Perfect Squares and Square Roots

Strand: Number
Outcomes: 1 and 2

Step 5: Follow-up on Assessment

Guiding Questions

What conclusions can be made from assessment information?
How effective have instructional approaches been?
What are the next steps in instruction?

A. Addressing Gaps in Learning

Review the concepts of perfect squares and their square roots by having students work with models, such as tiles and grid paper.
Provide time for students to reflect on their learning when using graphic organizers, such as the Frayer Models or Concept Definition Map.
Make sure that students are solving problems by drawing pictures and providing explanations to justify their thinking.
Remind students to use their divisibility rules to find factor pairs. Encourage students to write the factor pairs in an organized list to help determine the square root. If students are having difficulty identifying factors, you may want to provide them with multiplication tables.
Provide opportunities for students to develop number sense by encouraging them to refine their estimates of the square roots of non-perfect squares.

B. Reinforcing and Extending Learning

Students who have achieved or exceeded the outcomes will benefit from ongoing opportunities to apply and extend their learning. These activities should support students in developing a deeper understanding of the concept and should not progress to the outcomes in subsequent grades.

Consider strategies, such as the following.

Activity 1: Using 1 cm dot paper and square tiles, have students draw all the possible rectangles that will have an area of 60 square units. Challenge students to determine the number of rows that have to be added or removed to change each rectangular model into a square.

Activity 2: Students could play the game "Approaching the Root" with 3- or 4-digit numbers.

Activity 3: Solve the following problems. Solutions should contain diagrams and written explanations.

Fencing
Mattie is planning to fence a portion of her yard to create kennels for her three dogs. She wants the space large enough so there will be 4 m2 of space for each dog.

What should be the area of the fenced section?
Mattie would like the kennel to be a square. Approximate the length of each side of the fence needed to create a square fence.
How much fencing will be needed to create the kennel?
Chain-link fencing requires a support post at every corner and at least at every metre. Sketch a diagram of the kennel, including where you place the support posts.
Metal support posts cost $7.99 each and chain-link fencing costs $12.95/m. Determine the cost of materials to build the dog kennel.

Installing Carpet
A hotel wants to install an area carpet in the lobby of the hotel. The hotel lobby is 12 m by 8 m. They want the carpet to be square and fill not more than 80% of the lobby area.

What is the maximum area the carpet can cover?
What are the dimensions of the square carpet, to the nearest centimetre, that the hotel needs to order from the carpet company?