Tips & Strategies
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Build on your child's personal strengths: Praising your child is important- make sure they know you are proud of them for facing challenges, trying something new, or being brave. Try to find activities in which your child can demonstrate their strengths (music, sports, art, etc.). You could also try helping your child feel as though they are contributing around the house by providing them with jobs they can accomplish on their own.
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Have high expectations: Try not to have different expectations of your anxious child then you would of your other children. Be conscious, though, that the pace at which your anxious child accomplishes these expectations (going to birthday parties, talking to adults, etc.) may be different than that fo other children.
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Encourage independence: try not to step in and solve every problem for your child- this can lead to them thinking you don't believe they can accomplish tasks on their own. Teach your child how to reassure him/herself and model strategies for thinking through problems and responding to their own questions.
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Teach how to handle big feelings: Let your child know that it's ok to experience anxiety. Feelings are ok, and it can help to say how you feel sometimes.
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Try not to pass on your own fears: Try your best to not narrate your worries to your anxious child. Instead, try talking through situations in a neutral way, rather than in a negative light. Show your child that it is safe to explore.
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Work together as parents: Work together with your co-parent to develop a consistent approach to handling your child's anxieties that you both agree upon. Have clear and consistent limits and consequences outlined for your child, as well as showing love and acceptance.
Information from Worry Wise Kids:

How common are Anxiety Disorders?
Anxiety Disorders are quite common. At least one child in every elementary school classroom is likely to have an Anxiety Disorder (Cartwright-Hatton, McNicol & Doubleday, 2006).
However, less than 20% of students with Anxiety Disorders receive services for their problems because symptoms can be hard for parents or teachers to see (Mash & Wolfe 2019).
Can Children Grow out of Anxiety Disorders?
Sometimes they can. About 50% of cases of Anxiety Disorders have an illness duration of 8 years (Mash & Wolfe 2019). However, symptoms of Anxiety Disorders in childhood can be predictors of Anxiety Disorders more than 24 years later (Mash & Wolfe 2019).
Some subtypes of Anxiety Disorders are more likely to persist into adulthood, but others can fade with time. In either case, there are effective treatments available to help individuals experiencing Anxiety Disorders.

References:
Erk, Robert R. (2008). Counselling Treatment for Children and Adolescents with DSM-IV-TR Disorders. Pearson Education. Pp. 216-252.
Hay, Dale F. (2019). Emotional Development from Infancy to Adolescence: Pathways to Emotional Competence and Emotional Problems. Routeledge. Pp. 53-69.
Anxiety Disorders. (n.d.). Retrieved from https://www.learnalberta.ca/content/inmdict/html/anxiety_disorders.html
Mash, Eric J. and Wolfe, David A. (2019). Abnormal Child Psychology. Cengage. Pp. 356-401.
Parenting Tips for Anxious Kids. Retrieved from http://www.worrywisekids.org/node/36
Treatment Options
When it comes to treating anxiety, there are many different effective approaches, most of which are involve speaking with a counsellor to help overcome your child's fear.
Behaviour Therapy (Graded Exposure)
To put it simple, this method involves "facing your fears", although at a gradual pace and through providing support and techniques to manage the stress induced by the exposure to that which the child is afraid of. The goal fo this treatment is to provide the child with effective ways to cope with the anxiety, rather than to make the anxiety completely disappear. Successful graded exposure might look like repeated exposure to the child's fear which result in the child ranking the fear as less and less intense.
Other Behaviour Therapy approaches include Systematic Desensitization, where the child is made to feel safe and comfortable, then presenting him or her with the anxiety provoking stimuli. The goal would be to show the child they are Abel to relax around that which is cause them fear.
Flooding is another behaviour therapy technique. This is where the child is exposed to the thing or event which induces their anxiety for a prolonged period of time, until they realize that they are not in danger and become less anxious, This method is usually used in the case of specific phobias, and is most suitable to older children.
Cognitive-Behavioural Therapy (CBT)
This method involves teaching the child how thinking contributes to anxiety. The goal of this approach is to modify maladaptive thoughts and providing positive thoughts to replace them. Modelling, role-playing, exposure, and relaxation training can all be involved in this process. Often times CBT is paired with exposure treatments, as mentioned above, to achieve results.
Acceptance Commitment Therapy ACT
Acceptance Commitment Therapy aims to build psychological flexibility through acceptance and mindfulness strategies in order to achieve goals. The goal of ACT is not focussed on the symptoms of Anxiety Disorders, but rather at improving daily life.
Medication
There are a variety of medications that can be prescribed to treat anxiety. The most effective type, however, has been selective serotonin uptake inhibitors. These medications help manage the symptoms of Anxiety Disorders, especially OCD. Usually, one of the above therapies is first administered, then if medical professionals believe it to be in the child's interest, medication may also be prescribed.