Name: Erica Good
Process Standards: Problem Solving ___ Communications _x___ Reasoning _x___
Connections ____ Mathematical Representations ___x_
Content Standards: Numbers/Operations ____ Algebra __x__ Geometry___
Measurement ____ Data Analysis/Probability ____
Topic: Algebraic Function Machines
Grade Level: 3rd
Time: 1 hour
Rationale: Learning about function machines is a great way for students to develop their
problems solving skills. Students must solve for the “rule” of the problem. Developing
this skill helps students not only understand algebra, but leads to a better understanding
of cause and effect, social consequences, and furthers the understanding of basic addition,
subtraction, multiplication, and division.
Alabama Course of Study Objectives:
Standard 8) Complete a given geometric or numeric pattern.
Classroom Learning Objective(s): Students will demonstrate their ability to solve for a
function after reading Two of Everything by Lily Toy Hong and completing the Missing
Link worksheet which focuses on addition and multiplication functions.
Materials: Two of Everything by Lily Toy Hong, chart paper, pen, math journals for each
student, Missing Link worksheet (teacher generated-attached), computers with internet
Procedures:
Engage
-First I will read the book, Two of Everything by Lily Toy Hong.
-“What happened every time Mr. and Mrs. Haktak put something in the magic
pot?” (Answers may include—everything was doubled, when one thing went in
two came out, the objects were multiplied by 2)
-“So when they put in one coin, how many came out? What do you think was
happening inside the pot?”
-On a piece of chart paper, make a T chart that says
Into the magic pot
Out of the magic pot
Explore
-Read the story again and record the data. Your chart paper will look like…
Into the magic pot
Out of the magic pot
1 purse
2 purses
5 gold coins
10 gold coins
1 hairpin
2 hairpins
1 winter coat
2 winter coats
10 coins
20 coins
1 Mrs. Haktak
2 Mrs. Haktak
1 Mr. Haktak
2 Mr. Haktak
-“Look at the chart. What type of pattern do you see?”
-“Think of the magic pot as some sort of math problem. What type of math is
happening inside the pot? (x2)”
-“We if we wrote x2 in the middle here, would it be true every time?”
-Talk through each one and write x2 as you check
1 purse x2= 2 purses
5 gold coins x2= 10 coins
1 hairpin x2= 2 hairpins
1 winter coat x2=2 winter coat
Etc…
Explain:
-What would happen if we changed the magic pot to multiplying by 4?
-Which numbers would change?
-If the magic pot multiplied by 4, how many purses would Mr. and Mrs. Haktuk
have?
-If they put in 5 gold coins, and the magic pot was multiplying by 4, how many
coins would they have?
-What if our chart looked like this (draw on board)
In
1
2
3
4
Out
3
6
9
12
-Take a minute to figure out what would be happening in the magic pot.
-Allow students to work this out in their math journals.
-What is happening here?
Elaboration:
-What about if the chart looked like this?
In
2
3
4
5
Out
7
8
9
10
-This may be harder because the students will be looking for multiplication. Give
them a minute to figure it out. If they cannot seem to get it, give them a hint that
the magic pot might not necessarily be multiplying. It is important to let them
figure this out on their own if possible.
-explain that when looking for the rule, it might not always be multiplication. It
could be any type of math. It is important to look at how the number is changing.
-“Why would it be important to check the rule with all of the numbers and not just
the first one?”
-Have the students practice on their own
-Pass out the Missing Link Worksheet
-Allow students a few minutes to solve these problems as well as the “write your
own Missing Link problem”
-allow students to give a friend the problem they wrote and see if they can solve
it.
-Come back together and go over the answers and have them tell you how they
figured it out.
-Allow several students to share their Missing Link problem with the class and
see if the rest of the class can solve it.
-If there is time, allow students to play the function machine game at
http://teams.lacoe.edu/documentation/classrooms/amy/algebra/34/activities/functionmachine/functionmachine3_4.html
Assessment:
I will know that the students understand how to find the function if they complete
the Missing Link worksheet and write their own function problem with complete
accuracy.
Accommodations:
If a student is struggling, we will put out manipulatives. We will focus on simple
addition. You put one cube in a bag and pull out two. You put 2 cubes in a bag
and pull out three. You put 3 cubes in a bag and pull out 4. What is happening?
For a student who finds this too easy, I will have them create function machines
using harder math such as fractions or division.
Can you find the Missing Link?
Directions: Look at the pattern and see if you can find out the rule for the changing
numbers. Record the rule below.
In
Out
6
9
15
18
0
3
7
10
Rule: ______________
In
Out
4
4
7
7
1
1
2
2
Rule: ______________
In
4
20
5
25
1
20
3
15
Rule:_____________
In
Out
2
6
7
3
Out
Rule:_____________________
6
18
21
9
Rule:_____________
Write your own problem using your own rule. Have a friend solve for the rule
In
Out