants’ Reply Br.
16. But that case concerned a much broader class, more like the
original class this court rejected than the subclasses now at
issue. As the Seventh Circuit noted, the class there not only
sought “individualized relief,” but also “combined,” among
other groups, “all disabled students . . . who were not identified
as potentially eligible for services, not timely referred for
evaluation after identification, [and] not timely evaluated after
referral.” Id. at 495, 499. The subclasses in this case suffer from
no such flaw and seek class-wide injunctive relief.

    The District next argues that the class violates Rule
23(a)(3)’s typicality requirement because the parents’ claims
“vary from child-to-child.” Appellants’ Br. 42. This argument
should sound familiar: it is the District’s commonality
challenge in a new guise. Indeed, the District expressly claims
that the court “found typicality based on the same error it made
                                19
in finding commonality.” Id. 41. As we have already explained,
however, the district court made no such error. Specifically
analyzing typicality, it found a “sufficient nexus” between the
claims of the named plaintiffs and the claims of the members
of their respective subclasses. D.L. v. District of Columbia, 302
F.R.D. 1, 14 (D.D.C. 2013). We see no abuse of discretion.

    Rule 23(a)’s final requirement—adequacy—provides that
the named plaintiff must “fairly and adequately protect the
interests of the class.” Amchem Products, Inc. v. Windsor, 521
U.S. 591, 625 (1997) (quoting Fed. R. Civ. P. 23(a)(4)). This
rule “serves to uncover conflicts of interest between named
parties and the class they seek to represent.” Id. In this case, the
district court determined that notwithstanding the mootness of
their individual claims, the six named plaintiffs “displayed a
strong commitment to resolving this case” and “respond[ed] to
all developments in a timely and professional fashion.” D.L.,
302 F.R.D. at 14–16.

    Challenging this determination, the District argues that the
court “disregard[ed] the presumption” that “[w]hen a plaintiff’s
claim is moot, it makes her representation presumptively
inadequate.” Appellants’ Br. 42. The court did no such thing.
It acknowledged the adequacy concerns raised by the named
plaintiffs’ age progression and explained why they nonetheless
remained capable representatives. The Supreme Court,
moreover, has made clear that mootness and adequacy are
“separate issue[s]” and that plaintiffs with moot claims may
adequately represent a class. Geraghty, 445 U.S. at 407. With
the benefit of firsthand exposure to the parents and their
lawyers during the course of a then-eight-year-old case, the
district court found that the parents will “fairly and adequately
protect the interests of the class.” D.L., 302 F.R.D. at 14
(quoting Fed. R. Civ. P. 23(a)(4)). The District has given us no
basis for questioning that decision, especially given that the
                               20
district court pondered and rejected the exact arguments the
District now makes.

    Nor, contrary to the District’s argument, did the court err in
certifying subclasses under Rule 23(b)(2). To certify a class
under this provision, a single injunction must be able to
“provide relief to each member of the class.” Wal-Mart, 564
U.S. at 360. The district court’s comprehensive order does just
that. Rule 23(b)(2) exists so that parties and courts, especially
in civil rights cases like this, can avoid piecemeal litigation
when common claims arise from systemic harms that demand
injunctive relief. See Geraghty, 445 U.S. at 403 (discussing the
purpose of Rule 23); In re District of Columbia, 792 F.3d 96,
102 (D.C. Cir. 2015) (“Rule 23(b)(2) was intended for civil
rights cases.”). The Rule 23(b)(2) class action, in other words,
was designed for exactly this sort of suit.

                               IV.
    This brings us to the District’s challenges to the injunction.
IDEA authorizes courts to grant “such relief as [they]
determine[] is appropriate,” 20 U.S.C. § 1415(i)(2)(C)(iii),
which “entail[s] broad discretion and implicate[s] equitable
considerations,” Reid ex rel. Reid v. District of Columbia, 401
F.3d 516, 522 (D.C. Cir. 2005) (citation and internal quotation
marks omitted). Moreover, “it goes without saying that federal
courts must vigilantly enforce federal law and must not hesitate
in awarding necessary relief.” Horne v. Flores, 557 U.S. 433,
450 (2009).

