
562 F.3d 763 (2009)
UNITED STATES of America, Plaintiff-Appellee,
v.
Julio Cesar GARCIA-ROBLES, Defendant-Appellant.
No. 07-2209.
United States Court of Appeals, Sixth Circuit.
Argued: March 12, 2009.
Decided and Filed: April 9, 2009.
*764 ARGUED: Todd A. Shanker, Federal Defender Office, Detroit, Michigan, for Appellant. Michael R. Mueller, Assistant United States Attorney, Detroit, Michigan, for Appellee. ON BRIEF: Todd A. Shanker, Rafael Cerpa Villarruel, Federal Defender Office, Detroit, Michigan, for Appellant. Michael R. Mueller, Assistant United States Attorney, Detroit, Michigan, for Appellee.
Before: MOORE and WHITE, Circuit Judges; OLIVER, District Judge.[*]

OPINION
KAREN NELSON MOORE, Circuit Judge.
In June 2007, Julio Cesar Garcia-Robles ("Garcia-Robles") pleaded guilty to unlawful re-entry of an alien deported after an aggravated felony conviction. The district court and the parties agreed that Garcia-Robles's sentencing guidelines range was 30 to 37 months of incarceration. At sentencing, Garcia-Robles asked for a downward variance to a sentence of 24 months of incarceration. The government asked that the court impose a sentence within the guidelines range. The district court determined that, because of the severity of the offense and the fact that Garcia-Robles had previously returned to the United States after deportation, an upward variance was necessary. The district court sentenced Garcia-Robles to 96 months of incarceration. Garcia-Robles appeals this sentence and argues that the district court failed to give proper notice of this upward variance and that the sentence imposed was procedurally and substantively unreasonable.
We VACATE Garcia-Robles's sentence as procedurally unreasonable and REMAND for resentencing.

I. BACKGROUND
Garcia-Robles is a Mexican national. In 1997, Garcia-Robles was arrested in Utah with four grams of cocaine and pleaded guilty in state court to attempted possession with intent to distribute a controlled substance in the third degree and to providing false personal information to a police officer. He received a five-year suspended sentence for the first crime and was sentenced to 30 days in jail and 36 months of probation for the second. On December 4, 1997, Garcia-Robles was deported to Mexico. Following this deportation, Garcia-Robles illegally reentered the United States and was arrested in Utah again in 1999. Police stopped Garcia-Robles's car because it did not have a front license plate and found that he was driving under the influence and had three firearms in his vehicle. Garcia-Robles pleaded guilty in state court to purchase and possession of a dangerous weapon and to driving under the influence and was sentenced to 90 days in jail with 60 days suspended. After he served his state sentence, Garcia-Robles was charged in federal court with reentry of a deported alien. Garcia-Robles pleaded guilty and was sentenced to 46 months of incarceration and 36 months of supervised release. On September 18, *765 2002, Garcia-Robles was removed to Mexico.
The events that led to the current case occurred in March 2007 in Michigan. On March 8, 2007, law-enforcement officers stopped Garcia-Robles's car because it had expired license plate tabs. Garcia-Robles gave officers his name and told them that he was not present in the United States legally. Immigrations and Customs Enforcement identified Garcia-Robles and learned that he had been deported twice. Garcia-Robles was charged with and pleaded guilty to unlawful reentry after deportation after an aggravated felony in violation of 8 U.S.C. § 1326.
Before Garcia-Robles was sentenced, the government prepared a Presentence Report ("PSR") that indicated a sentencing range of 30 to 37 months of imprisonment based on a total offense level of 17 and a criminal history category of III. Garcia-Robles did not object to anything contained in the PSR. At sentencing, Garcia-Robles's counsel detailed the difficult life that Garcia-Robles had led and asked the district court to grant him a variance and to sentence him to 24 months of imprisonment. The government asked the district court to sentence Garcia-Robles within the 30-37 month guidelines range.
After hearing argument from the parties, the district court announced a sentence of 96 months of incarceration-59 months longer than the guidelines maximum. The district court explained that this significant variance was necessary because Garcia-Robles had committed a very serious offense, continued to violate the law, and was not supporting his four children. Additionally, the district court noted that a lengthy sentence was necessary because Garcia-Robles's previous sentence of 46 months of incarceration for illegal reentry had not deterred him from reentering the United States. After imposing sentence on September 18, 2007, the district court informed the parties' counsel that it would issue a written opinion, and "if they disagree with any of the findings or conclusions contained in the Opinion, [they] may file objections to that Opinion within five days of today." Joint Appendix ("J.A.") at 68 (Sent'g Tr. at 14). The day after the sentencing hearing, on September 19, 2007, the district court issued a written sentencing opinion. The written opinion noted Garcia-Robles's past problems with the law, the fact that he had used aliases, and the fact that there was no indication that he was supporting his children. The district court found that Garcia-Robles was "a person who consistently has lived his life such that the lives and safety of citizens have been endangered and jeopardized across this country." J.A. at 13 (Dist. Ct. Sent'g Op. at 4). Having concluded that Garcia-Robles was dangerous, the district court concluded that a significant sentence was necessary to protect the public and, especially given the fact that Garcia-Robles had previously returned to the United States after serving a 46-month sentence for illegal reentry, to deter Garcia-Robles from reentering the United States. Finally, the district court concluded that because Garcia-Robles had previously received a sentence longer than his current guidelines maximum, a disparity would result if Garcia-Robles were sentenced within the guidelines range. Judgment was entered against Garcia-Robles on September 21, 2007.
