# Place Value - Regrouping

Lessons for motivating and reinforcing place value concepts

### Method 1: Place Value Bankers

Overview: In this demonstration students will get to act out the roles of place holders.

Materials: place value blocks, or any manipulative to represent 1s, 10s, and 100s.

Background: This lesson was performed in a 1st-2nd grade multi-age setting. Before the demonstration many students were struggling with carrying and regrouping. Students were given a chance to be part of this activity on their own during individual practice time, and many chose to do so, saying that it was "fun." Within a few days after this, and other exercises, most students were regrouping with little difficulty.

Procedures:

In the Place Value Bank each teller works as a place holder. The bank needs at least 3 place holders for the 1s, 10s, and 100s. As a place holder, she must operate according to simple rules. She may accept deposits (addition) or withdraws (subtraction) of the place she is holding. However, she may never hold more than 9 (or less than 0) at a time. To follow these rules she may make appropriate trades with the place holders that work with her. For example, the ones place holder may group ten ones and "carry" them to the tens place holder. The tens place holder may "borrow" ten tens, (a block of 100) from the hundreds place holder.

While the transactions are occurring, an accountant-scribe should write the steps on the board.

Example 1: The bank has 372 units. Three 100s are held by Jeff, seven 10s are held by Alexis, and two 1s are held by Erika. Josh makes a deposit of 153. First Erika takes his three 1s to make a total of 5. Alexis takes his five 10s, which with her seven 10s makes twelve. She now has too many 10s so she "carries" ten of them (100) to Jeff. Josh deposits his one 100 with Jeff. Jeff's collection of 100s now totals 4.

Example 2: Simply reverse the steps mentioned so that Josh withdraws 153. For this to work, Alexis will have to "borrow" ten 10s from Jeff so that when Josh takes five from her twelve she still has seven.

### Method 2: Patterns

Purpose: The brilliance of place value is the way the same patterns work at any level so only a few patterns have to be learned.

Objective: Students will generalize carrying at any place by starting with small numbers that they already know.

Method: practice adding the same number in a sequence starting with small numbers. repeat this for numbers between 1 and 9. Once students have the idea, then move over one place value to the tens and repeat the same pattern. Once they have this move over to the hundreds. Once they have this pick a randon three digit number and mix all three levels.

Example of the steps
 Students should first get a lot of practice with the small numbers like the first column using different starting numbers, and adding different numbers. Students should discuss what happens to the tens column at each step. After doing the tens and hundreds patterns students should discuss whether the ones place was ever changed by the addition. Why not? Students should discuss what happens to the higher place when a carry occurs. When mixing the three columns together start with different digits. That way each column will produce a carry at a different time.

### The Digit Matching Game

Objective: Students will practice carrying and borrowing by playing to match digits.

Materials: two spinners with the digits 0 through 9, or two dice where at least one die has the digits 0, 9, 8, and 7.

Procedure:
 The game starts by having each student pick a digit which will be their target through out the game. The starting number is then set to 500. On each turn, the student spins both spinners and may either add or subtract, from the previous number, the digits he spins, in either order, with his goal being to produce his target digit. He gets a point for each time he matches his target digit. The answer may not go below 0 or above 1000, so addition or subtraction is required at the extremes.

Example:
 Start of Game: Derek picks 3 and Sam picks 6. 500 Round 1: Derek spins a 2 and a 3. He adds 23 to the 500 to get 1 point for matching his 3. 523 Sam roles a 7 and a 5. She notices that if she subtracts 57 she can get twp points by matching her target digit of 6 twice. 466 Round 2: Derek spins a 7 and a 9. He notices that adding 97 would result in 563 giving Sam a point also. So he subtracts 79 to get a point for matching his 3 387 Sam roles a 3 and a 1. She subtracts 31 and gets at point for matching her target of 6. Which gives Derek a point also for the 3 in the 100s place. 356