Guided Practice: What activities or exercises will the students complete with teacher guidance?
Students should work in groups of 3 or 4. Each student needs 1 or 2 half sheets of geo-dot paper, rulers, pencils or markers, and scissors. The text in quotes below is example dialogue the teacher may choose to use with students.On white board, write: "Quadrilateral: A polygon with four sides and four angles."
"Today we're going to take a closer look at quadrilaterals. In your group lean in and brainstorm the names of as many quadrilaterals as you can think of in one minute." Circulate and listen in on brainstorming, provide feedback and prompts when necessary.
After one minute, "OK, good work. Now I am going to give you five minutes to draw the quadrilaterals your group has named, and any others you can come up with. Talk to each other about who will draw what so that there are no duplicates in your group. Use the dots on the geo-dot paper and your rulers to make an accurate drawing of your quadrilaterals. Make it large enough that you can label it with its name. When you are happy with your drawings, cut them out carefully." These instructions are paraphrased in the power point on Slide 13. Allow five minutes for students to work, circulate and assist where necessary.
Depending on the student level and fluency regarding quadrilaterals the teacher might, at this point, choose to display the definitions of specific quadrilaterals such as the chart on Slide 14 of the A Closer Look at Quadrilaterals power point. Ask "Who has a rectangle?" Display the rectangle on the white board and ask: "What are the properties of a rectangle?" Accept and list all reasonable answers on the white board, in the language students offer, such as:
Opposite sides are the same.
The teacher should question and adjust where necessary.
- How can we make "4 angles" more specific? (4 right angles, 4- 90° angles.)
- What is mathematical vocabulary for "the same"? (Congruent, opposite sides are congruent.)
- What other properties of the opposite lines can you see? (Opposite sides are parallel.)
The final list on the board should be: Rectangle-
4 right angles,
Opposite sides are congruent and parallel.
On the board, draw a large double t-chart (3 columns). Title the chart "Quadrilaterals". One column should be headed "2 pairs of parallel sides", another "1 pair of parallel sides", and the third "No parallel sides".
Ask: "If I want to classify this rectangle based on parallel lines, where should I put it?" Use tape or magnets to post the rectangle in the first column, "2 pairs of parallel sides". "Who would like to post another quadrilateral on our chart?" In this fashion, continue until students have posted all quadrilaterals in the appropriate columns.
If students are familiar with the term "parallelogram" say: "What would be a more appropriate heading for the column we have labeled '2 pairs of parallel sides?'" (Parallelogram) Write parallelogram above "2 pairs of parallel sides".
If students do not know what a parallelogram is the teacher may use power point Slide 17, which is a graphic organizer defining parallelogram, and/or say: "Any quadrilateral whose opposite sides are parallel and congruent is called a parallelogram."
Write parallelogram above "2 pairs of parallel sides". "What quadrilateral has '1 pair of parallel sides'?"(Trapezoid) Write trapezoid above the second column, "1 pair of parallel sides".
If students are familiar with the term trapezium, say: "What about the third column, is there a word that means 'no parallel sides' for quadrilaterals?" (Trapezium) Write trapezium above "No parallel sides".
If students are not familiar with the term trapezium the teacher may use power point Slide 18, which is a graphic organizer defining trapezium, and/or say: "Mathematicians also have a word for a quadrilateral that has no parallel sides; that quadrilateral is called a trapezium." Write "trapezium" above "No parallel sides".
If he or she has not already done so, the teacher may choose this time to display Slide 14 on the power point which defines individual quadrilaterals, or display any chart defining quadrilaterals.
Continuing with the double t-chart, point to the first column.
Say: "How do we know that all of these quadrilaterals are parallelograms?" Accept and discuss all reasonable answers. (All of them have opposite sides that are parallel and congruent.) "So we know that rectangles, squares, and rhombuses are quadrilaterals that are parallelograms. Think about all of the properties of rectangles and squares."
"Lean in and talk about it with your group; are all squares also rectangles?" Allow time for small groups to discuss and debate, then call for an answer: (Yes, a square has 2 pairs of congruent sides, 2 pairs of parallel sides, and 4 right angles.)
"Are all rectangles also squares?" (No, many rectangles do not have 4 congruent sides.)
"Let's look at the relationship between squares and rhombuses. We have proved that they are both quadrilaterals that are parallelograms. Is a square also a rhombus? Lean in and talk about it." Again, allow time for discussion and debate, and then call for an answer. (Yes, a square is also a rhombus; it has 2 pairs of parallel sides, the sides are congruent, and there are 4 angles.)
"Is a rhombus also a square?" (No, many rhombuses do not have 4 right angles.)
Independent Practice: What activities or exercises will students complete to reinforce the concepts and skills developed in the lesson?
Students will write "Sometimes, Always, Never" statements and trade with classmates to solve them. The teacher may provide index cards or notebook paper for this activity.
Students should leave the answer space blank, but write their answer (sometimes, always, or never) on the back of the card.
Write on white board "Sometimes, Always, Never". Say, "We are going to spend a few minutes expressing what we have learned by writing Sometimes, Always, Never statements."
Write on white board to model for students:
A trapezoid is ___________________ a parallelogram. "What word belongs in the blank?" (never)
Allow a few minutes for students to write Sometimes, Always, Never statements, then an additional few minutes for them to trade with classmates.
Possible student responses:
- A rectangle is ____________________ a square. (sometimes)
- A square is ___________________ a rectangle. (always)
- A trapezium is ______________________ a quadrilateral. (always)
Circulate to prompt and support the students, encouraging them to use the lesson vocabulary as well as prior knowledge in their statements.