Deepening our understanding

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SWBAT use manipulatives to better understand the concept of solving equations and evaluating expressions

Big Idea

Hands on Equations is the miracle drug to saving Algebra

Do Now

15 minutes

To begin this lesson, I'm going to have students use the game 24.  I like this game because they can solve it mentally, but I like them to write the expression to reinforce the concept of parenthesis.  24 works like this.  The students are given 4 numbers.  They need to use all 4 numbers to make the number 24.  They can add, subtract, multiply or divide.  24 is a game that can be purchased for use in the classroom.

Here's an example:

6 5 1 1:  Students could write the following expression.  

6 x 1 x (5 - 1)

Then they would solve their own expression using orders of operations and see if they made 24.  The nice thing about this activity, is that there are more than one way to solve.

24 reinforces MP 1 by looking for an entry point and MP 6 because they need to use precision when they are writing their expressions.


Using Hands on Equations to deepen their understanding of Algebra

60 minutes

Hands on Equations is a kit that can be purchased for use within the classroom.  The theory behind HOE is that the students will develop a concrete, conceptual understanding of equations and expressions.  HOE can be used at anytime during the expressions and equations strands of common core.  I chose to use it right after I taught orders of operations and exponents.  I will be bring it back again when we start solving equations. 

Here's how it works: a snapshot of students talking HOE!

Student kits

blue pawns

white pawns


paper balance

Teacher kit:

Larger version of the student kit along with a balance for the presentation.

The teacher starts by showing the students that the pawn represents (x).  The term variable is NOT used as this can be confusing to kids. The first examples are easy.

x = 5, therefore 5 = 5

x = 2, therefore 2 = 2


x + 1 = 5, therefore x = 4, check 4 + 1 = 5, so 5 = 5

The problems become more complex quickly.

See example.

Students in 6th grade can go up to Lesson 7 which shows examples of the Distributive Property.  All examples, for now, are using positive numbers and addition. 

If your school cannot purchase the kits for you, you can find some examples of the lessons online. The kits can be easily be created by using chips instead of pawns and regular dice.  If you have access to dice with numbers on them that would be better so students can easily translate the quantity. 


10 minutes

To bring this lesson to a close, I'm going to have the students reflect and write about their learning.  I will give them an example of an equation and have them explain to me in words how they would go about solving.  Reflecting and writing is a good way for students to internalize their learning. You can collect this to get a good feel for the level of understanding among your students.