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Classroom Robotics-Mathematics Day 1- Pg. 1
Classroom
Robotics –
Mathematics
Day 1
Overview
Students will introduce the topic of algebra, explaining how
it is different from arithmetic. Students will then be exposed
to the idea of relationships in the forms of ratios and the
terms proportional and inversely proportional. Students will
be guided through this exposure by a worksheet.
Learning Objectives:
Students will be able to…


Describe proportionality and inverse proportionality
Express ratios in an algebraic way
Suitable Ages: 11+
Time Needed: 1hr 15 min
In this packet
Teacher’s Guide
Introduction to Algebra Worksheet
Answers to Introduction to Algebra Worksheet
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Classroom Robotics-Mathematics Day 1- Pg. 2
TEACHER’S GUIDE
Activity Goal
The goal of this activity is for participants to gain exposure to algebraic thinking and vocabulary.
Objectives
Students will be able to…


Describe proportionality and inverse proportionality
Express ratios in an algebraic way
Materials


Copies of Algebra Worksheet
Answer Key
Set Up
Familiarize yourself with the lesson plan and worksheet.


Robot Kits (optional)
First Build Building Guides (optional)
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Classroom Robotics-Mathematics Day 1- Pg. 3
Procedure
Time
10 min
30 min
10 min
35 min
< 75
minutes
Action
1. Explain the difference between arithematic and algebra.
Algebra is about finding relationships between things. Instead of
numbers alone, algebra focuses on ratios, proportions, and
inverse proportions.Emphasize why algebra is important to
robotics. Often the speed, forces and motion involved in
robotics is represented as a relationship and not just a number.
Tell them they will learn about this when they review simple
machines in science.
2. Pass out the worksheets and instruct students to complete
them. Have the students who finish quickly define “Algebra”,
“proportional”, and “inversly proportional” on the back of their
papers.
3. When the majority of students are finished, breifly review the
answers to make sure they understand the concepts.
4. Instruct the students to work on their First Build. They may need
pieces from their science class. They may also work on their
vocabulary sheets for Day 1 that they received in Language
Arts.
Materials Needed
Copies of Worksheet
Answer Key
Robot Kits
First Build Building Guides
We encourage and welcome your feedback!
Please fill out the feedback form based on your experience and observations and forward
it to <NETID>@utdallas.edu at the Science and Engineering Education Center.
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Classroom Robotics-Mathematics Day 1- Pg. 4
Name______________________________
Introduction to Algebra
Relationships Not Numbers
Addition, subtraction, multiplication and division are all part of arithmetic. This is the foundation of mathematics. Most
of your Math Class has focused on number manipulations like these. Algebra is different. Algebra focuses on the
relationships of numbers. Hopefully in the next few weeks you will see how important this field is.
This worksheet focuses on three aspects of the relationships of numbers: ratios, proportionality and inverse
proportionality.
Ratios are fractions that indicate how much of one thing relates to the amount of another. Speed is a simple ratio:
miles
.
hour
Ratios
What are the speeds of the following cars:

1.
Car travels 150 miles in 5 hours?
2.
Car travels 15 miles in ½ hour?
3.
Car travels 75 miles in 2 ½ hours?
4.
Car travels 60 miles in 2 hours?
5.
What is the speed of all these cars?
6.
Graph the points for each of these speeds and connect the points. What is the shape of the graph? What would the graph
look like if the car was traveling toward you from 150 miles away?
Classroom Robotics-Mathematics Day 1- Pg. 5
Distance
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Time
Distance
Rough graph of car coming toward you:
Time
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7.
Classroom Robotics-Mathematics Day 1- Pg. 6
In algebra we sometimes use letters to represent the actual numbers in a ratio. If we used “y” for distance and “x” for time
where would they go in this formula?
8.
miles
hour
Assuming that the car maintained a constant speed. How do y and x change over time?

