What's At the Root?

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SWBAT evaluate square roots of small perfect squares and cube roots of small perfect cubes. They will also be able to use the square root and cube root symbols to represent solutions.

Big Idea

Students will build examples of square and cubic numbers to make sense of roots. They will also be able to simplify expressions that use square and cube root symbols.

Warm Up

7 minutes

For today's Warm Up problems, I have included two questions that review concepts learned in previous grades. The first task asks students to write the equation of a line parallel to the one shown. Some students may need scaffolded prompting (e.g., What does parallel mean? What do we know about parallel lines? What is the equation of the given line?  Which part of that equation represents the slope?).  With appropriate questioning, most students will be able to provide an answer. For students who continue to struggle, even after questioning, I invite to tutoring offered during our school's advisory period.

The second problem requires students to recall the relationships formed by parallel lines cut by a transversal. I have an anchor poster hanging the classroom to which the students can refer if needed. I remind students of this resource as I circulate the room offering support during Warm Up. 

Objective/Proficiency Scale

2 minutes

I've included slides with both today's lesson objective as well as proficiency scale.  I review these slides with my students so that they are aware of the end goal of today's work time.

Exploration of Square and Cubic Numbers

16 minutes

Although some students may have previous experience with square and cubic numbers and their roots, the majority lack the conceptual understanding of these numbers. Today's Exploration time provide students the opportunity to interact with these numbers and make sense of them with manipulatives.

First, I ask students to build three or more squares. I then ask volunteers to bring one to the document camera to share with the class.  I record the number of squares used and ask the students to count the number squares used for one side of the square.  I record this number, too, hoping that as I continue, students will begin to see the pattern.  Once students can articulate what qualities make a square number, I ask them to record this information in their journal.  They also record examples of square numbers for future reference.

Next, I ask students to build cubes.  Before students begin, I ask them to describe the qualities of a cube.  I build a rectangular prism under the document camera and to create space for discussion about what constitutes a cube. Then, I ask the student to build at least three cubes using cubes (snap cubes or wooden cubes). Once students have built at least three cubes, I again ask for volunteers to bring an example to the document so we can record its details. Students then record their definition of cubic numbers in their journals write examples for future use.

Work Time

18 minutes

Once students have a working definition as well as manipulatives to support their work, I distribute Venn Diagram Mat and card sets for student pairs and explain the Work Time Activity. Students will spend 10 minute sorting the root cards onto the Venn diagram.  I show an example of each on the SmartBoard so students have a model to work from.  I then set the time and begin circulating the room watching for strategies used by students.

Once the timer sounds, I pull name sticks (from a class set in a cup) to bring students to the front to sort each of the cards onto the Venn diagram on the white board.  This allows student pairs to check their work and typically reveals at least one controversial response.  I then facilitate a class discussion by asking students to justify their thinking.  

Answer Out the Door

2 minutes

For closure, I have created a separate deck of perfect square and cubic numbers.  Students must give a correct response in order to be dismissed.  If a student misses a card, they remain seated and I come back to them with another card. For students who may struggle, I have mixed in smaller numbers that I can turn to so s/he has success out the door.