3.MD.7a: Finding Area by Tiling and Multiplication

Visual Models to Use

• Grid Paper - Draw rectangles on grid paper and count squares, then compare with multiplying length × width
• Array Models - Arrange objects in rows and columns to show the connection between arrays, multiplication, and area
• Area Models - Use rectangular diagrams labeled with dimensions to show how area relates to multiplication
• Square Tiles - Use physical square tiles to build rectangles and count the total, then verify by multiplying

Everyday Activities

1. Room Designer

Have your child measure the length and width of their bedroom in feet. Then have them draw it on grid paper (where each square is 1 square foot) and find the area by counting squares. Verify by multiplying length × width. Discuss why both methods give the same answer.

2. Tile Counter

In your kitchen, bathroom, or other tiled area, have your child count the number of tiles in one row and the number of rows. Then ask them to predict the total number of tiles using multiplication. Verify by counting all tiles individually.

3. Garden Planner

Design a rectangular garden on grid paper. If each square represents 1 square foot, have your child determine how many plants they can fit if each plant needs 1 square foot of space. Compare counting all squares with multiplying length × width.

4. Rectangle Hunt

Find rectangular objects around your home (book covers, placemats, device screens). Measure the length and width in inches, then calculate the area two ways: by drawing on grid paper and counting squares, and by multiplying the dimensions. Compare the results.

Strategies When Your Child Struggles

1. Start Small

Begin with small rectangles (2×3, 3×4) that your child can easily count and multiply. Once they see the pattern with small numbers, move to larger rectangles.

2. Use Concrete Materials

Use physical square tiles or cut out paper squares that your child can arrange into rectangles. The hands-on experience helps build understanding before moving to abstract concepts.

3. Draw and Label

Have your child draw rectangles on grid paper, label the dimensions, count the squares, and write the multiplication equation. This visual connection helps reinforce the relationship.

4. Connect to Arrays

If your child is familiar with multiplication arrays, point out that a rectangle of unit squares is just like a multiplication array. Each row has the same number of squares, just like each row in an array has the same number of objects.

5-Minute Practice Activities

1. Quick Draw and Check

Call out dimensions (e.g., "4 by 6"). Have your child quickly draw a rectangle with those dimensions on grid paper, count the squares, and check by multiplying. Repeat with different dimensions.

2. Area Prediction

Show your child a rectangle drawn on grid paper with dimensions labeled. Ask them to predict the area using multiplication, then verify by counting squares.

3. Missing Dimension

Draw a rectangle on grid paper, label one dimension, and tell your child the area. Have them figure out the missing dimension by counting or dividing.

4. Same Area, Different Dimensions

Challenge your child to find different rectangles that all have the same area (e.g., area of 24 square units could be 1×24, 2×12, 3×8, 4×6). Have them draw each rectangle on grid paper and verify by counting squares.

Mid-Year Expectations

By the middle of third grade, your child should be able to:

• Find the area of a rectangle by counting unit squares
• Understand that a rectangle can be covered with unit squares in rows and columns
• Recognize that the number of squares in a rectangle is related to its dimensions
• Begin to see the connection between counting squares and multiplication
• Draw rectangles with given dimensions on grid paper

End-of-Year Expectations

By the end of third grade, your child should be able to:

• Demonstrate that the area of a rectangle found by tiling is the same as multiplying the side lengths
• Explain why multiplying length × width gives the area of a rectangle
• Use multiplication to find the area of rectangles efficiently
• Apply the area formula (A = l × w) to solve simple problems
• Draw rectangles with a given area on grid paper

Mastery Signs

Your child has mastered this standard when they can:

• Independently find the area of rectangles using both tiling and multiplication
• Clearly explain the connection between counting squares and multiplying dimensions
• Choose the most efficient method (tiling or multiplication) based on the situation
• Apply their understanding to solve real-world area problems
• Find missing dimensions when given the area and one dimension
• Create different rectangles with the same area

Below Grade Level

For students who need additional support with basic area concepts and multiplication.

Download Practice Worksheet

At Grade Level

For students who are working at the expected level for this standard.

Download Grade Level Worksheet

Above Grade Level

For students who are ready for more challenging area problems.

Download Challenge Worksheet