After the September 19 opinion was filed, Garcia-Robles timely objected to the district court's sentence on September 26, 2007, and he filed his notice of appeal on September 28, 2007. Garcia-Robles objected on the grounds that the sentence was unduly severe and could not have taken the 18 U.S.C. § 3553(a) factors into account and to the fact that the district *766 court imposed this significant variance without alerting the parties to its intent to do so. Additionally, Garcia-Robles explained that the district court had relied on unreliable facts and had taken other information from the PSR out of context. On October 3, 2007, although the district court found Garcia-Robles's objections to be timely, nonetheless the district court overruled these objections in a single paragraph opinion that summarized the case and concluded that "[t]he Court has reviewed and considered [Garcia-Robles's] objections but adheres to the sentence of 96 months imposed on September 18, 2007." J.A. at 36-37 (Dist. Ct. Op. at 1-2).
Garcia-Robles raises three arguments in the current appeal. First, Garcia-Robles asserts that the district court erred because it failed to give notice of its intent to impose an upward variance.[1] Second, Garcia-Robles argues that his sentence was procedurally unreasonable because the district court failed to explain its reasons for overruling his objections to his sentence. Finally, Garcia-Robles argues that his sentence was substantively unreasonable because the district court considered unreliable information and failed to understand that Garcia-Robles's prior sentence for illegal reentry was based on a guideline that was later amended because it produced disproportionately high sentences.

II. ANALYSIS
On appeal, Garcia-Robles argues that his sentence is procedurally and substantively unreasonable. We conduct sentencing-reasonableness review as described in Gall v. United States, ___ U.S. ____, 128 S.Ct. 586, 597, 169 L.Ed.2d 445 (2007):
Regardless of whether the sentence imposed is inside or outside the Guidelines range, the appellate court must review the sentence under an abuse-of-discretion standard. It must first ensure that the district court committed no significant procedural error, such as failing to calculate (or improperly calculating) the Guidelines range, treating the Guidelines as mandatory, failing to consider the § 3553(a) factors, selecting a sentence based on clearly erroneous facts, or failing to adequately explain the chosen sentence-including an explanation for any deviation from the Guidelines range. Assuming that the district court's sentencing decision is procedurally sound, the appellate court should then consider the substantive reasonableness of the sentence imposed under an abuse-of-discretion standard. When conducting this review, the court will, of course, take into account the totality of the circumstances, including the extent of any variance from the Guidelines range. If the sentence is within the Guidelines range, the appellate court may, but is not required to, apply a presumption of reasonableness. But if the sentence is outside the Guidelines range, the court may not apply a presumption of unreasonableness. It may consider the extent of the deviation, but must give due deference to the district court's decision that the § 3553(a) factors, *767 on a whole, justify the extent of the variance. The fact that the appellate court might reasonably have concluded that a different sentence was appropriate is insufficient to justify reversal of the district court.
In deciding whether Garcia-Robles's sentence is procedurally reasonable, we consider three factors, whether the district court: "(1) properly calculated the applicable advisory Guidelines range; (2) considered the other § 3553(a) factors as well as the parties' arguments for a sentence outside the Guidelines range; and (3) adequately articulated its reasoning for imposing the particular sentence chosen, including any rejection of the parties' arguments for an outside-Guidelines sentence and any decision to deviate from the advisory Guidelines range." United States v. Bolds, 511 F.3d 568, 581 (6th Cir.2007). Garcia-Robles argues that his sentence is procedurally unreasonable because the district court failed to honor Garcia-Robles's right to speak meaningfully about his sentence and to explain its decision to overrule Garcia-Robles's objections to his sentence.