                               A.
   The District first argues that the injunction rests on two
mistakes of law—one concerning subclass three and the other
subclass four. “We review the district court’s conclusions of
                               21
law de novo.” United States v. Philip Morris, 566 F.3d 1095,
1110 (D.C. Cir. 2009).

    Recall that subclass three covers three-to-five-year-olds
who did not receive an eligibility determination within 120
days of being referred for an evaluation. To remedy this injury,
the court required the District to issue timely determinations in
95 percent of cases and to improve its performance annually
until it meets that benchmark. The District argues that this
requirement is “contrary to the plain language of IDEA”
because it “start[s] the clock” for eligibility determinations at
the date of referral rather than the date a parent or guardian
consents to a child’s evaluation. Appellants’ Br. 47. In support,
the District emphasizes that IDEA section 1414 requires an
eligibility determination “within 60 days of receiving parental
consent for the evaluation,” but it ignores the rest of the
sentence: “or, if the State establishes a timeframe within which
the evaluation must be conducted, within such timeframe.” 20
U.S.C. § 1414(a)(1)(C)(i)(I) (emphasis added). Exercising just
that option, the District passed a law—section 38-2561.02 of
the D.C. Code—which requires an eligibility determination
“within 120 days from the date that the student was referred
for an evaluation or assessment.” D.C. Code § 38-
2561.02(a)(1) (emphasis added). District law thus starts the
clock just when the court did, at referral rather than parental
consent. True, the District has amended section 38-2561.02 to
use parental consent as the trigger for the eligibility
determination timeline. See id. § 38–2561.02(a)(2)(A). But that
amendment, by its terms, will not become effective until “July
1, 2017, or upon funding, whichever occurs later.” Id.

    To be clear, the District still needs parental consent to
evaluate a child, see D.C. Code Mun. Reg. tit. 5, § 3005.2
(requiring reasonable efforts to obtain parental consent for
disability evaluations), and nothing in the injunction eliminates
                               22
that requirement. Indeed, the district court emphasized that “the
District should not be blamed for an untimely determination if
the parent does not reasonably participate in the . . . process,”
and noted that the District could adopt a parental delay policy
exempting cases in which parents cannot be reached or decline
to consent. D.L., 194 F. Supp. 3d at 71 (citing 34 C.F.R.
§ 300.301(d)(1)). In this way, the injunction excuses the
District from compliance where it is unable to meet its
deadlines through no fault of its own.

    The District brings a separate challenge to the remedy for
subclass four—children denied “smooth and effective”
transitions from Part C early intervention programs to Part B
preschool programs. In order to qualify as “smooth and
effective,” a transition must begin “not fewer than 90 days
before the [toddler’s] third birthday,” involve Part B and C
personnel, and deliver “seamless” services. See 20 U.S.C.
§ 1412(a)(9); 34 C.F.R. § 303.209(a)(3)(ii), (b)-(f). For this
subclass, the court fashioned a remedy familiar from subclass
three: a 95 percent compliance target, with incremental
improvement required each year. To avoid confusion, the court
made clear that the District could report a smooth transition so
long as children receive all “special education services” by
their third birthdays (or slightly later, for those with weekend,
holiday, and summer birthdays) and all “related services” by
fourteen days thereafter (or again, later in certain cases). D.L.,
194 F. Supp. 3d at 101. “Related services” are the “support
services required to assist a child” in benefitting from special
education. Endrew F., 137 S. Ct. at 994 (citing 20 U.S.C.
§ 1401(26), (29)) (internal quotation marks omitted). In other
words, the court ordered the District to provide core services
by age three and support services two weeks later.

