Summary

This lesson was designed to incorporate visual and kinesthetic aspects of learning how to complete the square of a quadratic formula. This visual aspects of the “tiles” gives students a deeper understanding of what it means to complete the square. While the kinesthetic aspect is a change for students and gives the classroom environment and opportunity to be more appeasing.

Print Settings

Printer Brand:

MakerBot

Printer:

MakerBot Replicator

Rafts:

Yes

Supports:

No

Resolution:

Standard

Infill:

10%

How I Designed This

Using the box and dice objects on Tinker Cad, I was able to create “chocolate bars”, “graham crackers” and “marshmallows” to represent the algebraic tiles within this lesson. These tiles give a fun visual aspect involved in the lesson to increase student engagement. Using specific colors and dimensions, I was able to create the objects to look similar to the themed tiles.

Grade: 10th – 12th
Subject: Algebra 2
Standards: MAFS.912.A-SSE.2.3:
Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression
b. Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.

Lesson Plan

Lesson Plan
• Duration: 42 Minutes
• Learning Objectives: Students will be able to complete the square of a quadratic expression and use that information to determine the maximum or minimum value of the expression. To do that they will move through the following steps.
 Concrete - completing the square using algebraic tiles
 Representational - completing the square using the box method
 Abstract - completing the square using algebraic methods and solving for maximum or minimum
• Prior Knowledge: Students should have an understanding of squaring a number and a term. They should also have a working knowledge of square roots. Students should have a foundational understanding of quadratics and what the maximum or minimum of a quadratic means. They should also understand what the "a" value in a quadratic means in terms of the direction a parabola opens.
• Guided Questions:

What do you think of when you hear the word “square”?
What are the attributes of a square as a geometric figure?
What does it look like when you square a number? A term? An expression?
Addition and subtraction are opposite operations, what is the opposite operation of squaring a number or expression?
• Materials:
o Computer
o Projection
o Note Packet/Worksheet
o Calculator
o Algebraic Tiles
• Instruction:
o Place students into cooperative groups of 3 or 4 prior to beginning the lesson, the concrete phase. Students should be grouped by ability level ensuring one stronger and one weaker student in each group. The teacher will begin the power point presentation working through the lesson and assigning practice to the groups. The teacher will circulate during the group activity providing feedback to students.
o The teacher will move to the next section of the lesson, the representational (box method) phase, and do work on the board. The teacher could direct and have a student do the work. After this section is complete the students will work on some guided practice problems.

o The final piece of this lesson teaches the student how to move from completing a simple square to finding the maximum or minimum of a quadratic using the vertex form of the quadratic equation. This is the abstract piece of the lesson. The teacher will work through the notes and the example problems with the class. After that is complete students will work on practice problems in their groups, in pairs, or individually depending on the class and teacher preference.
• Guided Practice:
o Students will complete the first guided practice activity in cooperative groups using themed algebraic tiles

o After students have learned the box method of completing the square they will complete a guided practice sheet either in pairs or small groups depending on the class.
• Closure: Students will complete a teacher made assessment following completion and review of the practice problems given in class.
• Summative Assessment: The teacher will determine whether or not learning targets have been reached by giving students a teacher made summative assessment.
• Formative Assessment: Teacher will gather information of understanding by observation while circulating during group activity. Misconceptions will be addressed as they are observed.
• Feedback to Students: Students will be given feedback throughout the progression of the lesson. They will receive feedback from:

Their peers are they work in their groups to explore the concepts they are learning.
The teacher during group work and some independent practice as she circulates the room.
Students will receive written feedback from teacher after independent work is turned in prior to summative assessment.
ACCOMMODATIONS & RECOMMENDATIONS
• Accommodations:
o This lesson moves through the stages of learning - concrete, representational, abstract. If a student is struggling in one stage allow them to practice more in the prior stage before moving on.

o Provide students with the work page for pre-made boxes.
Provide students with a copy of the power point and notes per their IEP (Individual education Plan) or Section 504 Plan.

o When grouping students make sure the students who need assistance are with students who will allow them to participate and not shut them out of the group.
• Extensions: More advanced students should be given problems that are more difficult at the beginning of the lesson. They could include problems using more fractions and decimals. The original problems can be adjusted by adding decimal values.

Completing the Square