## Chip Trading: Practicing Single-Digit Addition with Colored Chips Representing Ones, Tens, and Hundreds

• Lesson
Pre-K-2,3-5
1

This kinesthetic lesson involves using models to practice regrouping and to reinforce place value understanding. Students work together to play games involving bases 10 and 5. Students will also interpret models as numbers.

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 use  a document camera to demonstrate how the game works.

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.

Show how one player will play the game by displaying the Chip Trading game board with the 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.

Assessment Options

1. Stop students in the middle of the Land of 10 game and ask them to tell and write the value of their chips. Ask them to pretend they had 1 more blue chip, and ask how much they would have then. How do they know?
2. Ask students if they can find the value of the number represented on their board while playing the Land of 10 and the Land of 5.
3. Have students complete the Chip Trading activity sheet.

Extensions

1. Higher-achieving students can choose to play the game in many different bases. Usually, the smaller the base the more challenging the game, because sometimes students will need to make two or more trades in a single turn. Stop the students during the game and ask them which base they are using and how much their chips are worth.
2. Ask students to write out a set of rules for how to play, "Land of Six." Students can then share their rules with the class. Offer time after each student's presentation for either verbal feedback or written feedback.
3. Ask students to play in Land of 5, but the first player to reach a value of 100 chips wins. How will they know when someone has won? [4 reds will win the game since blues now have a value of 5 and reds now have a value of 5 × 5 = 25.] Allow them to play in different bases, but each time the winner must have 100 chips, and students have to determine how many chips of each color are needed.
4. Have students represent one base 10 numbers in two different bases and compare the results. What patterns do they observe between the representations in say base 4 compared to base 8? What is the greatest digit in base 4 and what is the greatest digit in base 8? Are more columns needed for one base than the other to represent the same base 10 number? If so, which base requires more columns and why?

Questions for Students

1. Why do you think our first game was called the Land of 10?

[In our system, when you have 10 ones we trade them for 1 ten.]

2. Depending on the base used, what is the maximum number of chips that can be in any column?

[For base n, there can be a maximum of n-1 chips in any given column.]

3. If a yellow in the Land of 10 is worth 1, how much is a blue worth? A red? A green?

[10, 100, 1000.]

4. What is the greatest digit that can be in any column for base 10?

[9.]

5. How do you know that a red is worth 100 in the Land of 10?

[You traded it for 10 blues, and each blue is worth 10. Ten 10’s make 100.]

Teacher Reflection

• Did you challenge all students at their level? What additional strategies for differentiation would be helpful?
• Did your students demonstrate understanding of their work with regrouping? How?
• What errors did you notice students making when regrouping with the chips or writing the the number?
• What other instructional strategies might you use to help students understand the need to regroup when the column has too many chips?
• How did students illustrate that they were actively engaged in the learning process?
• Did you find it necessary to make adjustments while teaching the lesson? If so, what adjustments, and were these adjustments effective?

### Learning Objectives

Students will:

• Add single-digit and double-digit numbers.
• Regroup numbers with chips representing quantities.
• Regroup numbers in other bases.

### NCTM Standards and Expectations

• Connect number words and numerals to the quantities they represent, using various physical models and representations.
• Use multiple models to develop initial understandings of place value and the base-ten number system
• Use a variety of methods and tools to compute, including objects, mental computation, estimation, paper and pencil, and calculators.
• Understand the place-value structure of the base-ten number system and be able to represent and compare whole numbers and decimals.
• Recognize equivalent representations for the same number and generate them by decomposing and composing numbers.

### Common Core State Standards – Mathematics

-Kindergarten, Algebraic Thinking

• CCSS.Math.Content.K.OA.A.1
Represent addition and subtraction with objects, fingers, mental images, drawings1, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations.

-Kindergarten, Algebraic Thinking

• CCSS.Math.Content.K.OA.A.2
Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem.

• CCSS.Math.Content.1.NBT.C.4
Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten.

• CCSS.Math.Content.2.NBT.B.5
Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.

• CCSS.Math.Content.2.NBT.B.6
Add up to four two-digit numbers using strategies based on place value and properties of operations.

• CCSS.Math.Content.2.NBT.B.7
Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds.

Grade 3, Num & Ops Base Ten

• CCSS.Math.Content.3.NBT.A.2
Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.

Grade 4, Num & Ops Base Ten

• CCSS.Math.Content.4.NBT.A.1
Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700 ÷ 70 = 10 by applying concepts of place value and division.

Grade 4, Num & Ops Base Ten

• CCSS.Math.Content.4.NBT.B.4
Fluently add and subtract multi-digit whole numbers using the standard algorithm.

Grade 5, Num & Ops Base Ten

• CCSS.Math.Content.5.NBT.A.1
Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left.

### Common Core State Standards – Practice

• CCSS.Math.Practice.MP1
Make sense of problems and persevere in solving them.
• CCSS.Math.Practice.MP6
Attend to precision.
• CCSS.Math.Practice.MP7
Look for and make use of structure.