    The District argues that the court had no authority to order
it to provide special education services by a child’s third
                               23
birthday—or for that matter, by any date certain. We disagree.
IDEA expressly requires states to ensure that an IEP “has been
developed and is being implemented” by “the third birthday”
of all toddlers transitioning from early intervention to
preschool. 20 U.S.C. § 1412(a)(9). Ignoring this statutory text,
the District points to a Department of Education regulation
requiring services to be delivered “as soon as possible” after
development of a child’s IEP. 34 C.F.R. § 300.323(c). The
statute, of course, is our guide, and it requires IEPs to be
implemented by the child’s third birthday. Moreover, the
regulation the District invokes, which concerns the provision
of special education services to students aged three to twenty-
one, has nothing to do with the transition to preschool for
children already identified as disabled. And if all this were not
enough, the regulation governing the “smooth transition”
condition requires—in language identical to the statute—that
an IEP “has been developed and is being implemented” by age
three, id. § 300.124(b), and a separate regulation obliges states
to make a FAPE available “no later than the child’s third
birthday,” id. § 300.101(b)(1)(i).

                               B.
    Next the District next makes a series of evidentiary
arguments: that the court chose unduly harsh compliance
targets, ignored improvements in the Child Find program, and
relied on inaccurate statistics. Our review of such objections is
“deferential—clear error as to any factual findings and abuse
of discretion as to the remedy.” Reid, 401 F.3d at 522.

    The first of these challenges concerns subclass one—three-
to-five-year-olds with disabilities whom the District failed to
find. The district court determined that at least 8.5 percent of
preschoolers should be enrolled in special education and
related services, but that just over 6 percent were. The court
based the 8.5 percent benchmark on expert testimony “related
                                24
to risk factors in the District, comparisons to other
jurisdictions, and incidence of developmental delays
nationwide.” D.L., 194 F. Supp. 3d at 49. Specifically, the court
found that although “nationally, about six percent of three-to-
five-year-olds are identified with developmental delays,” the
number is likely higher in the District because of its unique risk
factors, including unusually high rates of poverty, child
homelessness, single-parent and non-English-speaking
households, incidence of low birth weight and HIV/AIDS
infection, and participation in supplemental assistance
programs. Id. at 50. By way of comparison, the court noted that
“other urban jurisdictions” with similar risk profiles such as
Atlanta and Detroit identified “between 10 and 12 percent” of
children as eligible for special education. Id. at 49. “All of this
[evidence],” the court reasoned, “supports the conclusion that
the District must show that it is serving 8.5 percent of its
population,” i.e., the figure at the low end of its expected
identification rates. Id. at 51. The court ordered the District to
improve its performance half a percent each year until it
reaches 8.5 percent. Id.

    The District believes that this remedy suffers from three
flaws: (1) the 8.5 percent benchmark ignores “protective
factors” such as the existence of non-profits, which “buffer
children against the negative effects” of the risk factors in the
District and therefore reduce the number of children likely to
need special education services; (2) enrollment data, which the
injunction uses to measure the District’s success at finding
children, do not approximate Child Find compliance because
not all children identified as potentially needing IDEA services
ultimately enroll in special education programs; and (3) the
injunction improperly defines “enrollment” as receipt of all—
rather than only some—services promised in a child’s IEP.
Appellants’ Br. 45.
                               25
    The district court considered and rejected each of these
arguments. It took seriously the existence of protective factors
that might drive down special education rates, acknowledging
that “Washington D.C.’s network of non-profits likely does
indeed help to alleviate some of the negative developmental
effects of risk factors like high homelessness and poverty
rates.” D.L., 194 F. Supp. 3d at 52. Even so, the court
explained, the impact of non-profits and other city services was
“baked into” the numbers the parents’ expert had used because,
“to the extent that the non-profits do decrease rates of poverty
and homelessness, etc.,” that decrease was already reflected in
the District’s rates of homelessness, poverty, and other risk
factors. Id. As a result, the court reasoned, the data used to
design the remedy “incorporate[d] the positive effects” of
D.C.’s network of non-profits. Id. at 53.

