What is Hands-On Equations?
Hands-On Equations is a visual and kinesthetic system
developed for introducing students in
grades 3 to 8 to essential algebraic concepts. It is a
system designed to enhance student self-esteem and interest
in mathematics. In a few lessons students learn to solve
equations such as 4x + 3 = 3x + 9 and 2(2x + 1) = x + 8.
Later lessons teach additional concepts. The students
physically set up the equation using the game pieces and a
flat laminated balance and then proceed to carry out "legal
moves" to solve the equation. The legal moves are the
physical counterpart of the abstract mathematical principles
which are used to solve these equations.
What are the benefits of using Hands-On Equations?
- No algebraic prerequisites are required
- It is a game-like approach that fascinates students
- The gestures or "legal moves" used to solve the
equations reinforce the concepts at a deep kinesthetic
level
- The program can be used as early as the 3rd grade with
gifted students, 4th grade with average students and 5th
grade with LD students
- Students attain a high level of success with the
program (see research studies section)
- The program provides students with a strong foundation
for later algebraic studies
- The concepts and skills presented are essential for
success in an Algebra 1 class
Textbooks
A) THE
HANDS-ON EQUATIONS LEARNING SYSTEM
Complete
program for use with one student. Includes manuals for
Levels I, II, and III, worksheets, answer key, and one
student kit of game pieces with flat laminated balance.
Hands-On Equations
Sample Equations: Three Levels
Hands-On Equations consists of three levels. At each
level the students learn how to setup and solve the
equations using the game pieces; once they have mastered
this approach, they are taught how to setup and solve the
equations using only paper and pencil with the pictorial
notation.
Level I: Lessons #1 - #7:
Red Booklet. Students use the red cubes
and blue pawns to setup and solve:
Level II: Lessons #8 - #16:
Blue Booklet.
Students use the red cubes, blue pawns, and white pawns to
setup and solve:
Level III: Lessons #17 - #26:
Green Booklet.
Students use the red cubes, blue pawns, white pawns, and
green cubes to setup and solve:
B) THE HANDS-ON EQUATIONS VERBAL PROBLEMS BOOK
More than 300 verbal problems with solutions! Included
in this resource are number, consecutive number, age, coin
and distance problems. Problems are provided for Levels I,
II and III. There are verbal problems in this book for the
student starting out as well as for the advanced students
going into a regular algebra.
Verbal Problems Book
The examples below are taken from the
Hands-On Equations Verbal Problems Book.
This book contains more than 300 verbal problems including
number, consecutive number, age and distance problems for
all three Levels of Hands-On Equations. A sampling of the
types of problems presented in the book is shown below.
Within each section of the book the problems are graduated
in increasing order of difficulty. This makes the book a
valuable resource for teachers in grades 4 to 6, as well
as for teachers of pre-algebra and Algebra I students.
(The number in parenthesis indicates where the problem can
be found in the verbal problems book.)
Level I
1. Kathy's plant grew the same amount in January and
February. In March, it grew 3 inches. If the plant grew a
total of 13 inches during these three months, how much did
it grow during each of the other months? (Page 8/7)
2. Heather can buy 4 pizzas for the same price as 2 pizzas
and 8 one-dollar drinks. How much does each pizza cost?
(Page 9/16)
3. Celeste is 12 years older than Rosa. In four years, she
will be twice as old as Rosa will be then. How old is each
now? (Page 58/17)
4. Charlene has a container 1/2 filled with pennies. She
realizes that if she adds 12 pennies to the container, it
will then be 2/3 filled. How many pennies does the
container hold? (Page 77/18)
5. The average speed of an express train is 14 miles per
hour more than 1/3 the speed of a freight train. In two
hours the express train travels the same distance as the
freight train in three hours. Find the average speed of
each train. (Page 102/18)
Level II
1. The sum of two numbers is 10. Twice the first,
increased by the second number, is 10. Find the numbers.
(Page 27/18)
2. Jim has two lists of three consecutive even numbers.
The sum of the first number on each list is 10. If twice
the second number on the first list has the same value as
the first number on the second list, what are the two set
of consecutive even numbers? (Page 43/18)
3. If Jim's age is added to Sandra's age, the sum is 18.
If twice Jim's age is subtracted from Sandra's age, the
difference is 3. How old is each? (Page 68/22)
4. Charlotte has a total of 18 coins consisting of dimes
and nickels. If the number of nickels is 12 more than the
number of dimes, how many of each coin does she have?
(Page 92/28)
5. Bobby can paddle a canoe at 3 miles per hour. For 1
hour, Bobby paddles with the current and travels 4 miles
further then when paddling back against the current for
one hour. What is the canoe's speed when it travels with
the current? (Page 104/29)
Level III
1. When a number decreased by 4 is doubled, the result is
the same as the number increased by 6. Find the number.
(Page 28/25)
2. Charlotte has two lists of consecutive odd numbers. The
sum of the first number on each list is 10. When the 4th
number on the 1st list is doubled and then subtracted from
the first number on the second list, the result is the
same as the second number from the firs list, decreased by
14. Find the two sets of numbers. (Page 44/28)
3. Ten years ago, Marlene was 6 years older than 1/3rd of
her present age. How old is she now. (Page 60/30)
4. Two-thirds of a collection of 90 coins consists of
nickels. Of the remaining coins, the number of dimes is 10
more than 1/3rd the number of quarters. How many of each
type of coin is in the collection? (Page 78/24)
5. A private plane flying for two hours meets a headwind
that reduces its speed by 20 miles per hour. If it took
the plane a total of 5 hours to travel 440 miles, find the
speed of the plane prior to meeting the headwind. (Page
106/40)
