Summary
Students are challenged to create a perfect square with 10 tiles. They will discover which numbers can make a perfect square and what to do when it’s not a perfect square.
Essential Question(s)
How does the area of a square relate to the length of its side?
Learning Objectives
Identify the relationship between a square’s side length and its area
Identify the first 20 square numbers and their square roots
Estimate irrational square roots between perfect squares
Snapshot
Engage
Students create a claim and argue opposing viewpoints.
Explore
Students explore how to make perfect squares.
Explain
Students distinguish between rational and irrational numbers and estimate square roots.
Extend
Students participate in “Beat the Calculator” to estimate and correctly place square roots on a number line.
Evaluate
Students complete an exit ticket based on a real-world situation applying and explaining rational & irrational numbers.
Materials
Lesson Slides (attached)
Trifold handout (attached; one per student)
Square Numbers handout (attached; one per student)
Beat the Calculator Cards (attached; one per group)
Exit Ticket handout (attached; one per student)
Square color tiles (20-50 per student)
Sticky Notes (one stack per group)
Markers
Number Lines (optional)
Preparation
Engage
Posters placed in the room: “Cereal is a soup” “Cereal is not a soup”
Trifold handout: Print and fold before the lesson.
Explore
Square color tiles: Prepare individual bags with the desired amount of tiles for each student.
Explain
Number line: Prepare a number line on each of the four walls in your classroom for students to engage with.
Engage
15 Minute(s)
Use the attached Lesson Slides to follow along with the lesson. Begin with slide 3 and briefly read aloud the essential question: How does the area of a square relate to the length of its side? Then, move to slide 4 and read the objectives.
Transition to slide 5 and ask students to take out a piece of paper. Pose the following prompt:
Is cereal a soup?
Ask students to first write down their claim. Then, have them have them provide 1-3 pieces of evidence that support their claim.
Next, display slide 6 and explain to students that they will have a short debate over this topic. Direct students' attention to the posters on the wall, one that says “Cereal is a soup” and the other that says “Cereal is not a soup.” Ask them to move to the poster that their claim matches. Review expectations and debate guidelines with students.
Once students have debated the topic and are familiar with the format of a debate, ask them to return to their seats.
Move to slide 7 and pass out the attached Trifold handout to each student. Review the C.E.R.T.I.fy Your Thinking instructional strategy with students. Ask them to make a claim in response to the following question:
Is a square a rectangle?
Students should write their claim followed up with evidence and reasoning in the space provided on their trifold.
While students work on this, cover up the current signs on the wall with two signs stating “A square is a rectangle” and “A square is not a rectangle.”
Facilitate a debate following the same format with students over this topic.
End by explaining the conclusion that a square is a special type of rectangle that has to have 4 equal sides. All squares are rectangles, but not all rectangles are squares.
Explore
15 Minute(s)
Have students gather 30-50 color tiles.
Display slide 8. Challenge students to create a perfect square with exactly 10 color tiles. Play the one-minute timer and allow students individually to work through this challenge. Once they realize this can not be done, explore which area of tiles can create perfect squares.
Review slides 9 through 11 to explore different examples of squares.
Transition to slide 12. Pass out the attached Square Numbers handout to each student. Ask them to create and record perfect squares and their side lengths. Once a pattern is found, have them record all square numbers from 1-400.
Move to slide 13 and pose discussion questions and invite students to share their thoughts.
Explain
15 Minute(s)
Display slide 14 and direct students' attention to page 3 of their trifold. At the top of the page is a number line. Ask students to write the corresponding square root under each whole number on the number line.
Review the terminology with students on slides 15 and 16 and have them fill it in on their trifold.
Display slide 17 and review the following questions with students:
How does a square’s area relate to its side length?
What if a perfect square is impossible?
Play the 30-second timer and ask students to discuss these questions with their elbow partner. Then, invite students to share out their responses.
Take the next few minutes to use the number line to estimate irrational square roots.
Using a classroom number line on the wall, students will use sticky notes to place on the corresponding whole numbers (square root of 1 to square root of 400, placed on the whole numbers 1-20 on the number line). This will be a shared classroom number line that can be left up for student reference for however long the teacher sees fit.
Use the whole-class number line to model the following:
Model the example of a square root of 150. Ask students the following guiding questions to think about and respond to:
Is this on the number line?
Between which two perfect squares would 150 fall?
Students should determine that it is not on the number line and that 150 would fall between 144 and 169, which is the square roots of 12 and 13.
Ask students:
Is this on our number line (no)?
Between which two perfect squares would 150 fall?
They should see that it would fall between 144 and 169, which is the square roots 12 and 13.
Next, have students place sticky notes with a square root of 150 on the number line around where they would believe it would fall.
Practice locating and estimating non-perfect square numbers on the number line
Transition to slide 18 and tell students they are to complete the exercise provided on page 3 of their trifold. Explain to students that they will be reflecting on examples of non-perfect square roots and how to estimate them. Allow students time to complete the exercise. Circulate the room and provide support and guidance as needed.
Extend
30 Minute(s)
Move to slide 19 and place students into four teams. Invite students to play “Beat the calculator”. Explain to students that they will estimate an irrational square root on a number line. Teams will race to place a post-it note on their designated number line.
Assign specific wall space with a numberline for each group and have them face it.
Pass out a stack of sticky notes to each team.
When the teacher announces a square root, explain to students that they should write down on their sticky note the estimation of the irrational square root rounded to at least two decimal places.
Using the attached Beat the Calculator Cards, randomly choose a card and announce the square root on it. Have teams agree on a decimal estimation and write it on their sticky note. Then, ask their group’s “runner” to place the sticky note on the number line in the correct location between the two whole numbers.
Encourage students to pay attention to which whole number their decimal would lie closest to. Designate a class “calculator” who will use an actual calculator to determine the team with the closest estimation.
Evaluate
10 Minute(s)
Pass out the attached Exit Ticket handout to each student. Review the two questions on the handout and allow students time to work on it individually.
Collect completed handouts.
Resources
K20 Center. (n.d.). Claim, evidence, reasoning, test, improve (C.E.R.T.I.Fy your thinking). Strategies. https://learn.k20center.ou.edu/strategy/827
K20 Center. (2021, September 21). 30 Second Timer. YouTube. https://youtu.be/o9ViOMe_Wnk?si=la-FBoMrLAFNHl02
K20 Center. (2021, September 21). 1 Minute Timer. YouTube. https://youtu.be/6ilD555O_RE?si=_xfHcHI15ruuWbU1