David Schwendeman appeals the denial of his habeas corpus petition filed under 28 U.S.C. § 2254 . He contends the Washington state court jury that convicted him of two counts of vehicular assault was erroneously instructed, in violation of the fourteenth amendment to the United States Constitution. The jury was instructed they could infer Schwendeman had driven in a reckless manner, the predicate act required for his assault convictions, solely from evidence that he was speeding. We hold that the challenged instruction was constitutionally deficient and the error in giving it may not be excused as harmless. We reverse with instructions to the district court to grant the writ unless within a reasonable time Schwendeman is afforded a new trial.

There was plenty of evidence to support Schwendeman’s conviction. At around 11:30 p.m., after having spent two hours with six companions at a local tavern drinking beer, playing pool and dancing, Schwendeman and his friends left the tav ern in his pickup truck. Schwendeman drove. Two of his passengers rode up front in the cab with him, and four rode in the back in the truck bed. By his own admission, Schwendeman drove 37 miles per hour in a 25-mile-per-hour zone. According to the state’s evidence, he drove in excess of 39 miles per hour and one of his passengers testified he drove in excess of 50 miles per hour. He swerved back and forth on the road, he said to avoid hitting potholes, but there was other testimony that he was purposely trying to hit the potholes. He lost control of the truck and hit a telephone pole, causing injuries to his passengers.

Under Washington law, reckless driving is defined as driving a motor vehicle in wanton or willful disregard for the safety of persons or property. RCW 46.61.500(1). Given the evidence presented at his trial, Schwendeman’s conviction would be unremarkable. But, as sometimes occurs, the jury was not given a simple set of instructions which would have permitted them to consider all of the evidence and arrive at a verdict. Instead, the trial court gave the jury the following instruction number 7:

Schwendeman argues this instruction violated his right to due process under the fourteenth amendment because it permitted the jury to infer an element of the crime with which he was charged, reckless driving, simply from evidence that he drove in excess of the speed limit. The state argues to the contrary, and also contends that Schwendeman’s habeas petition should have been dismissed in any event because he failed to exhaust his state court remedies.

A. Exhaustion of State Remedies

On direct appeal, the Washington Court of Appeals affirmed Schwendeman’s convictions. The Washington Supreme Court denied his motion for discretionary review.

Schwendeman next filed a personal restraint petition with the Washington Court of Appeals. That petition was dismissed. He then filed a motion for discretionary review with the Washington Supreme Court. He argued that the trial court’s instruction number 7 created an unconstitutional inference of his guilt, and that his counsel’s failure to raise this issue on direct appeal constituted ineffective assistance of counsel. The Washington Supreme Court denied the motion for discretionary review.

Schwendeman then filed a habeas corpus petition in the district court. He alleged that jury instruction number 7 impermissi-bly permitted the jury to infer his guilt in violation of the fifth and fourteenth amendments, and that his counsel was ineffective because he did not raise this issue on direct appeal.

Under 28 U.S.C. § 2254 (b), “[a]n application for a writ of habeas corpus ... pursuant to the judgment of a State court shall not be granted unless it appears that the applicant has exhausted the remedies available in the courts of the State.” Section 2254 does not directly address the problem of mixed petitions. Rose v. Lundy, 455 U.S. 509, 516 , 102 S.Ct. 1198, 1202 , 71 L.Ed.2d 379 (1982). In Lundy , the Supreme Court held that a district court must dismiss “mixed petitions” that include both exhausted and unexhausted claims. Id. at 510 , 102 S.Ct. at 1199 . A claim is considered exhausted when it has been fairly presented to the highest state court. Tamapua v. Skimoda, 796 F.2d 261, 262 (9th Cir.1986); citing Picard v. Connor, 404 U.S. 270, 276 , 92 S.Ct. 509, 512-13 , 30 L.Ed.2d 438 (1971); and Middleton v. Cupp, 768 F.2d 1083, 1086 (9th Cir.1985). A habeas petitioner may, however, reformulate the claims made in state court; exhaustion requires only that the substance of the federal claim be fairly presented. Tamapua v. Shimoda, 796 F.2d at 262 .

Here, the parties agree that Schwende-man’s constitutional challenge to jury instruction number 7 was fairly presented to the Washington Supreme Court. We are also satisfied that Schwendeman raised the issue of ineffective assistance of counsel in his motion for discretionary review which he presented to the Washington Supreme Court. In denying that motion, the court stated: “[s]ince the instruction was not erroneous, petitioner’s appellate counsel did not represent him inadequately by failing to raise the issue on appeal.”

We conclude Schwendeman exhausted his state court remedies. We now consider the district court’s denial of his habeas petition on its merits.

B. Merits

Instruction number 7 allows, but does not require, the jury to infer recklessness solely from proof of excessive speed. The inference it allows is permissive.

Recently, in United States v. Rubio-Villareal, 967 F.2d 294 (9th Cir.1992) (en banc), we noted that a permissive inference jury instruction is constitutional “so long as it can be said ‘with substantial assurance’ that the inferred fact is ‘more likely than not to flow from the proved fact on which it is made to depend.’ ” Id. 967 F.2d at 296 (citing Ulster County v. Allen, 442 U.S. 140 , 166 n. 28, 99 S.Ct. 2213 , 2229 n. 28, 60 L.Ed.2d 777 (1979).

Although it is certainly true that excessive speed is probative of a jury’s determination of recklessness, here we cannot say with substantial assurance that the inferred fact of reckless driving more likely than not flowed from the proved fact of excessive speed. Under Ulster County , the instruction was constitutionally deficient. See Ulster County, 442 U.S. at 166 n. 28, 99 S.Ct. at 2229 n. 28; Rubio-Villareal, 967 F.2d at 294 .

A constitutionally deficient jury instruction requires reversal unless the error is harmless beyond a reasonable doubt. Id. at 296 n. 3. An error is harmless beyond a reasonable doubt when “there is no reasonable possibility that the error materially affected the verdict.” Id.

As we have said, there is ample evidence from which the jury could have found reckless driving. Schwendeman was driving an open-bed truck with passengers in the back at night down a road with potholes, swerving from side to side and exceeding the speed limit.

But instruction number 7 isolated speed as the only circumstance needed to permit the jury to find reckless driving and thereby convict Schwendeman. The jury was told, in effect, that it could ignore all the other evidence, consider only the evidence of Schwendeman’s speed, and if it found Schwendeman was exceeding the speed limit, that was enough to convict him — not of speeding, but of reckless driving.

By focusing the jury on the evidence of speed alone, the challenged instruction erroneously permitted the jury to find an element of the crime of which Schwende-man was convicted without considering all the evidence presented at trial. See Rubio-Villareal, 967 F.2d at 300 . We cannot say there is no reasonable possibility that the instruction did not materially affect the verdict. Accordingly, the error cannot be excused as harmless.

The district court’s denial of the petition for a writ of habeas corpus is reversed. This cause is remanded to the district court with instructions to issue the writ of habe-as corpus unless, within a reasonable time, Schwendeman is granted a new trial.

REVERSED and REMANDED for further proceedings.

. We did not reach the constitutional question in Rubio-Villareal , because there we held the permissive inference instruction was defective as a matter of federal law. See Rubio-Villareal, 967 F.2d at 297 . . We do not reach Schwendeman’s ineffective assistance of counsel claim.