Inclusion Criteria:

1. Children and adolescents aged 6 months to \< 18 years old with Low Grade Glioma (See Appendix I).
2. All patients must submit tumour tissue (fresh tumour tissue is recommended) and have pathological confirmation of LGG and determination of BRAF characteristics from the Hospital for Sick Children. Exceptions will be made for patients with neurofibromatosis type 1 who have not previously had a biopsy. NF1 patients are eligible without tissue confirmation but must have definitive clinical or radiographic evidence of tumour progression or risk for significant neurologic deterioration requiring immediate therapy. If a tissue sample for NF1 patients is available from a previous biopsy, it is required to be submitted for Central Review at the Hospital for Sick Children. Please refer to the lab manual for further details.
3. Patients must have progressive disease following surgical excision based on clear radiological or clinical evidence of progression, or an incomplete excision (\< 95% or \> 1.0 cm2 residual tumour) with necessity to begin treatment because of a risk of neurological impairment with progression.
4. All patients on study must have measurable tumour (\>1.0 cm2 of residual tissue if resection has been performed) within 28 days of enrollment.
5. Patients must have received no prior therapy including chemotherapy, biological modifiers and/or radiation treatment for the tumour with the exception of surgery.
6. Patient is able to start treatment within 14 working days after randomization.
7. Post pubertal teenagers who are sexually active agree to use two methods of contraception during the treatment period and for at least 6 months after the last dose of study drug. Please refer to Appendix V for a list of acceptable methods of contraception.
8. Lansky performance status \> 50% for patients \< 16 years of age. Karnofsky performance status \> 50% for patients ≥ 16 years of age.
9. Patients with neurologic deficits must have deficits that are stable for a minimum of 1 week prior to enrollment.
10. Patients receiving corticosteroids must be on a stable or decreasing dose for at least 1 week prior to enrollment.
11. Life expectancy \> 2 months at the time of enrollment.
12. Parents/guardians must provide written informed consent and to agree that they (and the patient) will comply with the study protocol.
13. Written assent by patient according to institutional guidelines.
14. Patients must have adequate bone marrow function within 2 weeks prior to enrollment:

* Hemoglobin ≥ 10 g/dL (may be supported )
* Neutrophil count ≥ 1.0 × 109/L
* Platelet count ≥ 100 × 109/L (transfusion independent)
15. Patients not on a therapeutic dose of an anti-coagulant must have an INR ≤ 1.5 and an aPTT ≤ 1.5x institutional ULN for age within 2 weeks prior to enrollment. Anti-coagulation is permitted prior to enrollment on the condition that the patient is, according to the local clinical practice guidelines or approved product labeling, adequately anti-coagulated prior to enrollment.
16. Patients must have satisfactory liver function within 2 weeks prior to enrollment:

* AST ≤ 3x institutional ULN for age
* ALT ≤ 3x institutional ULN for age
* Total Bilirubin ≤ 1.5x institutional ULN for age
17. Patients must have satisfactory renal parameters and meet the following criteria within 2 weeks prior to enrollment :

* Serum creatinine must be ≤ 1.5x ULN for age. If the serum creatinine is \> 1.5 × ULN, the glomerular filtration rate (either estimated or formal) must be \>90 mL/min/1.73 m2, for patient to be enrolled.
* Absence of clinically significant proteinuria, as defined by screening of the early morning urine (urine protein \< 1g/L and/or albumin/creatinine ratio \< 1.0 (mg/mmol)). If urine protein ≥ 1g/L, then Urine Protein Creatinine (UPC) ratio should be calculated. If UPC ratio \> 0.5, 24-hour urine protein should be obtained and the level should be \< 1000 mg/24 hours for patient enrollment. Note: UPC ratio of spot urine is an estimation of the 24 urine protein excretion - a UPC ratio of 1 is roughly equivalent to a 24-hour urine protein of 1 g. UPC ratio is calculated using one of the following formulas:

\[urine protein\]/\[urine creatinine\] - if both protein and creatinine are reported in mg/dL or \[(urine protein) x0.088\]/\[urine creatinine\] - if urine creatinine is reported in mmol/L

Quality of Life Correlative Study Inclusion Criteria (Optional):

1. Age ≥ 3 and \< 18 years.
2. English- or Spanish-speaking.
3. No known history of a significant neurodevelopmental disorder prior to diagnosis of LGG (e.g., Down syndrome, Fragile X, William's Syndrome, mental retardation). Patients with NF1 are not excluded.
4. No significant motor or sensory impairment that would prevent computer use and perception of the visual and auditory test stimuli.

Exclusion Criteria:

1. Children under 6 months of age.
2. Pregnant or lactating females.
3. Use of any investigational agent, systemic, targeted or immunotherapy prior to the first dose of study treatment.
4. Any bleeding diathesis or significant coagulopathy at risk of bleeding (i.e. in the absence of therapeutic anticoagulation).
5. Patients with evidence of new symptomatic CNS hemorrhage (\> grade I) on baseline MRI.
6. Any significant cardiovascular disease, e.g. aortic aneurysm requiring surgical repair or recent arterial thrombosis, CVAs, transient ischemic attacks (TIAs), and systemic hypertension (i.e., a systolic and diastolic BP ≥ 95th percentile for age, sex), prior history of hypertensive crisis or hypertensive encephalopathy or stroke, uncontrolled cardiac arrhythmia within 6 months prior to enrollment .
7. Any previous venous thromboembolism Grade 3 or higher (NCI CTCAE v. 4.03).
8. History of abdominal fistula, GI perforation, intra-abdominal abscess or active GI bleeding within 6 months prior to the first study treatment.
9. Unresolved infection.
10. An active peptic or duodenal ulcer.
11. Major surgical procedure (see Table 3 section 6.1.7), brain surgery, open biopsy or significant traumatic injury within 28 days prior to enrollment or the anticipation of the need for major (elective) surgery during the course of the study treatment.
12. Intermediate surgical procedure (see Table 3 section 6.1.7) within 2 weeks of enrollment.
13. Minor surgical procedures (see Table 3 section 6.1.7) within 3 days prior to the start of treatment (including the placement of a central line, including PICC line). Insertion of a port-a-cath will require a 7-day interval prior to the start of treatment.
14. Non-healing surgical wound.
15. A bone fracture that has not satisfactorily healed.
16. Concomitant use of the following:

* Aspirin (\> 325mg/day) within 10 days of enrollment
* Clopidogrel (\> 75mg/day) within 10 days of enrollment
* Use of therapeutic oral or parenteral anticoagulants or thrombolytic agents for therapeutic purposes with INR and aPTT outside therapeutic standards according to institutional guidelines within 10 days of first dose of Bevacizumab. Note: The use of full-dose oral or parenteral anticoagulants is permitted as long as the INR or aPTT is within therapeutic limits (according to the medical standard of the institution) and the patient has been on a stable dose of anticoagulants for at least two weeks at the time of the Baseline Visit. Prophylactic use of anticoagulants is allowed.
17. Hypersensitivity to Chinese hamster ovary (CHO) cell products or other recombinant human or humanized antibodies.