Grade level: 5-7
Can be modified for lower and higher grades.
Areas of Math engaged:
Arithmetic; addition, subtraction, multiplication and division.
(9)(10) Materials Needed:
paper
pencils
chalkboard or overhead
creativity
By creativity, I mean that the children
will have to use their knowledge of math to create new problems.
(1) Game
12 is similar to game 24, except we are trying to find 12 instead of 24.
I think this game can be modified to fit any number that your class is investigating.
This activity will investigate the number 12 and different ways you can
reach the number 12.
(2)
Prerequisites: Students should have a good understanding of the basic math
operations (adding, subtracting, multiplying and dividing). Students should
also be able to perform a couple of operations in one number sentence. Example:
3+4 x 2 = 14.
(3)(4)(5)
This activity can be real challenging for students. Students like to compete
with each other and this activity has enough room for the children to explore
and be creative. Although the "space" of the activity seems really
large, you can quickly narrow it by incorporating specifics into the question.
For example, instead of asking "How many ways can you get the number
12 by adding?", you can ask a narrower question, "What are some
of the ways you find twelve by adding even numbers?"
(6)
Class Plans: To introduce a topic like this, I would first explain to the
children that all numbers have characteristics, kind of like people's personalities.
I would then present the problems to the students. Together we would come
up with the simpler answers,(or most common) and then the children would
be set free to explore on their own. The students could present their findings
in a trivia manor. Triva = try having the students stump each other. If
twelve is to hard, you could start with a smaller number to build confidence
and then work your way up to the harder numbers.
(8)
One theme that you could look for, are patterns. Do the kids start off by
adding or multiplying the numbers to get 12? What operations do they use
first? Another theme could be using diversity in mathematics, trying to
find different ways of getting the same answer.
(7)(11)(12)(15)
*This activity starts with a warm-up to get the student's brain flowing. Start with something simple and then work your way up. Here is my warm up:
A. See how many ways you can get the number 12 by adding only odd numbers.
____ + ____ = 12
One of the more common answers could
be: 5 + 7 = 12. If you get this answer ask the students to branch
out by adding more than two numbers at a time. An example of this could
be: 1+1+1+1+1+1+1+1+1+1+1+1=12 That is a perfectly good answer as
well.
B. See how many ways you can get the number 12 by adding only even numbers.
____ + ____ = 12
A common example here could be:
8 + 4 =12. Again, if the problem gets too easy, have the students use
more than two numbers to add. An example of this could be: 2 + 4 + 6
= 12
** The next activity you can do, is to ask the children to find the number 12 with only using the numbers 5 and 7. This is a good place for children to start using different operations. Example: 5 + 5 + 7 - 5 = 12
It is important to remind the students,
that in this activity, they should remember to perform the operation from
left to right and not skip around. In other words, do not use parentheses.
If this is enough for one class day, have the children, for homework, come up with different ways to find the number 12 using at least 3 different operations. For example:
3 + 5 x 6 / 4 =12
For this activity, you can have students use parentheses. This example really says,
3 plus 5 = 8, 8 times 6 = 48, 48 divided by 4 = 12.
You can have students create a whole worksheet of these and then have them try to stump each other.
This is the whole purpose of the
activity. I want the children to become creative in the ways in which they
produce numbers. In this case, I have selected the number 12, but you can
use any number that you want. If students are having problems with this
activity, have them work backwards. Have them figure out ways of getting
12 down to zero. Have them brainstorm some of the numbers that equal 12.
(13) You could do follow up activities
on different numbers. Or like the warm-ups above, have the students work
with numbers that have decimals or fractions and do the same activity. For
example: .4 x 9 / 3 = 12 ( .4 times 9 = 3.6, 3.6 divided by 3 =12)