The Dragons - who welcome the Irish province to Rodney Parade for their GUINNESS PRO12 clash on Sunday - are unbeaten at home this season.
But they have only scored nine tries out of six games in the league and Jones knows that number must improve if they are to stand a chance against a free-flowing Ulster side.
"We played some attractive rugby last season and the season before but so far we haven't been able to get the ball through three pairs of hands," he said.
"That's something very much in our mind because if we are to be successful then we have to score at least 25 points. You are not going to do that by holding onto the ball all the time, the game has to have some width.
"It's something we are aware of and something we are working towards improving - if we are going to beat Ulster we have got to play."
Young gun Ollie Griffiths will make his first GUINNESS PRO12 start as the Dragons look to extend their home winning streak in the league to six games.
The Wales U20 star is one of five personnel changes made to the team that lost out to the Scarlets last weekend.
Fullback Carl Meyer gets the nod and joins the back three alongside wingers Ashton Hewitt and Nick Scott.
The centre pairing remains unchanged for the third week running as Adam Hughes and Adam Warren retain their places. 23-year-old Dorian Jones is named as fly-half and is joined in the halfbacks by scrum half Sarel Pretorius.
The front row sees one change made to it as prop Shaun Knight joins Boris Stankovich and hooker Elliot Dee. The second row has one change made to it as Cory Hill joins Rynard Landman. The back row includes Griffiths who joins Ed Jackson and Taulupe Faletau.
Ulster's six GUINNESS PRO12 games to date - like the Dragons - have all been won by the home side. Indeed the Ulstermen have not been victorious away from home since a trip to Connacht in April.
But Rory Best and Ruan Pienaar return to the Ulster squad as newly-installed director of rugby Les Kiss makes four personnel changes and three positional changes to the team that lost narrowly to Munster last weekend.
Peter Nelson returns to the side at fullback and is joined in the back three by Sammy Arnold and Rory Scholes, who replaces an injured Andrew Trimble. Paul Marshall and Stuart McCloskey are retained at scrumhalf and inside centre respectively.
Up front Kyle McCall comes into the team to replace Andrew Warwick at loosehead prop, joining acting captain Rob Herring and Wiehahn Herbst in the front row.
Dan Tuohy joins Franco van der Merwe in the second row, with Stephen Mulholland, who makes his first start for Ulster, named alongside Chris Henry and Robbie Diack in the back row.
And Ireland flanker Henry admits his side will need to produce their best.
"Dragons have had a similar run of form to us; their defence is particularly strong, they make teams work really hard, put them under pressure and frustrate players," he said.
"They tackle and bounce out of rucks and are a solid line constantly. We will have to come up with a few ideas to get through their line of defence but away from home and in a place like Rodney Parade you are talking about set-piece, maul, defence and not giving away penalties.
"(Taulupe) Faletau is obviously one of their danger men, so we need to start well. I think most of these games come down to the breakdown and I think that was something that was better for us last weekend.
"I think if we can get that right, and our game picks up, we can give any team a rattle away from home."
At Rodney Parade, 2.30pm. Live on S4C/BBC NI
Referee: Dudley Phillips (IRFU, 54th competition game)
Assistant Referees: Sean Brickell, Simon Rees (both WRU)
Citing Commissioner: Aurwel Morgan (WRU)
TMO: Tim Hayes (WRU)
Guinness PRO12
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