math+lesson+plan-gina


 * __The Digits Game using 4- and 5- Digit Numbers__**

Strategies for subtracting without using a standard subtraction algorithm

Grade Level: 5 Objectives: Students will develop, explain, and compare strategies for subtracting 4- and 5- digit numbers. Students will use a random set of digits to approximate a 4- or 5- digit number.

//GLE: M (N&O)-5-7: Makes estimates in a given situation by identifying when estimation is appropriate, selecting the appropriate method of estimation, determining the level of accuracy needed given the situation, analyzing the effect of the estimation method on the accuracy of results, and evaluating the reasonableness of solutions appropriate to grade level GLE’s across all content standards.//

Overhead Projector Numeral Cards- one deck for each pair of students Numeral Card Transparencies Student Sheet 8: Digits Game Score Sheet for each student Student Sheet 9: Problems from Digits Game for each student (homework)
 * Instructional Materials and Resources:**


 * Instructional Activities Tasks:**

Connect to prior knowledge: Remind the students that you can arrange digits in a number in any way they want in order to make different numbers. Connect to their prior knowledge by saying that when using 2 digit numbers, the number in the tens place is the most important for determining how high a number is, when using three digit numbers, the number in the one hundreds place is the most important, and so on. In this case, when using four digit numbers, the number in the thousands place is the most important, and the ten-thousand place is the most important for five digit numbers.
 * Opening**:

Introduction of the Digits Game: Display the following five transparent Numeral Cards on the overhead, or draw the cards on the board:

1 7 4 5 8

As students call out numbers, record them on the board or overhead. Then ask students for some numbers they can make with all five of the digits and record their suggestions.

Introduce to the students that we are going to be playing a game called the Digits Game. Say that they will be dealt five Numeral Cards, and that they need to arrange the digits to make a number as close as possible to the target number.

I will then write the following on the board:

Target number 5000

For this round, I will tell the students that the target number is 5000. There will be a different target for each round of the game. I will instruct the students that they can use as many of the digits as they want. The number they make can be over or under 5000. In order for them to find their score, they will figure out how far their number is from 5000. There will be no use of calculators for this lesson. **(RIBTS 5.4)**

I will then put the following cards on the board: 1, 7, 4, 5, and 8. Students will work in pairs to make a number as close as possible to the target and determine its distance from 5000. Students will use paper and pencil to record the number they make. I will circulate the room and talk to them about their strategies. I will encourage them to find the difference between 5000 and the numbers they make in a way that does not use a standard subtraction algorithm.

If students need help getting started, I will give them an example: If one student made the number 4571, and another made the number 5714, I will ask the students which is closer to 5000. I will ask them if they can arrange four of these digits to make a number that is even closer.

I will ask a few volunteers to tell what numbers they made and to explain the strategies they used to find the differences between their numbers and 5000. I will record each example on the board as a subtraction expression, written horizontally rather than vertically to help students focus on the numbers as whole quantities. For example:

5000-4875=125

I will explain to the students how to score the game by demonstrating with numbers students made, showing how to score with numbers both above and below the target.

I will give the example 5147, and ask how far apart 5147 and 5000 are from each other. Since the answer is 147, the students score would be 147. I will give another example using 4875 and ask how far apart 4875 is from 5000. The score here would be 125, and since the goal of the game is to get the lowest number, 125 is better than 147. **(RIBTS 2.5, 8.1, 8.2)**


 * Development**:

Playing the Game: I will distribute the deck of Numeral Cards to each pair of students. Students will remove the four Wild Cards from the deck for this game. I will also distribute a copy of Student Sheet 8, Digits Game Score Sheet. Students can use this sheet as a model to make additional score sheets as needed.

On the overhead, I will list the targets for each of the first three games. Students will use the same target for each round in the game. If necessary, I will adjust the difficulty level of the targets. **(RIBTS 8.3)**

Students will play at least one more game with targets they choose themselves. As students become more experienced with the game, I might ask them to play with larger targets such as 500,000.

I will go over the rules of the game. For each round, the dealer lays out one set of Numeral Cards that both players use, dealing one more card than there are digits in the target. Each player records the target, the closest number he or she made, and the difference between the numbers on the Game Score Sheet. **(RIBTS 5.4)**

As students begin, I will circulate the room to make sure everyone understands how to play. I will also observe what strategies students are using to make their numbers and to determine how close they are to the target. I will encourage the students to make two numbers, and then determine which is closer without actually finding the difference between each number and the target. For example, if the target is 6029, the available Numeral Cards are 2, 8, 5, 6, and 3, and a player has said that 6235 and 5863 are the closest numbers. **(RIBTS 2.7, 6.4, 6.8)**:


 * Closure**:

I will ask the students what they did in order to find which number is closest to the target by asking for a show of hands. Students might determine which one is closer in many ways:

Reasoning about the general distance between each number and the target: “I know that 6235 is more than 200 away from 6029, so 5863 is closer because it’s less than 200 away  (100 more is 5963, and another 100 more is 6063).”

Approximating numbers to multiples of 25, 50, or 100: “Round to 5863 to 5850 and 6029 to 6025. Then it would be 50 more to get to 5900, then 100 more, then 25, or 175 to the target, but its really less because its 5863. If you round 6235 to 6229, it would be 200 to the target, but really its even more.”

Expressing the distance between each number and the target as a sum of familiar numbers: “I know 6235 and 6029 are 1+70+100+35 apart. I added 1 to get from 6029 to 6030, then 70 to get to 6100, then 100, then 35. For the other pair, 5863 and 6029 are 7+30+100+29 apart. I started at 5863 and added 7 to get to 5870, then 30 to get to 5900, then 100 then 29. I know 5863 is closer because I know it’s going to add up less.”

I will say that these are all good strategies to use in order to determine which number is closer to the target. I will summarize that the main goal in this lesson is to determine what number is closest to another number without using a standard subtraction algorithm, and that these are all effective ways of doing that.

I will reserve a few minutes at the end of the session to review of one the problems on Student Sheet 9, Problems from the Digits Game. This is the homework sheet. I will choose one of the problems and ask students to share their strategies for finding the score.

I will know that the students understand the lesson by the strategies they used for finding the closest number to the target. I will review Student Sheet 8, Digits Game Score Sheet, as well as their oral responses in order to determine this. **(RIBTS 9.2)**
 * Assessment:**

If students seem to need more practice, I will suggest that they choose 4-digit targets that are multiples of 1000 or 100, such as 4000 or 2400. For more practice outside of the regular game format, they could find the largest and smallest numbers that can be made with each set of Numeral Cards dealt. Students who are ready for more of a challenge can choose 5- or 6-digit targets that have mostly nonzero digits. Students comfortable with digit numbers could use a 1-digit target, such as 1 or 3. They deal three Numeral Cards and make numbers with two decimal places. For example, a player with a target of 1 deals 0, 2 and 7. To get a number close to 1, the player might make 0.72 or 2.07.
 * Learning Factors**

Students will be grouped in pairs. Strong math students should be grouped with students who are not as strong in math. The partners will be boy-girl.
 * Environmental Factors:**