This is a generative activity. This activity was designed for third grade. It empahsizes the beginning levels of multiplication by teaching grouping and the beginning levels of division by teaching the concept of remainders. (1) It is possible for there to be different answers. (2) In order to do this activity, the students will need to have knowledge of addition and subtraction.
The students are going to design classrooms for different size classes. (2) First, you should point out how you arranged your classroom for that class. Emphasize how many groups there are and how many students are in each group. If your classroom is not arranged into groups illustrate how you could make groups for that class. You can use an overhead to illustrate this point or actually rearrange the students' desks.
Next divide the class into groups of varying abilities. (9) Give each group three pieces of white construction paper, unifix cubes, cardboard squares (used to trace the outline of the desks), a transparency with a marker.
(2,3,4,5) Then explain to reach group that they are new teachers. They have to plan their classrooms for three different numbered classes. Each classroom has a minimum number of students, set by the teacher, with no desks left over. The first class should be more than ten, the next more than twenty and the third more than thirty. For each instance, the group selects a number larger than the minimum. (10) They will use the unifix cubes to plan out the classroom. Then they draw the classroom, using the small pieces of cardboard to draw the desks. While the groups are working go around and monitor the groups. Make sure that all students are contributing to the design of the classrooms. (15) If a groups is stuck, give hints to possible answers. For example, if a groups has chosen the number twenty four, ask the class if their are two groups that can be formed (2 groups of 12).
(6)After the groups draw all three sample classrooms, have them draw the classroom for the "more than twenty" class on the transparency. Then have each group come up to the overhead projector with the transparency to explain what number they chose and how they grouped the desks. (6)During this time you should write down their results. When every group has explained their results, illustrate to the students numbers that occurred throughout the examples by circling them on the chart. (7) For example, one group selects twenty four with six groups of four and another group selects thirty six nine groups of four. Each classroom has groups of four with only the number of groups varying. (8) The students should see that certain numbers can be present in more than one answer.
The next step is to introduce the idea of remainders. Explain to the students that they are going to be teachers again. They are going to design three classrooms. One classroom will be more than ten, the next more than twenty and the third more than thirty. The numbers have to be different from the previous activity. In addition, they need to leave one desk for the teacher to use.
Once again divide the class up into groups of varying abilities. (9)Give them unifix cubes, three sheets of construction paper, a transparency with a pen and the cardboard tracers for drawing the desks. (10)Have the students plan out the classrooms with the unifix cubes. Then they can use the cardboard tracers to make the map. As they begin to work, monitor each group to make sure that everyone is participating. If a group is having problems assign each member a job to do for the task.
(6)After the groups finish designing the three classrooms, have them transfer the "more than twenty" classroom onto the transparency. Ask each group representative to bring up the transparency. Have the representative explain how the group arranged their classroom with an extra desk leftover. Copy down the number of total students and the way they grouped them on the transparency example.
(8)When all the groups are done, point out all of the reoccurring numbers in each of the examples. Illustrate how the groups arranged for the extra desk (Whether they chose an even number and added one or whether they chose a random number and worked with it). Show that once again certain numbers can be apart of other larger numbers as seen in the previous activity. Also point out that it is ok to have something leftover. Not every problem has to come out even.
(13)If you wish to address this idea
further, you could do other activities using this same principle. For example
you could up the number of remainders. You could also change the activity
to arrange something else. For example the students could be planning a
party for varying amounts of guests and they have to arrange chairs. This
is the great thing about a generative activity. You can do different things
with the same concept and the students discover things on their own.
Structured Outline
Classroom Grouping
Objective: The
students will be able to take a number and make groups of different amounts.
The students will be able to also make groups with remainders.
Grade Level: Third
grade
Math Area: Multiplication
(groups)
Previous Knowledge Needed: The
students should know how to add numbers more than ten and have some basic
knowledge of grouping.
Materials Needed:
white construction paper, unifix cubes, cardboard squares ( 1/2" x
1/2" ), transparencies, vis-a-vis pens, a sheet of butcher paper, an
overhead projector
Anticipatory Set: "Have
you ever wanted to be the teacher? Well today you are going to be teachers.
