In this lesson, students play a game using counters and a place value chart to practice and reinforce place value concepts in base 10. Students then repeat the game in base 5 and other bases to increase their understanding of regrouping.

For each student, copy and distribute the Chip Trading Activity Sheet, the Chip Trading Game Board, one die, and a set of yellow, blue, red, and green chips. Tell the students they will be playing the Chip Trading game today, and that you will demonstrate how the game works using an interactive whiteboard.

Briefly describe how players will roll a die and select chips based on the number they roll. They will use place value to regroup as they accumulate points. Regrouping continues through increasing place values until the greatest place value is attained.

Chip Trading Activity Sheet

Chip Trading Answer Key

Chip Trading Game Board

Show how one player will play the game by displaying the Chip Trading game board on your interactive whiteboard or by using a document camera__.__ First, show how Player 1 rolls a single die and takes the number of yellow chips indicated by the number shown on the die. Place the yellow chips in the yellow chip column. Although Player 2 should go next, for the sake of the demonstration, show subsequent turns for Player 1 to demonstrate regrouping. Proceed until regrouping is needed and demonstrate how a player will trade 10 yellow chips for one blue chip and place it in the correct column. For example, if there are 8 yellow chips and 5 more are added, trade 10 yellow chips for 1 blue chip, and place the blue chip in the correct column. There will now be 1 blue chip and 3 yellow chips. Tell students, “We have one ten (blue chip) and three ones (yellow chips) for a total value of 10 + 3 = 13.” Tell them that the same process will be used when they have 10 or more blue chips. You may wish to play the game further and ask students what the value on the board is after a red chip is introduced.

Explain that the opponent checks the regrouping to make sure it is done correctly. If a player makes an error, he or she loses a turn. The winner is the first player to trade for a red chip.

Now, pair students together and have them begin playing the game. (Only 1 game board is needed between the pair of students. They may use individual boards for the activity sheet or during individual assessment). You should circulate the room while students play the game and ask pairs what number is currently on their board. After students have played two or more games, tell them the game is called Land of 10 because they trade each time they have 10 chips of the same color. Write an equation on the board such as 10 yellows = 1 blue, 10 blues = 1 red, etc., to remind students how they usually trade.

With the remaining class time, move on to the Land of 5 game, which is similar but uses regrouping with smaller numbers.

Tell students they are now going to travel to the Land of 5. Ask them what the name of the game might indicate. [In the Land of 5 they play the same game, but players can only have up to 4 chips of any one color. If you have 5 chips, you must regroup.] Ask a pair of students to model the game on an interactive whiteboard or using a document camera. They should roll the dice until one player has more than 4 yellow chips, and then have the student trade 5 yellow chips for 1 blue chip. Ask students how many blue chips they will need before they can trade for a red chip. [5.] During the game, circulate the room and ask students what the number on their board represents in base 5. For example, some students may look at 234 in base 5 and think the number is two hundred thirty-four. Reinforce the concept that that in base 5, 234 means that there are two (twenty-fives), 3 (fives), and four (ones) for a total of 50 + 15 + 4 = 69. The winner of the game is the first to trade for a green chip. Allow students to play this game several times and watch to ensure that students are trading correctly.

Gather students again and display a number with blue and yellow chips using a whiteboard or document camera. Ask them if they can tell you how much these chips are worth, using the rules for the Land of 5. For example, model with 3 blue chips and 4 yellow chips worth a total of 19. Display several examples and ask the students to determine the value.

If time allows, the students may return to the game and choose which land they want to play in. They may even choose a new land. Or, you can have students work on the Chip Trading activity sheet as an assessment tool.

### Ideas for Differentiation

Lower-achieving students might not be ready to try the rules for the Land of 5. Instead, allow them to keep playing the game with base 10.

Allow struggling students to use calculators to check the value of the number represented on their board.

Another option could be to have them try the Land of 9. Since it is close to 10, it is easier to play and involves fewer trades. They would then trade every 9 yellows for a blue. The game ends when the first player trades for a red chip.

For even fewer trades still, you could use a base greater than 10, such as the Land of 20. To prevent from requiring too many chips, the winner could be the first player to obtain 5 blue chips. To speed up the game, you could also use a 20-sided die.