Grade: 6

Lesson Title: Area of Triangles and Parallelograms

Date: March 28

Curriculum Expectations ~ Construct a rectangle, triangle, square and parallelogram using a variety of tools given the area.

What do students need to know and be able to do? ~ understand the attributes of a parallelogram and triangle. ~ know and be able to determine the area/ formula to find area.~ understand that area is measured as a square unit.

Learning GoalsContent:Construct polygons when provided the area

Process:Solve problem reflecting on their prior knowledge of area. Students make connections between the area and dimensions of different polygons.

Lesson Components Anticipated Student Responses and Teacher

Prompts / QuestionsAction! ~ A polygon has an area of 36 square units. How many different parallelograms and triangles can you construct and what would be their dimensions?

Anticipated Student Responses and Possible Misconceptions~ finding area (using factors of 36 to determine the side lengths)~ counting wholes, miscounting halves (fractions of a whole)~ use of square unit rather than linear unit~ mix up perimeter and area~ focus on rectangles

Questions for Comparing~ Is a square a rectangle? ~ How is a triangle different than a rectangle?~ How is a parallelogram different than a rectangle?~ How do the areas compare?~ How are these figures the same or different?

Strategies Used to find AREA:~Counting the units inside the shape~ Multiplying the side lengths ~ Counting ½ units together as 1 whole unit.~ trial and error to determine correct dimensions~ add up all side lengths: perimeter~ Counting to determine area ~ Use formula (Length x width) or triangle formula~ develop a pattern: create a chart.

Sample 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~ A variety of shapes are given on the Smartboard. Some polygons fit the criteria whereas others don’t. Students are asked to find the area of each triangle and parallelograms.

~ The concepts that will elicited... attributes of a triangle and parallelogram, formula for area, dimensions, the concept of area, factors of a number, and square units of measurement.

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

~ base, height, area, square units~ parallel lines~ concept of a triangle having half the area of the rectangle with the same base or height.~ formulas

Lesson ComponentAfter / Consolidation / Reflecting and Connecting

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

~ Students will take a gallery walk of six target pieces. (selected based on strategies (e.g. factors, guess and check), types of shapes represented, different dimensions represented

~ Factors of 36 were evident.~ Knowledge of formulas for area.~ Knowledge of parallelograms and of triangles. ~ Understanding of what area is.~ Limited understanding of strategies needed to construct triangle with a given area.~ Beginning understanding of that different polygons and/ or different dimensions can give you the same

area.

~ Students will be asked to post 2 “I wonder...” statements on selected student work.~ Students, from specific groups, will respond and share their thoughts with the class.~ Teacher monitoring will ensure that the concepts are brought out and aligned with the learning goal.~ Teacher posted “I wonders..” may need to be added. ~ Learning goal elicited and posted. from student responses.

Some examples of “I wonders: ~ Why is the height so much bigger than the base?~ Why is the value of 72 used with the triangle?~ Is there another dimension for the square?~ How did you determine the dimensions for the rectangles / parallelograms?

Independent Practice: Exit Card Reflection Homework

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

~ Students will work independently on the learning task.

Task:~ Decide on a two digit number for an area. ~ Construct a triangle and a parallelogram with this area. You may not select a rectangle. ~ Label your drawing with the dimensions.

~ Determine if beginning and limited understandings explained above have improved.~ Target students accordingly.