You are going to set up three imaginary classroom for imaginary classes.
You will get to pick the number of students in each class, draw a map of
the classrooms and show the class how you designed one of your classrooms.
Behavioral Objective: After
today's lesson you are going to be able to take a number, arrange that number
into different groups.
Instructional Input: Look
at how the desks are arranged in our classroom. How many students do I have
in each group? How many groups do we have? Let's take the unifix cubes and
make a model of our classroom. Each cube equals one desk. Now let's draw
a map of our classroom using the construction paper and the tracers to draw
the desks.
Guided Practice: "Now,
each group is going to chose three different numbers. One number has to
be larger than ten. What is a number larger than ten? The next number will
be larger than twenty. What is an example of a number larger than twenty?
Finally the last number will be larger than thirty. What is a number larger
than thirty? These numbers are going to be the amount of students in each
class. You are going to design a classroom for all three classes. First
pick your numbers. Then get out that many unifix cubes. Make a model of
your classroom with the unifix cubes. Once you are sure that is how you
want you classroom to look, take the cardboard tracers and draw a map of
the classroom just like we did for ours. After you have completed all three
maps, draw the map of the "more than twenty" classroom on the
transparency with the pen." Go around and monitor each group to ensure
everyone is participating.
Discussion: "Now
each group has created classroom for different numbers of students. I would
like the group representative to bring up their transparency of the "more
than twenty" classroom when I call your group number. We are going
to see if there are some common numbers of groups or desks in our classrooms."
As each representative comes forward, you should copy down the total number
of students. Then below that number record the number of groups and the
number of members in each group. After all of the groups have explained
what they did, circle all of the common numbers from each example in red.
Point out to the students all of the common numbers. This helps then see
common factors of numbers.
Closing: "What
have you learned today?" The students will respond by saying that they
learned how to group and that groups can be made up of the same number.
Structured Extension
Classroom Grouping
with Remainders
Objective: The
students will be able to take a number and make groups of different amounts
with remainders.
Grade Level: Third
grade
Math Area: Multiplication
(groups)
Previous Knowledge Needed: The
students should know how to add numbers more than ten and have some basic
knowledge of grouping.
Materials Needed:
white construction paper, unifix cubes, cardboard squares ( 1/2" x
1/2" ), transparencies, vis-a-vis pens, a sheet of butcher paper, an
overhead projector
Anticipatory Set: "We
are going to become teachers again for the Math lesson. We did the lesson
where you picked a number and put the desks into groups. Now we are going
to do something new. You are still going to design classrooms for three
imaginary classes but this time you, as the teacher, need a desk for your
supplies. So now you have to have one desk by itself. In Math when one number
is remaining we call it a remainder. So when you leave that one desk out
you are making a remainder.
Behavioral Objective: After
today's lesson you will be able to divide a number into groups with one
leftover (a remainder).
Instructional Input: "Let's
take our unifix cubes and make a model of our classroom again. This time
let's include the one desk I have here by the blackboard." Use the
overhead so they can see your model. "Now let's draw a map of our classroom
using the cardboard tracers. When your map is finished put an X on the desk
leftover."
Guided Practice:
"Now it's your turn to create your three classrooms just like in the
other activity. Remember that one class has to be larger than ten, the second
larger than twenty and the third larger than thirty. You cannot use the
same numbers from the other activity. You must choose new numbers. Once
you have picked your numbers build a model of each classroom with the unifix
cubes. Then take your cardboard tracers and make a map of all three classrooms.
Remember to put an X on the desk leftover. Once you have done all that,
make a map of your "more than twenty" classroom on the transparency
with pen." Go around and monitor to ensure that all members of the
group are participating and they are including the one extra desk.
Discussion: Have a representative from each group bring their map on the transparency to the overhead. They should explain how many groups they have and how many desks are in each group. As they are doing this keep a chart of their total number, how many groups and how many members are in each group. Stress the different ways the students came up with a remainder of one. Once all the groups have presented their data ask different students to come and circle the common numbers that appear in each classroom map. Point out that once again a number can appear in many different groups.
Closing:
"What have we learned today?" The students should respond by saying
that they can break a number into groups and have one leftover (remainder).