Guanfacine for Hyperactivity in Children With Down Syndrome (HYPEbeGONE_DS)

Inclusion: 1. Parent/Legal Guardian can understand the consent process and is willing to provide informed consent/HIPAA authorization prior to the conduct of any study-related procedures. When applicable, the minor participant is willing to provide assent. 2. Participant has clinical diagnosis of non-mosaic DS. 3. Participant is between 6 and 12 years of age (inclusive) at time of consent. 4. Participant weight is ≥ 25 kg. 5. Participant has clinically significant symptoms of hyperactivity, inattention and impulsivity manifested as minimum scores of the following rating scales within 30 days of randomization: 1. A minimum score of 18 on the parent-reported ABC-H subscale, AND 2. A minimum score of moderate or greater (≥ 4) on the clinician reported Clinical Global Impression Severity (CGI-S) score specific to hyperactivity, inattention and impulsivity behaviors. 6. Participant has co-morbid medical screening and clearance to proceed with a non-stimulant medication trial with GIR within 30 days of randomization. 7. Participant is willing and able to comply with study procedures, including adherence to medication dosing schedule. Exclusion: 1. Participant has received guanfacine (any formulation) within 30 days of randomization. 2. Participant has received any of the following concomitant medication classes within 30 days of randomization: 1. Strong CYP3A4 inhibitors (e.g., boceprevir, clarithromycin, conivaptan, grapefruit juice, indinavir, itraconazole, ketoconazole, lopinavir/ritonavir, mibefradil, nefazodone, nelfinavir, posaconazole, ritonavir, saquinavir, telaprevir, telithromycin, and voriconazole) 2. Strong CYP3A4 inducers (e.g., avasimibe, carbamazepine, phenytoin, rifampin, and St. John's wort) 3. Participant has a psychiatric comorbidity, such as major depressive disorder, bipolar disorder, obsessive-compulsive disorder, or a psychotic disorder, that requires a pharmacological treatment other than guanfacine 4. For participants ≥ 8 years old at the time of consent, participant has a history of suicidality or positive screen on Ask Suicide-Screening Questions (asQ) Tool. 5. Participant is currently in or plans to participate in another interventional study. 6. Participant has a known hypersensitivity to guanfacine. 7. Participant has had a previous guanfacine treatment failure, as determined by their primary treating physician. 8. Participant has had a change in another medication intended to treat symptoms of hyperactivity, inattention, and impulsivity within the last 2 weeks. 9. Participant has had a seizure within the last 6 months. 10. Participant has had a change in their anti-convulsant dose within the last 4 weeks. 11. Participant has a cardiac-related condition including: 1. Significant symptomatic bradycardia; 2. 2nd degree or 3rd degree (complete) heart block; 3. Baseline heart rate (HR) or systolic blood pressure (BP) \> 2 standard deviations (SD) below mean for age as determined by medical examination; 4. History of aborted sudden cardiac death, unexplained syncope or near syncope, or historical use of a pacemaker as determined by medical history will require clearance by cardiology prior to enrollment; 5. Known history of congenital heart disease which requires ongoing care for monitoring or management will require clearance by cardiology prior to enrollment. 12. Participant has a history of untreated severe obstructive sleep apnea defined as obstructive apnea hypopnea index (OAHI) ≥ 10 events per hour or aortic regurgitation (AR). Participants with an OAHI index \> 10/hr are eligible if managed with continuous positive airway pressure (CPAP). 13. Participant has untreated thyroid disease. 14. Participant has a known hepatic impairment defined as aspartate aminotransferase (AST) or alanine aminotransferase (ALT) \> 2x the upper limit of normal (ULN) for age. 15. Participant has known impending or renal failure defined as: 1. Anuria diagnosed within 12 hours prior to enrollment; 2. Requiring renal replacement therapy. 16. Participant is pregnant. 17. Participant has any condition which would make the participant, in the opinion of the investigator, unsuitable for the study.