9.
Distance and Time are proportionate to each other with regards to speed. Explain.
Inverse Relationship
Find the missing number in each of the following equations:
1. 30 x ______= 60
2. 5 x ______= 60
3. 12 x ______= 60
4. 15 x ______= 60
5. 4 x ______= 60
6. 20 x ______= 60
7. 10 x ______= 60
8. 3 x ______= 60
9.
If the first number in each of these equations is called “x” and the second number is “y,” what happens to y when x
increases in value? __________________ what happens to x when y increases in value? ____________________
10. X and y are inversely proportional in this case. Explain.
11. In the following equation we will use F instead of x. We will use D instead of y. We will use W instead of 60. If the following
is true F x D = W what happens to D when you increase F, assuming that W stays the same?
12. Can you come up with a rule for the relationship of numbers that are multiplied and divided?
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Classroom Robotics-Mathematics Day 1- Pg. 7
Introduction to Algebra
Relationships not numbers
Addition, subtraction, multiplication and division are all part of arithmetic. This is the foundation of mathematics. Most
of your Math Class has focused on number manipulations like these. Algebra is different. Algebra focuses on the
relationships of numbers. Hopefully, in the next few weeks you will see how important this field is. This worksheet
focuses on three aspects of the relationships of numbers, ratios, proportionality and inverse proportionality.
Ratios are fractions that indicate how much of one thing relates to the amount of another. Speed is a simple ratio,
miles
.
hour
Ratios
What are the speeds of the following cars:

150miles
 30miles /hr
5hrs.
1.
Car travels 150 miles in 5 hours? Answer:
2.
Car travels 15 miles in ½ hour? Answer:
3.
Car travels 75 miles in 2 ½ hours? Answer:
4.
Car travels 60 miles in 2 hours? Answer:
5.
What is the speed of all these cars? 30 miles/hr
6.
Graph the points for each of these speeds and connect the points. What is the shape of the graph? What would the graph
look like if the car was traveling toward you from 150 miles away?

15miles
 30miles / hr
.5hrs.



75miles
 30miles /hr.
2.5hrs
60miles
 30miles /hr
2hrs.
Classroom Robotics-Mathematics Day 1- Pg. 8
Distance
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Time
Distance
Rough graph of car coming toward you:
represent
distance
Time
and “x” for time where would they go in
7. In algebra we sometimes use letters to
the actual numbers in a ratio. If we used “y” for
this formula?

miles
y
hour Answer: x

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Classroom Robotics-Mathematics Day 1- Pg. 9
8.
Assuming that the car maintained a constant speed. How do y and x change over time?
Using the numbers in the first
exercise they should see that miles and time go up together. As a car drives a longer time the car will go a longer distance.
9.
Distance and Time are proportionate to each other with regards to speed. Explain. They will go up and down together if the
speed remains the same. 5 miles/hr , 10 miles/2 hours, 20 mile/4 hours, etc. Their relationship is constant.
Inverse Relationship
Find the missing number in each of the following equations:
1. 30 x __2____= 60
2. 5 x ___12__= 60
3. 12 x __5____= 60
4. 15 x __4____= 60
5. 4 x __15___= 60
6. 20 x __3____= 60
7. 10 x __6____= 60
8. 3 x __20___= 60
9.
If the first number in each of these equations is called “x” and the second number is “y,” what happens to y when x
increases in value? ___goes down____ what happens to x when y increases in value? ___it too goes down_____________
10. X and y are inversely proportional in this case. Explain.
If the product is the same as x increases, y will decrease and vis versa.
11. In the following equation we will use F instead of x. We will use D instead of y. We will use W instead of 60. If the following
is true F x D = W what happens to D when you increase F, assuming that W stays the same?
D will go down if F increases, F will go down if D increases.
12. Can you come up with a rule for the relationship of numbers that are multiplied and divided? Numbers that are multiplied
are inversely related. Numbers that are divided are proportionate or directly related.