In this Grade 4 Saxon Math Intermediate 4 investigation, students explore multiplication through rectangular arrays and the area model, learning to calculate perimeter and area using square units such as square centimeters, square inches, and square feet. The lesson also introduces perfect squares and square roots, teaching students that squaring a number means multiplying it by itself and that the square root of a number is the side length of a square with that area. Students apply these concepts through hands-on activities estimating and finding perimeter and area on grid paper.
Section 1
📘 Multiplication Patterns, Area, Squares and Square Roots
To find the square root of a number, we find a number that, when multiplied by itself, equals the original number. We use the symbol .
Next, you’ll use visual models like arrays and squares to build a solid intuition for how squares and their roots work.
Section 2
Array
An array is a rectangular arrangement of numbers or symbols in columns and rows. It shows that the number of rows times the number of columns equals the total.
A 3x4 array of stars shows the multiplication fact: .
A 2x6 array of chairs illustrates the multiplication fact: .
A 5x3 array shows that 5 and 3 are factors of 15.
Think of an array as organizing things, like cookies on a baking sheet, into neat rows and columns. It's a visual way to see a multiplication problem in action! The number of rows times the number of columns gives the total count and also reveals the factors of that total.
Section 3
Area
The area is the amount of surface within the perimeter (boundary) of a flat figure. We measure area by counting the number of squares of a certain size needed to cover its surface.
A 6 cm by 4 cm rectangle's area is square cm.
A 3 in. by 3 in. square's area is square in.
Area is the space inside a shape, not the outline. It’s the total surface you can cover, like frosting on a square cake. We measure it by counting how many unit squares—like little cheese crackers—fit perfectly inside the boundary without any gaps or overlaps. It's all about total coverage!
Section 4
Square numbers
We say that we 'square a number' when we multiply a number by itself. The results, such as 1, 4, 9, 16, and 25, are called square numbers, or perfect squares.
To square 5, you calculate .
7 squared is .
The sequence of square numbers is or
Squaring a number is just multiplying it by itself. Why 'square'? Because the result is the area of a literal square! A 5x5 grid has 25 squares, so 5 squared is 25. These results, like 1, 4, 9, and 25, are called perfect squares because they form these perfect shapes.
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Section 1
📘 Multiplication Patterns, Area, Squares and Square Roots
To find the square root of a number, we find a number that, when multiplied by itself, equals the original number. We use the symbol .
Next, you’ll use visual models like arrays and squares to build a solid intuition for how squares and their roots work.
Section 2
Array
An array is a rectangular arrangement of numbers or symbols in columns and rows. It shows that the number of rows times the number of columns equals the total.
A 3x4 array of stars shows the multiplication fact: .
A 2x6 array of chairs illustrates the multiplication fact: .
A 5x3 array shows that 5 and 3 are factors of 15.
Think of an array as organizing things, like cookies on a baking sheet, into neat rows and columns. It's a visual way to see a multiplication problem in action! The number of rows times the number of columns gives the total count and also reveals the factors of that total.
Section 3
Area
The area is the amount of surface within the perimeter (boundary) of a flat figure. We measure area by counting the number of squares of a certain size needed to cover its surface.
A 6 cm by 4 cm rectangle's area is square cm.
A 3 in. by 3 in. square's area is square in.
Area is the space inside a shape, not the outline. It’s the total surface you can cover, like frosting on a square cake. We measure it by counting how many unit squares—like little cheese crackers—fit perfectly inside the boundary without any gaps or overlaps. It's all about total coverage!
Section 4
Square numbers
We say that we 'square a number' when we multiply a number by itself. The results, such as 1, 4, 9, 16, and 25, are called square numbers, or perfect squares.
To square 5, you calculate .
7 squared is .
The sequence of square numbers is or
Squaring a number is just multiplying it by itself. Why 'square'? Because the result is the area of a literal square! A 5x5 grid has 25 squares, so 5 squared is 25. These results, like 1, 4, 9, and 25, are called perfect squares because they form these perfect shapes.
Book overview
Jump across lessons in the current chapter without opening the full course modal.
Continue this chapter