- Hands on Equations–Making Algebra Kids’ Play
Beginning Hands-on Equations: Monday-Thursday at 9:00am
(12 classes; 75 minutes per class; 9:00am – 10:15am)
6/29, 6/30, 7/1, 7/2 7/6, 7/7, 7/8, 7/9 7/13, 7/14, 7/15, 7/16* 7/17 (*No class on 7/16. It will be made up on 7/17 @9am)
Advanced Hands-On Equations: Monday-Thursday at 9:00am
(12 classes; 75 minutes per class; 9:00am – 10:15am)
7/20, 7/21, 7/22, 7/23 7/27, 7/28, 7/29, 7/30 8/3, 8/4, 8/5, 8/6
Singapore Math Group class: Monday @10:30am (10:30-11:30am)
(6 classes; 60 minutes per class; 10:30-11:30am)
6/29, 7/6, 7/13, 7/20, 7/27, 8/3
Singapore Math Group class: Thursday @2:00pm (2:00-3:00pm)
(6 classes; 60 minutes per class; 2:00-3:00pm)
7/2, 7/9, 7/16* 7/17, 7/23, 7/30, 8/6 (*No class on 7/16. It will be made up on 7/17 @2pm)
Making Algebra Child’s Play
This class will prepare your children for Pre-Algebra class.
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
- 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
Word problems is the focus!
We spend 90% of the class time to deal with word problems with blocks/manipulatives!
A) HANDS-ON EQUATIONS LEARNING SYSTEM
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: Students use the red cubes and blue pawns to setup and solve:
Level II: Students use the red cubes, blue pawns, and white pawns to setup and solve:
Note: “Star,” written as “*”, is a new mathematical notation developed by Dr. Boremson. Star is another name for “the opposite of x,” normally written as “(-x)”.
Level III: Students use the red cubes, blue pawns, white pawns, and green cubes to setup and solve:
**Due to the time limit, we’ll only be able to cover Level 1 in these 10 sessions.
B) 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.
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?
2. Heather can buy 4 pizzas for the same price as 2 pizzas and 8 one-dollar drinks. How much does each pizza cost?
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?
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?
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.
1. The sum of two numbers is 10. Twice the first, increased by the second number, is 10. Find the numbers.
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?
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?
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?
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?
1. When a number decreased by 4 is doubled, the result is the same as the number increased by 6. Find the number.
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.
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?
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.