Grade: 5/6

Lesson Title: Area and Perimeter Relationships

Date: Mar 28

Curriculum Expectations Grade 5- create through investigation using a variety of tools and strategies, two-dimensional shapes with the same perimeter or the same area and determine, through investigation using a variety of tools and strategies, the relationships between the length and the width of a rectangle and its area and perimeterGrade 6-construct a rectangle, a square, a triangle, and a parallelogram, using a variety of tools, given the area and/or perimeter

What do students need to know and be able to do? -conceptual understanding of what area and perimeter are as well as familiarity with the terms-procedures (including formulaic ones) for determining area and perimeter of rectanglesLearning GoalsContent:Students will

create a variety of rectangles with the same area

analyse what happens to the perimeter as the dimensions of the rectangle change

Process:• We will select and use a

variety of concrete learning tools and appropriate computational strategies to investigate mathematical ideas and to solve problems.

• We will communicate mathematical thinking orally, visually, and in writing, using everyday language, mathematical vocabulary, and a variety of representations.

Lesson Components Anticipated Student Responses and Teacher

Prompts / QuestionsAction!

Task:

Create at least 3 different rectangles with the same area.

Explain what you notice about the perimeter of your shapes.

Anticipated Student Responses and Possible Misconceptions

1. Different rectangles can have the same area.

2. Rectangles with the same area can have different perimeters.

3. The longer the rectangle, the greater the perimeter; the more “square” the rectangle the smaller the perimeter.

4. Strategies for determining area include: counting squares, trial and error of multiplication facts, using factors of the area

Possible Misconception:

transferring geoboard representations onto grid paper; dot paper thought to be a more accessible toolSample Scaffolding Questions How else can you represent this?How are these ___the same or different?If I do ____, what will happen?How can you prove your answer or verify your estimate?How do you know?Have you found all the possibilities? How could you arrive at the same answer in a different way?

Minds-On AFL

1) Review vocabulary of area and perimeter. Ask students to define them. Record their definitions.

2) Ask a volunteer to show where we see the area and the perimeter of a concrete object (book).

3) Have students name the types of units they use to describe area (square units) and perimeter (linear units)

What are we listening and looking for from the student conversation and responses?

Area implies amount of surface covered by an object. Students run their hand over the surface of their desk. Area is the distance around an object. Students trace the outer edge of their desk to show its perimeter.

Lesson ComponentAfter / Consolidation / Reflecting and Connecting

Consolidation Highlights and Summary(Uncover Learning Goal, Success Criteria)

Clarify and support students in their use of some of the Math manipulatives, especially the grid paper as a tool, bringing out the ideas that it can be used to show scale (eg. 1 square on the paper represents one square unit)

These students traced centicube representations which made recording a challenge. They also noticed that the perimeter is different with every shape.

These students accurately created rectangles using a cm ruler to measure out the sides, rather than use the grid paper as a tool. They used multiplication of side lengths to determine/check the area.

The work of the group above showed that they were able to represent their geoboard

representation using the grid paper, where one square unit on the geoboard was one square on the grid. They used addition of side lengths to determine perimeter.

This group’s work also led the discussion about how a rectangle that is 3 x 4 is congruent to a 4 x 3 rectangle. It is simply rotated.

This groups work also showed the same idea as above, this time looking at a 4x2 and a 2 x 4 rectangle.

A) Two rectangles with the same lengths and widths will have the same area and perimeter AND are congruent. They are not two different rectangles.

B) As the length of the perimeter increases the width decreases.

Independent Practice: Exit Card Reflection Homework

Student Next Steps (Large Group/Small Group/Individual)

Exit Card

Three rectangles of equal area are on paper.

Determine perimeters.Describe what you notice about the perimeter of the rectangles?

Next Steps: Whole Group

1. Explicit instruction and Practice using tools:

geoboards; transfer to dot paper to represent what they see on geoboards (that each dot is one peg on the geoboard)

grid paper (use the

squares on the grid to represent the square units in their manipulative representation; scale)

2. Hands on opportunities to continue exploring how changes in the perimeter are determined by changes in the length and width without changing area.

3. Continue to develop math vocabulary and encourage math talk in small groups

4. Do the exit card, then move to other shapes, connecting to this learning.

Small group support – address confusion of area and volume