Each Friday Ms. Descartes' class plays the Place Value Game. Each student has 3 cards. Each card has a random 5-digit number on it. Ms. Descartes pulls a number from 1-9 from a hat and the students find the value of her number on all of their cards. The student with the highest total score wins.

Here's an example:

If a card contains the number 47229 and Ms. Descartes picks a 7, the card is worth 7000 points. If she picks a 2, it's worth 220 points.

Sylvia has the following cards:

If Ms. Descartes pulls a 3, how many points will Sylvia have?

What digit does she hope Ms. Descartes will pull next week so that she will have the highest possible score?

Extra:

Sylvia's friend Carina has these cards:

What's one digit that Ms. Descartes could pull next week that would give Carina a higher score than Sylvia? (Remember that both Sylvia and Carina have to compare scores using the number Ms. Descartes draws.)

Be sure to tell us the WHY of your answer.

You can email your answers to : adelfiom@sidwell.edu, bring your answers back to school in the fall, or mail them to us at:

Merry Adelfio and Raina Fishbane

Sidwell Friends School

3825 Wisconsin Ave. NW

Washington, DC 20016

These problems are from the Math Forum.