Counting
with 3's, 4's and Operations
Grade Level: 7-8
Materials: generative activity sheets: using the 3's, using the 4's, calculators
Goals: This activity will check students understanding of the
order of operations, the properties of operations and their inverses, and
promote cooperative learning. This activity will also help meet the TAAS
objectives.
Mandatory Set: As students arrive in class, hand out the generative activity that asks students to formulate one equation using three 3's. Allow students 15 minutes to complete.
Check for understanding: Walk around classroom monitoring and assisting students.
Modeling/Guided Practice: Review worksheet and solutions with students on the overhead. Have students share their answers. Periodically ask students questions or problems and check their answers.
Input/Objective
Discussion: The activity that we have completed is called a generative activity. Based on the name can anyone guess what I mean by "generative activity"
(student responses)
A generative activity is an activity that "generates" or produces a number of responses or answers. For example, you guys came up with many different solutions to the problems. This particular activity checked for your understanding and application of:
(review each of the points)
Ask the following questions:
1 How does this activity relate to things we have done before
Independent Practice
-Divide the class into groups of four
-Have students complete generative activity dealing with the number 4
-Require students to:
---------------------------------------------------------Day Two------------------------------------------
-Have students explain (in essay form):
Assessment
-Students will be graded on
Generative Lesson: Explanation
This challenging generative activity is designed to assess students understanding
of the order of operations, the properties of operations and their inverses,
and promote cooperative learning, in preparation for the TAAS test. The
activity challenges students knowledge in these areas:
*Properties of Addition (commutative)-it makes no difference in which order two numbers are added.
*Properties of Subtraction
*Properties of Multiplication-the commutative property, the role of zero and one in multiplication, and the distributive property
*Division Concepts-Fair Sharing (the idea that if a quantity is to be
separated evenly into a given number of subsets, then division expresses
the number in each subset). Also, the understanding that fractions are expressions
of division.
The activity can be done as a warm-up or extended to be a two day lesson that incorporates group work.
Since their are very few guidelines, the students will create a variety
of solutions. This "space" or range of answers is not too large
and will allow ideas to emerge. I have enclosed an example possible responses,
and also the actual activities that were completed by seventh grade math
students.
Generative Activity
Using three 3's, create equations to find values for numbers 1-10. You
need to arrange the 3's in any sequence. You may use any operation (addition,
subtraction, multiplication, and division). For example: 3+3/3 = 2. Then
once completed, check all answers using the computer.
1=
2=
3=
4=
5=
6=
7=
8=
9=
10=
Generative Activity
Using four 4's, create equations to find values for numbers 1-20. You
need to arrange the 4's in any sequence. Create at least two equations for
each value. You may use any operation (addition, subtraction, multiplication,
and division). For example: 44-44 = 0, 44/44 = 1. Then, once completed,
check all answers using calculators.
1= 11=
2= 12=
3= 13=
4= 14=
5= 15=
6= 16=
7= 17=
8= 18=
9= 19=
10= 20=
Student Work
Student 1:
Student 2:
Student 3:
