diff --git a/slides/k8s/namespaces.md b/slides/k8s/namespaces.md
index d9474118..a2ec544f 100644
--- a/slides/k8s/namespaces.md
+++ b/slides/k8s/namespaces.md
@@ -68,7 +68,7 @@
   kubectl -n blue get svc
   ```
 
-- We can also use *contexts*
+- We can also change our current *context*
 
 - A context is a *(user, cluster, namespace)* tuple
 
@@ -76,9 +76,9 @@
 
 ---
 
-## Creating a context
+## Viewing existing contexts
 
-- We are going to create a context for the `blue` namespace
+- On our training environments, at this point, there should be only one context
 
 .exercise[
 
@@ -87,29 +87,79 @@
   kubectl config get-contexts
   ```
 
-- Create a new context:
+]
+
+- The current context (the only one!) is tagged with a `*`
+
+- What are NAME, CLUSTER, AUTHINFO, and NAMESPACE?
+
+---
+
+## What's in a context
+
+- NAME is an arbitrary string to identify the context
+
+- CLUSTER is a reference to a cluster
+
+  (i.e. API endpoint URL, and optional certificate)
+
+- AUTHINFO is a reference to the authentication information to use
+
+  (i.e. a TLS client certificate, token, or otherwise)
+
+- NAMESPACE is the namespace
+
+  (empty string = `default`)
+
+---
+
+## Switching contexts
+
+- We want to use a different namespace
+
+- Solution 1: update the current context
+
+  *This is appropriate if we need to change just one thing (e.g. namespace or authentication).*
+
+- Solution 2: create a new context and switch to it
+
+  *This is appropriate if we need to change multiple things and switch back and forth.*
+
+- Let's go with solution 1!
+
+---
+
+## Updating a context
+
+- This is done through `kubectl config set-context`
+
+- We can update a context by passing its name, or the current context with `--current`
+
+.exercise[
+
+- Update the current context to use the `blue` namespace:
   ```bash
-  kubectl config set-context blue --namespace=blue \
-      --cluster=kubernetes --user=kubernetes-admin
+  kubectl config set-context --current --namespace=blue
+  ```
+
+- Check the result:
+  ```bash
+  kubectl config get-contexts
   ```
 
 ]
 
-We have created a context; but this is just some configuration values.
-
-The namespace doesn't exist yet.
-
 ---
 
-## Using a context
+## Using our new namespace
 
-- Let's switch to our new context and deploy the DockerCoins chart
+- Let's check that we are in our new namespace, then deploy the DockerCoins chart
 
 .exercise[
 
-- Use the `blue` context:
+- Verify that the new context is empty:
   ```bash
-  kubectl config use-context blue
+  kubectl get all
   ```
 
 - Deploy DockerCoins:
@@ -181,30 +231,19 @@ Note: it might take a minute or two for the app to be up and running.
 
 .exercise[
 
-- View the names of the contexts:
-  ```bash
-  kubectl config get-contexts
-  ```
-
 - Switch back to the original context:
   ```bash
-  kubectl config use-context kubernetes-admin@kubernetes
+  kubectl config set-context --current --namespace=
   ```
 
 ]
 
+Note: we could have used `--namespace=default` for the same result.
+
 ---
 
 ## Switching namespaces more easily
 
-- Defining a new context for each namespace can be cumbersome
-
-- We can also alter the current context with this one-liner:
-
-  ```bash
-  kubectl config set-context --current --namespace=foo
-  ```
-
 - We can also use a little helper tool called `kubens`:
 
   ```bash