EMB ERJ 145 ER/LR
Flight Crew Air Transport Pilot (ATP); Flight Crew Instrument; Flight Crew Multiengine
Distraction
Aircraft Equipment Problem Critical; Inflight Event / Encounter Weather / Turbulence
Flight Crew Overcame Equipment Problem; Flight Crew Took Evasive Action
Weather; Aircraft
We were flying from ZZZ to ZZZ1.  I was sitting in the right seat doing LCP (Line Check Pilot) training.  Mr. A was in the left seat doing CP (Check Pilot) training. The captains side airspeed and altitude became unreliable. We transferred controls to the first officers side. Mr. A ran the QRH.  The captains airspeed read 123 knots and we went down 500 feet. There was a 500 ft difference between the captains and FO's [First Officer] altitude. SPS (Shaker and Pusher System) Advance was displayed on the EICAS. The FO's airspeed was at 270. We descended immediately to FL240.  While in the descent we were given an altitude to descend to of FL220. We continued to ZZZ1 without incident. We elected to continue to ZZZ1 due to all the weather in the area. Around FL220 the captains airspeed seemed to return to match the FO's side. I still continued to fly and still proceeded as if the airspeed was unreliable. We landed with out incident .
Flight Crew reported airspeed and altimeter indication began to malfunction and elected to descend until indications matched on both Captain's and First Officer's instruments and elected to continue to destination airport.