Solving Two-Step Equations:Integrating Manipulatives and NUA

Strategies

Algeblocks® Lab 9-6 (High School)

Lab 6-5 (Middle School)

Objective: To solve equations requiring two or more steps. Materials:

Algeblocks® (x blocks and unit blocks) Sentence mat Colored cubes (4 different colors) Envelopes with various equations (one

and two-steps) Flow Maps with steps for solving

equations Post-its (Exit Survey)

Community Builder: Four Corners

Preset the 4 corners in the room (sports, color, number, season, etc.)

Ask a question to get students to the corners (i.e. What is your favorite color?)

Give directions for task (List-Group-Label) Ask another question to move groups to

new corners (i.e. What operation do you feel the most like today? Why?)

Reflection

Flow Map: Agenda

Community Builder:

4 Corners

Activity:List-Group-

Label

Flow Map:

Agenda

Problem of the Day

(POD)

Teach the Lesson:

Algeblocks®

Activity:Flow Maps

Reflection

Exit Survey

Introducing the Lesson(Problem of the Day)

1. X – 3 = -82. x = -5

3. -4x = -12How many “x’s”?Divide into ___

groups.1. -x = -32. X = +3

+

=

+

- -

Step 1: Set-up the Equation2x – 5 = 3

+

=

+

- -

Step 2: Add the same number of blocks to each side to make zero

pairs.2x – 5 = 3

+

=

+

- -

Step 3: Remove Zero Pairs from both sides (if needed).

2x – 5 = 3+

=

+

- -

Step 4: Ask, “How many x’s are there?”

Answer: ____Divide unit blocks into ___ groups.

+

=

+

- -

Flow Map Activity Model of One-Step Equations

Concrete Pictorial Symbolic Create Flow Maps of Two-Step

Equations Concrete,Pictorial, and Symbolic

Remember left to right One step per box Arrows in between each box

Flow Maps: One-step Equations

WordsSymbolic

Model the

equation

Add the same number to

each side to make zero

pairs

Remove zero pairs

Record the

answer

3 + x = 1 3 + x = 1

(+) -3 =-3X = 1 + (-3) X = -2

Flow Maps: One-step Equations

WordsSymbolic

Model the

equation

Ask: “How many “x’s?”Divide (unit

blocks) by the answer.

Remove all but ONE group from EACH

side.

Record the

answer

4x = 16There are 4

x’s 4x = 164 4

X = 4

Exit Survey

Solve the following equation on an index card. Remember to put your name at the top:

3x + 7 = -20

Model the equation

Add the same number of unit blocks to each side of

the mat.

Remove Zero Pairs from each side of the

mat.

Count unit blocks left and record your

answer.

Model the equation on the sentence mat.

Ask: “How many “x’s?”Divide (unit blocks) by

the answer.

Remove all but ONE group of blocks from

EACH side.

Count the number of unit blocks and record the

answer.

3 + x = 1

3 + x = 1 (+) -3 -3

3 + x = 1 (+) -3 -3 x = -2

3 + x = 1 x = -2

4x = 16

4x = 16 4 4

4x = 16 4 4

4x = 16 x = 4