Area by Multiplying Side Lengths
A 45-minute Grade 3 lesson connecting area to multiplication, where the formula is derived from the rows of an array rather than handed over as a rule.
Area by Multiplying Side Lengths is a free 45-minute Grade 3 maths lesson plan for Common Core standard 3.MD.C.7 — find area by multiplying side lengths. It is timed across 5 sections, gives the exact wording to use where the wording carries the mathematics, names 3 misconceptions with the teaching move that addresses each, and ends with an exit ticket and a printable worksheet with its answer key.
- Grade:
- Grade 3
- Length:
- 45 minutes
- Standard:
- 3.MD.C.7
Grade 3 · Measurement & Data
3.MD.C.7
Relate area to the operations of multiplication and addition.
Objective
Students will be able to find the area of a rectangle by multiplying its side lengths, and explain why that works.
Students are successful when they can
- Multiplies side lengths to find an area and states the square unit.
- Explains the multiplication in terms of rows of squares.
- Splits a rectangle into two and adds the areas to find the whole.
What you need
- Squared paper
- Square tiles
- Scissors for splitting rectangles
- The printable practice sheet linked at the end of this plan
The lesson
Warm-up — rows and row length
5 min- Show three rectangles on grids. For each, ask how many rows and how many squares in a row.
- Do not ask for the area yet. Naming the two numbers is what the formula is built from.
Teach — the formula is an array
14 min- Take a 5 by 8 rectangle. Five rows of eight squares. Write 5 × 8 = 40 square units.
- Say why: the squares are arranged in an array, so counting them is a multiplication. This is not a new rule.
- Ask what the side lengths measure. Five units and eight units — lengths, not squares. The answer is in square units and the sides are not.
- Now a 6 by 14 rectangle, which is beyond the tables. Cut it into 6 by 10 and 6 by 4.
- Sixty and twenty-four, so eighty-four. The two pieces are the distributive property, drawn.
- Finish with a missing side: an area of 48 and one side of 6. Divide to recover the other.
“Area is not a new formula. It is an array of squares, and multiplying the sides counts them the same way it always has.”
Guided practice — multiply, then split
12 min- Pairs find the area of rectangles by multiplying, checking one by counting squares.
- Then they take a rectangle too big for the tables and split it, recording both partial areas.
- Finally one missing-side problem each.
Independent practice
11 min- Students complete an area by multiplying page.
- Answers with the wrong unit — 40 units rather than 40 square units — are worth correcting every time.
Close
3 min- Give a rectangle 7 by 12 and ask for a split that makes it easy.
- 7 × 10 and 7 × 2, and the answer follows.
What goes wrong, and why
Each of these is a reasoning error rather than carelessness. The fix addresses the reasoning.
Adds the side lengths instead of multiplying.
Why: Two numbers and a rectangle, and addition is more familiar. This is also the perimeter calculation, which is a real thing done to rectangles.
Fix: Count the squares in a small case and compare with both answers. Only one matches, and the pupil finds out which.
Writes the area in units rather than square units.
Why: The unit has been carried over from the side lengths, which were measured in units, without noticing the quantity changed.
Fix: Point at one square on the grid. That is the unit being counted, and it is a square, so the answer counts squares.
Cannot find the area of a 6 by 14 rectangle because it is not in the tables.
Why: Area has been tied to recallable facts rather than to the structure, so an unfamiliar product looks like an unanswerable question.
Fix: Split it on squared paper and cut it apart. Two known facts, added. The rectangle makes the distributive property physical.
If they are not there yet
- Work with side lengths from the 2, 5 and 10 tables and check every answer by counting squares.
- Keep the grid under every rectangle so the array is visible behind the multiplication.
If they finish early
- Find the area of a compound shape by splitting it into two rectangles.
- Find all rectangles with whole number sides and an area of 36.
- Given the area and one side, find the other for a non-table case.
Exit ticket
A rectangle is 9 units by 4 units. What is its area? A different rectangle has area 35 square units and one side of 5. What is the other side?
What to look for: 36 square units and 7 units. An answer of 26 to the first is the perimeter; a missing unit on either answer is worth a note.
Printable practice for 3.MD.C.7
Free to print and copy, answer key included. Each sheet can generate a fresh set of problems for a retake.
- Area by MultiplyingWork out the area.
- Area of Bigger RectanglesWork out the area.
Questions about Area by Multiplying Side Lengths
How long does the Area by Multiplying Side Lengths lesson take?
45 minutes, split across 5 timed sections: warm-up 5 min, teach 14 min, guided practice 12 min, independent practice 11 min, close 3 min. The minutes are stated per section and add up to the stated length, so the plan can be cut or extended at a section boundary rather than abandoned halfway.
Which standard does Area by Multiplying Side Lengths teach?
CCSS.MATH.CONTENT.3.MD.C.7 — 3.MD.C.7, Measurement & Data for Grade 3: “Relate area to the operations of multiplication and addition.” In plain terms, find area by multiplying side lengths.
What do I need to teach this lesson?
Squared paper, square tiles, scissors for splitting rectangles and the printable practice sheet linked at the end of this plan. Everything listed is either ordinary classroom equipment or a free printable from this site — there is nothing to buy and nothing to prepare beyond photocopying.
What mistakes should I expect in this lesson?
Three, each a reasoning error rather than carelessness: adds the side lengths instead of multiplying; writes the area in units rather than square units and cannot find the area of a 6 by 14 rectangle because it is not in the tables. The plan gives the thinking behind each one and the teaching move that addresses the thinking rather than the symptom.
How do I know whether the lesson worked?
The exit ticket asks: “A rectangle is 9 units by 4 units. What is its area? A different rectangle has area 35 square units and one side of 5. What is the other side?.” 36 square units and 7 units. An answer of 26 to the first is the perimeter; a missing unit on either answer is worth a note. That tells you whether the class needs a reteach or a thirty-second conversation before you plan tomorrow.
Is there a worksheet to go with Area by Multiplying Side Lengths?
Yes — 2 printable 3.MD.C.7 worksheets, linked at the end of the plan and free like the rest of the site. Each one comes with an answer key and 25 versions, so the practice after the lesson can be a different paper on every desk.
Is Area by Multiplying Side Lengths free to use?
Yes. The plan, its printables and their answer keys are free to read, print and photocopy for your own class, with no account and no email capture. It was last reviewed on 5 September 2026. Please do not resell it or republish it as your own.
Last reviewed 2026-09-05. Aligned to 3.MD.C.7 of the Common Core State Standards for mathematics.