    As to enrollment rates, the court relied on the fact that the
District itself treats enrollment as a proxy for identification
when tracking and reporting its IDEA compliance. Adopting
the District’s own methods hardly amounts to an abuse of
discretion; quite to the contrary, it makes perfect sense. Nor, in
our view, was it unreasonable for the court to define
“enrollment” as provision of all services outlined in a child’s
IEP. After all, IDEA obliges states not only to find children
with disabilities, but also to give them services. See 20 U.S.C.
§ 1412(a)(1)(A) (requiring a FAPE to be made “available to all
children with disabilities”); (a)(2) (setting a goal of “full
educational opportunity”); (a)(3) (requiring states to develop
and implement effective Child Find policies). As the district
court put it, “the entire point of the Child Find requirement is
to provide services to children with disabilities,” a duty the
District is violating by offering children only some of the
services to which they are entitled. D.L., 194 F. Supp. 3d at 91.
                               26
    The District also challenges the injunction’s
“programmatic” requirements, which aim to improve data
collection and outreach efforts—for instance, by ordering
school officials to “publish printed materials targeted to parents
and guardians” about available services and to “maintain and
regularly update a list of primary referral sources.” Id. at 101.
The District insists that these requirements are tailored to
harms they addressed in response to the district court’s 2011
injunction. Perhaps so, but following a three-day trial with new
evidence, the district court found a slew of continuing
deficiencies in the District’s Child Find program, including
“material inconsistences in the District’s documents and
practice,” evidence that the District had yet to amend policies
the court ordered it to change five years earlier, and a two-year
decline in the District’s identification rates after the first
injunction was vacated in 2013. Id. at 99. Given this evidence,
we see no abuse of discretion in the district court’s decision to
again impose programmatic remedies.

    Next, the District mounts several challenges to the court’s
reliance on statistical evidence. Several of these arguments are,
in essence, objections to the liability finding. For example, the
District contends that “the generalized and procedural nature of
the findings does not support the conclusion that children were
denied a FAPE.” Appellants’ Br. 57. Other critiques focus on
the statistics the court used, which the District asserts are
inadequate to support “systemic relief.” Id. 54–55. In both
formulations, the District’s challenge fails.

    Not only does the District cite nothing for the proposition
that courts may not rely on statistical evidence, but it makes
perfect sense to use such evidence where, as here, the violations
amount to a systemic failure to find children. How else could
the court have demonstrated a failure to identify children with
disabilities except with numerical evidence that the District is
                               27
in fact failing to find and serve specified numbers of such
children? And how else could the court have remedied that
violation except by setting numerical goals to bring the District
into compliance with its IDEA obligations?

    Moreover, the District’s violation was clearly substantive.
Although it is true that “this court has at times required parents
to demonstrate that the student’s education was affected by any
procedural violations the school district might have
committed,” we have done so “only where the violation was
not obviously substantive.” Leggett v. District of Columbia,
793 F.3d 59, 67 (D.C. Cir. 2015) (quoting Lesesne ex rel. B.F.
v. District of Columbia, 447 F.3d 828, 834 (D.C. Cir. 2006))
(alterations and internal quotation marks omitted). The District
asserts that its failure to locate disabled children is a
“procedural” rather than substantive harm. Appellants’ Br. 57.
But twice in recent months the Supreme Court has confirmed
that access to a FAPE is a “substantive right.” Endrew F., 137
S. Ct. at 993; see also Fry v. Napoleon Community Schools,
137 S. Ct. 743, 749 (2017) (“An eligible child . . . acquires a
substantive right to [a FAPE] once the state accepts the IDEA’s
financial assistance.” (citation and internal quotation marks
omitted)). Disabled children are quite obviously denied a
FAPE when the District fails to find them at all.

                               C.
    Finally, we reach the District’s two deepest objections to
the injunction.

    First, the District contends that the court “should have erred
on the side of leaving control of the school system to state and
local authorities.” Appellants’ Br. 46. This argument
completely ignores the court’s restrained approach. Rather than
“assum[ing] control” of the District, id. 55, the court opted for
benchmarks and gradual deadlines, leaving the District with
                               28
flexibility in how to achieve compliance and time to do so. As
the parents explain, the injunction “require[s] [the District] to
do nothing more than what is required under IDEA,” and the
“programmatic requirements are limited to the basic elements
of an adequate Child Find program.” Appellees’ Br. 56. The
injunction balances the need for relief with deference to school
administrators, precisely what the court is supposed to do. See
Freeman v. Pitts, 503 U.S. 467, 489 (1992) (“[T]he court’s end
purpose must be to remedy the violation and, in addition, to
restore state and local authorities to the control of a school
system . . . .”).

