MANIPULATION OF

Number Groups

• Materials:
• -Uni-Fix cubes or any manipulative for students can be used for counting groups.
• -The teacher uses the same manipulative on the overhead so that all students may see.
• -Students need paper or a slate on which to write their answers.
• -A chart on which to write their answers.
  
• Pre-requisites:
• Students should be able to group different numbers or know how to add three or more numbers to write a math fact.
  
• Activity Length:
• This activity is credible as a day activity, but if discussion is extensive, it may carry over into the next day.
  
• Activity:

You are at the carnival and want to win a stuffed dinosaur.

You must score 24 points by playing the baseball toss to get the prize. Lucky for you, there are 4 balls to throw if needed. The bottles are marked from 1 - 15. Using each number once, find 5 ways to win

1. Hit any numbers, 1 - 15 to score 24 points . Remember, you have 4 balls you can throw if needed. Find 5 ways to win.
2. You hit the number 6 with the first ball. Find 5 ways to score 24 points using 4 balls.
3. You see the numbers 3 and 4 are close and easy to hit. What other numbers can you hit to win 5 times?
4. Generative:

When asking for their responses, there will be more than one correct answer. Although the numbers are restricted to 1-15, various answers can be given from the students that equal 24.

• Thinking with:

The students will use their manipulatives to group their numbers. Since each first or second grade student has 24 objects to arrange in groups, the numbers in their math fact can be determined easily. Each student can 'think with' the manipulative. By having objects to move, the students will be able to think about all different possibilities of calculating 24, or any other number. The task of adding multiple numbers can be tricky for the younger children. By thinking with concrete objects, the students can manipulate ideas of what will work.

1. Examples:

A.

10 + 9 + 5 = 24

4 + 8 + 12 = 24

2 + 15 + 7 = 24

3 + 7 + 10 + 4 = 24

15 + 2 + 5 + 2 = 24

B.

6 + 4 + 14 = 24

6 + 15 + 3 = 24

6 + 10 + 8 = 24

6 + 3 + 8 + 7 = 24

6 + 1 + 15 + 2 = 24

C.

3 + 4 + 15 + 2 = 24

3 + 4 + 10 + 7 = 24

3 + 4 + 12 + 5 = 24

3 + 4 + 6 + 11 = 24

3 + 4 + 9 + 8 = 24

4,5. Space:

The space to cover topics is large enough to have interesting discussions, yet at the same time is not too large, because certain ideas will be central to the topic. When looking at the answers given by the students, the topic about grouping, counting, and addition may arise. However, even those discussions have limitations. Since there are constraints on which numbers can be used, the students are not just plugging in any number, but arranging groups. These guides help the discussion to focus on a narrow topic.

1. Class plans:

Once the manipulatives are handed out to all students, began by stating the problem of the activity (needing 24 points). When the students know their task, allow them to explore their possibilities. Make sure to emphasize each student's example of four groups. After a sufficient amount of time, ask a student to come to the overhead and illustrate one of their answers. This is done by arranging the groups of the manipulative on the overhead. Next, the teacher can write the math fact on a chart. Finally, the discussion can occur. Began by asking about the patterns and reasoning that they used. Then let the rest of the discussion unfold.

1. Suggestions:

To prevent the possible solutions to a few easy ones, have peers demonstrate their answers to encourage others to shoot for higher goals. Also, you can say that there must be at least one example of all 4 balls. Since there are constraints on the problems, the answers will be three and four numbers.

8. Themes:

The major theme is grouping. The students group the manipulatives, finding numbers which equal to 24. When the students understand grouping, the concept of addition is easier to understand. Through addition, they become aware of the fact that different numbers can represent the same number. Some may even notice that certain numbers are used more often, were others are rarely used. The theme of common factors may also be included in the discussion.

1. Follow-up:

After the generative activity is completed, there are some other activities that will enhance and review the themes discussed. For example, you can practice adding more three and four numbers. Grouping must be mastered before they are able to fully understand the concept of addition.