Grade 3 · Math · Unit

Area and Perimeter

8 lessonsabout 4 weeks

The unit ends with three more days: a review day, the unit check, and a day to act on what the check showed.

Unit 6 of 8 in the Grade 3 Math Scope and Sequence

What's included in this unit

8 lessons in teaching order, each with its objective and a teacher note
24 practice pages to print, with an easier and a harder page where available
2 classroom tools for the projector
5 activities and pages that children do on a screen
8 check-up pages to collect

The whole unit in one file

Print every page of the unit at once, with the teacher guide first. The guide has one page per lesson: the objective, what to hand out, and the teacher note.

Teacher guide only (PDF)

The unit file, the teacher guide, and saved pages are included with the Teacher plan.

Your PDF is built in your browser, so it always has the newest version of every page.

Lessons

Lesson 1

Area: count the squares

Children find the area of a rectangle by counting its squares in rows and finish the multiplication for it.

StandardCommon Core 3.MD.C.7.aMeasurement and Data

3 class days

Day 1Teach: The Baking Tray · Practice on paper (Core page)
Day 2Practice and check: Practice on paper (Easier page, Harder page) · Practice on screen · Check-up page
Day 3Reteach and extend: Act on the check-up pages: reteach the children who are not there yet, with the tool and a new page from the maker; the others take a harder page.

Lesson 2

Area of a rectangle: multiply the side lengths

Children find the area of a rectangle by multiplying its two side lengths and say the area with its square unit (24 square feet).

StandardCommon Core 3.MD.C.7.bMeasurement and Data

2 class days

Day 1Teach: The Baking Tray · Practice on paper (Core page)
Day 2Practice and check: Practice on paper (Easier page, Harder page) · Check-up page

Warm up and teach

Open The Baking Tray on the projector.

Practice on paper

Area of a Rectangle: Multiply the Side Lengths
Core page Easier page Harder page

Check-up page

One more page of Area of a Rectangle: Multiply the Side Lengths to collect at the end of the lesson.

Teacher note

Common mistakes: Children add the two side lengths, or add all four sides (they find the perimeter). Others multiply correctly and say the unit of length: "24 feet" for 24 square feet.
Words to use: On the Baking Tray, set 4 rows of 6 buns: "How many buns? We don't have to count them one by one: 4 rows of 6 is 4 × 6." Give the tray a quarter turn: "6 rows of 4. Still 24." Draw a rectangle on the board and write 6 ft on top and 4 ft on the left side: "This time no squares are drawn. Picture squares 1 foot on each side. How many fit along the top? How many rows?" Write 4 × 6 = 24 and say the unit: "24 square feet. A square foot is a square that is 1 foot long and 1 foot wide."
What to watch for: On the easier page, the squares are still drawn in each rectangle, so a child can check the product by counting. On the page for everyone, only the two side lengths are written. Either order of the two factors is right (6 × 4 or 4 × 6). On the harder page, the sides go from 4 to 10, and two cards show a question mark on one side and print the area ("Area = 54 square meters"): the child finds the side. A child who multiplies 9 × 54 has not read the equation: ask, "What number times 9 makes 54?" The unit changes from card to card, and the area unit is printed with the boxes: have children read it aloud with their answer.

Lesson 3

Same area, different shape

Children compare rectangles and circle the one that covers the same number of squares as another.

StandardCommon Core 3.MD.C.6Measurement and Data

2 class days

Day 1Teach: Practice on paper (Core page)
Day 2Practice and check: Practice on paper (Easier page, Harder page) · Practice on screen · Check-up page

Practice on paper

Same Space, New Shape
Core page Easier page Harder page

Practice on screen

The Mosaic Menders — Area as Counting Unit Squares

Check-up page

One more page of Same Space, New Shape to collect at the end of the lesson.

Make more

Make more pages like this with the Shapes & Geometry maker.

Lesson 4

Area of an L-shape

Children cut an L-shaped figure into two rectangles, find the area of each by multiplying, and add the two areas.

StandardCommon Core 3.MD.C.7.dMeasurement and Data

2 class days

Day 1Teach: The Baking Tray · Practice on paper (Core page)
Day 2Practice and check: Practice on paper (Easier page, Harder page) · Check-up page

Warm up and teach

Open The Baking Tray on the projector.

Practice on paper

Area of an L-Shape
Core page Easier page Harder page

Check-up page

One more page of Area of an L-Shape to collect at the end of the lesson.

Teacher note

Common mistakes: Children multiply the two longest sides, as if the figure were a full rectangle. On the page without a grid, they use a side length of the whole figure for one of the parts (for example, 10 where the part is only 6 wide).
Words to use: On the Baking Tray, set 5 rows of 6 buns and crack the tray after the third row: "Two trays: 3 rows of 6 and 2 rows of 6. 18 + 12 = 30. Nothing was lost." The tray cannot make an L-shape, so go to the board and draw one on a grid: "This is not one rectangle. It is two rectangles pushed together. Where can one straight cut make two rectangles?" Draw the cut, name the parts A and B, write a product for each, and add. Cut the same figure the other way and add again: "The same area. Either cut is right."
What to watch for: On the easier page, the cut is drawn and the parts are named A and B. On the page for everyone, the figure is on a grid without the cut: the child draws the cut, and either of the two cuts is right. On the harder page, there is no grid and the six side lengths are written at the sides. Every length the child needs is printed, for either cut; nothing has to be subtracted. Have the child trace each part with a finger and say its two sides before writing a product. A child who takes the missing corner away from the full rectangle is right; ask for a cut as well, because the boxes add.

Lesson 5

Perimeter: walk the edge

Children find the perimeter of a rectangle by counting the unit edges all the way around.