     Second, the District argues that the court “strayed
impermissibly from the focus on individual relief that is [at] the
heart” of IDEA. Appellants’ Br. 56 (citing 20 U.S.C. § 1415).
As the District sees it, the “proper role” of IDEA’s judicial
enforcement provision “is individualized rather than systemic
relief.” Id. 55. In other words, the District believes that IDEA
precludes comprehensive injunctions. This is the last iteration
of an argument the District has pressed throughout this
litigation: IDEA claims ought to be handled one-by-one, not as
class actions cured through structural remedies.

    It is true that courts may remedy certain IDEA disputes,
such as a parent’s claim that a child’s IEP is defective, only
through “individualized” relief. See Jamie S., 668 F.3d at 495.
But to argue, as does the District, that this limitation also
applies to violations of the Child Find requirement ignores that,
unlike a parent worried about her child’s IEP, the parents in
this case challenge systemic defects in the District’s
identification and eligibility determination policies, which
harm all unidentified preschoolers and can only be remedied
by a comprehensive injunction designed to bring the District
into compliance with IDEA. See supra Part III.
                               29
    Even more important, the District’s argument would
eviscerate the very purpose of IDEA. When Congress enacted
the legislation that became IDEA, it was responding to the
“pervasive and tragic” failure to serve all children with
disabilities, Endrew F., 137 S. Ct. at 999, which is why it
imposed on states accepting IDEA funding an obligation to
“identif[y], locate[], and evaluate[]” all preschoolers with
disabilities, 20 U.S.C. § 1412(a)(3)(A). Yet the District, which
has enthusiastically accepted millions of dollars in IDEA
funding, now proposes to shift that burden back to the parents.
In the District’s view, it would be up to each and every parent,
many of whom are poor, homeless, and perhaps disabled
themselves, to somehow determine whether their children are
eligible for special education services and then to retain
counsel to sue the District to obtain the services to which they
are entitled. Given the purpose of IDEA, we cannot imagine a
more preposterous argument. And given the district court’s
finding that the District has failed, year after year, to comply
with IDEA’s Child Find requirement, we have no doubt that
the statute’s remedial provision—authorizing courts to “grant
such relief as [they] determine[] is appropriate,” 20 U.S.C.
§ 1415(i)(2)(C)(iii), and implicating “broad discretion” and
“equitable considerations,” Reid, 401 F.3d at 522—vests the
court with all the authority it needs to remedy those violations
through injunctive relief. For decades, courts across the country
have done just that, ordering or approving structural relief
when IDEA violations required it. See, e.g., Vaughn G. v.
Amprey, No. 96-1507, 1997 WL 378068, at *1 (4th Cir. 1997)
(recounting the “decade long struggle” between students and
the Baltimore City Public School (BCPS) system, which led to
a series of consent decrees restructuring BCPS’s special
education programs); D.D. v. New York City Board of
Education, No. 03-cv-2489, ECF No. 250 (E.D.N.Y. Apr. 25,
2007) (approving a decree requiring the New York State
Department of Education to amend its policies, coordinate with
                              30
other agencies, develop and implement training programs,
collect data, and propose new legislation to New York State
Assembly); Blackman v. District of Columbia, No. 97-cv-1629,
2006 WL 2456413 (D.D.C. Aug. 24, 2006) (approving an
expansive consent decree to remedy systemic IDEA violations
in the District of Columbia); James O. v. Marston, No. 86-cv-
0006, ECF Nos. 191–200 (D.N.H. Aug. 23, 1991) (requiring
the New Hampshire Department of Education to overhaul its
policies and procedures concerning children with disabilities in
detention centers and other state facilities).

                              V.
    Having considered each of the District’s challenges, we are
convinced that the district court made no mistake. So long as
the District of Columbia accepts federal funding, it is bound to
its pledge to find, evaluate, and serve all children with
disabilities. The district court neither erred nor abused its
discretion in holding the District to its word. We affirm in all
respects.

                                                   So Ordered.
