Lesson: Composing and Decomposing Shapes

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Lesson Objective

Student will be able to compose and decompose shapes.

Lesson Plan

Building Number Sense (5 minutes)

Skip count circle- have students skip count by 5’s or 10’s, be sure and start from a difficult number, unless your class needs to start at 0. Start at 450 or 785. (To make it even harder start at 781 or 232)

Mental Math Fluency (5 minutes)

“Name that shape” Hold up a shape and have students shout out name, you can make it competitive and have two students versus each other or just go through the whole class one student at a time.

Problem of the Day  (7 minutes)

Give a pair of squares to and a pair of isosceles triangles (just call them triangles not “isosceles triangles”) to students.

Use your shapes to create a rectangle and a rhombus. (Problem of the day will be explored in the mini lesson) (If a quick student points out that each of the squares are already “rectangles” then tell them to make a rectangle that is “not a square” or “does not have four equal sides”)

Mini Lesson

(12 minutes)

(The dialogue with “S” can be said by one student who is called on, or better yet, have students pair and share to discuss the answers and hopefully come up with the “S” exemplar answers as pairs)

Teacher (T): How did you make the rectangle?

Student (S): I put together (combined) the two squares.

T: How did you combine them?

S: I put them next to eachother

T: Now that you have a rectangle, could you make a two squares from it?

S: Yes, by spliting the rectangle in half.

T: Exactly, so we can use other shapes to create new shapes and we can also cut up (break down) shapes to make different shapes. There are two special math words for when we do these things, they are decompose and compose. When we decompose a shape we are breaking it down into different shapes (write on chart paper: Decompose-to split a shape into smaller shapes). When we compose a shape we are making a shape from two or more other shapes (write: Compose-to create a shape from two or more other shapes)

T: So with our triangles what shape did we compose?

S: We composed a rhombus.

T: And if we were to decompose the rhombus what shape would we have?

S: If we decompose our rhombus we would have two triangles.

Work Time (Zones, Independent, Group 30 minutes)

Pre-create or have students fold a cut a rectangular piece of paper into a square piece of paper then fold the square diagnollay and then cut down the fold then cut one of the triangles in half, then cut one of those triangles in half. Cut as shown:





So each student should have a rectangle, one large triangle, one medium triangle, and two small triangles.

Have students play with the shapes and compose new shapes from them some examples below:



Trapezoid                          Rhombus          Square       Quadrilateral


After students compose the shapes have them trace the outline onto new paper so the shapes look as below:




Choose students tracings to show to the class. Students then need to use their shapes to compose the shapes, using only the drawing of the outline, you may end up with some non-shapes and interesting combinations, these will work just as well for students learning how to visualize and compare sizes in decomposing and composing shapes for instance you may find a student making a shape like:





This is great but also make sure they compose the “normal” shapes with names and are using attribute words and shape names when composing and decomposing other students shapes.

After student compose other students outlined shapes they should draw on a piece of paper the shape they made and draw lines showing the decomposition, so the four steps are:

Student 1 composes shape                     Student 1 traces outline



Student 2 composes shape with cut up paper



Student 2 makes a drawing of composed shape





This activity can also be done in small groups or pairs where students build shapes and trace the outline then just have their group or pair try to compose the shape using just the outline.

Some questions to ask as students are composing each other’s shapes:

What shapes does the shape decompose into? (i.e. the shape decomposes into two triangles)
What did you use to compose the shape? (I used two triangles)
Is your shape the right size? (some students may use the wrong sized triangles so this will be a question to keep in mind)
What shape was composed by Darrian? (Darrian made a square) What did he compose his shape out of? (Darrian made his square with two triangles) Is there a different way you could compose a square? (Yes with three triangles or four triangles)





Math Reflection/Share (4 minutes)

(This is a time to share work and discuss critically a problem a student had or explain student work. Also this time can be used to ask a difficult question that takes the concept taught one more level up in bloom’s taxonomy)

Can you use circles to compose shapes? Show me with a drawing.
Can you decompose circles into shapes? Show me with a drawing.

(Yes you can use circles to compose shapes but you can’t make any shapes with names, just general “shapes”. You can also decompose circles, but again you don’t end up with two traditional shapes, you end up with two semi-circles)









1. What went well?


2. What would you change?

3. What needs explanation?

Students became very comfortable with composing and decomposing shapes.

Composing with the cut up paper was easy for most kids, but the transferring to drawing was somewhat difficult, so in the first go around make sure you clearly show how to compose and then draw the shape.

Though manipulative are a large part of this lesson students will mostly be tested on drawing and visualizing decomposition so make sure you push them to make the leap from concrete representation (manipulative) to abstract (drawing). My students were comfortable but if yours are not an idea is: get rid of the manipulatives and just show outlines of shapes and have students draw the outline and then draw in lines to decompose the shapes. So if it was an outline of a square they would draw a square and either split it into two triangles, two rectangles, four triangle, four squres, etc.

Lesson Resources

Shape Unit Day 4.doc  


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