Connecting Regrouping to Adding

Grade: 1st - early 2nd

Area of Math: Addition Skills

Specific Idea: Grouping, Regrouping, and Trading

Skills that must be mastered: Counting (2)

Length of Time Needed: 1 - 2 hours (2 class periods) (12)

Materials Needed: (9)

Paper

Pencil

Base Ten blocks (enough for each student to have 27 "ones" blocks and 2 "tens" blocks)

Some form of organizer to keep groups of blocks separated (6-inch rings or squares, colored paper, plastic lids, etc.); 2 per student

Procedures: (10, 11)

1) Discussion--Demonstrate an addition problem using the blocks on the overhead. Talk about how to combine the numbers to find a total. (6)

2) Pass out 2 organizers and 10 "ones" blocks to each student; allow time for exploration.

3) Ask students to count their blocks and draw how many they have (double check that everyone has ten blocks).

Example:

4) Ask the students to separate their blocks into two groups on the organizers and draw how many they have in each group.

Example:

5) Now, ask them to regroup the blocks and count how many they have total. Discussion--Do they have the same number as they did originally? Why? Have the students draw their equations and share their discoveries on the board. (6)

Example:

6) Be aware that a majority of students will answer with5+5. Other students' answers should encourage these students to find different combinations. (8, 1, 4, 15)

7) Have the students discover and draw numerous equations. (1, 4) Discussion--What happens when you regroup the two piles back together? Do you still have the same number? How does this relate to addition? Have someone explain an example on the board. (6, 8)

8) After using the manipulatives for a while, have the students write the equations traditionally. Draw one example on the overhead and write the traditional equation. (6)

Example:

9) At this time, give each student 10 more "ones" blocks. Instruct them to follow the same procedures as above: count and draw their total, separate the blocks into two groups and draw their findings, regroup the blocks and draw the equations.

10) Be aware that students will typically separate their blocks into two groups of ten. Have some students write their answers on the board, which should also encourage students to find more challenging combinations. (8, 1, 4, 15)

11) Now, pass out two "tens" blocks to each student. Have the students use the Base Ten blocks andtrade for groups of ten. Follow the procedures as discussed above, but trade for a ten block before writing the equation.

Example:

12) Discussion--What happens when they regroup? How are their answers similar to when they had ten blocks? How are the answers different? Do they get the same answer as before? Why or why not? (6, 8)

13) Now give each student 7 more "ones" blocks. Let them experiment with a total number that is odd. After they make discoveries, ask questions about the differences when working with a number that is odd. Discussion--How are their answers different from when they had an even number? What similarities can they find? (6, 8)

14) Wrap-up the activity. Discussion--What connections do they make between regrouping and adding? How are these two processes similar? How are they different? How many different combinations did they produce? What other connections do they make? (Write answers for these connections on the overhead.) (6, 1, 4, 8)

Follow-up Ideas: (13)

Use larger numbers, so that students will have to trade more often (greater than 30).

Use Base Ten blocks to solve equations; given the problem, find the answer (14+6=?).

Use Base Ten blocks to relate addition equations to subtraction equations (4+6=10. . .10-6=4).

Specific Examples with Children: (14)

1) Pre-Kindergarten Child, age 5: (7)

This child had a difficult time with this assignment. (3) He could count the objects accurately, but did not make the connection between the regrouping and adding. (8) When asked how many total blocks he would have when the two piles were regrouped, he made up a different number every time. Even though he was able to count the total number after the piles were regrouped, he was not able to begin thinking about trading the Base Ten blocks. (5) Therefore, I believe that this age was too young for this assignment.

2) Second Grade Child, age 8: (7)

In the beginning, this child found the assignment entirely too easy. (3) After separating the blocks into two groups, he immediately told me how many blocks were in each group and how many there were total. Therefore, I gave him ten more blocks, and the task was just as easy for him. (4) It was not until I gave him the seven extra blocks, that he showed some sort of difficulty. (3) However, he was still able to separate the blocks and eventually give me the total number. After spending a small amount of time with the Base Ten blocks, he was able to use them appropriately and effectively. (3) He made the general connections between regrouping and adding with little difficulty. (8) At this point, he seemed to finally enjoy the assignment and was benefiting from the activity. (3) Therefore, I concluded that this assignment was best geared toward first grade or early second grade students.