Decomposing Areas – Rectilinear Shapes Activity
- Grades
- Grade 3
- Pages
- 8
- File type
- Answer key
- Included
- Subject
- Math, Measurements
- Topic
- Composite Area, Rectilinear Shapes
- Resource types
- Worksheets
- Answer key
- Included
- Standards
- 3. MD.C.7
Product description
From the author
This is a Decomposing Areas Activity Pack.
There are 2 worksheets included.
For the first worksheet, students will:
-Cut out the whole rectilinear shape.
-Then cut (decompose) the whole shape into smaller rectilinear shapes to help determine the area of the whole.
-Each square represents 1 square inch (or 1 in²).
-Draw the outline of each smaller shape they created on the grid at the bottom of the page.
The recording page has space for up to six parts; the possible solution uses five. When they have done so, they will find the total area of the whole rectilinear shape.
An example of a possible solution is included.
For the second worksheet, students will:
-Look at the shapes shown on the graph paper.
-Draw lines to decompose them into squares or rectangles and write the areas of each before adding them up.
-Write their answers on the following page.
-The first one is done for them.
An answer key is included.
Both of these worksheets can be completed independently, in small groups, or as homework.
If this is a skill that has already been introduced and reviewed, this worksheet can be completed independently if you want to take a grade on it. Give students enough time to complete one (or both) of the worksheets without feeling rushed.
If this is a new skill, small groups would be great so that you can informally assess how well students are beginning to master this skill.
Small groups or homework will provide students with the additional practice they may need.
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In the classroom
Teaching tips & learning objectives
Learning objectives
Decompose a rectilinear figure into non-overlapping rectangles
Find the area of a rectangle by counting or calculating unit squares
Recognize area as additive by summing the areas of decomposed parts to find a whole figure's total area
Teaching tips
- Compare different ways of dividing the first shape and explain why the total area stays the same.
- Walk through the model figure before assigning the remaining graph-paper figures.
- Use the log page to organize area calculations while students mark their decompositions on the shapes.
Skills covered
Decomposing rectilinear shapes — students divide a whole figure into non-overlapping rectangles, either by physically cutting it apart or by drawing dividing lines on graph paper.
Area calculation — students find the area of each decomposed rectangle in square inches, using the grid's 1-square-inch units.
Recognizing area as additive — students sum the areas of the individual rectangles they created to determine the whole shape's total area.
Good to know
Questions teachers ask about this resource
Do the two worksheets use the same method for decomposing shapes?
No — the first has students physically cut a shape apart into pieces, while the second keeps the figure intact and has students draw dividing lines on graph paper instead.
Is there more than one correct way to decompose the shapes?
Yes — the first worksheet's own solution page is labeled as just one possibility, splitting the shape into five pieces that total 103 square inches, implying other valid divisions exist.
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Curriculum
Standards, concepts & topics
Standards
Standards
- 3. MD.C.7 — Relate area to the operations of multiplication and addition. a. Find the area of a rectangle with whole-number side lengths by tiling it, and show that the area is the same as would be found by multiplying the side lengths. b. Multiply side lengths to find areas of rectangles with whole-number side lengths in the context of solving real world and mathematical problems, and represent whole-number products as rectangular areas in mathematical reasoning. c. Use tiling to show in a concrete case that the area of a rectangle with wholenumber side lengths a and b + c is the sum of a × b and a × c. Use area models to represent the distributive property in mathematical reasoning. d. Recognize area as additive. Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the nonoverlapping parts, applying this technique to solve real world problems.
Core concepts
Core concepts
Area
Decomposing shapes
Rectilinear figures
Additive area
Topics
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