低齡學習者代數 - 有趣、具體的方法（1 級）

The Hands-on Equations program was developed by Dr. Henry Borenson as a way to give younger children access to understanding algebra concepts in a fun and concrete way. Borenson is known as the man who “made algebra child’s play.” 

In this class, learners will be introduced to the process of solving algebraic equations using a physical and visual model to solve for unknown variables. We will take abstract problems and turn them into problems that are concrete and easy to understand. Learners will leave this class with the confidence needed to tackle algebra while feeling proud of their ability to solve big kid problems! 

Learners will need to come to each class with hands-on equations materials. This is an absolute must for learners to get the most benefit from this class. You can either purchase a student kit online or print and create your own materials using the provided printable handouts. Printable activities will be available upon enrollment and should be downloaded and printed prior to class if you choose not to purchase the Hands-on Equations student kit. A link to the Hands-on Equations student kit will also be provided upon enrollment. I do highly recommend the Hands-on Equations kit!

Level 1 of Hands-on Equations introduces learners to the process of solving simple linear equations such as 3x + 2x + 4 = 20 + x or 2(2x + 3) = x + 9 where there is an unknown variable that must be isolated and then solved. Learners will use pawns and number cubes to represent algebra problems on a balance scale image. They will then simplify and solve for the unknown variable using a prescribed process. The class atmosphere will be fun and engaging for learners!

This class meets the NCTM Numbers and Operations standard for Mathematics Grades 3-5: Students will develop an understanding of algebra, problem solving, communication, and representation. Specifically, students will be able to:
•	Represent the idea of a variable as an unknown quantity using a letter or a symbol
•	Develop fluency in adding, subtracting, multiplying, and dividing whole numbers
•	Select and use various types of reasoning and methods of proof
•	Create and use representations to organize, record, and communicate mathematical ideas
•	Apply and adapt a variety of appropriate strategies to solve problems
•	Use the language of mathematics to express mathematical ideas precisely
•	Communicate mathematical thinking coherently and clearly to peers and teachers

The Hands-On Equations method was designed for young learners in grades 3 and up. This class is also appropriate for highly gifted young learners (2nd grade). Learners should have a strong foundation in basic addition and subtraction and should understand multiplication and have a beginning sense of multiplication facts through 12. This is a great class for accelerated learners who need a little more from their math classes. It’s also perfect for learners in grades 3-5 who are ready to begin solving basic linear equations. 

Learner progress will be evaluated both inside and outside class time. I will carefully observe each learner's ability to use the discussed strategies to solve problems in class. And, in order to fully benefit from this class, learners will complete an activity sheet after each lesson. This homework will correspond with the skills learned in each lesson. Grades can be provided for learners upon request.

Week 1: Learners will be introduced to the Hands-on Equations game pieces, including the balance scale, pawns, and number cubes. Learners will begin to explore the concepts of equations, variables, and unknowns. Learners will explore the process of solving linear equations using the Hands-on Equations method. (HOE Lesson 1 and HOE Lesson 2).

Week 2: Learners will continue exploring the process of solving linear equations using the Hands-on Equations method. Learners will be introduced to “legal moves” to help them solve equations. (HOE Lesson 3 and HOE Lesson 4).

Week 3: Learners will continue exploring the process of solving linear equations using the Hands-on Equations method. Learners will use “legal moves” to help them solve equations. They will also discover the distributive property through solving equations such as 2(2x + 3) = x + 9. (HOE Lesson 5 and HOE Lesson 6).

Week 4: Learners will continue exploring the process of solving linear equations using the Hands-on Equations method. Learners will use “legal moves” to help them solve equations. Learners will transfer their concrete, hands-on experience in solving algebraic linear equations to a pictorial system involving only paper and pencil. We will conclude this week by solving fun word problems using the Hands-on Equations method. (HOE Lesson 7 and HOE word problems).