Evaluating Treatment of ADHD in Children with Down Syndrome

Inclusion Criteria: * Stated willingness to comply with all study procedures and availability for the duration of the study. * Male or female, between the ages of 6.00-17.99 years at the time of consent. * Able to take oral (liquid) medication. * English is primary language. * Meets criteria for ADHD (hyperactivity, inattention, or combined) on the KSADS * Meets criteria for ADHD (hyperactivity, inattention, or combined) on the Vanderbilt (historically or currently, as indicated by a teacher/professional) Exclusion Criteria: * Current use of ADHD stimulant or non-stimulant medication and unwilling to discontinue for \>/= 3 days prior to starting the study. * Children with psychoses or bipolar disorder based on diagnostic interview with the parent. * Organic Brain Injury: Children must not have a history of head trauma with loss of consciousness, epilepsy, or any other organic disorder that could possibly affect brain function. * Specific heart conditions including the following: 1. QTc on baseline ECG\>470ms or QTC \> 500 in patients with repaired CHD, as determined by ECG 2. Brugada pattern, as determined by ECG 3. Baseline heart rate or systolic blood pressure \> 2 SD above mean for age as determined by medical examination. 4. 2nd or 3rd degree AV block, as determined by ECG 5. History of aborted sudden cardiac death or unexplained syncope as determined by medical history 6. History of a single ventricle as determined by medical history 7. Valvular regurgitation or stenosis \> mild, as determined by ECHO 8. Moderate or greater ventricular dysfunction, as determined by ECHO 9. Pulmonary hypertension, defined as right ventricular pressure \>33% systemic pressure or septal position consistent with \>mild right ventricular hypertension, as determined by ECHO 10. Use of a pacemaker as determined by medical history 11. Wolff Parkinson White/pre-ventricular excitation, as determined by ECG 12. Atrial, junctional, or ventricular tachyarrhythmia, as determined by ECG 13. Frequent premature ventricular contractions (PVCs) or premature atrial contractions (PACs), as determined by ECG 14. Abnormal T waves with inversion in V5 and/or V6, bizarre T wave morphology, notched biphasic T waves, or ST segment depression suggesting ischemia or inflammation, as determined by ECG 15. Moderate or larger atrial septal defect, as determined by ECHO 16. Ventricular septal defect \> small by ECHO 17. Valvar stenosis \> mild by ECHO 18. Aortic root dilation \> 2SD above mean by ECHO. * If participants meet any of the following heart conditions, they must be evaluated for the study by a cardiologist before beginning: 1. Right ventricular enlargement/right axis deviation, as determined by ECG 2. Intraventricular conduction delay \>120ms in child \>12 years old or \>100ms in child \<8 years old, as determined by ECG 3. Right or left bundle branch block, as determined by ECG * Treatment with a monoamine oxidase inhibitor (MAOI) or use of an MAOI within 14 days. * Active titration of non-ADHD, non-MAO psychotropic medication. Stable use of non-ADHD, non-MAO psychotropic medication, defined by no dose changes for \>/= 4 weeks before starting the study medication trial, will be allowed. * Known hypersensitivity or allergic reactions to methylphenidate or product components such as banana (due to bananas serving as flavoring in the formulation of the project's study interventions - Quillivant XR and the placebo). * Severe Obstructive Sleep Apnea (OSA) as rated by McGill index of 4 * Pregnancy. (Since there is limited information regarding the safety of Quillivant XR during pregnancy, a pregnancy test will be conducted at the medical screen for female participants who have commenced the menstrual cycle. If pregnancy is indicated, the participant will be excluded from the study as a precautionary measure).