StandardCommon Core 3.MD.D.8Measurement and Data

3 class days

Day 1Teach: All the Way Round · Practice on paper (Core page)
Day 2Practice and check: Practice on paper (Easier page, Harder page) · Practice on screen · Check-up page
Day 3Reteach and extend: Act on the check-up pages: reteach the children who are not there yet, with the tool and a new page from the maker; the others take a harder page.

Warm up and teach

Open All the Way Round on the projector.

Practice on paper

Walk the Edge
Core page Easier page Harder page

Practice on screen

The Mending Fences — Perimeter: the Distance Around

Check-up page

One more page of Walk the Edge to collect at the end of the lesson.

Make more

Make more pages like this with the Shapes & Geometry maker.

Lesson 6

Perimeter: find the missing side

Children find one unknown side length of a figure from its perimeter and the other side lengths, and write an equation with a letter for the unknown side.

StandardCommon Core 3.MD.D.8Measurement and Data

2 class days

Day 1Teach: All the Way Round · Practice on paper (Core page)
Day 2Practice and check: Practice on paper (Easier page, Harder page) · Check-up page

Warm up and teach

Open All the Way Round on the projector.

Practice on paper

Perimeter: Find the Missing Side
Core page Easier page Harder page

Check-up page

One more page of Perimeter: Find the Missing Side to collect at the end of the lesson.

Teacher note

Common mistakes: Children add the side lengths they see and write that sum as the answer, or they add the perimeter to it. In the rectangle with one side length given, they subtract that side once instead of twice, or they subtract it twice and write what is left as n without halving it.
Words to use: On All the Way Round, let the strand lie down: "The distance all the way around is one length." The tool shows no sides and no numbers, so go to the board. Draw a triangle with sides 10 ft and 6 ft and one side n: "The perimeter is 24 feet. Picture its strand laid straight: 24 feet long." Draw the strand as a bar cut into three pieces: 10, 6, n. Write 10 + 6 + n = 24. "10 + 6 is 16. What do we add to 16 to make 24?" n = 8. Check by adding all three sides.
What to watch for: On the easier page, the equation is printed under each figure and the child finds n. On the page for everyone, the child writes the equation on the line. The page has triangles, four-sided figures, and five-sided figures. On the harder page, the perimeters go up to 100, one figure is an L-shape with six sides, and two rectangles show one side length and the letter n on two sides. The printed side counts twice; what is left is n + n, so the child still has to split it in two (one side 9, perimeter 30: 9 + 9 + n + n = 30; 12 is left; n = 6). The figures are drawn in proportion (not actual size), so a child can see whether an answer looks right.

Lesson 7

Same perimeter, different area

Children compare rectangles and circle the one with the same distance around as another.

StandardCommon Core 3.MD.D.8Measurement and Data

2 class days

Day 1Teach: Practice on paper (Core page)
Day 2Practice and check: Practice on paper (Easier page, Harder page) · Practice on screen · Check-up page

Practice on paper

Same Fence, New Yard
Core page Easier page Harder page

Practice on screen

The Mending Fences — Perimeter: the Distance Around

Check-up page

One more page of Same Fence, New Yard to collect at the end of the lesson.

Make more

Make more pages like this with the Shapes & Geometry maker.

Lesson 8

Count the cubes

Children count all the unit cubes in a tower, also the ones they cannot see, and write the total.

Later gradeCommon Core 5.MD.C.4Measurement and Data

2 class days

Day 1Teach: Practice on paper (Core page)
Day 2Practice and check: Practice on paper (Easier page, Harder page) · Practice on screen · Check-up page

Practice on paper

Cube Towers
Core page Easier page Harder page

Practice on screen

Cube Towers (a page that checks the answers)

Check-up page

One more page of Cube Towers to collect at the end of the lesson.

Make more

Make more pages like this with the Measurement & Size maker.

Teacher note

Common mistakes: Children count only the cubes they can see in the drawing and leave out the hidden ones at the back and underneath. Or they count the square faces they see and get a number that is far too big.
Words to use: Build the tower with snap cubes first: "How many can you see from here? Now turn it around and take it apart. Count them all." Say: "Count layer by layer. How many cubes in the bottom layer? In the next one? Add the layers." Ask: "A cube on top must be sitting on something. What is under it?" Give the word: "The number of cubes that fill a shape is its volume."
What to watch for: Have each child build one tower from the page with cubes and compare the count with the written answer. A child who counts by layers ("6 and 6 and 6") is ready for volume as layers times the cubes in a layer.

Unit check: before and after

Two short paper checks made from this unit's own worksheets. Give Check A before you teach the unit and Check B after it, and you can see what changed. Each part belongs to one lesson.

Part 1: Lesson 1, Area: count the squares (1 task)
Part 2: Lesson 2, Area of a rectangle: multiply the side lengths (2 tasks)
Part 3: Lesson 3, Same area, different shape (1 task)
Part 4: Lesson 5, Perimeter: walk the edge (2 tasks)
Part 5: Lesson 6, Perimeter: find the missing side (2 tasks)
Part 6: Lesson 7, Same perimeter, different area (1 task)
Part 7: Lesson 8, Count the cubes (2 tasks)

Not in the check: Lesson 4. Worksheets that cannot be split into single tasks are left out.

Check A (PDF) · 3 pages Check B (PDF) · 3 pages

Printing a check counts as a download, like any worksheet.

Answer key A Answer key B Teacher pages: points, class record, and what to do next

The answer keys and the teacher pages come with the paid Teacher plan.

This is a classroom check of this unit's lessons. It is not a standardized test, and its points are not a grade.

Unit checks