Given the unique circumstances of this case, we hold that the district court's sentence was procedurally unreasonable because the district court failed to provide Garcia-Robles with an opportunity meaningfully to address the district court's chosen sentence. Based on the PSR and the government's position that the guideline range was reasonable, Garcia-Robles entered the sentencing hearing believing that he should be arguing against the backdrop of a 30-to-37-month sentence. Garcia-Robles was unaware that the district court was contemplating a significantly higher sentence and thus had no chance to argue against such a variance before the court announced its sentence. The Supreme Court has held that at sentencing, "[w]here the defendant or prosecutor presents nonfrivolous reasons for imposing a different sentence, however, the judge will normally go further and explain why he has rejected those arguments." Rita v. United States, 551 U.S. 338, 127 S.Ct. 2456, 2468, 168 L.Ed.2d 203 (2007). Under this precedent, the district court was required to consider, and to explain its rejection of, any non-frivolous arguments against the upward variance that Garcia-Robles made at sentencing. However, Garcia-Robles was not afforded the opportunity to make those arguments at sentencing.
Instead of permitting Garcia-Robles to address the variance during the sentencing hearing, the district court informed Garcia-Robles that the court would be issuing a written opinion and that Garcia-Robles could make written objections to that opinion. The day after the sentencing hearing, the district court issued a written sentencing opinion. However, in addition to issuing this explanation, the district court entered judgment before the time that he had granted Garcia-Robles to object had elapsed. Federal Rule of Criminal Procedure 35(a) states that a district court can correct a sentence that resulted from mathematical, technical, or clear error for seven days after sentencing. This rule implies that once the district court entered judgment, it was not free to change Garcia-Robles's sentence, no matter what his objections might be, except in very limited instances. See United States v. Arroyo, 434 F.3d 835, 838 (6th Cir.2006) ("The authority conferred by Rule 35(a) to a district court is extremely limited."). Additionally, the district court did not address Garcia-Robles's objections until after Garcia-Robles had filed his notice of appeal, an action which clearly divested the district court of jurisdiction. See Dunham v. United States, 486 F.3d 931, 935 (6th Cir.2007) ("The traditional rule is that *768 `a timely appeal divests the district court of jurisdiction to reconsider its judgment until the case is remanded by the Court of Appeals.'" (quoting Pittock v. Otis Elevator Co., 8 F.3d 325, 327 (6th Cir.1993))).
Given the sequence of events in this case, Garcia-Robles was never afforded an opportunity meaningfully to respond to the district court's decision to impose an upward variance. The district court chose to issue a written sentencing opinion and to permit Garcia-Robles to object to his sentence after that opinion issued rather than to permit oral objections during the sentencing hearing. However, the district court failed actually to provide that opportunity when it entered judgment before Garcia-Robles's time to object had elapsed and when it failed to respond to Garcia-Robles's objections until after its jurisdiction was divested by Garcia-Robles's notice of appeal. The district court imposed a significant upward variance without giving Garcia-Robles any opportunity meaningfully to respond to this substantial increase in sentence. Although the Supreme Court has held that a district court need not provide notice before imposing a variance based on § 3553(a) factors, in the same opinion the Court expressed its "confidence in the ability of district court judges and counsel-especially in light of Rule 32's other procedural protections-to make sure that all relevant matters relating to a sentencing decision have been considered before the final sentencing determination is made." Irizarry, 128 S.Ct. at 2203-04 (footnote omitted). In this case, the district court did not consider Garcia-Robles's objections to a significant upward variance until after the district court had entered judgment and Garcia-Robles had filed his notice of appeal. Because the district court had no jurisdiction to alter Garcia-Robles's sentence at the time it heard his objections to a greatly increased sentence, the district court failed to provide Garcia-Robles with an opportunity meaningfully to address the upward variance in his sentence. Accordingly, we VACATE Garcia-Robles's sentence as procedurally unreasonable and REMAND for resentencing. Because we conclude that Garcia-Robles's sentence is procedurally unreasonable, we do not consider at this time his arguments that his sentence is substantively unreasonable.

III. CONCLUSION
We VACATE Garcia-Robles's sentence as procedurally unreasonable and REMAND for resentencing.
NOTES
[*]  The Honorable Solomon Oliver, Jr., United States District Judge for the Northern District of Ohio, sitting by designation.
[1]  Garcia-Robles filed his appeal before the Supreme Court held that Federal Rule of Criminal Procedure 32(h) requires the district court to provide notice if it is considering an upward departure based on the guidelines, but not if it is considering an upward variance based on the § 3553(a) factors. Irizarry v. United States, ___ U.S. ____, 128 S.Ct. 2198, 2203, 171 L.Ed.2d 28 (2008). Garcia-Robles and the government agree that the district court granted a variance based on the § 3553(a) factors, and at oral argument Garcia-Robles conceded that under Irizarry, the district court was not required to give notice before imposing this variance. Accordingly, we do not discuss further Garcia-Robles's argument that notice was required under Rule 32(h).
